Model state effective Hamiltonian

The treatment developed here is based on the density matrix of quantum mechanics and extends previous work using wavefunctions.(42 5) The density matrix approach treats all energetically accessible electronic states in the same fashion, and naturally leads to average effective potentials which have been shown to give accurate results for electronically diabatic collisions. 19) The approach is taken here for systems where the dynamics can be described by a Hamiltonian operator, as it is possible for isolated molecules or in models where environmental effects can be represented by terms in an effective Hamiltonian. 

Hamiltonian equations, 610—615 minimal models, 615-618 multi-state effects, 624 pragmatic models, 618—621 spectroscopic properties, 598-610 linear molecules ... 

The main reason why existing MR CC methods as well as related MR MBPT cannot be considered as standard or routine methods is the fact that both theories suffer from the Intruder state problem or generally from the convergence problems. As is well known, both MR MBPT/CC theories are built on the concept of the effective Hamiltonian that acts in a relatively small model or reference space and provides us with energies of several states at the same time by diagonalization of the effective Hamiltonian. In order to warrant size-extensivity, both theories employ the complete model space formulations. Although conceptually simpler, the use of the complete model space makes the calculations rather... 

Some of the theoretical models used vary in each of the studies reported. These models were discussed in chapter 2, and the results are presented in each individual case below. In some cases, however, a detailed interpretation of the experimental UPS spectra requires the support of calculated density-of-valence-states (DOVS) curves. For that purpose, the valence effective Hamiltonian (VEH) method, which has been shown to provide accurate distributions of valence states for polymers and molecules, is used12-14. Even though it cannot be used for metal-containing systems (since the VEH potentials are not defined for metal atoms), the VEH approach is nevertheless of interest to determine the nature of the electronic wavefunctions (molecular orbitals) associated with a given UPS feature in the pristine polymer. 

The origin of the LR-SS difference was imputed to the incapability of the nonlinear effective solute Hamiltonian used in these solvation models to correctly describe energy expectation values of mixed solute states, i.e., states that are not stationary. Since in a perturbation approach such as the LR treatment the perturbed state can be seen as a linear combination of zeroth-order states, the inability of the effective Hamiltonian approach to treat mixed states causes an incorrect redistribution of the solvent terms among the various perturbation orders [32],... 

A modified effective Hamiltonian Goep is defined by replacing vxc by a model local potential vxc(r). The energy functional is made stationary with respect to variations of occupied orbitals that are determined by modified OEL equations in which Q is replaced by Goep- 84>i is determined by variations 8vxc(r) in these modified OEL equations. To maintain orthonormality, <5, can be constrained to be orthogonal to all occupied orbitals of the OEP trial state , so that (r) = J]a(l — na)i). First-order perturbation theory for the OEP Euler-Lagrange equations implies that... 

---