The ADF QM/MM Hybrid Potential
This section summarizes how the QM/MM hybrid potential is constructed in the IMOMM and AddRemove methods. A more detailed and formal discussion can be found in references [3] [2, 6]. The two basic components of the QM/MM potential are the potential arising from the electronic structure calculation of the QM model system and the potential arising from the molecular mechanics force field calculation.
In the IMOMM method the potential of the QM model system acts as a base where additional molecular mechanics potentials are added. When there are no covalent bonds that cross the QM/MM boundary the situation is straightforward. For example, consider a QM/MM simulation in which there are two molecules, one in the QM region and the other in the MM region such that no bonds cross the boundary. All MM potentials needed to define the MM molecule are included. Additionally, all non-bonded MM potentials between QM and MM atoms are included. All bonded MM potentials within the QM molecule are discarded because they are accounted for by the QM calculation.
When there are covalent bonds that cross the QM/MM boundary, the question of which MM potentials to accept and which to discard is not so easy to answer. Consider the system shown in Figure 1-2a, with one covalent bond that traverses the QM/MM boundary. Shown in Figure 1-2b is the equivalent QM model system with a capping hydrogen atom. In the IMOMM approach, MM potentials are only included if they depend on atoms that have no equivalent in the QM model system. Hence, any MM potential in which all atoms involved are QM atoms are NOT included in the total QM/MM potential, for instance the C2-C1 bond stretching or the C2-N3-H4 angle bending potentials. Furthermore, the C5-N3 bond stretching potential is also not included, because an equivalent in the QM model system exists, namely the N3-Hcap bond. The QM potential is assumed to adequately model the link bond. The same is true for the C2-N3-C5 bending potential. Again there is an equivalent in the QM model system that involves the capping hydrogen atom. The rule therefore also implies that any MM potentials in which only QM or LI atoms are involved, are NOT included in the hybrid QM/MM potential. On the other hand, all MM potentials that involve at least one or more MM atoms are included. For example, C2-N3-C5-O6 torsion potential is included because there is no equivalent in the QM model system and the O6 atom is a pure MM atom.
There is only one exception. It involves the non-bonded interactions between QM atoms and LI atoms. From the rules above this MM potential should be discarded. However, in the IMOMM method this potential is included. The reasoning is that this interaction in the real system is not adequately modeled in the QM model system.
Figure 1-2 a) QM/MM partitioning. b) The equivalent QM model system. The numeric subscripts simply refer to the atom numbering.
In the AddRemove model [3], things are less complicated. The classical LI atom is treated as a normal MM atom with corresponding MM potentials to both the MM and QM atoms. The same goes for the MM correction potentials of the capping atoms (only with the real QM atoms and other capping atoms). For the AddRemove model, it's best to view the setup as the setup of two systems, one with all real QM and MM atoms (case a) and one with the real QM atoms and the capping atoms (case b). For both you need to build up the force field; in the former case (a), all interactions involving only QM atoms are ignored (these are already present through the QM calculation), while in the latter case (b) all interactions without contributions from the capping atoms are ignored. The interactions of case (a) are the normal MM/MM and QM/MM interactions, while the interactions of case (b) are used for correcting the QM interactions of the capping atoms. This also means that an atomic force field type should be assigned to the capping atoms, which is being handled in the LINK_BONDS block.
