Mean-field dynamics with stochastic decoherence (MF-SD): A new algorithm for nonadiabatic mixed quantum/classical molecular-dynamics simulations with nuclear-induced decoherence

Abstract

The key factors that distinguish algorithms for nonadiabatic mixed quantum/classical ͑MQC͒ simulations from each other are how they incorporate quantum decoherence-the fact that classical nuclei must eventually cause a quantum superposition state to collapse into a pure state-and how they model the effects of decoherence on the quantum and classical subsystems. Most algorithms use distinct mechanisms for modeling nonadiabatic transitions between pure quantum basis states ͑"surface hops"͒ and for calculating the loss of quantum-mechanical phase information ͑e.g., the decay of the off-diagonal elements of the density matrix͒. In our view, however, both processes should be unified in a single description of decoherence. In this paper, we start from the density matrix of the total system and use the frozen Gaussian approximation for the nuclear wave function to derive a nuclear-induced decoherence rate for the electronic degrees of freedom. We then use this decoherence rate as the basis for a new nonadiabatic MQC molecular-dynamics ͑MD͒ algorithm, which we call mean-field dynamics with stochastic decoherence ͑MF-SD͒. MF-SD begins by evolving the quantum subsystem according to the time-dependent Schrödinger equation, leading to mean-field dynamics. MF-SD then uses the nuclear-induced decoherence rate to determine stochastically at each time step whether the system remains in a coherent mixed state or decoheres. Once it is determined that the system should decohere, the quantum subsystem undergoes an instantaneous total wave-function collapse onto one of the adiabatic basis states and the classical velocities are adjusted to conserve energy. Thus, MF-SD combines surface hops and decoherence into a single idea: decoherence in MF-SD does not require the artificial introduction of reference states, auxiliary trajectories, or trajectory swarms, which also makes MF-SD much more computationally efficient than other nonadiabatic MQC MD algorithms. The unified definition of decoherence in MF-SD requires only a single ad hoc parameter, which is not adjustable but instead is determined by the spatial extent of the nonadiabatic coupling. We use MF-SD to solve a series of one-dimensional scattering problems and find that MF-SD is as quantitatively accurate as several existing nonadiabatic MQC MD algorithms and significantly more accurate for some problems.

A general method to describe intersystem crossing dynamics in trajectory surface hopping

“…The latter effect can be partially mitigated using socalled decoherence corrections; the interested reader is referred to the according literature. [132,[136][137][138][139][140][141][142][143][144][145][146][147][148][149][150][151][152][153] Tunneling effects can also not be described with surface hopping although there exist several approaches to alleviate this deficiency, see, for example, Refs. [154][155][156][157][158].…”

Nonadiabatic dynamics in open quantum-classical systems: Forward-backward trajectory solution

“…These include mean-field and a variety of surface-hopping schemes [1][2][3][4][5][6][7] , methods based on semi-classical evaluations of path integral formulations of quantum mechanics [8][9][10][11][12][13][14][15][16][17][18][19][20] and descriptions based on the quantum-classical Liouville equation 21 . An important ingredient in any approach dealing with nonadiabatic dynamics is the manner in which quantum coherence and decoherence are taken into account in the dynamics.…”

Communication: Standard surface hopping predicts incorrect scaling for Marcus’ golden-rule rate: The decoherence problem cannot be ignored

“…Although FSSH dynamics do correctly predict a peak in rate as a function of driving 0 , our striking conclusion is that the FSSH algorithm does not recover the correct scaling (in V); FSSH rates scale as V instead of V 2 . Moving forward, we will invoke the well-known decoherence approach of Rossky and co-workers to collapse the electronic amplitude when appropriate, 14,15,[23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] and having done so, we will show that one now recovers the correct V 2 scaling. Thus, this work highlights the true significance of the decoherence problem: surface-hopping cannot recover the Marcus rates of the simplest possible nonadiabatic system without an adjustment for decoherence.…”