We report the first nonadiabatic molecular dynamics study based on the exact factorization of the electron–nuclear wave function. Our approach (a coupled-trajectory mixed quantum–classical, CT-MQC, ...scheme) is based on the quantum–classical limit derived from systematic and controlled approximations to the full quantum-mechanical problem formulated in the exact-factorization framework. Its strength is the ability to correctly capture quantum (de)coherence effects in a trajectory-based approach to excited-state dynamics. We show this by benchmarking CT-MQC dynamics against a revised version of the popular fewest-switches surface-hopping scheme that is able to fix its well-documented overcoherence issue. The CT-MQC approach is successfully applied to investigation of the photochemistry (ring-opening) of oxirane in the gas phase, analyzing in detail the role of decoherence. This work represents a significant step forward in the establishment of the exact factorization as a powerful tool to study excited-state dynamics, not only for interpretation purposes but mainly for nonadiabatic ab initio molecular dynamics simulations.
We present an exact single-electron picture that describes the correlated electron dynamics in strong laser fields. Our approach is based on the factorization of the electronic wave function as a ...product of a marginal and a conditional amplitude. The marginal amplitude, which depends only on one electronic coordinate and yields the exact one-electron density and current density, obeys a time-dependent Schrödinger equation with an effective time-dependent potential. The exact equations are used to derive an approximation that is a step towards general and feasible ab initio single-electron calculations for molecules. The derivation also sheds new light on the usual interpretation of the single-active electron approximation. From the study of model systems, we find that the exact and approximate single-electron potentials for processes with negligible two-electron ionization lead to qualitatively similar dynamics, but that the ionization barrier in the exact single-electron potential may be explicitly time dependent.
The ground state energy of a system of electrons (r=r_{1},r_{2},…) and nuclei (R=R_{1},R_{2},…) is proven to be a variational functional of the electronic density n(r,R) and paramagnetic current ...density j_{p}(r,R) conditional on R, the nuclear wave function χ(R), an induced vector potential A_{μ}(R) and a quantum geometric tensor T_{μν}(R). n, j_{p}, A_{μ} and T_{μν} are defined in terms of the conditional electronic wave function Φ_{R}(r). The ground state (n,j_{p},χ,A_{μ},T_{μν}) can be calculated by solving self-consistently (i) conditional Kohn-Sham equations containing effective scalar and vector potentials v_{s}(r) and A_{xc}(r) that depend parametrically on R, (ii) the Schrödinger equation for χ(R), and (iii) Euler-Lagrange equations that determine T_{μν}. The theory is applied to the E⊗e Jahn-Teller model.
Ultrafast dynamics with the exact factorization Agostini, Federica; Gross, E. K. U.
The European physical journal. B, Condensed matter physics,
09/2021, Volume:
94, Issue:
9
Journal Article
Peer reviewed
Open access
The exact factorization of the time-dependent electron–nuclear wavefunction has been employed successfully in the field of quantum molecular dynamics simulations for interpreting and simulating ...light-induced ultrafast processes. In this work, we summarize the major developments leading to the formulation of a trajectory-based approach, derived from the exact factorization equations, capable of dealing with nonadiabatic electronic processes, and including spin-orbit coupling and the non-perturbative effect of an external time-dependent field. This trajectory-based quantum-classical approach has been dubbed coupled-trajectory mixed quantum-classical (CT-MQC) algorithm, whose performance is tested here to study the photo-dissociation dynamics of IBr.
Graphic abstract
Trajectory-based mixed quantum-classical approaches to coupled electron–nuclear dynamics suffer from well-studied problems such as the lack of (or incorrect account for) decoherence in the trajectory ...surface hopping method and the inability of reproducing the spatial splitting of a nuclear wave packet in Ehrenfest-like dynamics. In the context of electronic nonadiabatic processes, these problems can result in wrong predictions for quantum populations and in unphysical outcomes for the nuclear dynamics. In this paper, we propose a solution to these issues by approximating the coupled electronic and nuclear equations within the framework of the exact factorization of the electron–nuclear wave function. We present a simple quantum-classical scheme based on coupled classical trajectories and test it against the full quantum mechanical solution from wave packet dynamics for some model situations which represent particularly challenging problems for the above-mentioned traditional methods.
We present a novel quantum-classical approach to nonadiabatic dynamics, deduced from the coupled electronic and nuclear equations in the framework of the exact factorization of the electron-nuclear ...wave function. The method is based on the quasiclassical interpretation of the nuclear wave function, whose phase is related to the classical momentum and whose density is represented in terms of classical trajectories. In this approximation, electronic decoherence is naturally induced as an effect of the coupling to the nuclei and correctly reproduces the expected quantum behavior. Moreover, the splitting of the nuclear wave packet is captured as a consequence of the correct approximation of the time-dependent potential of the theory. This new approach offers a clear improvement over Ehrenfest-like dynamics. The theoretical derivation presented in this Letter is supported by numerical results that are compared to quantum mechanical calculations.
We demonstrate that the molecular Berry phase and the corresponding nonanalyticity in the electronic Born-Oppenheimer wave function is, in general, not a true topological feature of the exact ...solution of the full electron-nuclear Schrödinger equation. For a numerically exactly solvable model we show that a nonanalyticity, and the associated geometric phase, only appear in the limit of infinite nuclear mass, while a perfectly smooth behavior is found for any finite nuclear mass.
The recently developed exact factorization approach condenses all electronic effects on the nuclear subsystem into scalar and vector potentials that appear in an effective time dependent Schrödinger ...equation. Starting from this equation, we derive subsystem Ehrenfest identities characterizing the energy, momentum, and angular momentum transfer between electrons and nuclei. An effective electromagnetic force operator induced by the electromagnetic field corresponding to the effective scalar and vector potentials appears in all three identities. The effective magnetic field has two components that can be identified with the Berry curvature calculated with (a) different Cartesian coordinates of the same nucleus and (b) arbitrary Cartesian coordinates of two different nuclei. (a) has a classical interpretation as the induced magnetic field felt by the nucleus, while (b) has no classical analog. Subsystem Ehrenfest identities are ideally suited for quantifying energy transfer in electron-phonon systems. With two explicit examples we demonstrate the usefulness of the new identities.
Safety requirements for bicycles are defined in different standards in Europe and worldwide. Nevertheless the payload of bicycles and the weight of the rider are not taken into account for the ...formulation of the test loads for mechanical tests. The average weight of bicycle users varies widely worldwide, and in recent years there has been a significant increase, especially in the industrialized nations, where electrically power assisted cycles in particular are experiencing very high demand. The influence of the rider's weight and driving style is determined by operating load measurements, based on the current fatigue tests the component damage ratio under variable amplitude loading is calculated in order to create a basis for a future reformulation.
Time-dependent density functional theory (TDDFT) is implemented in an all electron solid-state code for the case of fully unconstrained noncollinear spins. We use this to study intense, short, laser ...pulse-induced demagnetization in bulk Fe, Co, Ni and find that demagnetization can take place on time scales of <20 fs. It is demonstrated that this form of demagnetization is a two-step process: excitation of a fraction of electrons followed by spin-flip transitions mediated by spin–orbit coupling of the remaining localized electrons. We further show that it is possible to control the moment loss by tunable laser parameters, including frequency, duration, and intensity.
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