Related papers: Correlated Electron-Nuclear Dynamics with Conditio…
We develop a novel approach to the coupled motion of electrons and ions that focuses on the dynamics of the electronic subsystem. Usually the description of electron dynamics involves an electronic Schr\"odinger equation where the nuclear…
Solving the electronic Schr\"odinger equation for changing nuclear coordinates provides access to the Born-Oppenheimer potential energy surface. This surface is the key starting point for almost all theoretical studies of chemical processes…
For a given many-electron molecule, it is possible to define a corresponding one-electron Schr\"odinger equation, using potentials derived from simple atomic densities, whose solution predicts fairly accurate molecular orbitals for single-…
For a given many-electron molecule, it is possible to define a corresponding one-electron Schr\"odinger equation, using potentials derived from simple atomic densities, whose solution predicts fairly accurate molecular orbitals for single-…
Molecular rotation, vibration, internal rotation, isomerization, tunneling, intermolecular dynamics of weakly and strongly interacting systems, intra-to-inter-molecular energy transfer, hindered rotation and hindered translation over…
From non-linear theory of electromagnetism, suggested in (physics/9801031), follows that non-relativistic equation for scalar potential of electron in the field of nuclei is equivalent to respective Schr\"odinger equation. For mass and…
We present a novel mixed quantum-classical approach to the coupled electron-nuclear dynamics based on the exact factorization of the electron-nuclear wave function, recently proposed in [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys.…
The Schr\"odinger equation relates the electron wavefunction and the electric potential, which are emergent physical quantities. At that emergent level, the Schr\"odinger equation is either postulated as a principle of quantum physics or…
The electronic Schr\"odinger equation describes the motion of $N$ electrons under Coulomb interaction forces in a field of clamped nuclei. It is proved that its solutions for eigenvalues below the essential spectrum lie in the spectral…
Quantum trajectory calculations for electrons are a useful tool in the field of molecular dynamics, e.g. to understand processes in ultrafast spectroscopy. They have, however, two limitation: On the one hand, such calculations are typically…
A novel treatment of non-adiabatic couplings is proposed. The derivation starts from the long-known, but not well-known, fact that the wave function of the complete system of elctrons and nuclei can be written, without approximation, as a…
The exact factorization (EF) approach to coupled electron-ion dynamics recasts the time-dependent molecular Schr\"odinger equation as two coupled equations, one for the nuclear wavefunction and one for the conditional electronic…
Describing the dynamics of nuclei in molecules requires a potential energy surface, which is traditionally provided by the Born-Oppenheimer or adiabatic approximation. However, we also need to assign masses to the nuclei. There, the…
Born-Oppenheimer dynamics is shown to provide an accurate approximation of time-independent Schr\"odinger observables for a molecular system with an electron spectral gap, in the limit of large ratio of nuclei and electron masses, without…
Using a simple geometrical construction based upon the linear action of the Heisenberg--Weyl group we deduce a new nonlinear Schr\"{o}dinger equation that provides an exact dynamic and energetic model of any classical system whatsoever, be…
A theory of electronic friction is developed using the exact factorization of the electron-nuclear wavefunction. No assumption is made regarding the electronic bath, which can be made of independent or interacting electrons, and the nuclei…
The nonlinear Schrodinger equation is well known as a universal equation in the study of wave motion. In the context of wave motion at the free surface of an incompressible fluid, the equation accurately predicts the evolution of modulated…
We generalize the known solution of the Schr\"odinger equation, describing a particle confined to a triangular area, for a triangular graphene quantum dot with armchair-type boundaries. The quantization conditions, wave functions, and the…
The exact nuclear time-dependent potential energy surface arises from the exact decomposition of electronic and nuclear motion, recently presented in [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)]. Such…
It was recently shown that the exact potential driving the electron's dynamics in enhanced ionization of H$_2^+$ can have large contributions arising from dynamical electron-nuclear correlation, going beyond what any electrostatics-based…