Hamiltonian coupling

There is much flexibility in the way the mutation of one system to another can be represented. For example, if an atom type needs to be changed, it is possible to change the force field parameters for the interactions with this atom 

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E. Eliav, M.J. Vilkas, Y. Ishikawa, U. Kaldor, Extrapolated intermediate Hamiltonian coupled-cluster approach Theory and pilot application to electron affinities of alkali atoms, J. Chem. Phys. 122 (22) (2005) 224113. 

In recent years the solution of problems of large amplitude motions (LAM s) has usually been based on grid representations, such as DVR,[11, 12] of the Hamiltonians coupled with solution by sequential diagonalization and truncation (SDT[13, 9]) of the basis or by Lanczos[2] or other iterative nicthods[14]. More recently, filter diagonalization (ED) [5, 4] and spectral transforms of the iterative operator[15] have also been used. There has usually been a trade-off between the use of a compact basis with a dense Hamiltonian matrix, or a simple but very large D R with a sparse H and a fast matrix-vector product. 

The Hamiltonian coupling is not but it is generally reported as the coupling between the Lbwdin orthogonalized y/j) and y/. For only two states this takes the form,... 

The charge-transfer component further stabilizes the excimer in two ways. First, the intermolecular Coulomb interaction induces an attraction between the electron-hole pair, resulting in a weakly bound charge-transfer exciton. Second, the interchain one-electron Hamiltonian couples the charge-transfer component with the exciton component. 

We are interested in a situation where the extra particles in the lattice are described by a single band Hubbard Hamiltonian coupled to the acoustic phonons of the lattice as given in Equation 12.12 [ 128]. In the latter equation, the first and second terms describe the nearest-neighbor hopping of the extra-particles with hopping amplitudes J, and interactions V, computed for each microscopic model by band-structure calculations for Uj = 0, respectively. The third term is the phonon Hamiltonian. The fourth term is the phonon coupling obtained in lowest order in the displacement... 

The intricacies of QM/MM methods lie in the challenge of finding an appropriate treatment for the coupling between QM and MM regions as described by the term V qm/mm- Special care has to be taken that the QM/MM interface is described in an accurate and consistent way, in particular in combination with the Car-Parrinello scheme. Several mixed QM/MM Car-Parrinello methods have been implemented. In the fiilly Hamiltonian coupling scheme developed, bonds between QM and MM part of the system are treated with specifically designed pseudopotentials, whereas the remaining... 

The Fock-space and intermediate Hamiltonian coupled cluster methods were applied to the ground and excited levels of the second actinide element, thorium, and its heavy homo-logue eka-thorium (E122) [60], Two Fock-space schemes are used. The first starts with the NT + ion, with a closed-shell stmcture corresponding to a rare gas, and adds two electrons. 

Hamiltonian. Coupling between the vibrational modes is not eliminated by this transformation, but it is shifted from the kinetic energy, as in equation (1), to the potential energy (vide infra). 

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