Related papers: Computational error estimates for Born-Oppenheimer…
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…
We present the construction of an exponentially accurate time-dependent Born-Oppenheimer approximation for molecular quantum mechanics. We study molecular systems whose electron masses are held fixed and whose nuclear masses are…
We report on highly accurate calculations of Born-Oppenheimer potentials for excited $n\,\Sigma^{+}$ states of the hydrogen molecule for all possible combinations of singlet/triplet and gerade/ungerade symmetries up to $n=7$. A relative…
We report on accurate variational calculations of the Born-Oppenheimer potential for excited states of the hydrogen molecule with $\Pi$, $\Delta$, and $\Phi$ symmetries. The obtained potential energy curves reach the relative precision of…
The essence of atomic structure theory, quantum chemistry, and computational materials science is solving the multi-electron stationary Schr\"odinger equation. The Quantum Monte Carlo-based neural network wave function method has surpassed…
Ehrenfest, Born-Oppenheimer, Langevin and Smoluchowski dynamics are shown to be accurate approximations of time-independent Schr\"odinger observables for a molecular system avoiding caustics, in the limit of large ratio of nuclei and…
In this paper, we consider the time-dependent Born-Oppenheimer approximation (BOA) of a classical quantum molecule involving a possibly large number of nuclei and electrons, described by a Schr\"odinger equation. In the spirit of Born and…
The energies of molecular excited states arise as solutions to the electronic Schr\"{o}dinger equation and are often compared to experiment. At the same time, nuclear quantum motion is known to be important and to induce a red-shift of…
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)…
At non-zero temperature and when a system has low-lying excited electronic states, the ground-state Born--Oppenheimer approximation breaks down and the low-lying electronic states are involved in any chemical process. In this work, we use a…
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…
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…
Quantum-classical molecular dynamics, as a partial classical limit of the full quantum Schr\"odinger equation, is a widely used framework for quantum molecular dynamics. The underlying equations are nonlinear in nature, containing a quantum…
This paper describes a method to do ab initio molecular dynamics in electronically excited systems within the random phase approximation (RPA). Using a dynamical variational treatment of the RPA frequency, which corresponds to the…
In the present paper an example of entanglement between two different kinds of interacting particles, photons and electrons is analysed. The initial-value problem of the Schroedinger equation is solved non-perturbatively for the system of a…
Excited states of molecules lie in the heart of photochemistry and chemical reactions. The recent development in quantum computational chemistry leads to inventions of a variety of algorithms that calculate the excited states of molecules…
This paper is a continuation of a previous work about the study of the survival probability modelizing the molecular predissociation in the Born-Oppenheimer framework. Here we consider the critical case where the reference energy…
The role of electron-nuclear entanglement on the validity of the Born-Oppenheimer (BO) approximation is investigated. While nonadiabatic couplings generally lead to entanglement and to a failure of the BO approximation, surprisingly the…
Approximating ground and a fixed number of excited state energies, or equivalently low order Hamiltonian eigenvalues, is an important but computationally hard problem. Typically, the cost of classical deterministic algorithms grows…
Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical…