Hamiltonians subsystem electronic charges

The QM/MM interactions (Eqm/mm) are taken to include bonded and non-bonded interactions. For the non-bonded interactions, the subsystems interact with each other through Lennard-Jones and point charge interaction potentials. When the electronic structure is determined for the QM subsystem, the charges in the MM subsystem are included as a collection of fixed point charges in an effective Hamiltonian, which describes the QM subsystem. That is, in the calculation of the QM subsystem we determine the contributions from the QM subsystem (Eqm) and the electrostatic contributions from the interaction between the QM and MM subsystems as explained by Zhang et al. [13],... 

Figure 2. Uniform (1) and nonuniform (2-6) scaling paths of electronic charges in the complementary subsystems of M = (i4 B). The subsystem external potentials of the scaled hamiltonians for the starting and end points of each path are also listed, with the upper (lower) entries corresponding to ti (B).

The next and necessary step is to account for the interactions between the quantum subsystem and the classical subsystem. This is achieved by the utilization of a classical expression of the interactions between charges and/or induced charges and a van der Waals term [45-61] and we are able to represent the coupling to the quantum mechanical Hamiltonian by interaction operators. These interaction operators enable us to include effectively these operators in the quantum mechanical equations for calculating the MCSCF electronic wavefunction along with the response of the MCSCF wavefunction to externally applied time-dependent electromagnetic fields when the molecule is exposed to a structured environment [14,45-56,58-60,62,67,69-74],... 

Further elaboration of the hybrid models stipulated by the necessity to model chemical processes in polar solvents or in the protein environment of enzymes, or in oxide-based matrices of zeolites, requires the polarization of the QM subsystem by the charges residing on the MM atoms of the classically treated solvent, or protein, or oxide matrix. This polarization is described by renormalizing the one-electron part of the effective Hamiltonian for the QM subsystem ... 

In the previous Section we obtained the formula for junction between quantum and classical subsystems Eq. (13). The control for the types of interactions which are taken into account is an important characteristic of particular QM/MM scheme. The authors of Ref. [110] have proposed a classification of hybrid schemes based on the interaction between fragments. According to it, the simplest type of model is mechanical embedding (examples of this type of modelling are the IMOMM [38] and IMOMO [59] schemes by Morokuma) when both QM and MM systems are not polarized by each other and their interaction is represented by classical force fields only. In this context the choice of parameters of intersystem interaction can be crucially important, so, they are frequently optimized [97,118]. More elaborated model is that including polarization of the QM subsystem. This polarization can be covered by including the MM charges into one-electron part of the Hamiltonian of the QM subsystem ... 

What about the environment Think of the particle as a proton or a positive muon (. i+) which, being positively charged, would carry with it the electron cloud of, for example, a metallic system like niobium (Nb) [4], While the subsystem Hamiltonian entails coherent tunneling with a (resultant) frequency A... 

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