Definition of the QM region

Figure 10-2. (a) The non-Coulombic interactions of particles A and B may be renounced due to the size of the QM region. Particle C is located too close to the QM/MM border, hence non-Coulombic potentials have to be applied, (b) Definition of the QM core and QM layer region... 

The definition of the QM and MM regions is therefore critical for the validity of the QM/MM calculation. The smaller the QM region, the more affordable the computational cost, but care must be taken not to leave any critical electronic interactions out of the QM region. The importance of the choice of the QM/MM partition must, however, not hide the fact that both the QM and the MM descriptions must describe with sufficient accuracy interactions within the respective regions. 

F is the electronic wavefunction of the QM system which is a function of the coordinates, r, of the electrons and also depends on the coordinates of the nuclei in the quantum system, R, and of the atoms in the MM region, R. From the definition of the effective Hamiltonian in equation (1), the total energy of the system is ... 

The methods of MM are devoid of this failure since electron correlation effects are implicitly included in the atom-atom potentials . However, these methods are classical by definition and do not describe the quantum effects, which are essential in the overwhelming majority of problems, in fact in all the problems in which the electronic states should be considered explicitly. These considerations lead directly to the idea to separate the molecular system in two (or more) regions in such a way as to find the quantum effects taking place overwhelmingly in only one of them, while the other regions could be considered by classical methods. The QM/MM approaches are based on this idea. 

Hqu/mm is the Hamiltonian for the interaction between the QM and MM regions. It is the definition of this Hamiltonian which is crucial to the success of the hybrid potential method. Several forms for this term are possible but one of the simplest and probably the most widely used consists of a sum of electrostatic and Lennard-Jones terms. As in the MM potential, the electrostatic terms model the interactions between the charge distributions of different atoms whereas the Lennard-Jones terms model the short range repulsive and the longer range dispersion interactions which are not accounted for by the electrostatic interactions. For the case of mat initio QM method and an MM potential in which there are partial charges on the MM atoms, the interaction Hamiltonian will have the form ... 

AU the QM/MM methods dedicated to treat solution chemistry are based on the definition of two zones (i) an active region that is generally defined as a sphere around the reactive center and (ii) an environment region that embeds the active region. This is illustrated in Fig. 2.1. The active region generally includes the reactive center (the orange disk in Fig. 2.1) and at least the first coordination sphere and is described at the QM level. QM molecules will always be shown in... 

As mentioned, all continuous methods have the same basic definition for the potential energy (Eq. 2.14). The most important difference between the continuous methods lies in the form of the weight-functions method assigns them in perhaps the most intuitive manner. However, the PAP method also requires computation of a large number of computationally expensive QM/MM partitions for each conformation, since it includes all 2 possible partitions, with M the number of solvent molecules in the transition region. SAP, DAS and SCMP are considerably more economic altemalives that include only the most important contributions, typically M + 1. 

---