Recovering Marcus Theory Rates and Beyond without the Need for Decoherence Corrections: The Mapping Approach to Surface Hopping

Abstract

It is well-known that fewest-switches surface hopping (FSSH) fails to correctly capture the quadratic scaling of rate constants with diabatic coupling in the weak-coupling limit, as expected from Fermi's golden rule and Marcus theory. To address this deficiency, the most widely used approach is to introduce a "decoherence correction", which removes the inconsistency between the wave function coefficients and the active state. Here we investigate the behavior of a new nonadiabatic trajectory method, called the mapping approach to surface hopping (MASH), on systems that exhibit an incoherent rate behavior. Unlike FSSH, MASH hops between active surfaces deterministically and can never have an inconsistency between the wave function coefficients and the active state. We show that MASH not only can describe rates for intermediate and strong diabatic coupling but also can accurately reproduce the results of Marcus theory in the golden-rule limit, without the need for a decoherence correction. MASH is therefore a significant improvement over FSSH in the simulation of nonadiabatic reactions.

Unraveling the mechanisms of triplet state formation in a heavy-atom free photosensitizer

“…Thus BD-Ancould provide an interesting test-bed for recently developed approaches to calculating non-adiabatic transition rates applicable to high-dimensional anharmonic systems. 34,55,67,68,70–79 The S CT → S 0 transition poses a particular challenge, since it is deep in the inverted regime, nuclear quantum effects are very large and strong diabatic coupling means there may be some effects missed by FGR, which we have estimated using open quantum dynamics simulations. Furthermore in this study we have neglected non-Condon effects 80 and potential spin-vibronic effects, 81 which could also play a role in determine the rates of conversion between excited states in this system.…”

Quantum Quality with Classical Cost: Ab Initio Nonadiabatic Dynamics Simulations Using the Mapping Approach to Surface Hopping

“…The overcoherence problem is, therefore, resolved in MASH without the need for ad hoc decoherence corrections. For example, MASH accurately captures nonadiabatic thermal rates, whereas decoherence corrections are known to be needed for the analogous FSSH simulations. ,− …”

“…Such behavior is reminiscent of the use of surface hopping to calculate nonadiabatic thermal rates. In this case, the inconsistency error of FSSH is known to suppress the observed reaction rate and mean that the correct Δ 2 scaling behavior with respect to the diabatic coupling strength is not correctly reproduced. ,− More specifically in the thermal rate problem, it was found that, at short times, the two-hop trajectories between the ground-state reactant and product geometries were the ones that were responsible for the incorrectly suppressed reaction rate in FSSH . In the H 2 elimination process, the trajectories associated with an odd number of hops are important because the reaction proceeds from the excited to the ground electronic state.…”

“…MASH is constructed to describe the Born–Oppenheimer (adiabatic) force through the active surface and the nonadiabatic force through the velocity rescaling performed along the NACV. In addition, MASH has already been benchmarked on a range of model systems, ,, where it was regularly found to offer improvements over FSSH.…”

“… 33 , 39 − 42 More specifically in the thermal rate problem, it was found that, at short times, the two-hop trajectories between the ground-state reactant and product geometries were the ones that were responsible for the incorrectly suppressed reaction rate in FSSH. 38 In the H 2 elimination process, the trajectories associated with an odd number of hops are important because the reaction proceeds from the excited to the ground electronic state. As a result, we find that it is the three- and five-hop trajectories b that are the problem for FSSH.…”