From a6e96a188c323d06331c77063d0f7aabe1764038 Mon Sep 17 00:00:00 2001
From: DavideTisi <davide.tisi93@gmail.com>
Date: Wed, 13 Nov 2024 13:03:01 +0100
Subject: [PATCH 1/8] first commit

---
 docs/src/software/i-pi.sec                    |    1 +
 docs/src/topics/analysis.sec                  |    1 +
 examples/free-energy/README.rst               |    2 +
 examples/free-energy/data.zip                 |  Bin 0 -> 179081 bytes
 examples/free-energy/data/FES-md_hiq.bz2      |  Bin 0 -> 38245 bytes
 examples/free-energy/data/FES-pimd_hiq.bz2    |  Bin 0 -> 38190 bytes
 examples/free-energy/data/h5o2+.xyz           |    9 +
 .../free-energy/data/h5o2.dms4B.coeff.com.dat |  993 ++++++++
 .../free-energy/data/h5o2.pes4B.coeff.dat     | 2022 +++++++++++++++++
 examples/free-energy/data/input-md.xml        |   73 +
 examples/free-energy/data/input-md_hiq.xml    |   73 +
 examples/free-energy/data/input-pimd.xml      |   74 +
 examples/free-energy/data/input-pimd_hiq.xml  |   74 +
 examples/free-energy/data/plumed-md.dat       |   10 +
 examples/free-energy/data/plumed-md_hiq.dat   |   10 +
 examples/free-energy/data/plumed-pimd.dat     |   10 +
 examples/free-energy/data/plumed-pimd_hiq.dat |   10 +
 examples/free-energy/environment.yml          |   18 +
 examples/free-energy/free-energy.py           |   50 +
 19 files changed, 3430 insertions(+)
 create mode 100644 examples/free-energy/README.rst
 create mode 100644 examples/free-energy/data.zip
 create mode 100644 examples/free-energy/data/FES-md_hiq.bz2
 create mode 100644 examples/free-energy/data/FES-pimd_hiq.bz2
 create mode 100644 examples/free-energy/data/h5o2+.xyz
 create mode 100755 examples/free-energy/data/h5o2.dms4B.coeff.com.dat
 create mode 100755 examples/free-energy/data/h5o2.pes4B.coeff.dat
 create mode 100644 examples/free-energy/data/input-md.xml
 create mode 100644 examples/free-energy/data/input-md_hiq.xml
 create mode 100644 examples/free-energy/data/input-pimd.xml
 create mode 100644 examples/free-energy/data/input-pimd_hiq.xml
 create mode 100644 examples/free-energy/data/plumed-md.dat
 create mode 100644 examples/free-energy/data/plumed-md_hiq.dat
 create mode 100644 examples/free-energy/data/plumed-pimd.dat
 create mode 100644 examples/free-energy/data/plumed-pimd_hiq.dat
 create mode 100644 examples/free-energy/environment.yml
 create mode 100644 examples/free-energy/free-energy.py

diff --git a/docs/src/software/i-pi.sec b/docs/src/software/i-pi.sec
index 1ff3be9b..e7436f89 100644
--- a/docs/src/software/i-pi.sec
+++ b/docs/src/software/i-pi.sec
@@ -13,3 +13,4 @@ it on the `ipi-code website <http://ipi-code.org>`_, the `documentation pages
 - examples/pi-metad/pi-metad
 - examples/heat-capacity/heat-capacity
 - examples/pi-mts-rpc/mts-rpc
+- examples/free-energy/free-energy
diff --git a/docs/src/topics/analysis.sec b/docs/src/topics/analysis.sec
index a41e8820..2d56d7f9 100644
--- a/docs/src/topics/analysis.sec
+++ b/docs/src/topics/analysis.sec
@@ -7,3 +7,4 @@ for analysis or visualization purposes.
 - examples/gaas-map/gaas-map
 - examples/lpr/lpr
 - examples/roy-gch/roy-gch
+- examples/free-energy/free-energy
diff --git a/examples/free-energy/README.rst b/examples/free-energy/README.rst
new file mode 100644
index 00000000..7525c6b2
--- /dev/null
+++ b/examples/free-energy/README.rst
@@ -0,0 +1,2 @@
+Free energy methods
+=================== 
diff --git a/examples/free-energy/data.zip b/examples/free-energy/data.zip
new file mode 100644
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diff --git a/examples/free-energy/data/FES-pimd_hiq.bz2 b/examples/free-energy/data/FES-pimd_hiq.bz2
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HcmV?d00001

diff --git a/examples/free-energy/data/h5o2+.xyz b/examples/free-energy/data/h5o2+.xyz
new file mode 100644
index 00000000..a2d2ed17
--- /dev/null
+++ b/examples/free-energy/data/h5o2+.xyz
@@ -0,0 +1,9 @@
+7
+# CELL(abcABC):   13.38377    13.38377    13.38377    90.00000    90.00000    90.00000  cell{angstrom}  Traj: positions{angstrom} Step:           0  Bead:      10 
+       O  5.40450e-01 -9.74850e-01 -2.16580e-01
+       O  2.92484e+00 -8.39252e-01  1.52397e-01
+       H  1.83860e-01 -1.25804e+00 -1.07875e+00
+       H  1.74329e+00 -9.09278e-01 -1.00395e-01
+       H  3.29707e+00 -1.59324e+00  6.47253e-01
+       H  3.53033e+00 -6.08138e-01 -5.76078e-01
+       H  4.23316e-02 -1.94860e-01  9.22810e-02
diff --git a/examples/free-energy/data/h5o2.dms4B.coeff.com.dat b/examples/free-energy/data/h5o2.dms4B.coeff.com.dat
new file mode 100755
index 00000000..e17d2f50
--- /dev/null
+++ b/examples/free-energy/data/h5o2.dms4B.coeff.com.dat
@@ -0,0 +1,993 @@
+          dc
+     0.00000000000        0.231032055622        0.231032055622        0.231032055622    
+    0.231032055622        0.353903857962        0.353903857962        0.231032055622    
+     0.00000000000        0.231032055622        0.231032055622        0.231032055622    
+    0.353903857962        0.353903857962        0.231032055622        0.231032055622    
+     0.00000000000        0.231032055622        0.231032055622        0.353903857962    
+    0.353903857962        0.231032055622        0.231032055622        0.231032055622    
+     0.00000000000        0.231032055622        0.353903857962        0.353903857962    
+    0.231032055622        0.231032055622        0.231032055622        0.231032055622    
+     0.00000000000        0.353903857962        0.353903857962        0.353903857962    
+    0.353903857962        0.353903857962        0.353903857962        0.353903857962    
+     0.00000000000        0.197244964989        0.353903857962        0.353903857962    
+    0.353903857962        0.353903857962        0.353903857962        0.197244964989    
+     0.00000000000    
+          dw
+     0.00000000000        0.121909714310        0.121909714310        0.121909714310    
+    0.121909714310        0.189148319284        0.189148319284        0.121909714310    
+     0.00000000000        0.121909714310        0.121909714310        0.121909714310    
+    0.189148319284        0.189148319284        0.121909714310        0.121909714310    
+     0.00000000000        0.121909714310        0.121909714310        0.189148319284    
+    0.189148319284        0.121909714310        0.121909714310        0.121909714310    
+     0.00000000000        0.121909714310        0.189148319284        0.189148319284    
+    0.121909714310        0.121909714310        0.121909714310        0.121909714310    
+     0.00000000000        0.189148319284        0.189148319284        0.189148319284    
+    0.189148319284        0.189148319284        0.189148319284        0.189148319284    
+     0.00000000000        6.080029805686E-02    0.189148319284        0.189148319284    
+    0.189148319284        0.189148319284        0.189148319284        6.080029805686E-02
+     0.00000000000    
+          mm  2512  1332
+      coeffs
+     18.3687247418         4.12003419519        -110.958174035        -6.31233875343    
+     19.3977089261        -2.11027464466         2.71782480295        -19.7581562596    
+    0.534297545977        0.985535978259         1.42634669887         39.5581733333    
+    -6.78369615372        -4.91467707005        -6.80744637918        0.947054153953    
+    -2.36766153330         2.06899326007        0.239737657545         3.70977850339    
+     1.88603132867        0.224639798133        -3.53004986985       -0.475244479292    
+     2.10658528678        -4.21592527024       -0.454146243527        -1.69947881781    
+     7.54936469449        -1.34344523290         1.85330702038        0.817674338682    
+    0.516431093966         9.49717714570       -0.739363077633        -2.74328115097    
+     1.13702019050         5.95990781921         8.15163700811        4.493000028676E-02
+    -13.1503221543       -4.601865370837E-02    -1.16539454208        3.272748483055E-04
+     4.27016638025        0.672834774268        -3.24471969213       -0.372381302257    
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+    -2.17285760845       -0.166872772472       -0.521644760241        0.146817586889    
+    0.472368356341         1.39052516765         1.20696062713        8.550047307240E-02
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+     2.00483036103       -0.654988138732        -1.82405676451        3.611639728937E-02
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+     2.08810321067       -0.365756646427       -0.181760039880        -2.41534705603    
+     2.97352420417        0.507097549059        5.606906282491E-02    0.425150629744    
+   -0.928914063389        0.844473992136        0.876149567790       -0.170213323938    
+    -5.34895042288        0.415319253348        0.315063826447        -2.47280686025    
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+     1.81093702632        -3.30163415006        -9.29629156465         3.73698387411    
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+    -8.80288685178         6.40748282302         8.12553073398        0.918844166148    
+     3.64755044403        -8.89173514743        -11.9643042674         3.12244069944    
+     3.49795082018         1.53636704412       -8.383764707606E-02    -5.04451351326    
+   -0.178078767575         4.13693433815       -1.834627431636E-02    -1.19299359701    
+     2.09320835958         15.4179337813         6.19139998208        -4.71167138589    
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+   -0.113449777827       -0.541620698408        0.922552951045       -0.203152505428    
+   -0.360385104128        2.168842254278E-02    0.304367264304        4.567592460587E-02
+    1.862874082974E-02    0.371207081840        8.526937127619E-02    6.854118940025E-03
+     1.29341583503       -0.458512867841       -0.645321084515        0.141162256380    
+     2.42289306324        0.855114163345         1.12248557996        0.464228378265    
+   -0.451880309821       -0.351320648815        -2.33554576699       -0.692132019082    
+    -1.32792240575        -1.01959093262       -0.411306993228       -0.353793450506    
+   -0.607843381871         4.62176548506        0.296048502801       -0.691191192202    
+   -0.278311701724        0.842776819219         1.10503743491         2.77475056524    
+    0.120891303004       -0.418643455167        0.765758562067        7.873503575255E-02
+    0.672833452747       -7.681017017871E-02    8.642853423948E-02   -8.867417092108E-02
+   -0.302755372263       -0.890998307227       -0.943685587251        0.305777624586    
+   -0.354873820478       -0.242387307941       -0.712995560059         2.03086416455    
+   -0.333564074462         2.01577594078        -2.19302876967         2.61372004628    
+    2.236833847501E-02     1.69034238000        -1.32664456822         1.55531873720    
+   -0.116338439265         1.13737888261        -1.16979530945        -1.33713238455    
+   -0.376803090988        3.370355173555E-02    -1.32019036985       -0.371273743012    
+    0.583520317658        0.413998533402        0.444264164277       -0.204240218300    
+    0.160505709616        -1.85474950682       -0.933388889377         6.10769661265    
+    -1.16523160679        -2.10712694551        -1.13036742172        -5.78078441425    
+    -1.77923660606         2.20691875858        0.565206873107         2.06271781390    
+   -0.752736618388       -7.327083743835E-02    0.579659150450        -2.56211465038    
+    -2.62829828205        0.472076912234        0.437944220084        -3.03921513607    
+    -1.11118580122        0.388336651660        0.149347112609         1.79884245791    
+     1.16901138832         2.40919646045        -1.30326840650        0.683700956175    
+  err0 =      1.59E-02    1.06E-02    1.00E-02
+
diff --git a/examples/free-energy/data/h5o2.pes4B.coeff.dat b/examples/free-energy/data/h5o2.pes4B.coeff.dat
new file mode 100755
index 00000000..78ff3d62
--- /dev/null
+++ b/examples/free-energy/data/h5o2.pes4B.coeff.dat
@@ -0,0 +1,2022 @@
+          dc
+     0.00000000000        0.231032055622        0.231032055622        0.231032055622    
+    0.231032055622        0.353903857962        0.353903857962        0.231032055622    
+     0.00000000000        0.231032055622        0.231032055622        0.231032055622    
+    0.353903857962        0.353903857962        0.231032055622        0.231032055622    
+     0.00000000000        0.231032055622        0.231032055622        0.353903857962    
+    0.353903857962        0.231032055622        0.231032055622        0.231032055622    
+     0.00000000000        0.231032055622        0.353903857962        0.353903857962    
+    0.231032055622        0.231032055622        0.231032055622        0.231032055622    
+     0.00000000000        0.353903857962        0.353903857962        0.353903857962    
+    0.353903857962        0.353903857962        0.353903857962        0.353903857962    
+     0.00000000000        0.197244964989        0.353903857962        0.353903857962    
+    0.353903857962        0.353903857962        0.353903857962        0.197244964989    
+     0.00000000000    
+          dw
+     0.00000000000        0.121909714310        0.121909714310        0.121909714310    
+    0.121909714310        0.189148319284        0.189148319284        0.121909714310    
+     0.00000000000        0.121909714310        0.121909714310        0.121909714310    
+    0.189148319284        0.189148319284        0.121909714310        0.121909714310    
+     0.00000000000        0.121909714310        0.121909714310        0.189148319284    
+    0.189148319284        0.121909714310        0.121909714310        0.121909714310    
+     0.00000000000        0.121909714310        0.189148319284        0.189148319284    
+    0.121909714310        0.121909714310        0.121909714310        0.121909714310    
+     0.00000000000        0.189148319284        0.189148319284        0.189148319284    
+    0.189148319284        0.189148319284        0.189148319284        0.189148319284    
+     0.00000000000        6.080029805686E-02    0.189148319284        0.189148319284    
+    0.189148319284        0.189148319284        0.189148319284        6.080029805686E-02
+     0.00000000000    
+          mm      7785      59
+      coeffs
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+     6401.68015736        -13294.3798892        -1737.99955444         21030.2811764    
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+     34270.9824180         16206.7892175         34310.8914780         3302.86890949    
+     13035.8147765         260.228552685        -260.169658773        -1765.62280172    
+     1041.77066835        -602.391823940         458.000147562        -645.492523425    
+     341.615525989        -1111.85948491        -2747.61554687        -72.3211004188    
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+     1153.30877221         753.074394131         15389.5911540         5.33350725420    
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+     1528.45150397         334.539117882         14937.0419330        -178.202976683    
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+     2318.55115600         1084.17315585         32.0009851736         105.431675900    
+     761.123112259        -2217.06665098         657.104747611        -754.441598984    
+     431.615084418        -950.383903751         806.028661604        -1521.79813739    
+    -369.412764736         66.8858867446         15.2033231773        -52.2509138755    
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+     236.101992697         462.525022614         714.900500894        -2632.92754396    
+     469.307812646        -143.471063452         796.128399453         520.840279822    
+    -86.3814006184        -2010.78001255         832.720664474        -794.616971276    
+     1404.96103200         126.630445592        -269.461401490        -3.53859851794    
+     324.752937387        -365.851294770        -15.0540318736         726.102369707    
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+    -83.2694985267       -2.984765147315E-02    0.165212701673       -0.528921365948    
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+     1.39436949485        -6.97138370391         5.79219267365        -3.08878342553    
+     23.0643845723       -0.219814540057         12.2482295279       -5.831298153085E-03
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+     4.86392886231         3.80006700954         6.55614984680         4.71701457493    
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+    -6.53272906887        -37.0401253328       -9.144723246624E-02    7.385915765165E-03
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+   -0.173931484571       -0.458071622072        0.319537964255        0.165278315851    
+    0.236509120132       -0.203128294891       -0.763773854979        0.448180159765    
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+    -24.5985287804        -8.22492169529        0.236140288607        0.122960836668    
+    0.239963968350       -0.493451140157        -1.08517923177        2.679959045400E-02
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+    -1.33518537740        2.272848095376E-02   -0.649576318543        -23.9406405892    
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+    -9905.78023321         197.283335062         4336.37538595        -11666.8138674    
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+     3.09247356326         2263.63472216        -30.7010613521         29.6796972366    
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+     9.76280934891         80.6299948937        -22473.0487924         5.04372439510    
+    -1.11598309516         3209.22549846         55.4192016728        -60.1765481686    
+     26125.3668839         1.86318878675         31.9326978131        -261.476471682    
+    -79.4989264174        -172.672467975        -5360.64828765        -150.172507938    
+    -39.7643031773        -3330.31067894        0.527497449130         57.5748618416    
+    -959.031399349        -3.06551533982        -8.87062381055         203.357359557    
+    0.253947714466        0.996423578226         2747.73378150         34.7493032030    
+    -106.072787819         2962.93218535         40.1276918361         99.7598494309    
+    -5058.56250240        -20.5361879206         103.325926285        -3415.00250272    
+     26.9283882009         43.3199196283         7127.84061675         38.1012829905    
+     82.5654898697         9949.33156752         20.2521470433        -44.1108684004    
+     1799.08166310         2.88726734080        -239.333106561        -2891.25843939    
+     66.1992556584         103.270577231        -1541.79410081       -0.967090984060    
+     101.714991803        -2070.39082491    
+  n1 =   48189    err0 =      1.59E-04
diff --git a/examples/free-energy/data/input-md.xml b/examples/free-energy/data/input-md.xml
new file mode 100644
index 00000000..42bda7e1
--- /dev/null
+++ b/examples/free-energy/data/input-md.xml
@@ -0,0 +1,73 @@
+<simulation safe_stride='10' verbosity='medium'>
+    <ffsocket mode='unix' name='driver'>
+         <latency>  1.00000000e-04</latency> <address>zundel</address>
+   </ffsocket>
+   <ffplumed name="plumed">
+         <file mode="xyz">data/h5o2+.xyz</file>
+         <plumeddat> data/plumed-md.dat </plumeddat>
+         <plumed_extras> [doo, co1.lessthan, co2.lessthan, dc, mtd.bias ] </plumed_extras>
+   </ffplumed>
+   <total_steps>5000</total_steps>
+   <output prefix="meta-md">
+      <trajectory stride="10" filename="pos" cell_units="angstrom">positions{angstrom}</trajectory>
+      <trajectory stride="10" filename="colvar" bead="0" extra_type="doo,dc,mtd.bias"> extras_bias </trajectory>
+      <properties stride="10"> 
+      [ step, time, conserved, temperature{kelvin}, kinetic_md, 
+        potential, temperature{kelvin}(H), temperature{kelvin}(O), ensemble_bias ] 
+      </properties>
+   </output>
+   <prng>
+      <seed>18885</seed>
+   </prng>
+   <system>
+      <forces> 
+          <force forcefield="driver"></force>
+      </forces>
+      <initialize nbeads="1">
+        <file mode="xyz">data/h5o2+.xyz</file>
+        <cell>
+         [   25.29166, 0, 0, 0, 25.29166, 0, 0, 0, 25.29166 ]
+        </cell>
+      </initialize>
+      <ensemble>
+         <temperature units="kelvin"> 300.0 </temperature>
+         <bias>
+            <force forcefield="plumed"/>
+         </bias>
+      </ensemble>
+      <motion mode="dynamics">
+        <fixcom> False </fixcom>
+        <dynamics mode="nvt" splitting="baoab">
+         <timestep units="femtosecond"> 1.0 </timestep>
+<!--
+# Generated at http://cosmo-epfl.github.io/gle4md
+# Please cite:
+# M. Ceriotti, G. Bussi and M. Parrinello, J. Chem. Theory Comput. 6, 1170 (2010) 
+# M. Ceriotti, G. Bussi and M. Parrinello, Phys. Rev. Lett. 102, 020601 (2009)
+# Smart-sampling GLE. Enforces efficient sampling, focussing the effort on the slowest mode 
+# accessible by the simulation. Generated from the parameter file
+# library/smart/smart-0.5_6-2.a, 
+# and shifted so that they are effective to sample optimally 
+# a time scale of t_opt=1 picoseconds,
+# and do as well as possible upt to a cutoff frequency of 
+# νmax=100 THz [3336 cm^-1]
+-->  
+            <thermostat mode='gle'>
+              <A shape='(7,7)'>
+                [   8.191023526179e-4,    8.328506066524e-3,    1.657771834013e-3,    9.736989925341e-4,    2.841803794895e-4,   -3.176846864198e-5,   -2.967010478210e-4, 
+            -8.389856546341e-4,    2.405526974742e-2,   -1.507872374848e-2,    2.589784240185e-3,    1.516783633362e-3,   -5.958833418565e-4,    4.198422349789e-4, 
+            7.798710586406e-4,    1.507872374848e-2,    8.569039501219e-3,    6.001000899602e-3,    1.062029383877e-3,    1.093939147968e-3,   -2.661575532976e-3, 
+            -9.676783161546e-4,   -2.589784240185e-3,   -6.001000899602e-3,    2.680459336535e-5,   -5.214694469742e-5,    4.231304910751e-4,   -2.104894919743e-5, 
+            -2.841997149166e-4,   -1.516783633362e-3,   -1.062029383877e-3,    5.214694469742e-5,    1.433903506353e-9,   -4.241574212449e-5,    7.910178912362e-5, 
+            3.333208286893e-5,    5.958833418565e-4,   -1.093939147968e-3,   -4.231304910751e-4,    4.241574212449e-5,    2.385554468441e-8,   -3.139255482869e-5, 
+            2.967533789056e-4,   -4.198422349789e-4,    2.661575532976e-3,    2.104894919743e-5,   -7.910178912362e-5,    3.139255482869e-5,   2.432567259684e-11
+              ]
+              </A>
+            </thermostat>
+        </dynamics>
+      </motion>
+  </system>
+  <smotion mode="metad">
+     <metad> <metaff> [ plumed ] </metaff> </metad>
+  </smotion>
+</simulation>
diff --git a/examples/free-energy/data/input-md_hiq.xml b/examples/free-energy/data/input-md_hiq.xml
new file mode 100644
index 00000000..4208d757
--- /dev/null
+++ b/examples/free-energy/data/input-md_hiq.xml
@@ -0,0 +1,73 @@
+<simulation safe_stride='10' verbosity='low'>
+    <ffsocket mode='unix' name='driver'>
+         <latency>  1.00000000e-04</latency> <address>zundel</address>
+   </ffsocket>
+   <ffplumed name="plumed">
+         <file mode="xyz">data/h5o2+.xyz</file>
+         <plumeddat> data/plumed-md_hiq.dat </plumeddat>
+         <plumed_extras> [doo, co1.lessthan, co2.lessthan, dc, mtd.bias ] </plumed_extras>
+   </ffplumed>
+   <total_steps>2000000</total_steps>
+   <output prefix="meta-md_hiq">
+      <trajectory stride="200" filename="pos" cell_units="angstrom">positions{angstrom}</trajectory>
+      <trajectory stride="20" filename="colvar" bead="0" extra_type="doo,dc,mtd.bias"> extras_bias </trajectory>
+      <properties stride="20"> 
+      [ step, time, conserved, temperature{kelvin}, kinetic_md, 
+        potential, temperature{kelvin}(H), temperature{kelvin}(O), ensemble_bias ] 
+      </properties>
+   </output>
+   <prng>
+      <seed>18885</seed>
+   </prng>
+   <system>
+      <forces> 
+          <force forcefield="driver"></force>
+      </forces>
+      <initialize nbeads="1">
+        <file mode="xyz">data/h5o2+.xyz</file>
+        <cell>
+         [   25.29166, 0, 0, 0, 25.29166, 0, 0, 0, 25.29166 ]
+        </cell>
+      </initialize>
+      <ensemble>
+         <temperature units="kelvin"> 300.0 </temperature>
+         <bias>
+            <force forcefield="plumed"/>
+         </bias>
+      </ensemble>
+      <motion mode="dynamics">
+        <fixcom> False </fixcom>
+        <dynamics mode="nvt" splitting="baoab">
+         <timestep units="femtosecond"> 0.5 </timestep>
+<!--
+# Generated at http://cosmo-epfl.github.io/gle4md
+# Please cite:
+# M. Ceriotti, G. Bussi and M. Parrinello, J. Chem. Theory Comput. 6, 1170 (2010) 
+# M. Ceriotti, G. Bussi and M. Parrinello, Phys. Rev. Lett. 102, 020601 (2009)
+# Smart-sampling GLE. Enforces efficient sampling, focussing the effort on the slowest mode 
+# accessible by the simulation. Generated from the parameter file
+# library/smart/smart-0.5_6-2.a, 
+# and shifted so that they are effective to sample optimally 
+# a time scale of t_opt=1 picoseconds,
+# and do as well as possible upt to a cutoff frequency of 
+# νmax=100 THz [3336 cm^-1]
+-->  
+            <thermostat mode='gle'>
+              <A shape='(7,7)'>
+                [   8.191023526179e-4,    8.328506066524e-3,    1.657771834013e-3,    9.736989925341e-4,    2.841803794895e-4,   -3.176846864198e-5,   -2.967010478210e-4, 
+            -8.389856546341e-4,    2.405526974742e-2,   -1.507872374848e-2,    2.589784240185e-3,    1.516783633362e-3,   -5.958833418565e-4,    4.198422349789e-4, 
+            7.798710586406e-4,    1.507872374848e-2,    8.569039501219e-3,    6.001000899602e-3,    1.062029383877e-3,    1.093939147968e-3,   -2.661575532976e-3, 
+            -9.676783161546e-4,   -2.589784240185e-3,   -6.001000899602e-3,    2.680459336535e-5,   -5.214694469742e-5,    4.231304910751e-4,   -2.104894919743e-5, 
+            -2.841997149166e-4,   -1.516783633362e-3,   -1.062029383877e-3,    5.214694469742e-5,    1.433903506353e-9,   -4.241574212449e-5,    7.910178912362e-5, 
+            3.333208286893e-5,    5.958833418565e-4,   -1.093939147968e-3,   -4.231304910751e-4,    4.241574212449e-5,    2.385554468441e-8,   -3.139255482869e-5, 
+            2.967533789056e-4,   -4.198422349789e-4,    2.661575532976e-3,    2.104894919743e-5,   -7.910178912362e-5,    3.139255482869e-5,   2.432567259684e-11
+              ]
+              </A>
+            </thermostat>
+        </dynamics>
+      </motion>
+  </system>
+  <smotion mode="metad">
+     <metad> <metaff> [ plumed ] </metaff> </metad>
+  </smotion>
+</simulation>
diff --git a/examples/free-energy/data/input-pimd.xml b/examples/free-energy/data/input-pimd.xml
new file mode 100644
index 00000000..633cee81
--- /dev/null
+++ b/examples/free-energy/data/input-pimd.xml
@@ -0,0 +1,74 @@
+<simulation safe_stride='10' verbosity='medium'>
+    <ffsocket mode='unix' name='driver'>
+         <latency>  1.00000000e-04</latency> <address>zundel</address>
+   </ffsocket>
+   <ffplumed name="plumed">
+         <file mode="xyz">data/h5o2+.xyz</file>
+         <plumeddat> data/plumed-pimd.dat </plumeddat>
+         <plumed_extras> [doo, co1.lessthan, co2.lessthan, dc, mtd.bias ] </plumed_extras>
+   </ffplumed>
+   <total_steps>5000</total_steps>
+   <output prefix="meta-pimd">
+      <trajectory stride="10" filename="pos" cell_units="angstrom">positions{angstrom}</trajectory>
+      <trajectory stride="10" filename="xc" format="xyz">x_centroid{angstrom}</trajectory>
+      <trajectory stride="10" filename="colvar" bead="0" extra_type="doo,dc,mtd.bias"> extras_bias </trajectory>
+      <properties stride="10"> [ step, time, conserved, temperature{kelvin}, kinetic_cv, 
+            potential, temperature{kelvin}(H), temperature{kelvin}(O), ensemble_bias ] </properties>
+   </output>
+   <prng>
+      <seed>18885</seed>
+   </prng>
+   <system>
+      <forces> 
+          <force forcefield="driver"></force>
+      </forces>
+      <initialize nbeads="8">
+        <file mode="xyz">data/h5o2+.xyz</file>
+        <cell>
+         [   25.29166, 0, 0, 0, 25.29166, 0, 0, 0, 25.29166 ]
+        </cell>
+      </initialize>
+      <ensemble>
+         <temperature units="kelvin"> 300.0 </temperature>
+         <bias>
+           <force forcefield="plumed" nbeads="1">
+             <interpolate_extras> [ doo, dc, mtd.bias ] </interpolate_extras>
+           </force>
+         </bias>
+      </ensemble>
+      <motion mode="dynamics">
+        <fixcom> False </fixcom>
+        <dynamics mode="nvt" splitting="baoab">
+         <timestep units="femtosecond"> 1.0 </timestep>
+<!--
+# Generated at http://cosmo-epfl.github.io/gle4md
+# Please cite:
+# M. Ceriotti, G. Bussi and M. Parrinello, J. Chem. Theory Comput. 6, 1170 (2010) 
+# M. Ceriotti, G. Bussi and M. Parrinello, Phys. Rev. Lett. 102, 020601 (2009)
+# Smart-sampling GLE. Enforces efficient sampling, focussing the effort on the slowest mode 
+# accessible by the simulation. Generated from the parameter file
+# library/smart/smart-0.5_6-2.a, 
+# and shifted so that they are effective to sample optimally 
+# a time scale of t_opt=1 picoseconds,
+# and do as well as possible upt to a cutoff frequency of 
+# νmax=100 THz [3336 cm^-1]
+-->  
+            <thermostat mode='gle'>
+              <A shape='(7,7)'>
+                [   8.191023526179e-4,    8.328506066524e-3,    1.657771834013e-3,    9.736989925341e-4,    2.841803794895e-4,   -3.176846864198e-5,   -2.967010478210e-4, 
+            -8.389856546341e-4,    2.405526974742e-2,   -1.507872374848e-2,    2.589784240185e-3,    1.516783633362e-3,   -5.958833418565e-4,    4.198422349789e-4, 
+            7.798710586406e-4,    1.507872374848e-2,    8.569039501219e-3,    6.001000899602e-3,    1.062029383877e-3,    1.093939147968e-3,   -2.661575532976e-3, 
+            -9.676783161546e-4,   -2.589784240185e-3,   -6.001000899602e-3,    2.680459336535e-5,   -5.214694469742e-5,    4.231304910751e-4,   -2.104894919743e-5, 
+            -2.841997149166e-4,   -1.516783633362e-3,   -1.062029383877e-3,    5.214694469742e-5,    1.433903506353e-9,   -4.241574212449e-5,    7.910178912362e-5, 
+            3.333208286893e-5,    5.958833418565e-4,   -1.093939147968e-3,   -4.231304910751e-4,    4.241574212449e-5,    2.385554468441e-8,   -3.139255482869e-5, 
+            2.967533789056e-4,   -4.198422349789e-4,    2.661575532976e-3,    2.104894919743e-5,   -7.910178912362e-5,    3.139255482869e-5,   2.432567259684e-11
+              ]
+              </A>
+            </thermostat>
+        </dynamics>
+      </motion>
+  </system>
+  <smotion mode="metad">
+     <metad> <metaff> [ plumed ] </metaff> </metad>
+  </smotion>
+</simulation>
diff --git a/examples/free-energy/data/input-pimd_hiq.xml b/examples/free-energy/data/input-pimd_hiq.xml
new file mode 100644
index 00000000..fa637ce0
--- /dev/null
+++ b/examples/free-energy/data/input-pimd_hiq.xml
@@ -0,0 +1,74 @@
+<simulation safe_stride='10' verbosity='low'>
+    <ffsocket mode='unix' name='driver'>
+         <latency>  1.00000000e-04</latency> <address>zundel</address>
+   </ffsocket>
+   <ffplumed name="plumed">
+         <file mode="xyz">data/h5o2+.xyz</file>
+         <plumeddat> data/plumed-pimd_hiq.dat </plumeddat>
+         <plumed_extras> [doo, co1.lessthan, co2.lessthan, dc, mtd.bias ] </plumed_extras>
+   </ffplumed>
+   <total_steps>2000000</total_steps>
+   <output prefix="meta-pimd_hiq">
+      <trajectory stride="2000" filename="pos" cell_units="angstrom">positions{angstrom}</trajectory>
+      <trajectory stride="200" filename="xc" format="xyz">x_centroid{angstrom}</trajectory>
+      <trajectory stride="20" filename="colvar" bead="0" extra_type="doo,dc,mtd.bias"> extras_bias </trajectory>
+      <properties stride="20"> [ step, time, conserved, temperature{kelvin}, kinetic_cv, 
+            potential, temperature{kelvin}(H), temperature{kelvin}(O), ensemble_bias ] </properties>
+   </output>
+   <prng>
+      <seed>18885</seed>
+   </prng>
+   <system>
+      <forces> 
+          <force forcefield="driver"></force>
+      </forces>
+      <initialize nbeads="32">
+        <file mode="xyz">data/h5o2+.xyz</file>
+        <cell>
+         [   25.29166, 0, 0, 0, 25.29166, 0, 0, 0, 25.29166 ]
+        </cell>
+      </initialize>
+      <ensemble>
+         <temperature units="kelvin"> 300.0 </temperature>
+         <bias>
+           <force forcefield="plumed" nbeads="1">
+             <interpolate_extras> [ doo, dc, mtd.bias ] </interpolate_extras>
+           </force>
+         </bias>
+      </ensemble>
+      <motion mode="dynamics">
+        <fixcom> False </fixcom>
+        <dynamics mode="nvt" splitting="baoab">
+         <timestep units="femtosecond"> 0.5 </timestep>
+<!--
+# Generated at http://cosmo-epfl.github.io/gle4md
+# Please cite:
+# M. Ceriotti, G. Bussi and M. Parrinello, J. Chem. Theory Comput. 6, 1170 (2010) 
+# M. Ceriotti, G. Bussi and M. Parrinello, Phys. Rev. Lett. 102, 020601 (2009)
+# Smart-sampling GLE. Enforces efficient sampling, focussing the effort on the slowest mode 
+# accessible by the simulation. Generated from the parameter file
+# library/smart/smart-0.5_6-2.a, 
+# and shifted so that they are effective to sample optimally 
+# a time scale of t_opt=1 picoseconds,
+# and do as well as possible upt to a cutoff frequency of 
+# νmax=100 THz [3336 cm^-1]
+-->  
+            <thermostat mode='gle'>
+              <A shape='(7,7)'>
+                [   8.191023526179e-4,    8.328506066524e-3,    1.657771834013e-3,    9.736989925341e-4,    2.841803794895e-4,   -3.176846864198e-5,   -2.967010478210e-4, 
+            -8.389856546341e-4,    2.405526974742e-2,   -1.507872374848e-2,    2.589784240185e-3,    1.516783633362e-3,   -5.958833418565e-4,    4.198422349789e-4, 
+            7.798710586406e-4,    1.507872374848e-2,    8.569039501219e-3,    6.001000899602e-3,    1.062029383877e-3,    1.093939147968e-3,   -2.661575532976e-3, 
+            -9.676783161546e-4,   -2.589784240185e-3,   -6.001000899602e-3,    2.680459336535e-5,   -5.214694469742e-5,    4.231304910751e-4,   -2.104894919743e-5, 
+            -2.841997149166e-4,   -1.516783633362e-3,   -1.062029383877e-3,    5.214694469742e-5,    1.433903506353e-9,   -4.241574212449e-5,    7.910178912362e-5, 
+            3.333208286893e-5,    5.958833418565e-4,   -1.093939147968e-3,   -4.231304910751e-4,    4.241574212449e-5,    2.385554468441e-8,   -3.139255482869e-5, 
+            2.967533789056e-4,   -4.198422349789e-4,    2.661575532976e-3,    2.104894919743e-5,   -7.910178912362e-5,    3.139255482869e-5,   2.432567259684e-11
+              ]
+              </A>
+            </thermostat>
+        </dynamics>
+      </motion>
+  </system>
+  <smotion mode="metad">
+     <metad> <metaff> [ plumed ] </metaff> </metad>
+  </smotion>
+</simulation>
diff --git a/examples/free-energy/data/plumed-md.dat b/examples/free-energy/data/plumed-md.dat
new file mode 100644
index 00000000..6c839207
--- /dev/null
+++ b/examples/free-energy/data/plumed-md.dat
@@ -0,0 +1,10 @@
+# default units are LENGTH=nm ENERGY=kJ/mol TIME=ps
+doo: DISTANCE ATOMS=1,2 
+co1: DISTANCES GROUPA=1 GROUPB=3-7 LESS_THAN={RATIONAL R_0=0.14}
+co2: DISTANCES GROUPA=2 GROUPB=3-7 LESS_THAN={RATIONAL R_0=0.14}
+dc: COMBINE ARG=co1.lessthan,co2.lessthan COEFFICIENTS=1,-1 PERIODIC=NO
+mtd:   METAD ARG=doo,dc PACE=10 SIGMA=0.005,0.05 HEIGHT=4 FILE=HILLS-md BIASFACTOR=10 TEMP=300
+uwall: UPPER_WALLS ARG=doo AT=0.4 KAPPA=250
+
+PRINT ARG=doo,co1.*,co2.*,dc,mtd.*,uwall.* STRIDE=10 FILE=COLVAR-md
+FLUSH STRIDE=1
diff --git a/examples/free-energy/data/plumed-md_hiq.dat b/examples/free-energy/data/plumed-md_hiq.dat
new file mode 100644
index 00000000..cc5a5302
--- /dev/null
+++ b/examples/free-energy/data/plumed-md_hiq.dat
@@ -0,0 +1,10 @@
+# default units are LENGTH=nm ENERGY=kJ/mol TIME=ps
+doo: DISTANCE ATOMS=1,2 
+co1: DISTANCES GROUPA=1 GROUPB=3-7 LESS_THAN={RATIONAL R_0=0.14}
+co2: DISTANCES GROUPA=2 GROUPB=3-7 LESS_THAN={RATIONAL R_0=0.14}
+dc: COMBINE ARG=co1.lessthan,co2.lessthan COEFFICIENTS=1,-1 PERIODIC=NO
+mtd:   METAD ARG=doo,dc PACE=100 SIGMA=0.0025,0.025 HEIGHT=1 FILE=HILLS-md_hiq BIASFACTOR=8 TEMP=300
+uwall: UPPER_WALLS ARG=doo AT=0.4 KAPPA=250
+
+PRINT ARG=doo,co1.*,co2.*,dc,mtd.*,uwall.* STRIDE=20 FILE=COLVAR-md_hiq
+FLUSH STRIDE=1
diff --git a/examples/free-energy/data/plumed-pimd.dat b/examples/free-energy/data/plumed-pimd.dat
new file mode 100644
index 00000000..dcfd3478
--- /dev/null
+++ b/examples/free-energy/data/plumed-pimd.dat
@@ -0,0 +1,10 @@
+# default units are LENGTH=nm ENERGY=kJ/mol TIME=ps
+doo: DISTANCE ATOMS=1,2 
+co1: DISTANCES GROUPA=1 GROUPB=3-7 LESS_THAN={RATIONAL R_0=0.14}
+co2: DISTANCES GROUPA=2 GROUPB=3-7 LESS_THAN={RATIONAL R_0=0.14}
+dc: COMBINE ARG=co1.lessthan,co2.lessthan COEFFICIENTS=1,-1 PERIODIC=NO
+mtd:   METAD ARG=doo,dc PACE=10 SIGMA=0.005,0.05 HEIGHT=4 FILE=HILLS-pimd BIASFACTOR=10 TEMP=300
+uwall: UPPER_WALLS ARG=doo AT=0.4 KAPPA=250
+
+PRINT ARG=doo,co1.*,co2.*,dc,mtd.*,uwall.* STRIDE=10 FILE=COLVAR-pimd
+FLUSH STRIDE=1
diff --git a/examples/free-energy/data/plumed-pimd_hiq.dat b/examples/free-energy/data/plumed-pimd_hiq.dat
new file mode 100644
index 00000000..3c8689c6
--- /dev/null
+++ b/examples/free-energy/data/plumed-pimd_hiq.dat
@@ -0,0 +1,10 @@
+# default units are LENGTH=nm ENERGY=kJ/mol TIME=ps
+doo: DISTANCE ATOMS=1,2 
+co1: DISTANCES GROUPA=1 GROUPB=3-7 LESS_THAN={RATIONAL R_0=0.14}
+co2: DISTANCES GROUPA=2 GROUPB=3-7 LESS_THAN={RATIONAL R_0=0.14}
+dc: COMBINE ARG=co1.lessthan,co2.lessthan COEFFICIENTS=1,-1 PERIODIC=NO
+mtd:   METAD ARG=doo,dc PACE=100 SIGMA=0.0025,0.025 HEIGHT=1 FILE=HILLS-pimd_hiq BIASFACTOR=8 TEMP=300
+uwall: UPPER_WALLS ARG=doo AT=0.4 KAPPA=250
+
+PRINT ARG=doo,co1.*,co2.*,dc,mtd.*,uwall.* STRIDE=10 FILE=COLVAR-pimd_hiq
+FLUSH STRIDE=1
diff --git a/examples/free-energy/environment.yml b/examples/free-energy/environment.yml
new file mode 100644
index 00000000..05352af3
--- /dev/null
+++ b/examples/free-energy/environment.yml
@@ -0,0 +1,18 @@
+channels:
+  - plumed/label/nightly
+  - conda-forge
+dependencies:
+  - python=3.11
+  - pip
+  - gfortran
+  - make
+  - git
+  - plumed
+  - py-plumed  
+  - pip:
+    - ase==3.22.1
+    - git+https://github.com/i-pi/i-pi.git@main#egg=ipi
+    - matplotlib
+variables:
+  PYTHONPATH: 
+  PLUMED_KERNEL:
diff --git a/examples/free-energy/free-energy.py b/examples/free-energy/free-energy.py
new file mode 100644
index 00000000..adc4d8a0
--- /dev/null
+++ b/examples/free-energy/free-energy.py
@@ -0,0 +1,50 @@
+r"""
+Free energy methods
+==========================
+
+:Authors: Venkat Kapil `@venkatkapil24 <https://github.com/venkatkapil24/>`_
+          and Davide Tisi `@DavideTisi <https://github.com/DavideTisi/>`_
+
+This example shows how to perform free energy calculation on a
+effective Hamiltonian of a hydrogen atom in an effectively 1D double well
+from Ref. `Y. Litman et al., JCP (2022)
+<https://pubs.aip.org/aip/jcp/article/156/19/194107/2841188/Dissipative-tunneling-rates-through-the>`_
+"""
+
+# %%
+
+import os
+import subprocess
+import time
+
+import ipi.utils.parsing as pimdmooc
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+
+# %%
+# Model System
+# ------------
+#
+# We will consider the effective Hamiltonian of a hydrogen atom
+# in an effectively 1D double well from
+# Ref. `Y. Litman et al., JCP (2022)
+# <https://pubs.aip.org/aip/jcp/article/156/19/194107/2841188/Dissipative-tunneling-rates-through-the>`_
+# Its potential energy surface (PES) is described by the function
+# 
+# .. math::
+#
+#    V = A x^2 + B x^4 + \frac{1}{2} m \omega^2 y^2 + \frac{1}{2} m \omega^2 z^2
+# 
+# with:
+# 
+# .. math::
+#     
+#     \begin{align}
+#     m &= 1837.107~\text{a.u.}\\ 
+#     \omega &= 3800 ~\text{cm}^{-1} = 0.017314074~\text{a.u.}\\ 
+#     A &= -0.00476705894242374~\text{a.u.}\\
+#     B &= 0.000598024968321866~\text{a.u.}\\
+#     \end{align}
+#

From 79be02408fa873512f3af5c25a46753043344e33 Mon Sep 17 00:00:00 2001
From: DavideTisi <davide.tisi93@gmail.com>
Date: Wed, 13 Nov 2024 17:26:21 +0100
Subject: [PATCH 2/8] up to harmonic

---
 examples/free-energy/data.zip                 |  Bin 179081 -> 0 bytes
 examples/free-energy/data/FES-md_hiq.bz2      |  Bin 38245 -> 0 bytes
 examples/free-energy/data/FES-pimd_hiq.bz2    |  Bin 38190 -> 0 bytes
 examples/free-energy/data/h5o2+.xyz           |    9 -
 .../free-energy/data/h5o2.dms4B.coeff.com.dat |  993 --------
 .../free-energy/data/h5o2.pes4B.coeff.dat     | 2022 -----------------
 examples/free-energy/data/input-md.xml        |   73 -
 examples/free-energy/data/input-md_hiq.xml    |   73 -
 examples/free-energy/data/input-pimd.xml      |   74 -
 examples/free-energy/data/input-pimd_hiq.xml  |   74 -
 examples/free-energy/data/plumed-md.dat       |   10 -
 examples/free-energy/data/plumed-md_hiq.dat   |   10 -
 examples/free-energy/data/plumed-pimd.dat     |   10 -
 examples/free-energy/data/plumed-pimd_hiq.dat |   10 -
 examples/free-energy/environment.yml          |    1 +
 examples/free-energy/free-energy.py           |  321 +++
 16 files changed, 322 insertions(+), 3358 deletions(-)
 delete mode 100644 examples/free-energy/data.zip
 delete mode 100644 examples/free-energy/data/FES-md_hiq.bz2
 delete mode 100644 examples/free-energy/data/FES-pimd_hiq.bz2
 delete mode 100644 examples/free-energy/data/h5o2+.xyz
 delete mode 100755 examples/free-energy/data/h5o2.dms4B.coeff.com.dat
 delete mode 100755 examples/free-energy/data/h5o2.pes4B.coeff.dat
 delete mode 100644 examples/free-energy/data/input-md.xml
 delete mode 100644 examples/free-energy/data/input-md_hiq.xml
 delete mode 100644 examples/free-energy/data/input-pimd.xml
 delete mode 100644 examples/free-energy/data/input-pimd_hiq.xml
 delete mode 100644 examples/free-energy/data/plumed-md.dat
 delete mode 100644 examples/free-energy/data/plumed-md_hiq.dat
 delete mode 100644 examples/free-energy/data/plumed-pimd.dat
 delete mode 100644 examples/free-energy/data/plumed-pimd_hiq.dat

diff --git a/examples/free-energy/data.zip b/examples/free-energy/data.zip
deleted file mode 100644
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diff --git a/examples/free-energy/data/h5o2+.xyz b/examples/free-energy/data/h5o2+.xyz
deleted file mode 100644
index a2d2ed17..00000000
--- a/examples/free-energy/data/h5o2+.xyz
+++ /dev/null
@@ -1,9 +0,0 @@
-7
-# CELL(abcABC):   13.38377    13.38377    13.38377    90.00000    90.00000    90.00000  cell{angstrom}  Traj: positions{angstrom} Step:           0  Bead:      10 
-       O  5.40450e-01 -9.74850e-01 -2.16580e-01
-       O  2.92484e+00 -8.39252e-01  1.52397e-01
-       H  1.83860e-01 -1.25804e+00 -1.07875e+00
-       H  1.74329e+00 -9.09278e-01 -1.00395e-01
-       H  3.29707e+00 -1.59324e+00  6.47253e-01
-       H  3.53033e+00 -6.08138e-01 -5.76078e-01
-       H  4.23316e-02 -1.94860e-01  9.22810e-02
diff --git a/examples/free-energy/data/h5o2.dms4B.coeff.com.dat b/examples/free-energy/data/h5o2.dms4B.coeff.com.dat
deleted file mode 100755
index e17d2f50..00000000
--- a/examples/free-energy/data/h5o2.dms4B.coeff.com.dat
+++ /dev/null
@@ -1,993 +0,0 @@
-          dc
-     0.00000000000        0.231032055622        0.231032055622        0.231032055622    
-    0.231032055622        0.353903857962        0.353903857962        0.231032055622    
-     0.00000000000        0.231032055622        0.231032055622        0.231032055622    
-    0.353903857962        0.353903857962        0.231032055622        0.231032055622    
-     0.00000000000        0.231032055622        0.231032055622        0.353903857962    
-    0.353903857962        0.231032055622        0.231032055622        0.231032055622    
-     0.00000000000        0.231032055622        0.353903857962        0.353903857962    
-    0.231032055622        0.231032055622        0.231032055622        0.231032055622    
-     0.00000000000        0.353903857962        0.353903857962        0.353903857962    
-    0.353903857962        0.353903857962        0.353903857962        0.353903857962    
-     0.00000000000        0.197244964989        0.353903857962        0.353903857962    
-    0.353903857962        0.353903857962        0.353903857962        0.197244964989    
-     0.00000000000    
-          dw
-     0.00000000000        0.121909714310        0.121909714310        0.121909714310    
-    0.121909714310        0.189148319284        0.189148319284        0.121909714310    
-     0.00000000000        0.121909714310        0.121909714310        0.121909714310    
-    0.189148319284        0.189148319284        0.121909714310        0.121909714310    
-     0.00000000000        0.121909714310        0.121909714310        0.189148319284    
-    0.189148319284        0.121909714310        0.121909714310        0.121909714310    
-     0.00000000000        0.121909714310        0.189148319284        0.189148319284    
-    0.121909714310        0.121909714310        0.121909714310        0.121909714310    
-     0.00000000000        0.189148319284        0.189148319284        0.189148319284    
-    0.189148319284        0.189148319284        0.189148319284        0.189148319284    
-     0.00000000000        6.080029805686E-02    0.189148319284        0.189148319284    
-    0.189148319284        0.189148319284        0.189148319284        6.080029805686E-02
-     0.00000000000    
-          mm  2512  1332
-      coeffs
-     18.3687247418         4.12003419519        -110.958174035        -6.31233875343    
-     19.3977089261        -2.11027464466         2.71782480295        -19.7581562596    
-    0.534297545977        0.985535978259         1.42634669887         39.5581733333    
-    -6.78369615372        -4.91467707005        -6.80744637918        0.947054153953    
-    -2.36766153330         2.06899326007        0.239737657545         3.70977850339    
-     1.88603132867        0.224639798133        -3.53004986985       -0.475244479292    
-     2.10658528678        -4.21592527024       -0.454146243527        -1.69947881781    
-     7.54936469449        -1.34344523290         1.85330702038        0.817674338682    
-    0.516431093966         9.49717714570       -0.739363077633        -2.74328115097    
-     1.13702019050         5.95990781921         8.15163700811        4.493000028676E-02
-    -13.1503221543       -4.601865370837E-02    -1.16539454208        3.272748483055E-04
-     4.27016638025        0.672834774268        -3.24471969213       -0.372381302257    
-   -0.134731368050         1.63990410999        -8.86642070873        -3.05628691211    
-   -0.631025689309        0.161863921727        -7.36179176839         1.85276734455    
-     1.50628479372        0.218481846774        -194.555337820        -8.42174497191    
-     67.0589425824        -11.1403612635         2.05516496698        0.612724911804    
-   -0.396997868573        -17.4769870048       -0.485320898722         12.0232024236    
-    -1.36943057306        -11.7287041117         69.0377886090         33.1162478246    
-     16.0892644861         7.18428206095        -4.18614191608         16.0058587155    
-    -2.49247355286        -41.9756611769         13.2405879642       -0.268768847066    
-    0.374403417629       -0.156537854690        0.853302837391        -1.45677258650    
-    3.032300498335E-03   -0.128057669399        0.549707747298        -2.97735711027    
-    -1.07303954971         1.04808484519       -0.241317492649        9.495242090019E-02
-    -4.75335920219        0.650237776988        0.646629088529       -0.478724424692    
-    0.906123208627        -3.57318832565         6.98927192298        0.872073657945    
-     2.14081276173        -11.6815592215        0.693713034190       -0.643043816426    
-   -0.475995445393       -0.370462083409        -5.50328292715        -3.66996785597    
-     8.51546390742        -3.69184194026        -5.63935777658       -0.239561388064    
-    0.911127462886         12.0092135156         1.05566230303         1.79329213224    
-    5.543286442803E-02     1.49861810331         3.24038940982         4.43622627617    
-    -2.55031308804        -2.39708285896        0.200343114214        -2.08203453592    
-    -9.42307668485        8.117966894921E-02    0.935902160681        -2.25195298876    
-     2.62393965639        0.575259935802        0.784344737301        -6.86813837336    
-     5.40513672839         2.55211749307        -5.22289614922       -0.496430080834    
-    -1.06883174924        5.293055978468E-02   -0.246234436406       -0.956460515707    
-     2.89694519592        -2.09780877269         1.19108403777        -1.30843573909    
-     2.41180777322         2.55673424855         1.23770857365       -0.177601898901    
-     1.98869673860       -0.218942533530        -1.42495129719        3.244824713953E-02
-   -0.231737286290        0.217169395930         6.36601133050       -0.308791291168    
-   -0.468197744660        -1.13142816111       -5.133026447702E-02    0.197511214661    
-    0.234861112741       -0.308826853058        2.292711155854E-03    8.779809977873E-02
-    8.365847858396E-02    0.681090141613        -1.09195456295        0.727804252951    
-   -6.213776525946E-02    8.887173885662E-02   -8.466569373781E-03     1.75504450293    
-   -4.607154249042E-02    0.272445188536       -0.207698309951        -16.1473933014    
-    0.573977660188        0.712223080339         4.80675313450        0.359445694252    
-   -0.856203654023        -2.09627557147       -1.409931247934E-02   -0.384662259276    
-    -1.07377822610       -3.466367943995E-02     5.28850618719         12.2850707299    
-   -0.341852450407        -2.16075207900        7.202011748734E-02    0.309327819198    
-    -16.7918096069         4.47116144847        -4.17410032786        0.981094039669    
-    3.182503676147E-02   -4.370149914074E-02   -0.114215848270        0.346801621607    
-   -1.447900513607E-02    0.457153513501        2.303740587807E-02   -0.293177283763    
-    -1.31980911880       -0.667742423352        0.434171333694       -4.341046647839E-02
-   -7.120633724809E-02     1.43040404509       -0.406918828788        0.491567025385    
-   -0.162792202557        0.417829216338       -0.151447545581        0.254261486421    
-   -6.094098446964E-02    0.757364701599        0.939767558881        -1.25659506720    
-     1.06957325748       -0.348045658168       -8.302643439485E-02    0.378201429226    
-   -0.124018566946       -8.850997726065E-02    0.386896375544       -0.543196104483    
-   -1.916785090866E-03   -0.791601527926       -0.139326811997         2.05827838776    
-   -0.930912645522        0.149092960572        0.214296461120         1.14596170380    
-   -0.468348010288        5.358126388218E-03    0.923522390554       -5.430825414843E-02
-   -0.595595684205       -0.862769051979        6.021177481791E-02   -0.358722486761    
-    1.812511299604E-02   -0.765689099267        0.787656194239        6.323153749952E-02
-   -0.381828377362       -0.795439734158       -0.208719432981         1.13508437649    
-    5.810313324736E-02    0.122767491810        3.995570561960E-02    0.181101483007    
-   -5.514816857095E-03    0.198411560469        8.244800525288E-02   -0.237387574975    
-    0.138092520490        -1.30271867319       -0.649484372647        0.508980234936    
-    7.005289426679E-02    0.191156666769         13.9471341689        -1.20709681342    
-    -3.31934818635        -12.0587716827        0.410698853759        -2.40851344378    
-     7.24886174860        -1.01388617014         5.78721682185       -0.938600190226    
-    0.256604871925        -8.49515356064        -7.74958379233         7.62120005896    
-    -5.59412240170       -0.122430762182        -2.51369390948         22.2496023723    
-    -4.70559305731         3.80151292400         1.91307885093       -0.323151581534    
-    0.531595461721        2.650368280935E-02     1.41417022422        -3.22523622100    
-   -0.520943208203       -0.128974941285         1.53899835531        -4.02030203474    
-    0.234034194646         1.86000810689       -0.285112679630        0.442409202127    
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-   -0.672288899863        0.751999084788       -0.993876459579        0.504542562301    
-   -0.754704642881        -1.10073758273        0.505933145122       -0.672134063550    
-    0.308803132791       -0.631045890876        -2.15724182107        -1.14980757363    
-   -0.594365231613       -0.335011779684         1.54052442857        0.674230789261    
-     1.34765790310        -4.09404746293        -2.08876660240        -1.18495936592    
-   -0.859088914083        0.668198051706        0.445077008404        0.288155763530    
-   -0.736954291503       -0.203498365471        -1.71731393417        -1.03803525686    
-    0.840281092138        -2.13087513010        0.628204764097        0.701226209450    
-    -1.55522761687       -0.662914517777        -1.04683021422        0.164333329462    
-   -0.763274093458        6.688477850494E-03    -1.16217976560         1.62720625744    
-    0.791036656629        0.796280393613        0.430176907243       -7.075979729590E-02
-     5.70991477032        0.141757273310        0.847337058020       -0.461073497848    
-    0.349381962685       -0.552583436451        -3.15120955092       -0.791942646308    
-     1.24047277926        -1.70864383764        6.602481970099E-02   -5.799659733020E-02
-    0.324756738868         3.80527955971         3.33566254205        0.278902582205    
-    0.230632271066        -4.17067144371        -1.30009640076         1.96352459250    
-    -2.78231494924        -3.24158875715        -3.45591544725         4.58088650664    
-    -2.47868595311        0.465103396040         2.47560347339       -0.754498177152    
-     4.08608737007        -5.80530816427        -3.18732028585       -0.855318215273    
-    -1.41063857752        -2.58518246704        -3.01142036236         3.59241318923    
-     2.87893827914         1.06950191623        -3.09160052250       -0.407600925959    
-    0.185382112516       -0.768455783651        2.650561564211E-02   -0.769015221448    
-    8.109074332583E-02    -1.43369499615         1.73620471601       -0.982477910310    
-    0.328744425966         1.68314365389        0.994799034856        -2.17092253176    
-   -0.419054360597        0.176252956444        0.630085620358       -0.623998670879    
-   -0.183324760377        -2.23233425375       -0.575803829764       -0.358633437582    
-    -2.17285760845       -0.166872772472       -0.521644760241        0.146817586889    
-    0.472368356341         1.39052516765         1.20696062713        8.550047307240E-02
-    0.320967048608         1.46652065926        0.913168179129         2.53219422046    
-     2.00483036103       -0.654988138732        -1.82405676451        3.611639728937E-02
-    0.191434509809        -2.40513621301        4.267543930321E-03   -1.891912876288E-02
-     2.08810321067       -0.365756646427       -0.181760039880        -2.41534705603    
-     2.97352420417        0.507097549059        5.606906282491E-02    0.425150629744    
-   -0.928914063389        0.844473992136        0.876149567790       -0.170213323938    
-    -5.34895042288        0.415319253348        0.315063826447        -2.47280686025    
-     2.91281984746         1.94941081078        0.450524562561         1.05163505541    
-     1.81093702632        -3.30163415006        -9.29629156465         3.73698387411    
-    -2.83097449273         4.57138876125        -6.24388000860       -1.944538916554E-02
-     2.19999774414        -3.21503380499        -8.34274123111        -9.49477499134    
-     1.80864129243         3.13741970539         2.01323347639        -2.77000624430    
-   -0.919254966096        0.605037384062       -0.260010936319         3.43384482251    
-    -8.80288685178         6.40748282302         8.12553073398        0.918844166148    
-     3.64755044403        -8.89173514743        -11.9643042674         3.12244069944    
-     3.49795082018         1.53636704412       -8.383764707606E-02    -5.04451351326    
-   -0.178078767575         4.13693433815       -1.834627431636E-02    -1.19299359701    
-     2.09320835958         15.4179337813         6.19139998208        -4.71167138589    
-    -1.85159437885        -3.27563586542         2.86999916399       -0.771296283307    
-   -0.403551144187        0.144989037390        0.317675788803       -0.621840960900    
-   -0.103451511969       -0.174625905203        0.765550657691        1.931204332037E-02
-    0.730951775035         1.20427717318        -1.19783678620        0.527673630251    
-    0.613629025723        0.421283533295       -0.902154262435         1.38123622246    
-   -0.113449777827       -0.541620698408        0.922552951045       -0.203152505428    
-   -0.360385104128        2.168842254278E-02    0.304367264304        4.567592460587E-02
-    1.862874082974E-02    0.371207081840        8.526937127619E-02    6.854118940025E-03
-     1.29341583503       -0.458512867841       -0.645321084515        0.141162256380    
-     2.42289306324        0.855114163345         1.12248557996        0.464228378265    
-   -0.451880309821       -0.351320648815        -2.33554576699       -0.692132019082    
-    -1.32792240575        -1.01959093262       -0.411306993228       -0.353793450506    
-   -0.607843381871         4.62176548506        0.296048502801       -0.691191192202    
-   -0.278311701724        0.842776819219         1.10503743491         2.77475056524    
-    0.120891303004       -0.418643455167        0.765758562067        7.873503575255E-02
-    0.672833452747       -7.681017017871E-02    8.642853423948E-02   -8.867417092108E-02
-   -0.302755372263       -0.890998307227       -0.943685587251        0.305777624586    
-   -0.354873820478       -0.242387307941       -0.712995560059         2.03086416455    
-   -0.333564074462         2.01577594078        -2.19302876967         2.61372004628    
-    2.236833847501E-02     1.69034238000        -1.32664456822         1.55531873720    
-   -0.116338439265         1.13737888261        -1.16979530945        -1.33713238455    
-   -0.376803090988        3.370355173555E-02    -1.32019036985       -0.371273743012    
-    0.583520317658        0.413998533402        0.444264164277       -0.204240218300    
-    0.160505709616        -1.85474950682       -0.933388889377         6.10769661265    
-    -1.16523160679        -2.10712694551        -1.13036742172        -5.78078441425    
-    -1.77923660606         2.20691875858        0.565206873107         2.06271781390    
-   -0.752736618388       -7.327083743835E-02    0.579659150450        -2.56211465038    
-    -2.62829828205        0.472076912234        0.437944220084        -3.03921513607    
-    -1.11118580122        0.388336651660        0.149347112609         1.79884245791    
-     1.16901138832         2.40919646045        -1.30326840650        0.683700956175    
-  err0 =      1.59E-02    1.06E-02    1.00E-02
-
diff --git a/examples/free-energy/data/h5o2.pes4B.coeff.dat b/examples/free-energy/data/h5o2.pes4B.coeff.dat
deleted file mode 100755
index 78ff3d62..00000000
--- a/examples/free-energy/data/h5o2.pes4B.coeff.dat
+++ /dev/null
@@ -1,2022 +0,0 @@
-          dc
-     0.00000000000        0.231032055622        0.231032055622        0.231032055622    
-    0.231032055622        0.353903857962        0.353903857962        0.231032055622    
-     0.00000000000        0.231032055622        0.231032055622        0.231032055622    
-    0.353903857962        0.353903857962        0.231032055622        0.231032055622    
-     0.00000000000        0.231032055622        0.231032055622        0.353903857962    
-    0.353903857962        0.231032055622        0.231032055622        0.231032055622    
-     0.00000000000        0.231032055622        0.353903857962        0.353903857962    
-    0.231032055622        0.231032055622        0.231032055622        0.231032055622    
-     0.00000000000        0.353903857962        0.353903857962        0.353903857962    
-    0.353903857962        0.353903857962        0.353903857962        0.353903857962    
-     0.00000000000        0.197244964989        0.353903857962        0.353903857962    
-    0.353903857962        0.353903857962        0.353903857962        0.197244964989    
-     0.00000000000    
-          dw
-     0.00000000000        0.121909714310        0.121909714310        0.121909714310    
-    0.121909714310        0.189148319284        0.189148319284        0.121909714310    
-     0.00000000000        0.121909714310        0.121909714310        0.121909714310    
-    0.189148319284        0.189148319284        0.121909714310        0.121909714310    
-     0.00000000000        0.121909714310        0.121909714310        0.189148319284    
-    0.189148319284        0.121909714310        0.121909714310        0.121909714310    
-     0.00000000000        0.121909714310        0.189148319284        0.189148319284    
-    0.121909714310        0.121909714310        0.121909714310        0.121909714310    
-     0.00000000000        0.189148319284        0.189148319284        0.189148319284    
-    0.189148319284        0.189148319284        0.189148319284        0.189148319284    
-     0.00000000000        6.080029805686E-02    0.189148319284        0.189148319284    
-    0.189148319284        0.189148319284        0.189148319284        6.080029805686E-02
-     0.00000000000    
-          mm      7785      59
-      coeffs
-     6014.42584772        -16998.5888786        -28720.3983510        -130.909484662    
-     6401.68015736        -13294.3798892        -1737.99955444         21030.2811764    
-    -1969.65614041         750.668385422        -251.010149590         59.1057858385    
-    -4201.58395761         2327.14993219        -852.095323263         5356.92858640    
-    -27638.2197481        -10268.2657606         6839.78130117         5386.09624032    
-     7470.08240706         269.588444298         440.916885041         5162.94530486    
-     12232.9800926        -30619.6473616        -10951.1189538        -8546.95711923    
-    -74160.2027297        -12528.2171441        -249.489192360        -6939.14716046    
-     34270.9824180         16206.7892175         34310.8914780         3302.86890949    
-     13035.8147765         260.228552685        -260.169658773        -1765.62280172    
-     1041.77066835        -602.391823940         458.000147562        -645.492523425    
-     341.615525989        -1111.85948491        -2747.61554687        -72.3211004188    
-    -92.4714132873        -573.359936013         290.259364772         1187.34451163    
-     1545.85285421        -2227.48012631        -1642.14706375        -3053.66066865    
-     2370.18372303        -2308.20802048         35.9543609839        -1905.55205781    
-     11352.7485100        -2140.03981192         21079.1977262        -881.963527156    
-     120.079855353        -50.1605942722         1163.29418195        -5193.78112021    
-     8527.89716782        -2437.10964435         1952.85080106        -27498.5366006    
-    -1176.51430359        -466.238885398        -1724.99985191        -9980.05397028    
-     9762.72279138        -9265.81239775         2410.65407166        -14715.6552968    
-     26.7405799845         260.698739641         970.012051099         663.061163062    
-     168.276327902        -190.080846852         582.598071431         88.5282547067    
-    -1634.16832296        -702.910361595         395.636979551        -53.9477613640    
-     41.4628629544         284.135182848         1438.18016829        -640.551642753    
-     973.768002525         613.344917072         701.652944581        -1810.22455617    
-     1153.30877221         753.074394131         15389.5911540         5.33350725420    
-     365.610690298        -1556.60572406         2209.32348073        -9981.06256686    
-     1528.45150397         334.539117882         14937.0419330        -178.202976683    
-    -43.0517335143         556.406011061         67.8838938295        -511.756369882    
-     137.794056975         640.392720852         340.903919254         1480.34355940    
-     2318.55115600         1084.17315585         32.0009851736         105.431675900    
-     761.123112259        -2217.06665098         657.104747611        -754.441598984    
-     431.615084418        -950.383903751         806.028661604        -1521.79813739    
-    -369.412764736         66.8858867446         15.2033231773        -52.2509138755    
-    -115.768583332        -43.9945478366        -6.73726317705         224.638793144    
-    -33.0434113849        -172.456003602        -61.5606564574        -66.4634563535    
-     17.8616648495        -2.18477888285        -48.0235216528        -68.2843129631    
-    -72.7134041892         38.8588995223        -204.752285364        -93.8568820227    
-     41.5060545421        -160.618961983        -56.4327243839        -52.8141124498    
-    -49.1474718746         111.476387293        -37.1222150720         100.266619245    
-     236.101992697         462.525022614         714.900500894        -2632.92754396    
-     469.307812646        -143.471063452         796.128399453         520.840279822    
-    -86.3814006184        -2010.78001255         832.720664474        -794.616971276    
-     1404.96103200         126.630445592        -269.461401490        -3.53859851794    
-     324.752937387        -365.851294770        -15.0540318736         726.102369707    
-    -42.7151846540        -9.84629835969        -23.4793053366        -18.9857328530    
-     6.91231765345        -80.8709708243        -97.2151704715         76.3173284667    
-     35.3015351986         14.1316409097         61.7644624945        -206.814864336    
-    -223.885134582        -125.690733486        -37.5666205432        -86.5948844179    
-    -76.7631601819         14.6432318423         276.595905418         143.421931279    
-    -43.3177901180        -152.922269592        -62.9979771910        -6.51044342375    
-    -31.2451503811        -77.2913258346         59.4486922712        -8.24335043571    
-    -112.457264607         268.193058150         8.88547669314        -74.6054163970    
-    -79.5869898574        -24.6414699588         23.4821108611        -106.562105275    
-     75.3003724385        -292.455898902        -6212.93924884         6842.51181268    
-     6839.67511240        -64535.7604843        -3271.64093643         294.457342384    
-    -2609.63310437         5913.01642301         21970.1969271        -24576.4024496    
-    -6885.72817129        -13944.4187754        -55999.9106429        -2110.83882810    
-     287.072331540         6285.10148622         4201.29133290        -6691.94877586    
-     78052.4794552         22466.6160039         58167.5916927        -4.42327396096    
-    -535.064096384        -3821.13007954         1034.93109727        -1430.02003674    
-     386.436471104         382.811272146         865.614364274         658.968618215    
-    -5103.66634778        -488.487199779        -254.565329050        -2547.52536294    
-    -871.367826404        -786.308629241         1818.33561328        -4658.11873435    
-     1000.01695764         1051.09393874         4940.06566027        -6357.34144689    
-    -1292.04296983         64937.9792074         18878.3996201         277.689852466    
-     8009.08877241         6278.75921662        -8054.53208371        -46108.9386055    
-    -32247.5370231         32595.8588611        -12.0071373433         1989.97743469    
-    -996.308414609        -4801.89761035        -3024.17452678        -838.590607090    
-     360.438845109        -2076.30403108         1370.58835916         7389.58552151    
-    -308.858477230        -402.505310598         6266.29124969        -10246.0034066    
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-     4317.92978271        -29514.2346356         3676.13276766         1713.49826275    
-     1.44110339329        -100.242387127        -71.2704747691        -119.912029796    
-    -73.8384333312         42.0269387597        -104.169242728         104.958780484    
-     844.472927127         486.984564421         324.068147805         45.9818460216    
-     82.9997083017        -316.854776122        -608.445815478         288.591883210    
-     561.409161678         152.703087931         190.730207780         61.5024995435    
-    -331.709734435        -106.329145641         488.865772887         896.018169376    
-    -616.587040772        -841.333419032        -223.766293526         33.4423388440    
-    -3067.02948376        -5144.41441829         9747.83091924         2779.25110491    
-    -1622.14066168         1239.60488707         3311.65342865         2173.18793453    
-    -1222.36106727        -5151.24379654         6266.67283950        -17588.7625276    
-    -269.652595166        -7840.42815431        -275.202088909        -193.314075065    
-    -612.812709991        -705.133496553        -8083.77357959        -359.136606207    
-    -108.308218197         338.810464147        -298.793382582         41.4849055625    
-     631.591259037         619.893255151         3245.82495412        -1986.54061294    
-    -447.196252791         178.338617480         2138.79930064         399.713429818    
-    -373.547340610         201.685337692        -481.221984202         394.963242114    
-    -601.938508127        -678.014590988         118.412831305         204.578420607    
-     2592.39575956         861.209382495        -127.609360443         152.823073043    
-     300.862884083        -355.236589600         2.21949581003         997.235534756    
-     2147.32532458        -383.154679944         477.013414425         882.115318942    
-    -326.296672332         360.285623244         1827.99212666        -199.022041729    
-     969.693077630        -60415.0876566        -14111.9706051         404.365694705    
-    -14987.4685354         59013.5511603         29837.8861289         23954.4873024    
-    -258.023766129        -12418.7416743         43.8089902104        -454.022353772    
-    -2310.74110603         4396.10255064         956.884204630         1457.83259072    
-    -6876.34411527         579.597773090        -6386.33964494        -6864.14764162    
-    -27.8510157909        -380.576522817        -709.283480495         1359.86845927    
-     7544.70565858         4043.43311204        -4593.38191110        -10596.3756196    
-    -14834.8316988         1425.42522133        -1962.43979464         1914.84297531    
-    -19.7046983010         27.2677437041        -224.103650218        -155.171505966    
-     62.1226113318         5.08800351198        -292.554247344        -148.329353797    
-    -407.375033702        -1171.93594013        -184.205164144         100.069640714    
-    -242.725701525         799.197870831         1235.06167548         88.5606538523    
-    -792.177722777         585.334723050         1076.78764507         441.617454239    
-     733.784186962        -198.615324010        -582.837955970        -937.674728527    
-    -683.075004826         1960.65566835         3053.56037226        -5254.04527508    
-    -548.688246815         1228.30418557        -20224.5299601        -17300.7506980    
-     10861.1262987        -5228.65906300        -7405.72756507         757.552022490    
-    -357.865282794        -1196.95228586         1794.54781046         11253.9060573    
-    -170.360916731         12304.7490527         278.731406642        -141.683866636    
-     1206.67228740         102.610436059        -5091.52919640         311.884646460    
-     173.545135935        -156.222861114         190.057494461        -89.1153571021    
-     277.245445635         1062.74851406        -3016.58720669         758.203535055    
-     154.920819915         841.159087897        -2526.11818037         1178.93565621    
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-     6.42461376745        -6.18111119162        -9.63400368831        -3.73423548093    
-    -1.33588704996        -1.59306934199        -13.0633700608         17.8424712284    
-    -54.4774124893        -22.6898928764        -25.5690132024        -14.5824782586    
-    -15.4493367532        -11.5507289735        -47.5598930379        -8.05577890783    
-    -8.50207221496         22.8107866591         12.3916995496         6.08165751794    
-    -13.3879945630        -10.9088864386        -8.44438830269        -3.98048322967    
-    -8.51215704109        -22.4394096353       -0.806047939405        -10.0840287711    
-     10.1738182020        -12.2034576341         5.20540123988        -13.9257507049    
-    -6.53272906887        -37.0401253328       -9.144723246624E-02    7.385915765165E-03
-   -8.339124278885E-03   -5.174777948008E-02    0.119186698208       -0.134947849391    
-   -0.173931484571       -0.458071622072        0.319537964255        0.165278315851    
-    0.236509120132       -0.203128294891       -0.763773854979        0.448180159765    
-    -1.36437433324        -5.11475838142         15.6012945930        -3.88778069560    
-   -0.985649225244        -23.5144647931        -2.89238150172       -0.579044934586    
-     16.4353733021        -1.45427258982        -3.36210280258        -1.73113784408    
-     1.53600184907         13.1259265468        -23.0015614090        -5.00441657059    
-     3.64900434224         35.8844107761         23.6401558579        -11.7427405504    
-    -24.5985287804        -8.22492169529        0.236140288607        0.122960836668    
-    0.239963968350       -0.493451140157        -1.08517923177        2.679959045400E-02
-    0.435747602729       -0.148419331061        -1.24753866778       -0.859142546239    
-    -1.33518537740        2.272848095376E-02   -0.649576318543        -23.9406405892    
-    -44.6247310915         183.830361633         763.417072915        -253604.511731    
-    -370.929637571        -2047.74838086         6917.10745094         920.626839836    
-     5056.22826271         641621.724088        -178.056813952         117.293010290    
-    -210926.138277         222.407547218         330.905857064        -44515.9098159    
-    -184.751493198        -2515.82723091         476410.906895         47.8210984192    
-    -1.24593791268        -19157.9640272         26.9759690537         2994.93538737    
-    -585151.241409        -48.7525670441        -251.589678850         72988.2691552    
-    -4.52092245144         12.4676117536        -9212.63754467         14.9150390126    
-    -79.2693043830        -22867.5035630        -134.082912206        -15.9356145210    
-     3375.38149781         84.8839984588        -594.890297546         231291.695838    
-     23.3336344148        -175.093508635         201995.496857         49.0195366015    
-     153.235407529        -26920.8500352        -95.5490653732         1049.73038921    
-    -303668.474400         34.6552192357        -311.381398005        -2573.26572672    
-    -305.655896132         2184.69468892         13351.6717913        -19.4335088884    
-     22.7880169392         1316.62773983         338.538970175        -4827.30719818    
-    -18129.8411475         174.345465098         160.419963332        -34637.0590103    
-    -2.78053700935        -26.2242919731         1101.71974646        -58.8139202173    
-    -98.8160075054         15.1250045898         131.900467723         220.416287569    
-     8383.39797581        -415.650550225         73.8910895718        -1186.32825537    
-    -503.372540353         307.881743445        -7673.13149217         256.320882685    
-     185.711576043         9477.91352564         34.4424213332        -788.077678066    
-    -9905.78023321         197.283335062         4336.37538595        -11666.8138674    
-    -326.179235603        -83.9813555197         47738.8205697         28.5696329768    
-    -2.73993966358        -9073.82800669         66.4488629448         172.917975210    
-     2607.39258932         199.967722471        -266.640726784        -12941.3036574    
-     528.349274510        -143.390238176         27029.4505576         689.776665915    
-    -274.140232150         37171.1111280        -414.419315434        -635.146360978    
-    -28002.4180028        -523.899881838         816.008797252        -3565.81328530    
-    -1.62711490926         2.26634705322         2487.28008654        -4.39736790732    
-     3.09247356326         2263.63472216        -30.7010613521         29.6796972366    
-     1051.32925090         3.80964614356        -39.1238957038        -20357.1207856    
-     9.76280934891         80.6299948937        -22473.0487924         5.04372439510    
-    -1.11598309516         3209.22549846         55.4192016728        -60.1765481686    
-     26125.3668839         1.86318878675         31.9326978131        -261.476471682    
-    -79.4989264174        -172.672467975        -5360.64828765        -150.172507938    
-    -39.7643031773        -3330.31067894        0.527497449130         57.5748618416    
-    -959.031399349        -3.06551533982        -8.87062381055         203.357359557    
-    0.253947714466        0.996423578226         2747.73378150         34.7493032030    
-    -106.072787819         2962.93218535         40.1276918361         99.7598494309    
-    -5058.56250240        -20.5361879206         103.325926285        -3415.00250272    
-     26.9283882009         43.3199196283         7127.84061675         38.1012829905    
-     82.5654898697         9949.33156752         20.2521470433        -44.1108684004    
-     1799.08166310         2.88726734080        -239.333106561        -2891.25843939    
-     66.1992556584         103.270577231        -1541.79410081       -0.967090984060    
-     101.714991803        -2070.39082491    
-  n1 =   48189    err0 =      1.59E-04
diff --git a/examples/free-energy/data/input-md.xml b/examples/free-energy/data/input-md.xml
deleted file mode 100644
index 42bda7e1..00000000
--- a/examples/free-energy/data/input-md.xml
+++ /dev/null
@@ -1,73 +0,0 @@
-<simulation safe_stride='10' verbosity='medium'>
-    <ffsocket mode='unix' name='driver'>
-         <latency>  1.00000000e-04</latency> <address>zundel</address>
-   </ffsocket>
-   <ffplumed name="plumed">
-         <file mode="xyz">data/h5o2+.xyz</file>
-         <plumeddat> data/plumed-md.dat </plumeddat>
-         <plumed_extras> [doo, co1.lessthan, co2.lessthan, dc, mtd.bias ] </plumed_extras>
-   </ffplumed>
-   <total_steps>5000</total_steps>
-   <output prefix="meta-md">
-      <trajectory stride="10" filename="pos" cell_units="angstrom">positions{angstrom}</trajectory>
-      <trajectory stride="10" filename="colvar" bead="0" extra_type="doo,dc,mtd.bias"> extras_bias </trajectory>
-      <properties stride="10"> 
-      [ step, time, conserved, temperature{kelvin}, kinetic_md, 
-        potential, temperature{kelvin}(H), temperature{kelvin}(O), ensemble_bias ] 
-      </properties>
-   </output>
-   <prng>
-      <seed>18885</seed>
-   </prng>
-   <system>
-      <forces> 
-          <force forcefield="driver"></force>
-      </forces>
-      <initialize nbeads="1">
-        <file mode="xyz">data/h5o2+.xyz</file>
-        <cell>
-         [   25.29166, 0, 0, 0, 25.29166, 0, 0, 0, 25.29166 ]
-        </cell>
-      </initialize>
-      <ensemble>
-         <temperature units="kelvin"> 300.0 </temperature>
-         <bias>
-            <force forcefield="plumed"/>
-         </bias>
-      </ensemble>
-      <motion mode="dynamics">
-        <fixcom> False </fixcom>
-        <dynamics mode="nvt" splitting="baoab">
-         <timestep units="femtosecond"> 1.0 </timestep>
-<!--
-# Generated at http://cosmo-epfl.github.io/gle4md
-# Please cite:
-# M. Ceriotti, G. Bussi and M. Parrinello, J. Chem. Theory Comput. 6, 1170 (2010) 
-# M. Ceriotti, G. Bussi and M. Parrinello, Phys. Rev. Lett. 102, 020601 (2009)
-# Smart-sampling GLE. Enforces efficient sampling, focussing the effort on the slowest mode 
-# accessible by the simulation. Generated from the parameter file
-# library/smart/smart-0.5_6-2.a, 
-# and shifted so that they are effective to sample optimally 
-# a time scale of t_opt=1 picoseconds,
-# and do as well as possible upt to a cutoff frequency of 
-# νmax=100 THz [3336 cm^-1]
--->  
-            <thermostat mode='gle'>
-              <A shape='(7,7)'>
-                [   8.191023526179e-4,    8.328506066524e-3,    1.657771834013e-3,    9.736989925341e-4,    2.841803794895e-4,   -3.176846864198e-5,   -2.967010478210e-4, 
-            -8.389856546341e-4,    2.405526974742e-2,   -1.507872374848e-2,    2.589784240185e-3,    1.516783633362e-3,   -5.958833418565e-4,    4.198422349789e-4, 
-            7.798710586406e-4,    1.507872374848e-2,    8.569039501219e-3,    6.001000899602e-3,    1.062029383877e-3,    1.093939147968e-3,   -2.661575532976e-3, 
-            -9.676783161546e-4,   -2.589784240185e-3,   -6.001000899602e-3,    2.680459336535e-5,   -5.214694469742e-5,    4.231304910751e-4,   -2.104894919743e-5, 
-            -2.841997149166e-4,   -1.516783633362e-3,   -1.062029383877e-3,    5.214694469742e-5,    1.433903506353e-9,   -4.241574212449e-5,    7.910178912362e-5, 
-            3.333208286893e-5,    5.958833418565e-4,   -1.093939147968e-3,   -4.231304910751e-4,    4.241574212449e-5,    2.385554468441e-8,   -3.139255482869e-5, 
-            2.967533789056e-4,   -4.198422349789e-4,    2.661575532976e-3,    2.104894919743e-5,   -7.910178912362e-5,    3.139255482869e-5,   2.432567259684e-11
-              ]
-              </A>
-            </thermostat>
-        </dynamics>
-      </motion>
-  </system>
-  <smotion mode="metad">
-     <metad> <metaff> [ plumed ] </metaff> </metad>
-  </smotion>
-</simulation>
diff --git a/examples/free-energy/data/input-md_hiq.xml b/examples/free-energy/data/input-md_hiq.xml
deleted file mode 100644
index 4208d757..00000000
--- a/examples/free-energy/data/input-md_hiq.xml
+++ /dev/null
@@ -1,73 +0,0 @@
-<simulation safe_stride='10' verbosity='low'>
-    <ffsocket mode='unix' name='driver'>
-         <latency>  1.00000000e-04</latency> <address>zundel</address>
-   </ffsocket>
-   <ffplumed name="plumed">
-         <file mode="xyz">data/h5o2+.xyz</file>
-         <plumeddat> data/plumed-md_hiq.dat </plumeddat>
-         <plumed_extras> [doo, co1.lessthan, co2.lessthan, dc, mtd.bias ] </plumed_extras>
-   </ffplumed>
-   <total_steps>2000000</total_steps>
-   <output prefix="meta-md_hiq">
-      <trajectory stride="200" filename="pos" cell_units="angstrom">positions{angstrom}</trajectory>
-      <trajectory stride="20" filename="colvar" bead="0" extra_type="doo,dc,mtd.bias"> extras_bias </trajectory>
-      <properties stride="20"> 
-      [ step, time, conserved, temperature{kelvin}, kinetic_md, 
-        potential, temperature{kelvin}(H), temperature{kelvin}(O), ensemble_bias ] 
-      </properties>
-   </output>
-   <prng>
-      <seed>18885</seed>
-   </prng>
-   <system>
-      <forces> 
-          <force forcefield="driver"></force>
-      </forces>
-      <initialize nbeads="1">
-        <file mode="xyz">data/h5o2+.xyz</file>
-        <cell>
-         [   25.29166, 0, 0, 0, 25.29166, 0, 0, 0, 25.29166 ]
-        </cell>
-      </initialize>
-      <ensemble>
-         <temperature units="kelvin"> 300.0 </temperature>
-         <bias>
-            <force forcefield="plumed"/>
-         </bias>
-      </ensemble>
-      <motion mode="dynamics">
-        <fixcom> False </fixcom>
-        <dynamics mode="nvt" splitting="baoab">
-         <timestep units="femtosecond"> 0.5 </timestep>
-<!--
-# Generated at http://cosmo-epfl.github.io/gle4md
-# Please cite:
-# M. Ceriotti, G. Bussi and M. Parrinello, J. Chem. Theory Comput. 6, 1170 (2010) 
-# M. Ceriotti, G. Bussi and M. Parrinello, Phys. Rev. Lett. 102, 020601 (2009)
-# Smart-sampling GLE. Enforces efficient sampling, focussing the effort on the slowest mode 
-# accessible by the simulation. Generated from the parameter file
-# library/smart/smart-0.5_6-2.a, 
-# and shifted so that they are effective to sample optimally 
-# a time scale of t_opt=1 picoseconds,
-# and do as well as possible upt to a cutoff frequency of 
-# νmax=100 THz [3336 cm^-1]
--->  
-            <thermostat mode='gle'>
-              <A shape='(7,7)'>
-                [   8.191023526179e-4,    8.328506066524e-3,    1.657771834013e-3,    9.736989925341e-4,    2.841803794895e-4,   -3.176846864198e-5,   -2.967010478210e-4, 
-            -8.389856546341e-4,    2.405526974742e-2,   -1.507872374848e-2,    2.589784240185e-3,    1.516783633362e-3,   -5.958833418565e-4,    4.198422349789e-4, 
-            7.798710586406e-4,    1.507872374848e-2,    8.569039501219e-3,    6.001000899602e-3,    1.062029383877e-3,    1.093939147968e-3,   -2.661575532976e-3, 
-            -9.676783161546e-4,   -2.589784240185e-3,   -6.001000899602e-3,    2.680459336535e-5,   -5.214694469742e-5,    4.231304910751e-4,   -2.104894919743e-5, 
-            -2.841997149166e-4,   -1.516783633362e-3,   -1.062029383877e-3,    5.214694469742e-5,    1.433903506353e-9,   -4.241574212449e-5,    7.910178912362e-5, 
-            3.333208286893e-5,    5.958833418565e-4,   -1.093939147968e-3,   -4.231304910751e-4,    4.241574212449e-5,    2.385554468441e-8,   -3.139255482869e-5, 
-            2.967533789056e-4,   -4.198422349789e-4,    2.661575532976e-3,    2.104894919743e-5,   -7.910178912362e-5,    3.139255482869e-5,   2.432567259684e-11
-              ]
-              </A>
-            </thermostat>
-        </dynamics>
-      </motion>
-  </system>
-  <smotion mode="metad">
-     <metad> <metaff> [ plumed ] </metaff> </metad>
-  </smotion>
-</simulation>
diff --git a/examples/free-energy/data/input-pimd.xml b/examples/free-energy/data/input-pimd.xml
deleted file mode 100644
index 633cee81..00000000
--- a/examples/free-energy/data/input-pimd.xml
+++ /dev/null
@@ -1,74 +0,0 @@
-<simulation safe_stride='10' verbosity='medium'>
-    <ffsocket mode='unix' name='driver'>
-         <latency>  1.00000000e-04</latency> <address>zundel</address>
-   </ffsocket>
-   <ffplumed name="plumed">
-         <file mode="xyz">data/h5o2+.xyz</file>
-         <plumeddat> data/plumed-pimd.dat </plumeddat>
-         <plumed_extras> [doo, co1.lessthan, co2.lessthan, dc, mtd.bias ] </plumed_extras>
-   </ffplumed>
-   <total_steps>5000</total_steps>
-   <output prefix="meta-pimd">
-      <trajectory stride="10" filename="pos" cell_units="angstrom">positions{angstrom}</trajectory>
-      <trajectory stride="10" filename="xc" format="xyz">x_centroid{angstrom}</trajectory>
-      <trajectory stride="10" filename="colvar" bead="0" extra_type="doo,dc,mtd.bias"> extras_bias </trajectory>
-      <properties stride="10"> [ step, time, conserved, temperature{kelvin}, kinetic_cv, 
-            potential, temperature{kelvin}(H), temperature{kelvin}(O), ensemble_bias ] </properties>
-   </output>
-   <prng>
-      <seed>18885</seed>
-   </prng>
-   <system>
-      <forces> 
-          <force forcefield="driver"></force>
-      </forces>
-      <initialize nbeads="8">
-        <file mode="xyz">data/h5o2+.xyz</file>
-        <cell>
-         [   25.29166, 0, 0, 0, 25.29166, 0, 0, 0, 25.29166 ]
-        </cell>
-      </initialize>
-      <ensemble>
-         <temperature units="kelvin"> 300.0 </temperature>
-         <bias>
-           <force forcefield="plumed" nbeads="1">
-             <interpolate_extras> [ doo, dc, mtd.bias ] </interpolate_extras>
-           </force>
-         </bias>
-      </ensemble>
-      <motion mode="dynamics">
-        <fixcom> False </fixcom>
-        <dynamics mode="nvt" splitting="baoab">
-         <timestep units="femtosecond"> 1.0 </timestep>
-<!--
-# Generated at http://cosmo-epfl.github.io/gle4md
-# Please cite:
-# M. Ceriotti, G. Bussi and M. Parrinello, J. Chem. Theory Comput. 6, 1170 (2010) 
-# M. Ceriotti, G. Bussi and M. Parrinello, Phys. Rev. Lett. 102, 020601 (2009)
-# Smart-sampling GLE. Enforces efficient sampling, focussing the effort on the slowest mode 
-# accessible by the simulation. Generated from the parameter file
-# library/smart/smart-0.5_6-2.a, 
-# and shifted so that they are effective to sample optimally 
-# a time scale of t_opt=1 picoseconds,
-# and do as well as possible upt to a cutoff frequency of 
-# νmax=100 THz [3336 cm^-1]
--->  
-            <thermostat mode='gle'>
-              <A shape='(7,7)'>
-                [   8.191023526179e-4,    8.328506066524e-3,    1.657771834013e-3,    9.736989925341e-4,    2.841803794895e-4,   -3.176846864198e-5,   -2.967010478210e-4, 
-            -8.389856546341e-4,    2.405526974742e-2,   -1.507872374848e-2,    2.589784240185e-3,    1.516783633362e-3,   -5.958833418565e-4,    4.198422349789e-4, 
-            7.798710586406e-4,    1.507872374848e-2,    8.569039501219e-3,    6.001000899602e-3,    1.062029383877e-3,    1.093939147968e-3,   -2.661575532976e-3, 
-            -9.676783161546e-4,   -2.589784240185e-3,   -6.001000899602e-3,    2.680459336535e-5,   -5.214694469742e-5,    4.231304910751e-4,   -2.104894919743e-5, 
-            -2.841997149166e-4,   -1.516783633362e-3,   -1.062029383877e-3,    5.214694469742e-5,    1.433903506353e-9,   -4.241574212449e-5,    7.910178912362e-5, 
-            3.333208286893e-5,    5.958833418565e-4,   -1.093939147968e-3,   -4.231304910751e-4,    4.241574212449e-5,    2.385554468441e-8,   -3.139255482869e-5, 
-            2.967533789056e-4,   -4.198422349789e-4,    2.661575532976e-3,    2.104894919743e-5,   -7.910178912362e-5,    3.139255482869e-5,   2.432567259684e-11
-              ]
-              </A>
-            </thermostat>
-        </dynamics>
-      </motion>
-  </system>
-  <smotion mode="metad">
-     <metad> <metaff> [ plumed ] </metaff> </metad>
-  </smotion>
-</simulation>
diff --git a/examples/free-energy/data/input-pimd_hiq.xml b/examples/free-energy/data/input-pimd_hiq.xml
deleted file mode 100644
index fa637ce0..00000000
--- a/examples/free-energy/data/input-pimd_hiq.xml
+++ /dev/null
@@ -1,74 +0,0 @@
-<simulation safe_stride='10' verbosity='low'>
-    <ffsocket mode='unix' name='driver'>
-         <latency>  1.00000000e-04</latency> <address>zundel</address>
-   </ffsocket>
-   <ffplumed name="plumed">
-         <file mode="xyz">data/h5o2+.xyz</file>
-         <plumeddat> data/plumed-pimd_hiq.dat </plumeddat>
-         <plumed_extras> [doo, co1.lessthan, co2.lessthan, dc, mtd.bias ] </plumed_extras>
-   </ffplumed>
-   <total_steps>2000000</total_steps>
-   <output prefix="meta-pimd_hiq">
-      <trajectory stride="2000" filename="pos" cell_units="angstrom">positions{angstrom}</trajectory>
-      <trajectory stride="200" filename="xc" format="xyz">x_centroid{angstrom}</trajectory>
-      <trajectory stride="20" filename="colvar" bead="0" extra_type="doo,dc,mtd.bias"> extras_bias </trajectory>
-      <properties stride="20"> [ step, time, conserved, temperature{kelvin}, kinetic_cv, 
-            potential, temperature{kelvin}(H), temperature{kelvin}(O), ensemble_bias ] </properties>
-   </output>
-   <prng>
-      <seed>18885</seed>
-   </prng>
-   <system>
-      <forces> 
-          <force forcefield="driver"></force>
-      </forces>
-      <initialize nbeads="32">
-        <file mode="xyz">data/h5o2+.xyz</file>
-        <cell>
-         [   25.29166, 0, 0, 0, 25.29166, 0, 0, 0, 25.29166 ]
-        </cell>
-      </initialize>
-      <ensemble>
-         <temperature units="kelvin"> 300.0 </temperature>
-         <bias>
-           <force forcefield="plumed" nbeads="1">
-             <interpolate_extras> [ doo, dc, mtd.bias ] </interpolate_extras>
-           </force>
-         </bias>
-      </ensemble>
-      <motion mode="dynamics">
-        <fixcom> False </fixcom>
-        <dynamics mode="nvt" splitting="baoab">
-         <timestep units="femtosecond"> 0.5 </timestep>
-<!--
-# Generated at http://cosmo-epfl.github.io/gle4md
-# Please cite:
-# M. Ceriotti, G. Bussi and M. Parrinello, J. Chem. Theory Comput. 6, 1170 (2010) 
-# M. Ceriotti, G. Bussi and M. Parrinello, Phys. Rev. Lett. 102, 020601 (2009)
-# Smart-sampling GLE. Enforces efficient sampling, focussing the effort on the slowest mode 
-# accessible by the simulation. Generated from the parameter file
-# library/smart/smart-0.5_6-2.a, 
-# and shifted so that they are effective to sample optimally 
-# a time scale of t_opt=1 picoseconds,
-# and do as well as possible upt to a cutoff frequency of 
-# νmax=100 THz [3336 cm^-1]
--->  
-            <thermostat mode='gle'>
-              <A shape='(7,7)'>
-                [   8.191023526179e-4,    8.328506066524e-3,    1.657771834013e-3,    9.736989925341e-4,    2.841803794895e-4,   -3.176846864198e-5,   -2.967010478210e-4, 
-            -8.389856546341e-4,    2.405526974742e-2,   -1.507872374848e-2,    2.589784240185e-3,    1.516783633362e-3,   -5.958833418565e-4,    4.198422349789e-4, 
-            7.798710586406e-4,    1.507872374848e-2,    8.569039501219e-3,    6.001000899602e-3,    1.062029383877e-3,    1.093939147968e-3,   -2.661575532976e-3, 
-            -9.676783161546e-4,   -2.589784240185e-3,   -6.001000899602e-3,    2.680459336535e-5,   -5.214694469742e-5,    4.231304910751e-4,   -2.104894919743e-5, 
-            -2.841997149166e-4,   -1.516783633362e-3,   -1.062029383877e-3,    5.214694469742e-5,    1.433903506353e-9,   -4.241574212449e-5,    7.910178912362e-5, 
-            3.333208286893e-5,    5.958833418565e-4,   -1.093939147968e-3,   -4.231304910751e-4,    4.241574212449e-5,    2.385554468441e-8,   -3.139255482869e-5, 
-            2.967533789056e-4,   -4.198422349789e-4,    2.661575532976e-3,    2.104894919743e-5,   -7.910178912362e-5,    3.139255482869e-5,   2.432567259684e-11
-              ]
-              </A>
-            </thermostat>
-        </dynamics>
-      </motion>
-  </system>
-  <smotion mode="metad">
-     <metad> <metaff> [ plumed ] </metaff> </metad>
-  </smotion>
-</simulation>
diff --git a/examples/free-energy/data/plumed-md.dat b/examples/free-energy/data/plumed-md.dat
deleted file mode 100644
index 6c839207..00000000
--- a/examples/free-energy/data/plumed-md.dat
+++ /dev/null
@@ -1,10 +0,0 @@
-# default units are LENGTH=nm ENERGY=kJ/mol TIME=ps
-doo: DISTANCE ATOMS=1,2 
-co1: DISTANCES GROUPA=1 GROUPB=3-7 LESS_THAN={RATIONAL R_0=0.14}
-co2: DISTANCES GROUPA=2 GROUPB=3-7 LESS_THAN={RATIONAL R_0=0.14}
-dc: COMBINE ARG=co1.lessthan,co2.lessthan COEFFICIENTS=1,-1 PERIODIC=NO
-mtd:   METAD ARG=doo,dc PACE=10 SIGMA=0.005,0.05 HEIGHT=4 FILE=HILLS-md BIASFACTOR=10 TEMP=300
-uwall: UPPER_WALLS ARG=doo AT=0.4 KAPPA=250
-
-PRINT ARG=doo,co1.*,co2.*,dc,mtd.*,uwall.* STRIDE=10 FILE=COLVAR-md
-FLUSH STRIDE=1
diff --git a/examples/free-energy/data/plumed-md_hiq.dat b/examples/free-energy/data/plumed-md_hiq.dat
deleted file mode 100644
index cc5a5302..00000000
--- a/examples/free-energy/data/plumed-md_hiq.dat
+++ /dev/null
@@ -1,10 +0,0 @@
-# default units are LENGTH=nm ENERGY=kJ/mol TIME=ps
-doo: DISTANCE ATOMS=1,2 
-co1: DISTANCES GROUPA=1 GROUPB=3-7 LESS_THAN={RATIONAL R_0=0.14}
-co2: DISTANCES GROUPA=2 GROUPB=3-7 LESS_THAN={RATIONAL R_0=0.14}
-dc: COMBINE ARG=co1.lessthan,co2.lessthan COEFFICIENTS=1,-1 PERIODIC=NO
-mtd:   METAD ARG=doo,dc PACE=100 SIGMA=0.0025,0.025 HEIGHT=1 FILE=HILLS-md_hiq BIASFACTOR=8 TEMP=300
-uwall: UPPER_WALLS ARG=doo AT=0.4 KAPPA=250
-
-PRINT ARG=doo,co1.*,co2.*,dc,mtd.*,uwall.* STRIDE=20 FILE=COLVAR-md_hiq
-FLUSH STRIDE=1
diff --git a/examples/free-energy/data/plumed-pimd.dat b/examples/free-energy/data/plumed-pimd.dat
deleted file mode 100644
index dcfd3478..00000000
--- a/examples/free-energy/data/plumed-pimd.dat
+++ /dev/null
@@ -1,10 +0,0 @@
-# default units are LENGTH=nm ENERGY=kJ/mol TIME=ps
-doo: DISTANCE ATOMS=1,2 
-co1: DISTANCES GROUPA=1 GROUPB=3-7 LESS_THAN={RATIONAL R_0=0.14}
-co2: DISTANCES GROUPA=2 GROUPB=3-7 LESS_THAN={RATIONAL R_0=0.14}
-dc: COMBINE ARG=co1.lessthan,co2.lessthan COEFFICIENTS=1,-1 PERIODIC=NO
-mtd:   METAD ARG=doo,dc PACE=10 SIGMA=0.005,0.05 HEIGHT=4 FILE=HILLS-pimd BIASFACTOR=10 TEMP=300
-uwall: UPPER_WALLS ARG=doo AT=0.4 KAPPA=250
-
-PRINT ARG=doo,co1.*,co2.*,dc,mtd.*,uwall.* STRIDE=10 FILE=COLVAR-pimd
-FLUSH STRIDE=1
diff --git a/examples/free-energy/data/plumed-pimd_hiq.dat b/examples/free-energy/data/plumed-pimd_hiq.dat
deleted file mode 100644
index 3c8689c6..00000000
--- a/examples/free-energy/data/plumed-pimd_hiq.dat
+++ /dev/null
@@ -1,10 +0,0 @@
-# default units are LENGTH=nm ENERGY=kJ/mol TIME=ps
-doo: DISTANCE ATOMS=1,2 
-co1: DISTANCES GROUPA=1 GROUPB=3-7 LESS_THAN={RATIONAL R_0=0.14}
-co2: DISTANCES GROUPA=2 GROUPB=3-7 LESS_THAN={RATIONAL R_0=0.14}
-dc: COMBINE ARG=co1.lessthan,co2.lessthan COEFFICIENTS=1,-1 PERIODIC=NO
-mtd:   METAD ARG=doo,dc PACE=100 SIGMA=0.0025,0.025 HEIGHT=1 FILE=HILLS-pimd_hiq BIASFACTOR=8 TEMP=300
-uwall: UPPER_WALLS ARG=doo AT=0.4 KAPPA=250
-
-PRINT ARG=doo,co1.*,co2.*,dc,mtd.*,uwall.* STRIDE=10 FILE=COLVAR-pimd_hiq
-FLUSH STRIDE=1
diff --git a/examples/free-energy/environment.yml b/examples/free-energy/environment.yml
index 05352af3..35f747cc 100644
--- a/examples/free-energy/environment.yml
+++ b/examples/free-energy/environment.yml
@@ -11,6 +11,7 @@ dependencies:
   - py-plumed  
   - pip:
     - ase==3.22.1
+    - chemiscope
     - git+https://github.com/i-pi/i-pi.git@main#egg=ipi
     - matplotlib
 variables:
diff --git a/examples/free-energy/free-energy.py b/examples/free-energy/free-energy.py
index adc4d8a0..9f941f5b 100644
--- a/examples/free-energy/free-energy.py
+++ b/examples/free-energy/free-energy.py
@@ -17,6 +17,9 @@
 import subprocess
 import time
 
+import ipi
+import ase.io
+import chemiscope
 import ipi.utils.parsing as pimdmooc
 import numpy as np
 import matplotlib.pyplot as plt
@@ -48,3 +51,321 @@
 #     B &= 0.000598024968321866~\text{a.u.}\\
 #     \end{align}
 #
+# Let's define a function to visualize the PES!
+#
+
+def PES(x, y , z):
+    """
+    PES from Ref. `Y. Litman et al., JCP (2022)`
+    """
+    
+    A = -0.00476705894242374
+    B = 0.000598024968321866 
+    k = 1837.107 * 0.017314074**2
+    
+    return A * x**2 + B * x**4 + k * y**2 / 2 +  k * z**2 / 2
+
+# %%
+# The PES, in three dimensions, can be drawn with xy contours
+# (each contour corresponds to kB T with T = 300 K), for various z values. 
+#
+
+x = np.linspace(-3,3,21)
+y = np.linspace(-0.5,0.5,21)
+
+X, Y = np.meshgrid(x, y)
+Z = PES(X, Y, 0)
+
+
+contour_levels = [np.min(Z) + 0.00095004347 * i for i in range(12)]
+
+plt.title(r'$V(x,y,0)$')
+plt.xlabel(r'$x$ [a.u.]')
+plt.ylabel(r'$y$ [a.u.]')
+plt.contour(X, Y, Z, levels=contour_levels)
+plt.show()
+
+# %%
+# **Questions**:
+#
+# 1. Looking at the contours can you tell
+# if delocalization of the system to its other minimum is
+# a rare event with respect to the time scale of
+# the system's vibrations?
+# 
+# 2. Feel free to plot it for various z values.
+# Does the plot change? What does it tell you
+# about the coupling between the modes?
+#
+#
+
+# %%
+# Calculating the free energy of a hamiltonian
+# ============================================
+#
+# The harmonic approximation
+# --------------------------
+#
+# The harmonic approximation to the PES is essentially
+# a truncated Taylor series expansion to second
+# order around one of its minima.
+# :math:`V^{\text{harm}} = V(q_0) + \frac{2}{2} \left.\frac{\partial^2 V}{\partial q^2}\right|_{q_0} (q - q_0)^2`  
+# where :math:`q = (x,y,z)`
+# is a position vector and :math:`q_0 = \text{arg min}_{q} V` is
+# the position where the PES has a local minimum.
+#
+# Let's use the i-PI code to optimize the PES with respect to its position
+# to find :math:`q_0` and :math:`V^{\text{harm}}`.
+#
+
+# %%
+# Step 1: fixed cell geometry optimization
+# ----------------------------------------
+# 
+# To find :math:`q_0` we will use the fixed-cell geometry
+# optimization feature of i-PI! The inputs are
+# into the `geop` directory.
+#
+# You will find the i-PI input file. Have a look at the
+# `input.xml` file and see if you can understand its various parts.
+#
+# The snippet that implements the geometry optimization feature is 
+#
+# .. code-block:: xml
+#
+#    <motion mode='minimize'>
+#      <optimizer mode='bfgs'>
+#        <tolerances>
+#          <energy> 1e-5 </energy>
+#          <force> 1e-5 </force>
+#          <position> 1e-5 </position>
+#        </tolerances>
+#      </optimizer>
+#    </motion>
+#
+#
+# In essence, the geometry optimization is implemented as a
+# motion class. At every step instead of performing "dynamics" we will
+# simply move towards a local minimum of the PES. There are
+# many algorithms for locally optimizing high-dimensional functions;
+# here we use the robust
+# `BFGS <https://en.wikipedia.org/wiki/Broyden%E2%80%93Fletcher%E2%80%93Goldfarb%E2%80%93Shanno_algorithm>`_
+# method. The tolerances set thershold values for changes in the energy,
+# positions and forces, that are sufficient to deem an optimization converged. 
+#
+
+# %%
+# Installing the Python driver
+#
+# i-PI comes with a FORTRAN driver, which however has to be installed
+# from source. We use a utility function to compile it. Note that this requires
+# a functioning build system with `gfortran` and `make`.
+
+ipi.install_driver()
+# %%
+# To perform a fixed-cell geomerty optimization
+# the bash script command should look like: 
+# 
+# .. code-block:: bash
+#
+#      i-pi geop/input.xml > log.i-pi $
+#      sleep(5)
+#      i-pi-driver -u -h geop -m doublewell_1D & 
+# 
+# The same can be achieved from Python using `subprocess.Popen`
+
+
+ipi_process = subprocess.Popen(["i-pi", "geop/input.xml"])
+time.sleep(5)  # wait for i-PI to start
+driver_process =subprocess.Popen(
+            ["i-pi-driver", "-u", "-h", "geop", "-m", "doublewell_1D"]
+        )
+    
+# %%
+# If you run this in a notebook, you can go ahead and start loading
+# output files *before* i-PI and lammps have finished running, by
+# skipping this cell
+
+ipi_process.wait()
+driver_process.wait()
+    
+# %%
+#
+# The number of steps taken for an optimization calculation depends on
+# the system (the PES), the optimization method,
+# and the initial configuration. Here,
+# we initialize the system from :math:`q = (2.0, 0.2, -0.5)`
+# as seen in the `geop/init.xyz` file.
+#
+# You can analyze your optimization calculation by plotting
+# the potential energy vs steps and confirm if the potential
+# energy has indeed converged to the set threshold!
+# 
+# The final frame of the `geop.pos_0.xyz` file gives 
+# with chemiscope we can wisualize the minimzation 
+# trajectory and its energies.
+#
+
+geop_out,_geop = ipi.read_output('geop.out')
+geop_traj = ipi.read_trajectory("geop.pos_0.xyz")
+
+chemiscope.show(
+    frames=geop_traj,
+    properties={
+        "steps": { "values" : np.arange(len(geop_traj)),
+                  "target" : "structure"},
+        "U":{"values": geop_out['potential'],
+              "target" : "structure"},
+    }, 
+    settings=chemiscope.quick_settings(
+        x="steps", y="U", trajectory=True
+    ),
+    mode="structure",
+)
+
+# %%
+# Step 2: harmonic calculation
+# ----------------------------
+#
+# To compute the system's Hessian we will use the vibrations feature of i-PI. 
+# Go through the `input.xml` file.
+# The snippet that implements the vibrations feature is 
+# 
+# .. code-block:: xml
+#
+#    <motion mode='vibrations'>
+#      <vibrations mode='fd'>
+#        <pos_shift> 0.001 </pos_shift>
+#        <energy_shift> 0.001 </energy_shift>
+#        <prefix> phonons </prefix>
+#        <asr> none </asr>
+#      </vibrations>
+#    </motion>
+#
+# The system's Hessian is computed using the finite difference method.
+# This approach approximates the ij-th element of the Hessian in terms
+# of the forces acting at infinitisemally displaced positions around the minimum:
+#
+# .. math::
+#
+#      \frac{\partial^2 V}{\partial q^2}_{ij} \approx - \frac{1}{2 \epsilon}
+#      \left(\left.f_{i}\right|_{q_{j} + \epsilon} - \left.f_{i}\right|_{q_{j}
+#      - \epsilon} \right)
+#
+# At every step instead of performing "dynamics", we will displace a degree of
+# freedom along :math:`\pm \epsilon` and estimate one row of the Hessian. `pos_shift` sets
+# the value of :math:`\epsilon` while `asr` zeros out the blocks of the Hessian due to continuous
+# symmetries (translations or rotations for solids or clusters). In this example,
+# we set this option to `none` as our system doesn't possess any continuous symmetries.
+#
+
+# %%
+# The initial configuration for this calculation should correspond to an
+# opitimized position. You can obtain this from the last frame of the geop trajectory. 
+
+ase.io.write('init_harm.xyz',geop_traj,format='extxyz')
+
+# %%
+# The `bash` command for this would be
+# 
+# .. code-block:: bash
+#
+#      i-pi harm/input.xml > log.i-pi $
+#      sleep(5)
+#      i-pi-driver -u -h vib -m doublewell_1D & 
+# 
+# Again we will use `subprocess.Popen`
+
+ipi_process = subprocess.Popen(["i-pi", "harm/input.xml"])
+time.sleep(5)  # wait for i-PI to start
+driver_process =subprocess.Popen(
+            ["i-pi-driver", "-u", "-h", "vib", "-m", "doublewell_1D"]
+        )
+
+# %%
+# If you run this in a notebook, you can go ahead and start loading
+# output files *before* i-PI and lammps have finished running, by
+# skipping this cell
+
+ipi_process.wait()
+driver_process.wait()
+
+# %%
+# The Hessian can be recovered from the `harm.phonons.hess`file. 
+# You can use the snippet below to plot the harmonic approximation
+# to the PES
+#
+
+def PES_harm(x,y,z):
+    """
+    Harmonic approximation to the PES from Ref. `Y. Litman et al., JCP (2022)` around 
+    a local minimum. Note this function is only valid for the example!
+    """
+    
+    return V0 + hess[0,0] * (x - q0[0])**2 / 2 + hess[1,1] * (y - q0[1])**2 / 2 + hess[2,2] * (z - q0[2])**2 / 2
+
+hess = np.loadtxt('harm.phonons.hess', comments='#')
+q0 = ipi.read_trajectory('init_harm.xyz')[0].positions[0] / 0.529177
+V0 = np.loadtxt('harm.out', ndmin=2)[0,1]
+
+x = np.linspace(-3,3,21)
+y = np.linspace(-0.5,0.5,21)
+
+X, Y = np.meshgrid(x, y)
+
+contour_levels = [np.min(Z) + 0.00095004347 * i for i in range(12)]
+
+plt.title(r'$V(x,y,0)$')
+plt.xlabel(r'$x$ [a.u.]')
+plt.ylabel(r'$y$ [a.u.]')
+plt.contour(X, Y, PES(X, Y, 0), levels=contour_levels)
+plt.show()
+
+plt.title(r'$V^{\mathrm{harm}}(x,y,0)$')
+plt.xlabel(r'$x$ [a.u.]')
+plt.ylabel(r'$y$ [a.u.]')
+plt.contour(X, Y, PES_harm(X, Y, 0), levels=contour_levels)
+plt.show()
+
+# %%
+# The harmonic calculation also  gives us the frequency modes
+# from the dynamical matrix (mass scaled hessian)!
+#
+
+W2s = np.loadtxt('harm.phonons.eigval')
+print ('Harmonic Frequencies')
+for w2 in W2s:
+    print('%10.5f cm^-1'% (w2**0.5 * 219474))
+
+# %% 
+# These frequencies can be used to calculate the quantum harmonic
+# free energy of the system -- an approxiamtion to its true free energy!
+#
+
+def quantum_harmonic_free_energy(Ws, T):
+    """
+    Receives a list of frequencies in atomic units and the temperature 
+    in Kelvin. Returns the system's harmonic free energy.
+    """
+    
+    hbar = 1
+    kB = 3.1668116e-06
+    
+    return V0 + -kB * T * np.log(1 - np.exp(-hbar * Ws / (kB * T))).sum() 
+
+print ('Quantum Harmonic free energy: %15.8f [a.u.]'% (quantum_harmonic_free_energy(W2s**0.5, 300)))
+print ('Quantum Harmonic free energy: %15.8f [eV]'% (quantum_harmonic_free_energy(W2s**0.5, 300) * 27.211386))
+print ('Quantum Harmonic  free energy: %15.8f [kJ/mol]' % (quantum_harmonic_free_energy(W2s**0.5, 300) * 2625.4996))
+
+# %%
+#
+# The exact free energy for the system when localized in one of
+# the wells is still around 0.65 kJ/mol off w.r.t the harmonic limit. 
+#
+
+F = -7.53132797e-05 + quantum_harmonic_free_energy(W2s**0.5, 300)
+
+print ('Exact Quantum free energy: %15.8f [a.u.]'% (F))
+print ('Exact Quantum free energy: %15.8f [eV]'% (F * 27.211386))
+print ('Exact Quantum free energy: %15.8f [kJ/mol]' % (F * 2625.4996))
+

From ac15f6861d3cd0b524fa89be7563a3908837c38f Mon Sep 17 00:00:00 2001
From: DavideTisi <davide.tisi93@gmail.com>
Date: Wed, 13 Nov 2024 17:39:48 +0100
Subject: [PATCH 3/8] start anharmonic

---
 examples/free-energy/free-energy.py | 40 ++++++++++++++++++++++++++++-
 1 file changed, 39 insertions(+), 1 deletion(-)

diff --git a/examples/free-energy/free-energy.py b/examples/free-energy/free-energy.py
index 9f941f5b..3368f911 100644
--- a/examples/free-energy/free-energy.py
+++ b/examples/free-energy/free-energy.py
@@ -291,7 +291,7 @@ def PES(x, y , z):
 driver_process.wait()
 
 # %%
-# The Hessian can be recovered from the `harm.phonons.hess`file. 
+# The Hessian can be recovered from the `harm.phonons.hess` file. 
 # You can use the snippet below to plot the harmonic approximation
 # to the PES
 #
@@ -369,3 +369,41 @@ def quantum_harmonic_free_energy(Ws, T):
 print ('Exact Quantum free energy: %15.8f [eV]'% (F * 27.211386))
 print ('Exact Quantum free energy: %15.8f [kJ/mol]' % (F * 2625.4996))
 
+# %%
+# 
+# Harmonic to anharmonic
+# ----------------------
+#
+# Calculating free energies beyond the harmonic approximation is non-trivial.
+# There exist a familty of methods that can  solve the vibrational Schroedinger
+# Equation by approximating the anharmonic component of the PES, yielding an amharmonic
+# free energy. While highly effective for low-dimensional or mildly anharmonic systems,
+# the method of resort for *numerically-exact amharmonic free energies* of solid and clusters
+# is the thermodynamic integration method combined with the path-integral method 
+# ( for applications see Refs.
+# `M. Rossi et al, PRL (2016) <https://doi.org/10.1103/PhysRevLett.117.115702>`_,
+# `V. Kapil et al, JCTC (2019) <https://doi.org/10.1021/acs.jctc.9b00596>`_,
+# `V. Kapil et al, PNAS (2022) <https://doi.org/10.1073/pnas.2111769119>`_).
+#  
+#
+# The central idea is to reversibly change the potential from harmonic to anharmonic
+# by defining a :math:`\lambda`-dependent Hamiltonian 
+#
+# .. math::
+#    \hat{H}(\lambda) = \hat{T} + \lambda
+#    \hat{V}^{\text{harm}}  + (1 - \lambda) \hat{V}
+#
+# The  the anharmonic free energy is calculated as the reversible work done
+# along the fictitious path in :math:`\lambda`-space
+#
+# .. math::
+#     F = F^{\text{harm}} + \left< \hat{V} -
+#     \hat{V}^{\text{harm}} \right>_{\lambda}
+#
+#
+# where :math:`\left< \hat{O} \right>_{\lambda}` 
+# is the path-integral estimator for a positon dependent operator 
+# for :math:`\hat{H}(\lambda)`.
+
+
+

From 13aeefcce7765f97096819a8ed7949863e3e8818 Mon Sep 17 00:00:00 2001
From: DavideTisi <davide.tisi93@gmail.com>
Date: Wed, 13 Nov 2024 17:42:04 +0100
Subject: [PATCH 4/8] add folders

---
 examples/free-energy/geop/init.xyz  |  3 +++
 examples/free-energy/geop/input.xml | 30 +++++++++++++++++++++++++++++
 examples/free-energy/harm/input.xml | 27 ++++++++++++++++++++++++++
 3 files changed, 60 insertions(+)
 create mode 100644 examples/free-energy/geop/init.xyz
 create mode 100644 examples/free-energy/geop/input.xml
 create mode 100644 examples/free-energy/harm/input.xml

diff --git a/examples/free-energy/geop/init.xyz b/examples/free-energy/geop/init.xyz
new file mode 100644
index 00000000..18501ba9
--- /dev/null
+++ b/examples/free-energy/geop/init.xyz
@@ -0,0 +1,3 @@
+1
+# CELL(GENH): 100.0 0.0 0.0 0.0 100.0 0.0 0.0 0.0 100.0 positions{angstrom} cell{angstrom}
+H 2.0 0.2 -0.5 
diff --git a/examples/free-energy/geop/input.xml b/examples/free-energy/geop/input.xml
new file mode 100644
index 00000000..68ed7233
--- /dev/null
+++ b/examples/free-energy/geop/input.xml
@@ -0,0 +1,30 @@
+<simulation mode='static' verbosity='high'>
+  <output prefix='geop'>
+    <properties stride='1' filename='out'>  [ step, potential ] </properties>
+    <trajectory filename='pos' stride='1'> positions </trajectory>
+  </output>
+  <total_steps> 1000 </total_steps>
+  <prng>
+    <seed> 32342 </seed>
+  </prng>
+  <ffsocket name='driver' mode='unix' pbc='false'>
+    <address> geop </address>
+  </ffsocket>
+  <system>
+    <initialize nbeads='1'>
+      <file mode='xyz'> geop/init.xyz </file>
+    </initialize>
+    <forces>
+      <force forcefield='driver'> </force>
+    </forces>
+    <motion mode='minimize'>
+      <optimizer mode='bfgs'>
+        <tolerances>
+          <energy> 1e-5 </energy>
+          <force> 1e-5 </force>
+          <position> 1e-5 </position>
+        </tolerances>
+      </optimizer>
+    </motion>
+  </system>
+</simulation>
diff --git a/examples/free-energy/harm/input.xml b/examples/free-energy/harm/input.xml
new file mode 100644
index 00000000..a44e04d7
--- /dev/null
+++ b/examples/free-energy/harm/input.xml
@@ -0,0 +1,27 @@
+<simulation mode='static' verbosity='high'>
+  <output prefix='harm'>
+    <properties stride='10' filename='out'>  [ step, potential ] </properties>
+  </output>
+  <total_steps> 5000 </total_steps>
+  <prng>
+    <seed> 32342 </seed>
+  </prng>
+  <ffsocket name='lmp' mode='unix' pbc='true'>
+    <address> vib </address>
+  </ffsocket>
+  <system>
+    <initialize nbeads='1'>
+      <file mode='ase'> init_harm.xyz </file>
+    </initialize>
+    <forces>
+      <force forcefield='lmp'> </force>
+    </forces>
+    <motion mode='vibrations'>
+      <vibrations mode='fd'>
+        <pos_shift> 0.001 </pos_shift>
+        <prefix> phonons </prefix>
+        <asr> none </asr>
+      </vibrations>
+    </motion>
+  </system>
+</simulation>

From 105214a0886e461b053c4c7f7d6343802f69128b Mon Sep 17 00:00:00 2001
From: DavideTisi <davide.tisi93@gmail.com>
Date: Wed, 13 Nov 2024 18:15:59 +0100
Subject: [PATCH 5/8] last-part

---
 examples/free-energy/free-energy.py | 60 ++++++++++++++++++++++++++++-
 1 file changed, 59 insertions(+), 1 deletion(-)

diff --git a/examples/free-energy/free-energy.py b/examples/free-energy/free-energy.py
index 3368f911..96b30941 100644
--- a/examples/free-energy/free-energy.py
+++ b/examples/free-energy/free-energy.py
@@ -263,7 +263,7 @@ def PES(x, y , z):
 # The initial configuration for this calculation should correspond to an
 # opitimized position. You can obtain this from the last frame of the geop trajectory. 
 
-ase.io.write('init_harm.xyz',geop_traj,format='extxyz')
+ase.io.write('init_harm.xyz',geop_traj[-1],format='extxyz')
 
 # %%
 # The `bash` command for this would be
@@ -405,5 +405,63 @@ def quantum_harmonic_free_energy(Ws, T):
 # is the path-integral estimator for a positon dependent operator 
 # for :math:`\hat{H}(\lambda)`.
 
+# %%
+#
+# Step 3: Harmonic to anharmonic thermodynamic integration
+# --------------------------------------------------------
+#
+# A full quantum thermodynamic integration calculation requires
+# knowledge of the harmonic reference. Luckily we have just performed these
+# calculations! 
+#
+
+# %%
+# Classical Statistical Mechanics
+# -------------------------------
+#
+# Let's first compute the anharmonic free energy difference within the classical approximation.
+# 
+# To create the input file for I-PI we need to defines a "mixed"
+# :math:`\lambda`-dependent Hamiltonian. Let's see the new most important parts. 
+#
+# This i-PI calculation includes two "forcefield classes" 
+#
+# .. code-block:: xml
+# 
+#    <!-->  defines the anharmonic PES <-->
+#    <ffsocket name='driver' mode='unix' matching='any' pbc='false'>
+#        <address> f0 </address>
+#        <latency> 1e-3 </latency>
+#    </ffsocket>
+# 
+# a standard socket 
+# 
+# and 
+# 
+# .. code-block:: xml
+#
+#    <!-->  defines the harmonic PES <-->
+#    <ffdebye name='debye'>
+#            <hessian shape='(3,3)' mode='file'> HESSIAN-FILE </hessian>
+#            <x_reference mode='file'> X-REF-FILE <!--> relative path to a file containing the optimized positon vector <-->   </x_reference>
+#            <v_reference> V-REF <!-->  the value of the PES at its local minimum <-->   </v_reference>
+#    </ffdebye>
+# 
+# an intrinsic harmonic forcefield that builds the harmonic potential.
+# This requires :math:`q_0`, :math:`V(q_0)` and the full Hessian. 
+# `HESSIAN-FILE` is `harm.phonons.hess` which is the file containing the
+# full hessian.
+# X-REF-FILE is a file with the optimized positon vector  
+# 
+
+with open('ref.data','w') as xref:
+    for pos in geop_traj[-1].positions:
+        xref.write(f'{pos[0]}  {pos[1]}  {pos[2]} \n')
+
+# V-REF can be obtained from the potential energy in `harm.out`
+
+V-ref = np.readtxt('harm.out')
+print(V-ref)
+
 
 

From a09d177d021d0186fef2c488a22b518db7629be5 Mon Sep 17 00:00:00 2001
From: DavideTisi <davide.tisi93@gmail.com>
Date: Tue, 10 Dec 2024 18:08:48 +0100
Subject: [PATCH 6/8] finish and works

---
 examples/free-energy/cti/init.xyz    |   3 +
 examples/free-energy/environment.yml |   2 +-
 examples/free-energy/free-energy.py  | 644 +++++++++++++++++++++------
 examples/free-energy/qti/init.xyz    |   3 +
 4 files changed, 526 insertions(+), 126 deletions(-)
 create mode 100644 examples/free-energy/cti/init.xyz
 create mode 100644 examples/free-energy/qti/init.xyz

diff --git a/examples/free-energy/cti/init.xyz b/examples/free-energy/cti/init.xyz
new file mode 100644
index 00000000..8032e3da
--- /dev/null
+++ b/examples/free-energy/cti/init.xyz
@@ -0,0 +1,3 @@
+1
+# CELL(abcABC):  188.97261   188.97261   188.97261    90.00000    90.00000    90.00000  Step:          13  Bead:       0 positions{atomic_unit}  cell{atomic_unit}
+       H  1.99641e+00 -6.18337e-10  1.54584e-09
diff --git a/examples/free-energy/environment.yml b/examples/free-energy/environment.yml
index 35f747cc..c18b1d79 100644
--- a/examples/free-energy/environment.yml
+++ b/examples/free-energy/environment.yml
@@ -8,9 +8,9 @@ dependencies:
   - make
   - git
   - plumed
-  - py-plumed  
   - pip:
     - ase==3.22.1
+    - pyfftw
     - chemiscope
     - git+https://github.com/i-pi/i-pi.git@main#egg=ipi
     - matplotlib
diff --git a/examples/free-energy/free-energy.py b/examples/free-energy/free-energy.py
index 96b30941..69535352 100644
--- a/examples/free-energy/free-energy.py
+++ b/examples/free-energy/free-energy.py
@@ -17,13 +17,12 @@
 import subprocess
 import time
 
-import ipi
 import ase.io
 import chemiscope
+import ipi
 import ipi.utils.parsing as pimdmooc
-import numpy as np
 import matplotlib.pyplot as plt
-
+import numpy as np
 
 
 # %%
@@ -35,18 +34,18 @@
 # Ref. `Y. Litman et al., JCP (2022)
 # <https://pubs.aip.org/aip/jcp/article/156/19/194107/2841188/Dissipative-tunneling-rates-through-the>`_
 # Its potential energy surface (PES) is described by the function
-# 
+#
 # .. math::
 #
 #    V = A x^2 + B x^4 + \frac{1}{2} m \omega^2 y^2 + \frac{1}{2} m \omega^2 z^2
-# 
+#
 # with:
-# 
+#
 # .. math::
-#     
+#
 #     \begin{align}
-#     m &= 1837.107~\text{a.u.}\\ 
-#     \omega &= 3800 ~\text{cm}^{-1} = 0.017314074~\text{a.u.}\\ 
+#     m &= 1837.107~\text{a.u.}\\
+#     \omega &= 3800 ~\text{cm}^{-1} = 0.017314074~\text{a.u.}\\
 #     A &= -0.00476705894242374~\text{a.u.}\\
 #     B &= 0.000598024968321866~\text{a.u.}\\
 #     \end{align}
@@ -54,24 +53,26 @@
 # Let's define a function to visualize the PES!
 #
 
-def PES(x, y , z):
+
+def PES(x, y, z):
     """
     PES from Ref. `Y. Litman et al., JCP (2022)`
     """
-    
+
     A = -0.00476705894242374
-    B = 0.000598024968321866 
+    B = 0.000598024968321866
     k = 1837.107 * 0.017314074**2
-    
-    return A * x**2 + B * x**4 + k * y**2 / 2 +  k * z**2 / 2
+
+    return A * x**2 + B * x**4 + k * y**2 / 2 + k * z**2 / 2
+
 
 # %%
 # The PES, in three dimensions, can be drawn with xy contours
-# (each contour corresponds to kB T with T = 300 K), for various z values. 
+# (each contour corresponds to kB T with T = 300 K), for various z values.
 #
 
-x = np.linspace(-3,3,21)
-y = np.linspace(-0.5,0.5,21)
+x = np.linspace(-3, 3, 21)
+y = np.linspace(-0.5, 0.5, 21)
 
 X, Y = np.meshgrid(x, y)
 Z = PES(X, Y, 0)
@@ -79,9 +80,9 @@ def PES(x, y , z):
 
 contour_levels = [np.min(Z) + 0.00095004347 * i for i in range(12)]
 
-plt.title(r'$V(x,y,0)$')
-plt.xlabel(r'$x$ [a.u.]')
-plt.ylabel(r'$y$ [a.u.]')
+plt.title(r"$V(x,y,0)$")
+plt.xlabel(r"$x$ [a.u.]")
+plt.ylabel(r"$y$ [a.u.]")
 plt.contour(X, Y, Z, levels=contour_levels)
 plt.show()
 
@@ -92,7 +93,7 @@ def PES(x, y , z):
 # if delocalization of the system to its other minimum is
 # a rare event with respect to the time scale of
 # the system's vibrations?
-# 
+#
 # 2. Feel free to plot it for various z values.
 # Does the plot change? What does it tell you
 # about the coupling between the modes?
@@ -109,7 +110,7 @@ def PES(x, y , z):
 # The harmonic approximation to the PES is essentially
 # a truncated Taylor series expansion to second
 # order around one of its minima.
-# :math:`V^{\text{harm}} = V(q_0) + \frac{2}{2} \left.\frac{\partial^2 V}{\partial q^2}\right|_{q_0} (q - q_0)^2`  
+# :math:`V^{\text{harm}} = V(q_0) + \frac{2}{2} \left.\frac{\partial^2 V}{\partial q^2}\right|_{q_0} (q - q_0)^2`
 # where :math:`q = (x,y,z)`
 # is a position vector and :math:`q_0 = \text{arg min}_{q} V` is
 # the position where the PES has a local minimum.
@@ -121,7 +122,7 @@ def PES(x, y , z):
 # %%
 # Step 1: fixed cell geometry optimization
 # ----------------------------------------
-# 
+#
 # To find :math:`q_0` we will use the fixed-cell geometry
 # optimization feature of i-PI! The inputs are
 # into the `geop` directory.
@@ -129,7 +130,7 @@ def PES(x, y , z):
 # You will find the i-PI input file. Have a look at the
 # `input.xml` file and see if you can understand its various parts.
 #
-# The snippet that implements the geometry optimization feature is 
+# The snippet that implements the geometry optimization feature is
 #
 # .. code-block:: xml
 #
@@ -151,7 +152,7 @@ def PES(x, y , z):
 # here we use the robust
 # `BFGS <https://en.wikipedia.org/wiki/Broyden%E2%80%93Fletcher%E2%80%93Goldfarb%E2%80%93Shanno_algorithm>`_
 # method. The tolerances set thershold values for changes in the energy,
-# positions and forces, that are sufficient to deem an optimization converged. 
+# positions and forces, that are sufficient to deem an optimization converged.
 #
 
 # %%
@@ -164,31 +165,33 @@ def PES(x, y , z):
 ipi.install_driver()
 # %%
 # To perform a fixed-cell geomerty optimization
-# the bash script command should look like: 
-# 
+# the bash script command should look like:
+#
 # .. code-block:: bash
 #
 #      i-pi geop/input.xml > log.i-pi $
 #      sleep(5)
-#      i-pi-driver -u -h geop -m doublewell_1D & 
-# 
+#      i-pi-driver -u -h geop -m doublewell_1D &
+#
 # The same can be achieved from Python using `subprocess.Popen`
 
+ipi_process = None
+if not os.path.exists("geop.out"):
+    ipi_process = subprocess.Popen(["i-pi", "geop/input.xml"])
+    time.sleep(5)  # wait for i-PI to start
+    driver_process = subprocess.Popen(
+        ["i-pi-driver", "-u", "-h", "geop", "-m", "doublewell_1D"]
+    )
 
-ipi_process = subprocess.Popen(["i-pi", "geop/input.xml"])
-time.sleep(5)  # wait for i-PI to start
-driver_process =subprocess.Popen(
-            ["i-pi-driver", "-u", "-h", "geop", "-m", "doublewell_1D"]
-        )
-    
 # %%
 # If you run this in a notebook, you can go ahead and start loading
 # output files *before* i-PI and lammps have finished running, by
 # skipping this cell
 
-ipi_process.wait()
-driver_process.wait()
-    
+if ipi_process is not None:
+    ipi_process.wait()
+    driver_process.wait()
+
 # %%
 #
 # The number of steps taken for an optimization calculation depends on
@@ -200,26 +203,22 @@ def PES(x, y , z):
 # You can analyze your optimization calculation by plotting
 # the potential energy vs steps and confirm if the potential
 # energy has indeed converged to the set threshold!
-# 
-# The final frame of the `geop.pos_0.xyz` file gives 
-# with chemiscope we can wisualize the minimzation 
+#
+# The final frame of the `geop.pos_0.xyz` file gives
+# with chemiscope we can wisualize the minimzation
 # trajectory and its energies.
 #
 
-geop_out,_geop = ipi.read_output('geop.out')
+geop_out, _geop = ipi.read_output("geop.out")
 geop_traj = ipi.read_trajectory("geop.pos_0.xyz")
 
 chemiscope.show(
     frames=geop_traj,
     properties={
-        "steps": { "values" : np.arange(len(geop_traj)),
-                  "target" : "structure"},
-        "U":{"values": geop_out['potential'],
-              "target" : "structure"},
-    }, 
-    settings=chemiscope.quick_settings(
-        x="steps", y="U", trajectory=True
-    ),
+        "steps": {"values": np.arange(len(geop_traj)), "target": "structure"},
+        "U": {"values": geop_out["potential"], "target": "structure"},
+    },
+    settings=chemiscope.quick_settings(x="steps", y="U", trajectory=True),
     mode="structure",
 )
 
@@ -227,10 +226,10 @@ def PES(x, y , z):
 # Step 2: harmonic calculation
 # ----------------------------
 #
-# To compute the system's Hessian we will use the vibrations feature of i-PI. 
+# To compute the system's Hessian we will use the vibrations feature of i-PI.
 # Go through the `input.xml` file.
-# The snippet that implements the vibrations feature is 
-# 
+# The snippet that implements the vibrations feature is
+#
 # .. code-block:: xml
 #
 #    <motion mode='vibrations'>
@@ -261,69 +260,79 @@ def PES(x, y , z):
 
 # %%
 # The initial configuration for this calculation should correspond to an
-# opitimized position. You can obtain this from the last frame of the geop trajectory. 
+# opitimized position. You can obtain this from the last frame of the geop trajectory.
 
-ase.io.write('init_harm.xyz',geop_traj[-1],format='extxyz')
+ase.io.write("init_harm.xyz", geop_traj[-1], format="extxyz")
 
 # %%
 # The `bash` command for this would be
-# 
+#
 # .. code-block:: bash
 #
 #      i-pi harm/input.xml > log.i-pi $
 #      sleep(5)
-#      i-pi-driver -u -h vib -m doublewell_1D & 
-# 
+#      i-pi-driver -u -h vib -m doublewell_1D &
+#
 # Again we will use `subprocess.Popen`
 
-ipi_process = subprocess.Popen(["i-pi", "harm/input.xml"])
-time.sleep(5)  # wait for i-PI to start
-driver_process =subprocess.Popen(
-            ["i-pi-driver", "-u", "-h", "vib", "-m", "doublewell_1D"]
-        )
+ipi_process = None
+if not os.path.exists("harm.out"):
+    ipi_process = subprocess.Popen(["i-pi", "harm/input.xml"])
+    time.sleep(5)  # wait for i-PI to start
+    driver_process = subprocess.Popen(
+        ["i-pi-driver", "-u", "-h", "vib", "-m", "doublewell_1D"]
+    )
 
 # %%
 # If you run this in a notebook, you can go ahead and start loading
 # output files *before* i-PI and lammps have finished running, by
 # skipping this cell
 
-ipi_process.wait()
-driver_process.wait()
+if ipi_process is not None:
+    ipi_process.wait()
+    driver_process.wait()
 
 # %%
-# The Hessian can be recovered from the `harm.phonons.hess` file. 
+# The Hessian can be recovered from the `harm.phonons.hess` file.
 # You can use the snippet below to plot the harmonic approximation
 # to the PES
 #
 
-def PES_harm(x,y,z):
+
+def PES_harm(x, y, z):
     """
-    Harmonic approximation to the PES from Ref. `Y. Litman et al., JCP (2022)` around 
+    Harmonic approximation to the PES from Ref. `Y. Litman et al., JCP (2022)` around
     a local minimum. Note this function is only valid for the example!
     """
-    
-    return V0 + hess[0,0] * (x - q0[0])**2 / 2 + hess[1,1] * (y - q0[1])**2 / 2 + hess[2,2] * (z - q0[2])**2 / 2
 
-hess = np.loadtxt('harm.phonons.hess', comments='#')
-q0 = ipi.read_trajectory('init_harm.xyz')[0].positions[0] / 0.529177
-V0 = np.loadtxt('harm.out', ndmin=2)[0,1]
+    return (
+        V0
+        + hess[0, 0] * (x - q0[0]) ** 2 / 2
+        + hess[1, 1] * (y - q0[1]) ** 2 / 2
+        + hess[2, 2] * (z - q0[2]) ** 2 / 2
+    )
+
 
-x = np.linspace(-3,3,21)
-y = np.linspace(-0.5,0.5,21)
+hess = np.loadtxt("harm.phonons.hess", comments="#")
+q0 = ipi.read_trajectory("init_harm.xyz")[0].positions[0] / 0.529177
+V0 = np.loadtxt("harm.out", ndmin=2)[0, 1]
+
+x = np.linspace(-3, 3, 21)
+y = np.linspace(-0.5, 0.5, 21)
 
 X, Y = np.meshgrid(x, y)
 
 contour_levels = [np.min(Z) + 0.00095004347 * i for i in range(12)]
 
-plt.title(r'$V(x,y,0)$')
-plt.xlabel(r'$x$ [a.u.]')
-plt.ylabel(r'$y$ [a.u.]')
+plt.title(r"$V(x,y,0)$")
+plt.xlabel(r"$x$ [a.u.]")
+plt.ylabel(r"$y$ [a.u.]")
 plt.contour(X, Y, PES(X, Y, 0), levels=contour_levels)
 plt.show()
 
-plt.title(r'$V^{\mathrm{harm}}(x,y,0)$')
-plt.xlabel(r'$x$ [a.u.]')
-plt.ylabel(r'$y$ [a.u.]')
+plt.title(r"$V^{\mathrm{harm}}(x,y,0)$")
+plt.xlabel(r"$x$ [a.u.]")
+plt.ylabel(r"$y$ [a.u.]")
 plt.contour(X, Y, PES_harm(X, Y, 0), levels=contour_levels)
 plt.show()
 
@@ -332,45 +341,56 @@ def PES_harm(x,y,z):
 # from the dynamical matrix (mass scaled hessian)!
 #
 
-W2s = np.loadtxt('harm.phonons.eigval')
-print ('Harmonic Frequencies')
+W2s = np.loadtxt("harm.phonons.eigval")
+print("Harmonic Frequencies")
 for w2 in W2s:
-    print('%10.5f cm^-1'% (w2**0.5 * 219474))
+    print("%10.5f cm^-1" % (w2**0.5 * 219474))
 
-# %% 
+# %%
 # These frequencies can be used to calculate the quantum harmonic
 # free energy of the system -- an approxiamtion to its true free energy!
 #
 
+
 def quantum_harmonic_free_energy(Ws, T):
     """
-    Receives a list of frequencies in atomic units and the temperature 
+    Receives a list of frequencies in atomic units and the temperature
     in Kelvin. Returns the system's harmonic free energy.
     """
-    
+
     hbar = 1
     kB = 3.1668116e-06
-    
-    return V0 + -kB * T * np.log(1 - np.exp(-hbar * Ws / (kB * T))).sum() 
 
-print ('Quantum Harmonic free energy: %15.8f [a.u.]'% (quantum_harmonic_free_energy(W2s**0.5, 300)))
-print ('Quantum Harmonic free energy: %15.8f [eV]'% (quantum_harmonic_free_energy(W2s**0.5, 300) * 27.211386))
-print ('Quantum Harmonic  free energy: %15.8f [kJ/mol]' % (quantum_harmonic_free_energy(W2s**0.5, 300) * 2625.4996))
+    return V0 + -kB * T * np.log(1 - np.exp(-hbar * Ws / (kB * T))).sum()
+
+
+print(
+    "Quantum Harmonic free energy: %15.8f [a.u.]"
+    % (quantum_harmonic_free_energy(W2s**0.5, 300))
+)
+print(
+    "Quantum Harmonic free energy: %15.8f [eV]"
+    % (quantum_harmonic_free_energy(W2s**0.5, 300) * 27.211386)
+)
+print(
+    "Quantum Harmonic  free energy: %15.8f [kJ/mol]"
+    % (quantum_harmonic_free_energy(W2s**0.5, 300) * 2625.4996)
+)
 
 # %%
 #
 # The exact free energy for the system when localized in one of
-# the wells is still around 0.65 kJ/mol off w.r.t the harmonic limit. 
+# the wells is still around 0.65 kJ/mol off w.r.t the harmonic limit.
 #
 
 F = -7.53132797e-05 + quantum_harmonic_free_energy(W2s**0.5, 300)
 
-print ('Exact Quantum free energy: %15.8f [a.u.]'% (F))
-print ('Exact Quantum free energy: %15.8f [eV]'% (F * 27.211386))
-print ('Exact Quantum free energy: %15.8f [kJ/mol]' % (F * 2625.4996))
+print("Exact Quantum free energy: %15.8f [a.u.]" % (F))
+print("Exact Quantum free energy: %15.8f [eV]" % (F * 27.211386))
+print("Exact Quantum free energy: %15.8f [kJ/mol]" % (F * 2625.4996))
 
 # %%
-# 
+#
 # Harmonic to anharmonic
 # ----------------------
 #
@@ -379,15 +399,15 @@ def quantum_harmonic_free_energy(Ws, T):
 # Equation by approximating the anharmonic component of the PES, yielding an amharmonic
 # free energy. While highly effective for low-dimensional or mildly anharmonic systems,
 # the method of resort for *numerically-exact amharmonic free energies* of solid and clusters
-# is the thermodynamic integration method combined with the path-integral method 
+# is the thermodynamic integration method combined with the path-integral method
 # ( for applications see Refs.
 # `M. Rossi et al, PRL (2016) <https://doi.org/10.1103/PhysRevLett.117.115702>`_,
 # `V. Kapil et al, JCTC (2019) <https://doi.org/10.1021/acs.jctc.9b00596>`_,
 # `V. Kapil et al, PNAS (2022) <https://doi.org/10.1073/pnas.2111769119>`_).
-#  
+#
 #
 # The central idea is to reversibly change the potential from harmonic to anharmonic
-# by defining a :math:`\lambda`-dependent Hamiltonian 
+# by defining a :math:`\lambda`-dependent Hamiltonian
 #
 # .. math::
 #    \hat{H}(\lambda) = \hat{T} + \lambda
@@ -401,8 +421,8 @@ def quantum_harmonic_free_energy(Ws, T):
 #     \hat{V}^{\text{harm}} \right>_{\lambda}
 #
 #
-# where :math:`\left< \hat{O} \right>_{\lambda}` 
-# is the path-integral estimator for a positon dependent operator 
+# where :math:`\left< \hat{O} \right>_{\lambda}`
+# is the path-integral estimator for a positon dependent operator
 # for :math:`\hat{H}(\lambda)`.
 
 # %%
@@ -412,7 +432,7 @@ def quantum_harmonic_free_energy(Ws, T):
 #
 # A full quantum thermodynamic integration calculation requires
 # knowledge of the harmonic reference. Luckily we have just performed these
-# calculations! 
+# calculations!
 #
 
 # %%
@@ -420,48 +440,422 @@ def quantum_harmonic_free_energy(Ws, T):
 # -------------------------------
 #
 # Let's first compute the anharmonic free energy difference within the classical approximation.
-# 
+#
 # To create the input file for I-PI we need to defines a "mixed"
-# :math:`\lambda`-dependent Hamiltonian. Let's see the new most important parts. 
+# :math:`\lambda`-dependent Hamiltonian. Let's see the new most important parts.
 #
-# This i-PI calculation includes two "forcefield classes" 
+# This i-PI calculation includes two "forcefield classes"
 #
 # .. code-block:: xml
-# 
+#
 #    <!-->  defines the anharmonic PES <-->
 #    <ffsocket name='driver' mode='unix' matching='any' pbc='false'>
 #        <address> f0 </address>
 #        <latency> 1e-3 </latency>
 #    </ffsocket>
-# 
-# a standard socket 
-# 
-# and 
-# 
+#
+# a standard socket
+#
+# and
+#
 # .. code-block:: xml
 #
 #    <!-->  defines the harmonic PES <-->
 #    <ffdebye name='debye'>
-#            <hessian shape='(3,3)' mode='file'> HESSIAN-FILE </hessian>
-#            <x_reference mode='file'> X-REF-FILE <!--> relative path to a file containing the optimized positon vector <-->   </x_reference>
-#            <v_reference> V-REF <!-->  the value of the PES at its local minimum <-->   </v_reference>
+#            <hessian shape='(3,3)' mode='file'> HESSIAN_FILE </hessian>
+#            <x_reference mode='file'> X_REF_FILE <!--> relative path to a file containing the optimized positon vector <-->   </x_reference>
+#            <v_reference> V_REF <!-->  the value of the PES at its local minimum <-->   </v_reference>
 #    </ffdebye>
-# 
+#
 # an intrinsic harmonic forcefield that builds the harmonic potential.
-# This requires :math:`q_0`, :math:`V(q_0)` and the full Hessian. 
-# `HESSIAN-FILE` is `harm.phonons.hess` which is the file containing the
+# This requires :math:`q_0`, :math:`V(q_0)` and the full Hessian.
+# `HESSIAN_FILE` is `harm.phonons.hess` which is the file containing the
 # full hessian.
-# X-REF-FILE is a file with the optimized positon vector  
-# 
+# X_REF_FILE is a file with the optimized positon vector
+#
+
 
-with open('ref.data','w') as xref:
+HESSIAN_FILE = "harm.phonons.hess"
+X_REF_FILE = "ref.data"
+with open(X_REF_FILE, "w") as xref:
     for pos in geop_traj[-1].positions:
-        xref.write(f'{pos[0]}  {pos[1]}  {pos[2]} \n')
+        xref.write(f"{pos[0]}  {pos[1]}  {pos[2]} \n")
+
+# %%
+# V_REF can be obtained from the potential energy in `harm.out`
+
+V_REF = np.loadtxt("harm.out")[1]
+print(V_REF)
+
+# %%
+# To model a Hamiltonian with a linear combination of the harmonic and
+# the anharmonic potential you can define the weights for the force
+# components as
+#
+# .. code-block:: xml
+#
+#     <forces>
+#         <force forcefield='debye' weight=''> </force>  <!-->  set this to lambda <-->
+#         <force forcefield='driver' weight=''> </force> <!-->  set this to 1 - lambda <-->
+#     </forces>
+#
+# You can print out the harmonic and the anharmonic
+# components as a <property> in the output class
+#
+# .. code-block:: xml
+#
+#     <properties filename='pots' stride='10' flush='10'>
+#         [ pot_component_raw(0), pot_component_raw(1) ]
+#     </properties>
+#
+# A typical TI calculation requires multiple simulations,
+# one for each lambda and a postprocessing step to integrate the free
+# energy difference. In this example, we use six linearly-spaced points i.e.
+# :math:`\lambda\in\left[0, 0.2, 0.4, 0.6, 0.8, 1.0\right]`,
+# and create a set of files for each calculation.
+
+# %%
+# Let's generate the input files for the TI calculations
+
+for idx, i in enumerate(["0.0", "0.2", "0.4", "0.6", "0.8", "1.0"]):
+    with open(f"cti/input_{i}.xml", "w") as f:
+        strfile = """<simulation verbosity='low'>
+   <output prefix='cti_{i}'>
+      <properties filename='out' stride='10' flush='10'> [ step, time{{picosecond}}, conserved, temperature{{kelvin}}, kinetic_cv, potential, pressure_cv, volume, ensemble_temperature ] </properties>
+      <properties filename='pots' stride='10' flush='10'> [ pot_component_raw(0), pot_component_raw(1) ] </properties>
+      <trajectory filename='pos1' stride='10' bead='0' flush='10'> positions </trajectory>
+      <trajectory filename='xc' stride='10' flush='10'> x_centroid </trajectory>
+      <checkpoint stride='4000'/>
+   </output>
+   <total_steps> 10000 </total_steps>
+   <prng><seed>31415</seed></prng>
+   <ffsocket name='driver' mode='unix' matching='any' pbc='false'>
+       <address> f{idx} </address>
+       <latency> 1e-3 </latency>
+   </ffsocket>
+   <ffdebye name='debye'>
+	   <hessian shape='(3,3)' mode='file'> {HESSIAN_FILE} </hessian>
+	   <x_reference mode='file'> {X_REF_FILE} </x_reference>
+	   <v_reference> {V_REF}  </v_reference>
+   </ffdebye>
+   <system>
+      <initialize nbeads='1'>
+	 <file mode='xyz'> ./cti/init.xyz </file>
+         <velocities mode='thermal' units='kelvin'> 300 </velocities>
+      </initialize>
+      <forces>
+         <force forcefield='debye' weight='{i}'> </force>
+         <force forcefield='driver' weight='{im1:2.1f}'> </force>
+      </forces>
+      <motion mode='dynamics'>
+	 <fixcom> False </fixcom>
+         <dynamics mode='nvt'>
+            <timestep units='femtosecond'> 1.00 </timestep>
+            <thermostat mode='pile_l'>
+                <tau units='femtosecond'> 100 </tau>
+            </thermostat>
+         </dynamics>
+      </motion>
+      <ensemble>
+         <temperature units='kelvin'> 300 </temperature>
+      </ensemble>
+   </system>
+</simulation>
+""".format(
+            HESSIAN_FILE=HESSIAN_FILE,
+            X_REF_FILE=X_REF_FILE,
+            V_REF=V_REF,
+            i=i,
+            idx=idx,
+            im1=1 - float(i),
+        )
+        f.write(strfile)
+
+# %%
+# You can run i-PI simulataneous in these directories, the bash command would look like:
+#
+# .. code-block:: bash
+#
+#    for x in 0.0 0.2 0.4 0.6 0.8 1.0 ; do
+#       cd ${x}
+#       i-pi cti/input_${x}.xml > log${x}.i-pi &
+#       cd ..
+#    done
+#
+#    wait 5
+#
+#    for x in {0..10..2}; do
+#       i-pi-driver -u -h f${x} -m doublewell_1D &
+#    done
+#
+
+for idx, i in enumerate(["0.0", "0.2", "0.4", "0.6", "0.8", "1.0"]):
+    ipi_process = None
+    if not os.path.exists(f"cti_{i}.out"):
+        ipi_process = subprocess.Popen(["i-pi", f"cti/input_{i}.xml"])
+        time.sleep(5)  # wait for i-PI to start
+        driver_process = subprocess.Popen(
+            ["i-pi-driver", "-u", "-h", f"f{idx}", "-m", "doublewell_1D"]
+        )
+    # in a jupiter notebook comments the next 3 lines to be able to
+    # load the outputs before the run ends
+    if ipi_process is not None:
+        ipi_process.wait()
+        driver_process.wait()
+
+# %%
+#
+# When the calculations have finished,
+# you can use the following snippet to analyze the
+# mean force along the path and estimat its integral!
+
+du_list = []
+duerr_list = []
+
+dir_list = ["0.0", "0.2", "0.4", "0.6", "0.8", "1.0"]
+l_list = [float(l) for l in dir_list]
+
+for i in dir_list:
+
+    filename = f"cti_{i}.pots"
+    data, _data = ipi.read_output(filename)
+
+    du = data["pot_component_raw(1)"] - data["pot_component_raw(0)"]
+    du_list.append(du.mean())
+    duerr_list.append(du.std() / len(du) ** 0.5)
+
+
+du_list = np.asarray(du_list)
+duerr_list = np.asarray(duerr_list)
+
+plt.plot(l_list, (du_list) * 2625.4996, color="blue")
+plt.fill_between(
+    l_list,
+    y1=(du_list - duerr_list) * 2625.4996,
+    y2=(du_list + duerr_list) * 2625.4996,
+    color="blue",
+    alpha=0.2,
+)
+plt.title("Classical thermodynamic integration")
+plt.xlabel(r"$\lambda$")
+plt.ylabel(r"$\left<U - U^{\mathrm{harm}}\right>_{\lambda}$ [kJ/mol]")
+plt.show()
 
-# V-REF can be obtained from the potential energy in `harm.out`
 
-V-ref = np.readtxt('harm.out')
-print(V-ref)
+# %%
+# Since we are working within classical stat mech,
+# we should use the classical harmonic reference to estimate
+# the classical anharmonic free energy.
+
+
+def classical_harmonic_free_energy(Ws, T):
+    """
+    Receives a list of frequencies in atomic units and
+    the temperature in Kelvin. Returns the system's harmonic free energy.
+    """
+
+    hbar = 1
+    kB = 3.1668116e-06
+
+    return V0 + kB * T * np.log(hbar * Ws / (kB * T)).sum()
 
 
+df, dferr = np.trapz(x=l_list, y=du_list), np.trapz(x=l_list, y=duerr_list**2) ** 0.5
+
+F = classical_harmonic_free_energy(W2s**0.5, 300)
+
+print("Classical harmonic free energy: %15.8f [a.u.]" % (F))
+print("Classical harmonic free energy: %15.8f [eV]" % (F * 27.211386))
+print("Classical harmonic free energy: %15.8f [kJ/mol]" % (F * 2625.4996))
+print("")
+
+F = classical_harmonic_free_energy(W2s**0.5, 300) + df
+Ferr = dferr
+
+
+print("Classical anharmonic free energy: %15.8f +/- %15.8f [a.u.]" % (F, Ferr))
+print(
+    "Classical anharmonic free energy: %15.8f +/- %15.8f [eV]"
+    % (F * 27.211386, Ferr * 27.211386)
+)
+print(
+    "Classical anharmonic free energy: %15.8f +/- %15.8f [kJ/mol]"
+    % (F * 2625.4996, Ferr * 2625.4996)
+)
+print("")
+F = -7.53132797e-05 + quantum_harmonic_free_energy(W2s**0.5, 300)
+
+print("Exact free energy: %15.8f [a.u.]" % (F))
+print("Exact free energy: %15.8f [eV]" % (F * 27.211386))
+print("Exact free energy: %15.8f [kJ/mol]" % (F * 2625.4996))
+
+
+# %%
+# Quantum Statistical Mechanics
+# -----------------------------
+#
+# The quantum anharmonic free energy can be calculated using the path-integral
+# method. The main difference in the input file is the number of replicas!
+# Let's construct the input file:
+
+for idx, i in enumerate(["0.0", "0.2", "0.4", "0.6", "0.8", "1.0"]):
+    with open(f"qti/input_{i}.xml", "w") as f:
+        strfile = """<simulation verbosity='low'>
+   <output prefix='qti_{i}'>
+      <properties filename='out' stride='10' flush='10'> [ step, time{{picosecond}}, conserved, temperature{{kelvin}}, kinetic_cv, potential, pressure_cv, volume, ensemble_temperature ] </properties>
+      <properties filename='pots' stride='10' flush='10'> [ pot_component_raw(0), pot_component_raw(1) ] </properties>
+      <trajectory filename='pos1' stride='10' bead='0' flush='10'> positions </trajectory>
+      <trajectory filename='xc' stride='10' flush='10'> x_centroid </trajectory>
+      <checkpoint stride='4000'/>
+   </output>
+   <total_steps> 10000 </total_steps>
+   <prng><seed>31415</seed></prng>
+   <ffsocket name='driver' mode='unix' matching='any' pbc='false'>
+       <address> f{idx} </address>
+       <latency> 1e-3 </latency>
+   </ffsocket>
+   <ffdebye name='debye'>
+	   <hessian shape='(3,3)' mode='file'> {HESSIAN_FILE} </hessian>
+	   <x_reference mode='file'> {X_REF_FILE} </x_reference>
+	   <v_reference> {V_REF}  </v_reference>
+   </ffdebye>
+   <system>
+      <initialize nbeads='32'>
+	 <file mode='xyz'> ./qti/init.xyz </file>
+         <velocities mode='thermal' units='kelvin'> 300 </velocities>
+      </initialize>
+      <forces>
+         <force forcefield='debye' weight='{i}'> </force>
+         <force forcefield='driver' weight='{im1:2.1f}'> </force>
+      </forces>
+      <motion mode='dynamics'>
+	 <fixcom> False </fixcom>
+         <dynamics mode='nvt'>
+            <timestep units='femtosecond'> 1.00 </timestep>
+            <thermostat mode='pile_l'>
+                <tau units='femtosecond'> 100 </tau>
+            </thermostat>
+         </dynamics>
+      </motion>
+      <ensemble>
+         <temperature units='kelvin'> 300 </temperature>
+      </ensemble>
+   </system>
+</simulation>
+""".format(
+            HESSIAN_FILE=HESSIAN_FILE,
+            X_REF_FILE=X_REF_FILE,
+            V_REF=V_REF,
+            i=i,
+            idx=idx,
+            im1=1 - float(i),
+        )
+        f.write(strfile)
+
+
+# %%
+# You can run i-PI simulataneous.
+
+for idx, i in enumerate(["0.0", "0.2", "0.4", "0.6", "0.8", "1.0"]):
+    ipi_process = None
+    if not os.path.exists(f"qti_{i}.out"):
+        ipi_process = subprocess.Popen(["i-pi", f"qti/input_{i}.xml"])
+        time.sleep(5)  # wait for i-PI to start
+        driver_process = [
+            subprocess.Popen(
+                ["i-pi-driver", "-u", "-h", f"f{idx}", "-m", "doublewell_1D"]
+            )
+            for i in range(32)
+        ]
+    # in a jupiter notebook comments the next 3 lines to be able to
+    # load the outputs before the run ends
+    if ipi_process is not None:
+        ipi_process.wait()
+        for i in range(32):
+            driver_process[i].wait()
+
+# %%
+# The data analysys is done with the following snippets
+
+Q_du_list = []
+Q_duerr_list = []
+
+Q_dir_list = ["0.0", "0.2", "0.4", "0.6", "0.8", "1.0"]
+Q_l_list = [float(l) for l in Q_dir_list]
+
+for i in Q_dir_list:
+    filename = f"qti_{i}.pots"
+    data, _data = ipi.read_output(filename)
+
+    du = data["pot_component_raw(1)"] - data["pot_component_raw(0)"]
+    Q_du_list.append(du.mean())
+    Q_duerr_list.append(du.std() / len(du) ** 0.5)
+
+
+Q_du_list = np.asarray(Q_du_list)
+Q_duerr_list = np.asarray(Q_duerr_list)
+
+plt.plot(
+    Q_l_list,
+    (Q_du_list) * 2625.4996,
+    color="red",
+    label="Quantum thermodynamic integration",
+)
+plt.fill_between(
+    Q_l_list,
+    y1=(Q_du_list - Q_duerr_list) * 2625.4996,
+    y2=(Q_du_list + Q_duerr_list) * 2625.4996,
+    color="red",
+    alpha=0.2,
+)
+plt.plot(
+    l_list,
+    (du_list) * 2625.4996,
+    color="blue",
+    label="Classical thermodynamic integration",
+)
+plt.fill_between(
+    l_list,
+    y1=(du_list - duerr_list) * 2625.4996,
+    y2=(du_list + duerr_list) * 2625.4996,
+    color="blue",
+    alpha=0.2,
+)
+plt.legend()
+plt.xlabel(r"$\lambda$")
+plt.ylabel(r"$\left<U - U^{\mathrm{harm}}\right>_{\lambda}$ [kJ/mol]")
+
+# %%
+# Then show the free energy
+
+df, dferr = (
+    np.trapz(x=Q_l_list, y=Q_du_list),
+    np.trapz(x=Q_l_list, y=Q_duerr_list**2) ** 0.5,
+)
+
+F = quantum_harmonic_free_energy(W2s**0.5, 300)
+
+print("Quantum harmonic free energy: %15.8f [a.u.]" % (F))
+print("Quantum harmonic free energy: %15.8f [eV]" % (F * 27.211386))
+print("Quantum harmonic free energy: %15.8f [kJ/mol]" % (F * 2625.4996))
+print("")
+
+F = quantum_harmonic_free_energy(W2s**0.5, 300) + df
+Ferr = dferr
+
+
+print("Quantum anharmonic free energy: %15.8f +/- %15.8f [a.u.]" % (F, Ferr))
+print(
+    "Quantum anharmonic free energy: %15.8f +/- %15.8f [eV]"
+    % (F * 27.211386, Ferr * 27.211386)
+)
+print(
+    "Quantum anharmonic free energy: %15.8f +/- %15.8f [kJ/mol]"
+    % (F * 2625.4996, Ferr * 2625.4996)
+)
+print("")
+F = -7.53132797e-05 + quantum_harmonic_free_energy(W2s**0.5, 300)
 
+print("Exact free energy: %15.8f [a.u.]" % (F))
+print("Exact free energy: %15.8f [eV]" % (F * 27.211386))
+print("Exact free energy: %15.8f [kJ/mol]" % (F * 2625.4996))
diff --git a/examples/free-energy/qti/init.xyz b/examples/free-energy/qti/init.xyz
new file mode 100644
index 00000000..8032e3da
--- /dev/null
+++ b/examples/free-energy/qti/init.xyz
@@ -0,0 +1,3 @@
+1
+# CELL(abcABC):  188.97261   188.97261   188.97261    90.00000    90.00000    90.00000  Step:          13  Bead:       0 positions{atomic_unit}  cell{atomic_unit}
+       H  1.99641e+00 -6.18337e-10  1.54584e-09

From 0c492093fe5de3c7776a744a601f94d197f77fa9 Mon Sep 17 00:00:00 2001
From: DavideTisi <davide.tisi93@gmail.com>
Date: Tue, 10 Dec 2024 18:35:59 +0100
Subject: [PATCH 7/8] linter

---
 examples/free-energy/free-energy.py | 85 ++++++++++++++++++-----------
 1 file changed, 52 insertions(+), 33 deletions(-)

diff --git a/examples/free-energy/free-energy.py b/examples/free-energy/free-energy.py
index 69535352..763b4f7e 100644
--- a/examples/free-energy/free-energy.py
+++ b/examples/free-energy/free-energy.py
@@ -20,7 +20,6 @@
 import ase.io
 import chemiscope
 import ipi
-import ipi.utils.parsing as pimdmooc
 import matplotlib.pyplot as plt
 import numpy as np
 
@@ -110,7 +109,8 @@ def PES(x, y, z):
 # The harmonic approximation to the PES is essentially
 # a truncated Taylor series expansion to second
 # order around one of its minima.
-# :math:`V^{\text{harm}} = V(q_0) + \frac{2}{2} \left.\frac{\partial^2 V}{\partial q^2}\right|_{q_0} (q - q_0)^2`
+# :math:`V^{\text{harm}} = V(q_0) +
+# \frac{1}{2} \left.\frac{\partial^2 V}{\partial q^2}\right|_{q_0} (q - q_0)^2`
 # where :math:`q = (x,y,z)`
 # is a position vector and :math:`q_0 = \text{arg min}_{q} V` is
 # the position where the PES has a local minimum.
@@ -150,7 +150,7 @@ def PES(x, y, z):
 # simply move towards a local minimum of the PES. There are
 # many algorithms for locally optimizing high-dimensional functions;
 # here we use the robust
-# `BFGS <https://en.wikipedia.org/wiki/Broyden%E2%80%93Fletcher%E2%80%93Goldfarb%E2%80%93Shanno_algorithm>`_
+# `BFGS` (Broyden-Fletcher-Goldfarb-Shanno) quasi-Newton
 # method. The tolerances set thershold values for changes in the energy,
 # positions and forces, that are sufficient to deem an optimization converged.
 #
@@ -252,8 +252,10 @@ def PES(x, y, z):
 #      - \epsilon} \right)
 #
 # At every step instead of performing "dynamics", we will displace a degree of
-# freedom along :math:`\pm \epsilon` and estimate one row of the Hessian. `pos_shift` sets
-# the value of :math:`\epsilon` while `asr` zeros out the blocks of the Hessian due to continuous
+# freedom along :math:`\pm \epsilon` and estimate one row of the Hessian.
+# `pos_shift` sets
+# the value of :math:`\epsilon` while `asr` zeros out the blocks
+# of the Hessian due to continuous
 # symmetries (translations or rotations for solids or clusters). In this example,
 # we set this option to `none` as our system doesn't possess any continuous symmetries.
 #
@@ -396,9 +398,11 @@ def quantum_harmonic_free_energy(Ws, T):
 #
 # Calculating free energies beyond the harmonic approximation is non-trivial.
 # There exist a familty of methods that can  solve the vibrational Schroedinger
-# Equation by approximating the anharmonic component of the PES, yielding an amharmonic
+# Equation by approximating the anharmonic component of
+# the PES, yielding an amharmonic
 # free energy. While highly effective for low-dimensional or mildly anharmonic systems,
-# the method of resort for *numerically-exact amharmonic free energies* of solid and clusters
+# the method of resort for *numerically-exact amharmonicfree energies*
+# of solid and clusters
 # is the thermodynamic integration method combined with the path-integral method
 # ( for applications see Refs.
 # `M. Rossi et al, PRL (2016) <https://doi.org/10.1103/PhysRevLett.117.115702>`_,
@@ -439,7 +443,8 @@ def quantum_harmonic_free_energy(Ws, T):
 # Classical Statistical Mechanics
 # -------------------------------
 #
-# Let's first compute the anharmonic free energy difference within the classical approximation.
+# Let's first compute the anharmonic free
+# energy difference within the classical approximation.
 #
 # To create the input file for I-PI we need to defines a "mixed"
 # :math:`\lambda`-dependent Hamiltonian. Let's see the new most important parts.
@@ -463,8 +468,12 @@ def quantum_harmonic_free_energy(Ws, T):
 #    <!-->  defines the harmonic PES <-->
 #    <ffdebye name='debye'>
 #            <hessian shape='(3,3)' mode='file'> HESSIAN_FILE </hessian>
-#            <x_reference mode='file'> X_REF_FILE <!--> relative path to a file containing the optimized positon vector <-->   </x_reference>
-#            <v_reference> V_REF <!-->  the value of the PES at its local minimum <-->   </v_reference>
+#            <x_reference mode='file'> X_REF_FILE
+#        <!--> relative path to a file containing the optimized positon vector <-->
+#            </x_reference>
+#            <v_reference> V_REF
+#        <!-->  the value of the PES at its local minimum <-->
+#            </v_reference>
 #    </ffdebye>
 #
 # an intrinsic harmonic forcefield that builds the harmonic potential.
@@ -494,10 +503,10 @@ def quantum_harmonic_free_energy(Ws, T):
 #
 # .. code-block:: xml
 #
-#     <forces>
-#         <force forcefield='debye' weight=''> </force>  <!-->  set this to lambda <-->
-#         <force forcefield='driver' weight=''> </force> <!-->  set this to 1 - lambda <-->
-#     </forces>
+#   <forces>
+#      <force forcefield='debye' weight=''> </force>  <!-->  set this to lambda <-->
+#      <force forcefield='driver' weight=''> </force> <!-->  set this to 1 - lambda <-->
+#   </forces>
 #
 # You can print out the harmonic and the anharmonic
 # components as a <property> in the output class
@@ -521,9 +530,14 @@ def quantum_harmonic_free_energy(Ws, T):
     with open(f"cti/input_{i}.xml", "w") as f:
         strfile = """<simulation verbosity='low'>
    <output prefix='cti_{i}'>
-      <properties filename='out' stride='10' flush='10'> [ step, time{{picosecond}}, conserved, temperature{{kelvin}}, kinetic_cv, potential, pressure_cv, volume, ensemble_temperature ] </properties>
-      <properties filename='pots' stride='10' flush='10'> [ pot_component_raw(0), pot_component_raw(1) ] </properties>
-      <trajectory filename='pos1' stride='10' bead='0' flush='10'> positions </trajectory>
+      <properties filename='out' stride='10' flush='10'> [ step, time{{picosecond}},
+      conserved, temperature{{kelvin}}, kinetic_cv, potential, pressure_cv,
+      volume, ensemble_temperature ] </properties>
+      <properties filename='pots' stride='10' flush='10'>
+      [ pot_component_raw(0), pot_component_raw(1) ] </properties>
+      <trajectory filename='pos1' stride='10' bead='0' flush='10'>
+        positions
+      </trajectory>
       <trajectory filename='xc' stride='10' flush='10'> x_centroid </trajectory>
       <checkpoint stride='4000'/>
    </output>
@@ -534,13 +548,13 @@ def quantum_harmonic_free_energy(Ws, T):
        <latency> 1e-3 </latency>
    </ffsocket>
    <ffdebye name='debye'>
-	   <hessian shape='(3,3)' mode='file'> {HESSIAN_FILE} </hessian>
-	   <x_reference mode='file'> {X_REF_FILE} </x_reference>
-	   <v_reference> {V_REF}  </v_reference>
+       <hessian shape='(3,3)' mode='file'> {HESSIAN_FILE} </hessian>
+       <x_reference mode='file'> {X_REF_FILE} </x_reference>
+       <v_reference> {V_REF}  </v_reference>
    </ffdebye>
    <system>
       <initialize nbeads='1'>
-	 <file mode='xyz'> ./cti/init.xyz </file>
+      <file mode='xyz'> ./cti/init.xyz </file>
          <velocities mode='thermal' units='kelvin'> 300 </velocities>
       </initialize>
       <forces>
@@ -548,7 +562,7 @@ def quantum_harmonic_free_energy(Ws, T):
          <force forcefield='driver' weight='{im1:2.1f}'> </force>
       </forces>
       <motion mode='dynamics'>
-	 <fixcom> False </fixcom>
+      <fixcom> False </fixcom>
          <dynamics mode='nvt'>
             <timestep units='femtosecond'> 1.00 </timestep>
             <thermostat mode='pile_l'>
@@ -584,7 +598,7 @@ def quantum_harmonic_free_energy(Ws, T):
 #
 #    wait 5
 #
-#    for x in {0..10..2}; do
+#    for x in {0..10}; do
 #       i-pi-driver -u -h f${x} -m doublewell_1D &
 #    done
 #
@@ -613,7 +627,7 @@ def quantum_harmonic_free_energy(Ws, T):
 duerr_list = []
 
 dir_list = ["0.0", "0.2", "0.4", "0.6", "0.8", "1.0"]
-l_list = [float(l) for l in dir_list]
+l_list = [float(lst) for lst in dir_list]
 
 for i in dir_list:
 
@@ -702,9 +716,14 @@ def classical_harmonic_free_energy(Ws, T):
     with open(f"qti/input_{i}.xml", "w") as f:
         strfile = """<simulation verbosity='low'>
    <output prefix='qti_{i}'>
-      <properties filename='out' stride='10' flush='10'> [ step, time{{picosecond}}, conserved, temperature{{kelvin}}, kinetic_cv, potential, pressure_cv, volume, ensemble_temperature ] </properties>
-      <properties filename='pots' stride='10' flush='10'> [ pot_component_raw(0), pot_component_raw(1) ] </properties>
-      <trajectory filename='pos1' stride='10' bead='0' flush='10'> positions </trajectory>
+      <properties filename='out' stride='10' flush='10'> [ step, time{{picosecond}},
+      conserved, temperature{{kelvin}}, kinetic_cv, potential,
+      pressure_cv, volume, ensemble_temperature ] </properties>
+      <properties filename='pots' stride='10' flush='10'>
+      [ pot_component_raw(0), pot_component_raw(1) ] </properties>
+      <trajectory filename='pos1' stride='10' bead='0' flush='10'>
+         positions
+      </trajectory>
       <trajectory filename='xc' stride='10' flush='10'> x_centroid </trajectory>
       <checkpoint stride='4000'/>
    </output>
@@ -715,13 +734,13 @@ def classical_harmonic_free_energy(Ws, T):
        <latency> 1e-3 </latency>
    </ffsocket>
    <ffdebye name='debye'>
-	   <hessian shape='(3,3)' mode='file'> {HESSIAN_FILE} </hessian>
-	   <x_reference mode='file'> {X_REF_FILE} </x_reference>
-	   <v_reference> {V_REF}  </v_reference>
+       <hessian shape='(3,3)' mode='file'> {HESSIAN_FILE} </hessian>
+       <x_reference mode='file'> {X_REF_FILE} </x_reference>
+       <v_reference> {V_REF}  </v_reference>
    </ffdebye>
    <system>
       <initialize nbeads='32'>
-	 <file mode='xyz'> ./qti/init.xyz </file>
+      <file mode='xyz'> ./qti/init.xyz </file>
          <velocities mode='thermal' units='kelvin'> 300 </velocities>
       </initialize>
       <forces>
@@ -729,7 +748,7 @@ def classical_harmonic_free_energy(Ws, T):
          <force forcefield='driver' weight='{im1:2.1f}'> </force>
       </forces>
       <motion mode='dynamics'>
-	 <fixcom> False </fixcom>
+      <fixcom> False </fixcom>
          <dynamics mode='nvt'>
             <timestep units='femtosecond'> 1.00 </timestep>
             <thermostat mode='pile_l'>
@@ -781,7 +800,7 @@ def classical_harmonic_free_energy(Ws, T):
 Q_duerr_list = []
 
 Q_dir_list = ["0.0", "0.2", "0.4", "0.6", "0.8", "1.0"]
-Q_l_list = [float(l) for l in Q_dir_list]
+Q_l_list = [float(lst) for lst in Q_dir_list]
 
 for i in Q_dir_list:
     filename = f"qti_{i}.pots"

From 4c0e5429ae1da4443af78852b5c16406126fedd5 Mon Sep 17 00:00:00 2001
From: DavideTisi <davide.tisi93@gmail.com>
Date: Tue, 10 Dec 2024 20:19:44 +0100
Subject: [PATCH 8/8] separate graph

---
 examples/free-energy/free-energy.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/examples/free-energy/free-energy.py b/examples/free-energy/free-energy.py
index 763b4f7e..f804d2f1 100644
--- a/examples/free-energy/free-energy.py
+++ b/examples/free-energy/free-energy.py
@@ -332,6 +332,8 @@ def PES_harm(x, y, z):
 plt.contour(X, Y, PES(X, Y, 0), levels=contour_levels)
 plt.show()
 
+# %%
+
 plt.title(r"$V^{\mathrm{harm}}(x,y,0)$")
 plt.xlabel(r"$x$ [a.u.]")
 plt.ylabel(r"$y$ [a.u.]")