Hamiltonian hybridization

MMVB is a hybrid force field, which uses MM to treat the unreactive molecular framework, combined with a valence bond (VB) approach to treat the reactive part. The MM part uses the MM2 force field [58], which is well adapted for organic molecules. The VB part uses a parametrized Heisenberg spin Hamiltonian, which can be illustrated by considering a two orbital, two electron description of a sigma bond described by the VB determinants... 

The SM1-SM3 methods model solvation in water with various degrees of sophistication. The SM4 method models solvation in alkane solvents. The SM5 method is generalized to model any solvent. The SM5.42R method is designed to work with HF, DFT or hybrid HF/DFT calculations, as well as with AMI or PM3. SM5.42R is implemented using a SCRF algorithm as described below. A description of the differences between these methods can be found in the manual accompanying the AMSOL program and in the reviews listed at the end of this chapter. Available Hamiltonians and solvents are summarized in Table 24.1. 

The hybrid Hamiltonian, which depends on both spatial and titration coordinates, can be written in terms of van der Waals, Coulomb, and GB electrostatic energies,... 

Laio, A. VandeVondele, J. Rothlisberger, U., A Hamiltonian electrostatic coupling scheme for hybrid Car-Parrinello molecular dynamics simulations, J. Chem. Phys. 2002,116, 6941-6947... 

The basic formalism of the X-dynamics method has taken various forms in its application to problems of interest. In an early prototype calculation to assess umbrella sampling in chemical coordinates, the X-dynamics method was used to evaluate the relative free energy of hydration for a set of small molecules which included both nonpolar (C2H6,) and polar (CH3OH, CH3SH, and CH3CN) solutes.1 By assigning a separate X variable to the Lennard-Jones and Coulomb interactions, a linear partition of the potential part of the hybrid Hamiltonian was constructed... 

The inter/intramolecular potentials that have been described may be viewed as classical in nature. An alternative is a hybrid quantum-mechanical/classical approach, in which the solute molecule is treated quantum-mechanically, but interactions involving the solvent are handled classically. Such methods are often labeled QM/MM, the MM reflecting the fact that classical force fields are utilized in molecular mechanics. An effective Hamiltonian Hefl is written for the entire solute/solvent system ... 

In scheme (9) we could have substituted on the diagonal S(S -i-1)/2 for As a-ASb and BSa-BSb- As it stands, the matrix is a hybrid because it contains matrix elements on the off-diagonal and operators on the diagonal. The present form of (9) is, however, despite its awkward form, a more useful starting point for setting up a spin Hamiltonian for the description of trinuclear and tetranuclear clusters containing delocalized dimers. 

DIFFERENT ORBITAL SYMMETRIES FULLY HYBRIDIZED HAMILTONIAN... 

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