Quantum mechanical charge field framework

Nuclear size corrections of order (Za) may be obtained in a quite straightforward way in the framework of the quantum mechanical third order perturbation theory. In this approach one considers the difference between the electric field generated by the nonlocal charge density described by the nuclear form factor and the field of the pointlike charge as a perturbation operator [16, 17]. 

Having left the framework of field theory outlined in chapter 7 and thus having avoided any need for subsequent renormalization procedures, the mass and charge of the electron are now the physically observable quantities, and therefore do not bear a tilde on top. In contrast to quantum electrodynamics, the radiation field is no longer a dynamical degree of freedom in a many-electron theory which closely follows nonrelativistic quantum mechanics. Vector potentials may only be incorporated as external perturbations in the many-electron Hamiltonian of Eq. (8.62). From the QED Eqs. (7.13), (7.19), and (7.20), the Hamiltonian of a system of N electrons and M nuclei is thus described by the many-particle Hamiltonian of Eq. (8.66). In addition, we refer to a common absolute time frame, although this will not matter in the following as we consider only the stationary case. 

Gao and coworkers proposed the X-Pol framework by combining the fragment-based electronic structure theory with a molecular mechanical force field. Unlike the traditional force fields, X-Pol does not require bond stretching, angle, and torsion terms because they are represented explicitly by quantum mechanics. The polarization and charge transfer between fragments are also evaluated quantum mechanically. Furthermore, X-Pol can be used to model chemical reactions. 

Biological systems can be treated at various different levels within a Car-Parrinello approach. One possibility is to use intelligently designed cluster models of the active site. Currently, systems of typically a few himdred atoms can be treated at the full quantum level. In addition, a static external field that captures the electrostatic field of the surrounding protein can be introduced. A common procedure is to parameterize the external electrostatic field in terms of point charges from empirical protein force fields. The most comprehensive approach for the treatment of biological systems within a Car-Parrinello framework are mixed quantum/classical QM/MM simulations. In these hybrid simulations, the reactive part of the system is treated within a standard Car-Parrinello scheme, whereas the surroimding protein is described with an empirically derived force field. In this way, electrostatic as well as steric and mechanic effects of the environment can be taken explicitly into account. 

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