Partitioning of the Vibrational-Electronic Hamiltonian. Ab Initio Correlated Calculations of the First Vibronic Transitions for Some Simple Molecules

Int J of Quantum Chemistry

Baňacký

Zajac

1992

The electron-vibrational problem of the general nonadiabatic molecular systems has been solved by means of the quasi-particle transformations. The SCF ab initio solution of the nonadiabatic fermion Hamiltonian yields stabilization of the electronic ground-state energy due to electron-phonon interaction and it also gives the corrections to the one-and two-particle terms. Two two-particle correction yields effective attractive electron-electron interaction, but in the form different from Frolich's effective electron-electron interaction term. In contrast to the standard electron-phonon Hamiltonian of solid-state physics that does not take into account the possible effects of nonadiabaticity of a system, the presented nonadiabatic theory yields also one-particle corrections. The presence of this term in the Hamiltonian might play a crucial role in the theory of superconductivity since the superconductors are nonadiabatic systems. Since the quasi-particle theory of vibrational energy calculations for nonadiabatic molecules is extremely extensive and will be published elsewhere [lo], we restrict ourselves only to the schematic way of derivation, with the focus being placed on the fermion part of the nonadiabatic e1.-vibr. Hamiltonian.

“…(4. 8)]. The two-particle Hamiltonian, i.e., the correction AH", has been obtained in the form (4.14) and (4.15), which yields the Cooper-pairs formation [(4.21)].…”

Section: Basjackmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonadiabatic theory of electron–vibrational coupling: New basis for microscopic interpretation of superconductivity

Int J of Quantum Chemistry

Baňacký

Zajac

1992

“…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.…”

Section: Svreek B A~~a C K + and Zajacmentioning

confidence: 99%

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

Int J of Quantum Chemistry

Baňacký

Zajac

1992

An exact solution for the electron-vibrational problem of the nonadiabatic molecular system has been obtained. By the quasi-particle transformation technique, the fermionic Hamiltonian has been derived and solved at the ab initio level. Results clearly and unambiguously show that the gap formation due to nonadiabatic electron-phonon coupling is mediated by the one-particle electron-phonon interaction term, whereas the two-particle one represents just a correction to the correlation energy. The temperature dependence of the gap and electronic specific heat connected with the electron-phonon coupling have also been derived.

“…Most of the equations and concepts were subsequently published in a series of papers [14][15][16][17][18][19][20][21]. However, some essential ingredients were missing in my original formulation, namely the inclusion of the COM problem.…”

Section: Introductionmentioning

confidence: 99%

“…However, some essential ingredients were missing in my original formulation, namely the inclusion of the COM problem. In particular, in the works [14][15][16][17] the molecular adiabatic corrections were wrong derived without having regard for Born-Handy ansatz.…”

Section: Introductionmentioning

confidence: 99%

Centre-of-Mass Separation in Quantum Mechanics: Implications for the Many-Body Treatment in Quantum Chemistry and Solid State Physics

Advances in the Theory of Quantum Systems in Chemistry and Physics

2011

We address the question to what extent the centre-of-mass (COM) separation can change our view of the many-body problem in quantum chemistry and solid state physics. It was shown that the many-body treatment based on the electron-vibrational Hamiltonian is fundamentally inconsistent with the Born-Handy ansatz so that such a treatment can never respect the COM problem. Born-Oppenheimer (B-O) approximation reveals some secret: it is a limit case where the degrees of freedom can be treated in a classical way. Beyond the B-O approximation they are inseparable in principle. The unique covariant description of all equations with respect to individual degrees of freedom leads to new types of interaction: besides the known vibronic (electron-phonon) one the rotonic (electron-roton) and translonic (electron-translon) interactions arise. We have proved that due to the COM problem only the hypervibrations (hyperphonons, i.e. phonons + rotons + translons) have true physical meaning in molecules and crystals; nevertheless, the use of pure vibrations (phonons) is justified only in the adiabatic systems. This fact calls for the total revision of our contemporary knowledge of all nonadiabatic effects, especially the Jahn-Teller effect and superconductivity. The vibronic coupling is responsible only for removing of electron (quasi)degeneracies but for the explanation of symmetry breaking and forming of structure the rotonic and translonic coupling is necessary.