Communication: The correct interpretation of surface hopping trajectories: How to calculate electronic properties

Abstract

In a recent paper, we presented a road map for how Tully's fewest switches surface hopping (FSSH) algorithm can be derived, under certain circumstances, from the mixed quantum-classical Liouville equation. In this communication, we now demonstrate how this new interpretation of surface hopping can yield significantly enhanced results for electronic properties in nonadiabatic calculations. Specifically, we calculate diabatic populations for the spin-boson problem using FSSH trajectories. We show that, for some Hamiltonians, without changing the FSSH algorithm at all but rather simply reinterpreting the ensemble of surface hopping trajectories, we recover excellent results and remove any and all ambiguity about the initial condition problem.

Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations

“…Although MF-GQME offers probably the highest possible accuracy for the lowest possible cost, other similar calculations can be carried out using other dynamics methods such as FSSH, linearized and partially linearized approaches, and higher tier methods [2,5,7,8,17]. Indeed, at the opposite end of the hierarchy, very computationally demanding approaches such as the momentum-jump solution to the QCLE [11] can be made tractable when combined within the GQME framework [25], greatly expanding its regime of applicability.…”

“…At present, this means that one is typically limited to using MFT, or Tully's fewest switches surface hopping (FSSH) algorithm and its variants [13][14][15][16][17], or linearized path integral approaches [18][19][20].…”

How to calculate linear absorption spectra with lifetime broadening using fewest switches surface hopping trajectories: A simple generalization of ground-state Kubo theory

“…25 In order to develop an expression for the dipole-dipole correlation function, we will make use of the recently developed definition of the nuclear-electronic density matrix consistent with an ensemble of FSSH trajectories. 48,49 As FSSH has been extensively discussed in the literature, we will not provide a description of it here. 25,48,52 In the formalism developed in this section, we will consider systems for which, in the diabatic representation, the transition dipole moment is position independent and couples the ground state to a single (bright) excited state.…”

“…23,[45][46][47] In doing so, we obtained a well-defined expression for the mixed quantum-classical nuclear-electronic density matrix that is consistent with a swarm of FSSH trajectories. 48,49 Our analysis makes it clear that information from both FSSH electronic wavefunctions and FSSH active adiabatic surfaces is necessary to build up the proper nuclear-electronic density matrix. Using this FSSH nuclear-electronic density matrix, we believe we can now calculate any electronic property of interest directly from an ensemble of surface hopping trajectories.…”

Surface hopping outperforms secular Redfield theory when reorganization energies range from small to moderate (and nuclei are classical)

“…First, until recently, it was unclear how to initialize a surface hopping calculation over a linear combination of adiabatic states; 40 this conundrum has now been resolved. 41,42 Second, many researchers have likely presumed that FSSH must fail in the Redfield regime. After all, in the Redfield regime, electronic coherence is important (unlike the Marcus regime wherein wavepackets separate irreversibly) and FSSH cannot capture recoherences (wavepacket separation and recombination).…”