Perturbation theory localized

Atoms in Molecules Electron Transfer Calculations Electronic Wavefunctions Analysis Hyperconjugation Intermolecular Interactions by Perturbation Theory Localized MO SCF Methods Natural Orbitals NMR Chemical Shift Computation Ab Initio Rotational Barriers Barrier Origins Valence Bond Curve Crossing Models. 

Highest occupied molecular orbital Intermediate neglect of differential overlap Linear combination of atomic orbitals Local density approximation Local spin density functional theory Lowest unoccupied molecular orbital Many-body perturbation theory Modified INDO version 3 Modified neglect of diatomic overlap Molecular orbital Moller-Plesset... 

The first type of interaction, associated with the overlap of wavefunctions localized at different centers in the initial and final states, determines the electron-transfer rate constant. The other two are crucial for vibronic relaxation of excited electronic states. The rate constant in the first order of the perturbation theory in the unaccounted interaction is described by the statistically averaged Fermi golden-rule formula... 

Pipek J, Bogar F (1999) Many-Body Perturbation Theory with Localized Orbitals - Kapuy s Approach. 203 43-61... 

A transition linearly coupled to the phonon field gradient will experience, from the perturbation theory perspective, a frequency shift and a drag force owing to phonon emission/absorption. Here we resort to the simplest way to model these effects by assuming that our degree of freedom behaves like a localized boson with frequency (s>i. The corresponding Hamiltonian reads... 

Importantly, the value of the results gained in the present section is not limited to the application to actual systems. Eq. (4.2.11) for the GF in the Markov approximation and the development of the perturbation theory for the Pauli equation which describes many physical systems satisfactorily have a rather general character. An effective use of the approaches proposed could be exemplified by tackling the problem on the rates of transitions of a particle between locally bound subsystems. The description of the spectrum of the latter considered in Ref. 135 by means of quantum-mechanical GF can easily be reformulated in terms of the GF of the Pauli equation. 

As reviewed above, when a solute is placed in a dielectric medium, it electrically polarizes that medium. The polarized medium produces a local electrostatic field at the site of the solute, this field polarizes the solute, and the polarized solute interacts with the polarized medium. The interaction is typically too large to be treated by perturbation theory, and some sort of self-consistent treatment of polarized solute and polarized medium is more appropriate. At this point several options present themselves. It promotes orderly discussion to classify these... 

Starting from the normal mode approximation, one can introduce anharmonicity in different ways. Anharmonic perturbation theory [206] and local mode models [204] may be useful in some cases, where anharmonic effects are small or mostly diagonal. Vibrational self-consistent-field and configuration-interaction treatments [207, 208] can also be powerful and offer a hierarchy of approximation levels. Even more rigorous multidimensional treatments include variational calculations [209], diffusion quantum Monte Carlo, and time-dependent Hartree approaches [210]. 

H. J. Werner, F. R. Manby, and P. J. Knowles, Fast linear scaling second order Mpller Plesset perturbation theory (MP2) using local and density fitting approximations. J. Chem. Phys. 118, 8149 8160 (2003). 

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