Related papers: On Corrections to the Born-Oppenheimer Approximati…
We propose a procedure to analyze the relation between the exact factorization of the electron-nuclear wave function and the Born-Oppenheimer approximation. We define the adiabatic limit as the limit of infinite nuclear mass. To this end,…
A first principles quantum formalism to describe the non-adiabatic dynamics of electrons and nuclei based on a second quantization representation (SQR) of the electronic motion combined with the usual representation of the nuclear…
The Born-Oppenheimer approximation leads to the counterintuitive result of a vanishing electronic flux density upon vibrational dynamics in the electronic ground state. To circumvent this long known issue, we propose using pairwise…
We propose a novel method to describe realistically ionization processes with absorbing boundary conditions in basis expansion within the formalism of the so-called Non-Adiabatic Quantum Molecular Dynamics. This theory couples…
The quantum mechanical motion of the atomic nuclei is considered over a single- or a multi-dimensional subspace of electronic states which is separated by a gap from the rest of the electronic spectrum over the relevant range of nuclear…
The molecular Schr\"odinger equation is rewritten in terms of non-unitary equations of motion for the nuclei (or electrons) that depend parametrically on the configuration of an ensemble of generally defined electronic (or nuclear)…
An alternative method is introduced to solve a simple two-dimensional models describing vibrational excitation and dissociation processes during the electron-molecule collisions. The model works with one electronic and one nuclear degree of…
The combined quantum electron-nuclear dynamics is often associated with the Born-Huang expansion of the molecular wave function and the appearance of nonadiabatic effects as a perturbation. On the other hand, native multicomponent…
The diagonal Born-Oppenheimer correction (DBOC) stems from the diagonal second derivative coupling term in the adiabatic representation, and it can have an arbitrary large magnitude when a gap between neighbouring Born-Oppenheimer (BO)…
The adiabatic approximation is a natural approach for the description of phenomena induced by low frequency laser radiation because the ratio of the laser frequency to the characteristic frequency of an atom or a molecule is a small…
An approach to non-adiabatic dynamics of atoms in molecular and condensed matter systems under general non-equilibrium conditions is proposed. In this method interaction between nuclei and electrons is considered explicitly up to the second…
The standard wave function approach for the treatment of neutrino oscillations fails in situations where quantum ensembles at a finite temperature with or without an interacting background plasma are encountered. As a first step to treat…
We develop a density matrix formalism to describe coupled electron-nuclear dynamics. To this end we introduce an effective Hamiltonian formalism that describes electronic transitions and small (quantum) nuclear fluctuations along a…
Nuclear quantum phenomena beyond the Born-Oppenheimer approximation are known to play an important role in a growing number of chemical and biological processes. While there exists no unique consensus on a rigorous and efficient…
We apply the Born--Oppenheimer approximation to a harmonic diatomic molecule with one electron. We compare the exact and approximate results not only for the internal degrees of freedom but also for the motion of the center of mass. We…
We study a general problem of the translational/rotational/vibrational/electronic dynamics of a diatomic molecule exposed to an interaction with an arbitrary external electromagnetic field. The theory developed in this paper is relevant to…
Every physical regime is some sort of approximation of reality. One lesser-known realm that is the semiquantal regime, which may be used to describe systems with both classical and quantum subcomponents. In the present review, we discuss…
This paper provides a complete self-consistent nonlinear theory for electron plasma waves, within the framework of the adiabatic approximation. The theory applies whatever the variations of the wave amplitude, provided that they are slow…
The coupling of electronic and vibrational motion is studied by two canonical transformations namely normal coordinate transformation and momentum transformation on molecular Hamiltonian. It is shown that by these transformations we can…
In this work we develop tools that enable the study of non-adiabatic effects with variational and diffusion Monte Carlo methods. We introduce a highly accurate wave function ansatz for electron-ion systems that can involve a combination of…