Laser-induced electron localization in H₂⁺: mixed quantum-classical dynamics based on the exact time-dependent potential energy surface

Abstract

We study the exact nuclear time-dependent potential energy surface (TDPES) for laser-induced electron localization with a view to eventually developing a mixed quantum-classical dynamics method for strong-field processes. The TDPES is defined within the framework of the exact factorization [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett., 2010, 105, 123002] and contains the exact effect of the couplings to the electronic subsystem and to any external fields within a scalar potential. We compare its features with those of the quasistatic potential energy surfaces (QSPES) often used to analyse strong-field processes. We show that the gauge-independent component of the TDPES has a mean-field-like character very close to the density-weighted average of the QSPESs. Oscillations in this component are smoothened out by the gauge-dependent component, and both components are needed to yield the correct force on the nuclei. Once the localization begins to set in, the gradient of the exact TDPES tracks one QSPES and then switches to the other, similar to the description provided by surface-hopping between QSPESs. We show that evolving an ensemble of classical nuclear trajectories on the exact TDPES accurately reproduces the exact dynamics. This study suggests that the mixed quantum-classical dynamics scheme based on evolving multiple classical nuclear trajectories on the exact TDPES will be a novel and useful method to simulate strong field processes.

Surface hopping in laser-driven molecular dynamics

“…The studies justify the SH methodology for the laser-driven case. At the same time, the investigations also conclude the present, controversially led debate about the applicability of BOSs or IBOSs in SH schemes [10][11][12], because both are not appropriate. These conclusions are valid for (and at the same time limited to) laser fields where the Floquet treatment of the time-dependent Hamiltonian approximately applies.…”

“…In close analogy, the SH mechanism can create branches of classical trajectories at avoided crossings. The findings [6] justify, albeit qualitatively but anyhow convincingly, the SH methodology on BOSs, in the field-free case.For the laser-driven dynamics, any validation of SH is still lacking and the appropriate choice of the applicable PES is discussed controversially, at present [10][11][12]. In fact, the hitherto purely intuitively chosen PES in SH models are fundamentally different from each other, and include BOSs [10,[13][14][15][16][17], instantaneous BOSs (IBOSs) [18][19][20][21][22] as well as Floquet surfaces (FSs) [22][23][24].…”

Libra: An open-Source “methodology discovery” library for quantum and classical dynamics simulations

“…Although quantum mechanical calculations can be coded in a way that does not require intermediate objects, the ability to have both "AO" and "PrimitiveG" objects is convenient for many purposes. For instance, they can be used in the floating spherical Gaussian orbital (FSGO) [36][37][38] calculations; they can represent semi-classical electron in the electron force field (eFF) calculations [39,40] or in quantized Hamiltonian dynamics; [41][42][43] they can be used as the time-evolving basis functions (either electronic or nuclear) in propagation of the TD-SE [44][45][46] (e.g., in the FMS [47] or wavepacket propagation [48,49] contexts). The molecular integrals and their derivatives are overloaded to take argument of the "PrimitiveG" and "AO" data type, to simplify quantum-chemical calculations to the intuitive, compact, and object-oriented procedures.…”

An exact factorization perspective on quantum interferences in nonadiabatic dynamics

“…The molecular wavefunction can, for example, be represented exactly by a simple factorization 37,38 in terms of a time-dependent nuclear wavefunction and a time-dependent electronic wavefunction, parametrically dependent on the nuclear positions. When inserted into the molecular time-dependent Schrödinger equation, the Exact Factorization (EF) leads to coupled equations driving the dynamics of the two components of the wavefunction: a timedependent Schrödinger equation [39][40][41][42] describes the evolution a) Electronic address: agostini@mpi-halle.mpg.de of the nuclear wavefunction, where the effect of the electrons is fully accounted for by a time-dependent vector potential and a time-dependent scalar potential (or time-dependent potential energy surface, TDPES); electronic dynamics is generated by an evolution equation where the coupling to the nuclei is expressed by the so-called electron-nuclear coupling operator. [43][44][45][46][47] The EF has been developed both in the time-independent [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64] and in the time-dependent [37][38][39][40][41][42][43][65][66][67][68] versions and analyzed under different perspectives.…”