Beyond born oppenheimer theories and its implication to quantum dynamics

Ville J. Härkönen

We combine the recently developed many-body Green's function theory for electrons and nuclei with the exact factorization of the wave function. The existing Born-Oppenheimer Green's functions are shown to be special cases of our exact approach. We consider the limitations of the laboratory frame formulation of the Green's function theory and discuss why the body-fixed frame formulation is needed in order to go beyond the Born-Oppenheimer theory. We give exact forms of the electronic and nuclear Green's functions written in terms of the exact factorized states, providing a systematic approach beyond the Born-Oppenheimer approximation. The lowest order approximation to the exact electronic Green's function is found to be an expected value of the Born-Oppenheimer electronic Green's function with respect to the nuclear density.

Holger Friedrich Hofmann

John A. Parkhill, Thomas Markovich, David G. Tempel +1 more

In this work, we develop an approach to treat correlated many-electron dynamics, dressed by the presence of a finite-temperature harmonic bath. Our theory combines a small polaron transformation with the second-order time-convolutionless master equation and includes both electronic and system-bath correlations on equal footing. Our theory is based on the ab initio Hamiltonian, and is thus well-defined apart from any phenomenological choice of basis states or electronic system-bath coupling model. The equation-of-motion for the density matrix we derive includes non-markovian and non-perturbative bath effects and can be used to simulate environmentally broadened electronic spectra and dissipative dynamics, which are subjects of recent interest. The theory also goes beyond the adiabatic Born-Oppenheimer approximation, but with computational cost scaling such as the Born-Oppenheimer approach. Example propagations with a developmental code are performed, demonstrating the treatment of electron-correlation in absorption spectra, vibronic structure, and decay in an open system. An untransformed version of the theory is also presented to treat more general baths and larger systems.

Geoffrey L. Price, Baker, B. Mitchell, Palle E. T. Jørgensen +1 more

Ville J. Härkönen, Robert van Leeuwen, Eberhard K. U. Gross

The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here resolves the problems arising from the translational and rotational invariance of this Hamiltonian that afflict the existing many-body Green's function theories. We derive a coupled set of exact equations for the electronic and nuclear Green's functions and provide a systematic way to approximately compute the properties of arbitrary many-body systems of electrons and nuclei beyond the Born-Oppenheimer approximation. The case of crystalline solids is discussed in detail.

Vladimir S. Filinov