Fewest switches surface hopping with Baeck-An couplings

Abstract

In the Baeck-An (BA) approximation, first-order nonadiabatic coupling vectors are given in terms of adiabatic energy gaps and the second derivative of the gaps with respect to the coupling coordinate. In this paper, a time-dependent (TD) BA approximation is derived, where the couplings are computed from the energy gaps and their second time-derivatives. TD-BA couplings can be directly used in fewest switches surface hopping, enabling nonadiabatic dynamics with any electronic structure methods able to provide excitation energies and energy gradients. Test results of surface hopping with TD-BA couplings for ethylene and fulvene show that the TD-BA approximation delivers a qualitatively correct picture of the dynamics and a semiquantitative agreement with reference data computed with exact couplings. Nevertheless, TD-BA does not perform well in situations conjugating strong couplings and small velocities. Considered the uncertainties in the method, TD-BA couplings could be a competitive approach for inexpensive, exploratory dynamics with a small trajectories ensemble. We also assessed the potential use of TD-BA couplings for surface hopping dynamics with time-dependent density functional theory (TDDFT), but the results are not encouraging due to singlet instabilities near the crossing seam with the ground state.

Simulations of molecular photodynamics in long timescales

“…From a technical standpoint, performing nonadiabatic dynamics with FSSH amounts to repeating the following sequence: Read initial conditions (geometry, velocity, initial electronic state and initial time-dependent wave function coefficients).Compute electronic energies and energy gradients (usually through an external code).Obtain time-derivative couplings (either nonadiabatic coupling vectors, through wave function overlap matrices, or approximated methods [98]).Solve the classical EOM.Solve the quantum EOM (a locally approximated time-dependent Schrödinger equation).Decide on whether to hop to another state or not.Go back to step (i) with the updated set of conditions. Going between steps requires conveying information either internally (from (v) to (vi), for instance) or through some external program ((i) to (ii), for example). A straightforward approach is to use a primary driver that will call a set of scripts or programs sequentially, each communicating through text files.…”

“… Compute electronic energies and energy gradients (usually through an external code). Obtain time-derivative couplings (either nonadiabatic coupling vectors, through wave function overlap matrices, or approximated methods [ 98 ]). Solve the classical EOM.…”

“…Obtain time-derivative couplings (either nonadiabatic coupling vectors, through wave function overlap matrices, or approximated methods [ 98 ]).…”

The Newton-X platform: new software developments for surface hopping and nuclear ensembles

“…For all methods available in Newton-X, nonadiabatic couplings can be calculated with the time-dependent Baeck-An approach 23 (TD-BA), which approximates the time-derivative couplings in terms of the energy gaps and their second time-derivatives ( )…”

“…In recent years, Newton-X became the host of novel methods for nonadiabatic couplings without wavefunctions, 23 zero-point-energy leakage corrections, 24 and nonadiabatic dynamics induced by incoherent light, 25 in complex-valued potential energy surfaces, 26 and including multiple chromophores. 27 All these features, together with interfaces to numerous third-party programs spanning methods from MRCI to machine learning potentials, make Newton-X one of the richest software platforms for mixed quantum-classical simulations.…”