Define compare_confs_fl as a cheaper preprocess for compare_confs

Compare two Cartesian coordinates representing conformers using first and last atom distances.
If the `fl_distances` are the similar, the distance matrices are computed and returned.

arc/species/converter.py

@@ -2011,6 +2011,43 @@ def compare_zmats(z1, z2, r_tol=0.01, a_tol=2, d_tol=2, verbose=False, symmetric
                           symmetric_torsions=symmetric_torsions)
 
 
+def compare_confs_fl(xyz1: dict,
+                      xyz2: dict,
+                      rtol: float = 0.01,
+                      dmat2: Optional[np.ndarray] = None,
+                      fl_distance2: Optional[float] = None,
+                      ) -> Tuple[Optional[float], Optional[float], Optional[np.ndarray], Optional[np.ndarray]]:
+    """
+    Compare two Cartesian coordinates representing conformers using first and last atom distances. If the distances are the same,
+    the distance matrices are computed and returned.
+
+    The relative difference (``rtol`` * fl_distance1) is compared against the absolute difference abs(fl_distance1 - fl_distance2).
+
+    Args:
+        xyz1 (dict): Conformer 1.
+        xyz2 (dict): Conformer 2.
+        rtol (float): The relative tolerance parameter (see Notes).
+        dmat2 (np.ndarray, optional): The distance matrix of conformer 2.
+        fl_distance2 (float, optional): The first and last atom distance of conformer 2.
+
+    Returns:
+        Tuple containing distances and matrices:
+        - (fl_distance1, fl_distance2, dmat1, dmat2): First-to-last distances and distance matrices for both conformers.
+    """
+    xyz1, xyz2 = check_xyz_dict(xyz1), check_xyz_dict(xyz2)
+    dmat1 = None
+    fl_distance1 = np.linalg.norm(np.array(xyz1['coords'][0]) - np.array(xyz1['coords'][-1]))
+    if fl_distance2 is None:
+        fl_distance2 = np.linalg.norm(np.array(xyz2['coords'][0]) - np.array(xyz2['coords'][-1]))
+    if abs(fl_distance1-fl_distance2)/fl_distance1>rtol:
+        return fl_distance1, fl_distance2, dmat1, dmat2
+    if dmat1 is None:
+        dmat1 = xyz_to_dmat(xyz1)
+    if dmat2 is None:
+        dmat2 = xyz_to_dmat(xyz2)
+    return fl_distance1, fl_distance2, dmat1, dmat2
+
+
 def compare_confs(xyz1: dict,
                   xyz2: dict,
                   rtol: float = 0.01,