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.