Speed up identical molecule detection (#2025)

* speed up molecule comparison (should help with #2008)

* update docstring and releasehistory

* remove trailing whitespace

* Apply some suggestions from code review

* Apply suggestions from code review

Co-authored-by: Josh A. Mitchell <[email protected]>

* fix whitespace

---------

Co-authored-by: Josh A. Mitchell <[email protected]>

Author: j-wags

docs/releasehistory.md

@@ -13,6 +13,7 @@ Releases follow the `major.minor.micro` scheme recommended by [PEP440](https://w
 ### Behavior changes
 
 - [PR #2026](https://github.com/openforcefield/openff-toolkit/pull/2026): Makes `Molecule.__repr__` more succinct for large molecules.
+- [PR #2025](https://github.com/openforcefield/openff-toolkit/pull/2025): Speeds up `Molecule.ordered_connection_table_hash`, but changes the specific hash outputted for a given molecule. The meaning of hash identity within a single OpenFF Toolkit version is unchanged. Updates documentation to state that these this method is only intended for comparing Molecule objects using the same version of the OpenFF Toolkit, and that hashes may not be stable between versions. 
 - [PR #2041](https://github.com/openforcefield/openff-toolkit/pull/2041): Drop testing on Python 3.10
 
 ### Bugfixes

openff/toolkit/topology/molecule.py

@@ -25,6 +25,7 @@
 
 """
 
+import hashlib
 import json
 import operator
 import pathlib
@@ -750,11 +751,11 @@ def atom2(self):
 
     @property
     def atom1_index(self) -> int:
-        return self.molecule.atoms.index(self._atom1)
+        return self._atom1.molecule_atom_index
 
     @property
     def atom2_index(self) -> int:
-        return self.molecule.atoms.index(self._atom2)
+        return self._atom2.molecule_atom_index
 
     @property
     def atoms(self):
@@ -1255,17 +1256,28 @@ def __hash__(self):
         return hash(self.to_smiles())
 
     def ordered_connection_table_hash(self) -> int:
-        """Compute an ordered hash of the atoms and bonds in the molecule"""
+        """
+        Compute an ordered hash of the atoms and bonds in the molecule.
+
+        This hash method is intended for comparison of Molecule objects at
+        runtime, and hashes from one version of the software should not be
+        compared with hashes generated using different versions.
+        """
         if self._ordered_connection_table_hash is not None:
             return self._ordered_connection_table_hash
 
+        # Pre-assign molecule atom indices in O(N) time to avoid use of List.index to get index of each one
+        # in O(N^2) time
+        for index, atom in enumerate(self.atoms):
+            atom._molecule_atom_index = index
+
         id = ""
         for atom in self.atoms:
-            id += f"{atom.symbol}_{atom.formal_charge}_{atom.stereochemistry}__"
+            id += f"{atom.atomic_number}_{atom.formal_charge.magnitude}_{atom.stereochemistry}__"
         for bond in self.bonds:
             id += f"{bond.bond_order}_{bond.stereochemistry}_{bond.atom1_index}_{bond.atom2_index}__"
 
-        self._ordered_connection_table_hash = hash(id)
+        self._ordered_connection_table_hash = hashlib.sha3_224(id.encode("utf-8")).hexdigest()
         return self._ordered_connection_table_hash
 
     @classmethod
@@ -1971,23 +1983,22 @@ def from_smiles(
         return molecule
 
     def _is_exactly_the_same_as(self, other):
-        for atom1, atom2 in zip(self.atoms, other.atoms):
-            if (
-                (atom1.atomic_number != atom2.atomic_number)
-                or (atom1.formal_charge != atom2.formal_charge)
-                or (atom1.is_aromatic != atom2.is_aromatic)
-                or (atom1.stereochemistry != atom2.stereochemistry)
-            ):
-                return False
-        for bond1, bond2 in zip(self.bonds, other.bonds):
-            if (
-                (bond1.atom1_index != bond2.atom1_index)
-                or (bond1.atom2_index != bond2.atom2_index)
-                or (bond1.is_aromatic != bond2.is_aromatic)
-                or (bond1.stereochemistry != bond2.stereochemistry)
-            ):
-                return False
-        return True
+        # Pre-assign molecule atom indices in O(N) time to avoid use of List.index to get index of each one
+        # in O(N^2) time
+        for index, atom in enumerate(self.atoms):
+            atom._molecule_atom_index = index
+        for index, atom in enumerate(other.atoms):
+            atom._molecule_atom_index = index
+
+        self_id = (
+            tuple((atom.atomic_number, atom.formal_charge.magnitude, atom.stereochemistry) for atom in self.atoms),
+            tuple((bond.bond_order, bond.stereochemistry, bond.atom1_index, bond.atom2_index) for bond in self.bonds),
+        )
+        other_id = (
+            tuple((atom.atomic_number, atom.formal_charge.magnitude, atom.stereochemistry) for atom in other.atoms),
+            tuple((bond.bond_order, bond.stereochemistry, bond.atom1_index, bond.atom2_index) for bond in other.bonds),
+        )
+        return self_id == other_id
 
     @staticmethod
     def are_isomorphic(