TIES Protocol¶
Superimposition and defining the alchemical region¶
Any two pairs are superimposed using a recursive joint traversal of two molecules starting from any two pairs.
A heuristics (which can be turned off) is used where the more rare atoms that are present across the two molecules are used as the starting points for the traversal, decreasing substantially the computational cost.
Charge treatment¶
Currently TIES 20 supports the transformation between ligands that have the same net charge.
We employ a dual topology approach which divides the atoms in each transformation into three groups:
Joint region. This is the region of the molecule where the atoms are the same meaning that they are shared across the two ligands in the transformation.
Disappearing region. Atoms present only in the starting ligand of the transformation which are fully represented at lambda=0 and which will be scaled accordingly during the lambda progression.
Appearing region. Atoms present only in the ending ligand of the transformation and therefore not present at lambda=0. These atoms start appearing during the lambda progression and are fully represented at lambda=1.
When the two ligands in a transformation are superimposed together, the treatment of charges depends on which group they belong to.
Joint region: matched atoms and their charges¶
In the joint region of the transformation, first –q-pair-tolerance is used to determine whether the two original atoms are truly the same atoms. If their charges differ by more than this value (default 0.1e), then the two atoms will be added to the alchemical regions (Disappearing and appearing).
It is possible that a lot of matched atoms in the joint region, with each pair being within 0.1e of each other, cumulatively have rather different charges between the starting and the ending ligand. For this reason, TIES 20 sums the differences between the starting and the ending atoms in the joint region, and if the total is larger than -netqtol (default 0.1e) then we further expand the alchemical region until the “appearing” and “disappearing” regions in the joint region are of a sufficiently similar net charge.
Abiding by -netqtol rule has the further effect that, inversely, the alchemical regions (disappearing and appearing regions), will have very similar net charges - which is a necessary condition for the calculation of the partial derivative of the potential energy with respect to the lambda.
If -netqtol rule is violated, different schemes for the removal of the matched atoms in the joint region are tried to satisfy the net charge limit. The scheme that removes fewest matched pairs, is used. In other words, TIES 20 is trying to use the smallest alchemical region possible while satisfying the rule.
Note that we are not summing together the absolute differences in charges in the joint region. This means that if one atom pair has 0.02e charge difference, and another pair has -0.02e charge difference, then their total is zero. In other words, we are not worried about the distribution of the differences in charges in the joint region.
The hydrogen charges are considered by absorbing them into the heavy atoms.
The charges in the joint region for each pair are averaged.
The last step is redistribution, where the final goal is that the net charge is the same in the Appearing and in the Disappearing alchemical region. After averaging the charges in the joint region, its overall charge summed with the charge of each alchemical region should be equal to the whole molecule net charge: \(q_{joint} + q_{appearing} == q_{joint} + q_{disappearing} == q_{molecule}\). Therefore, after averaging the charges, \(q_{molecule} - q_{joint} - q_{appearing}\) is distributed equally in the region \(q_{appearing}\). The same rule is applied in \(q_{disappearing}\).