Concepts and Terminology¶
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  [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 , 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.
Nomenclature and Terminology¶
This section summarizes the naming conventions that are used throughout this document. Some of the terminology has already been described in the previous section. Since the nomenclature describing the link bonds can be somewhat confusing we recommend that special attention be given to this section.
Full QM/MM system vs. QM model system¶
When performing a combined QM/MM simulation, the molecular system is divided into QM and MM regions as shown in Figure 1-1a. We will refer to the total hybrid system as the ‘full system’ or sometimes we will refer to it as the ‘real system’. The ‘QM model system’ is the capped system for which the electronic structure calculation is performed. Figure 1-1a shows the full system and Figure 1-1b depicts the corresponding QM model system.
QM, MM and LI atom types¶
In the ADF QM/MM input, each atom in the full system must be designated as a QM, MM or LI atom, where LI refers to link. Figure 1-1c shows these designations for the example system. Although two atoms are involved in a LINK bond, we only designate the atom in the MM region as the LI atom. We do so because this atom corresponds to a capping atom in the QM model system. In systems where there are no covalent bonds that cross the QM/MM boundary, there will be no LI atoms.
There are several different meanings of the term atom and atom type that have arisen because of the hybrid nature of the QM/MM method, see the following items.
QM/MM type or QM/MM atom type (MM, QM or LI)¶
Refers to the partitioning of the full system into QM and MM regions. As described above, there are only three QM/MM types allowed: QM, MM, and LI. Each atom in the full system is assigned a QM/MM atom type in the MM_CONNECTION_TABLE subkey block.
Force Field atom type¶
The atom type used in the force field calculation. Each atom in the full system is assigned a force field atom type in the MM_CONNECTION_TABLE subkey block of the input. Force field atom types assigned to each atom must correspond to atom types defined in the Force field file. Force field atom types must be assigned to all atoms, even the QM atoms because the non-bonded interactions between QM and MM atoms are treated by a molecular mechanics potential.
ADF atoms or ADF fragments¶
The atom types used for the electronic structure calculation of the model system. These are the atoms or fragments defined in the FRAGMENTS key block in a standard ADF calculation. The ADF fragment types used for the capping atoms are defined in the LINK_BONDS subkey block. Note that capping atoms can only be single atom fragments, not compound fragments as allowed by ADF.
Partitioning into QM and MM regions¶
In a QM/MM simulation the basic question is how to partition the system into QM and MM regions. When studying an active site of a catalyst, for example, one must decide where to put the QM/MM boundary. Putting the boundary too close to the reaction center will question the chemical realism of the model. On the other hand, if one makes the boundary too far away, the computational expense of the QM calculation may become problematic. Each system is different in this respect and the user must make the proper tests to validate the appropriateness of the QM/MM partitioning used. We strongly suggest that the reader examines the literature on QM/MM methods and understands the basic limitations of the approach.
Below we give examples of QM/MM partitioning that should not or can not be used. For comparison, we also give some representative examples of QM/MM partitioning that the program does allow. In the examples, the region enclosed in the dotted polygon represents the QM region and the atoms labeled with ‘LI’ are the so-called Link atoms.
First, the QM/MM boundary should not cut across double, triple or aromatic bonds as shown in Figure 1-3. In these examples, a simple capping atom does not satisfy the valence of the QM fragment and the electronic structure of the QM model system would be drastically different from that of the ‘real’ system.
Figure 1-3 Examples of partitioning that should not be used because the link bonds are double or aromatic bonds.
Next, figure 1-4a depicts examples of partitioning that are not allowed because the LI atom has a covalent bond to more than one QM atom. A LI atom can only be bonded to one QM atom. Figure 1-4b shows the opposite, which is allowed. In other words, one QM atom can be bonded to more than one LI atom. This is due to the partitioning scheme that was used and the geometric relationship expressed in Equation 1.1, which restricts the position of the link atom, based on the QM and dummy atom. Note that there is no limit to the number of LI atoms or link bonds, just that each LI atom can only be bonded to one QM atom.
Figure 1-4 a) Examples of partitioning that are not allowed because the LI atom has a covalent bond to more than one QM atom. b) The allowed reverse of the examples showed in (a). A LI atom can only bond to one QM atom.
Then, figure 1-5 provides some representative examples of partitioning that the program does allow. Example a shows a typical solute-solvent QM/MM partitioning where there are no link bonds at all. Example b depicts two separate molecules each possessing a QM and a MM region. We emphasize that any number of molecules and link bonds can be used. Recall that in the IMOMM/ADF method all link bonds have a different a parameter associated with them, each specified by the user, upon which the energy depends (and which are difficult to choose or generalize). In example b there would be four independent a parameters. Example c seems very similar to the earlier example in Figure 1-3. The difference is that the ring in Figure 1-cd is not aromatic and consequently the link bonds in example d cross single bonds. Example d shows a single molecule, with two QM regions separated a MM region. For this example, two equivalent pedagogic representations of the sample partitioning are displayed. Example e is a complex organometallic system that we have tested the QM/MM approach on.
Figure 1-5 Representative examples of QM/MM partitioning that can be used in ADF QM/MM ADF.