The quasiparticle concept in vibrational–electronic problems in molecules. I. Partitioning of the vibrational–electronic Hamiltonian

Abstract

AbSttSdThe partitioning of the vibrational-electronic Hamiltonian is presented. This partitioning is based on a new quasiparticle transformation that is constructed in such a way that the adiabatic approximation is included into the unperturbed Hamiltonian; nonadiabacity, anharmonicity, and electron correlation are treated as perturbations. We also present the second quantization treatment for bosons. The many body perturbation theory expansion for the vibrational-electronic Hamiltonian is suggested. A comparison of this approach is made with gradient techniques.

Molecular aspects of superconductivity: The role of the one‐particle term at the gap formation

“…We have solved this problem in analogy with the adiabatic case [4], but now, two-step successive quasi-particle transformations have been used [6]. The motion of the new fermions obtained after the second transformation depends on nuclear coordinates and, what is novel, also on nuclear momenta.…”

“…Recently, the ab initio theory based on the quasi-particle transformation technique has been formulated [4] and numerically verified [5]. The new fermionsquasiparticles emerging after the transformation-follow the nuclear motion adiabatically.…”

Rovibrational Energies of Triatomic Molecules by Means of the Rayleigh–Schrödinger Perturbation Theory

“…[5]) provides adiabatic potentials and nonadiabatic couplings (formally identical with Eqs. [8], [10], and [11]) in terms of the dynamical variable r. The corresponding system of ordinary Schrödinger equations is equivalent to the original three-dimensional eigenvalue problem and its solution provides finally the sought, numerically "exact" energies.…”

“…These procedures range from approximate low-order perturbation theory schemes to numerically robust and accurate basis-set procedures (see Refs. (4) and (8) and references therein). Standard perturbation procedures allow separate treatments of individual states and are numerically inexpensive, but they turn out to be mostly unstable and rather inaccurate.…”

Localization, conductivity, and superconductivity

“…The symmetry‐broken unrestricted Hartree–Fock solution gives a much better agreement with the experimental 1 s ionization energy than the symmetry‐restricted Hartree–Fock solution 23, but the wave function is not symmetry adapted. Further improvement of the wave function leads, however, to restored symmetry properties, where the final wave function is a superposition of equal amounts of 1 s holes 24. Hence localization is not real but depends on calculation method.…”