A mapping approach to surface hopping

Abstract

We present a nonadiabatic classical-trajectory approach that offers the best of both worlds between fewest-switches surface hopping (FSSH) and quasiclassical mapping dynamics. This mapping approach to surface hopping (MASH) propagates the nuclei on the active adiabatic potential-energy surface, like in FSSH. However, unlike in FSSH, transitions between active surfaces are deterministic and occur when the electronic mapping variables evolve between specified regions of the electronic phase space. This guarantees internal consistency between the active surface and the electronic degrees of freedom throughout the dynamics. MASH is rigorously derivable from exact quantum mechanics as a limit of the quantum-classical Liouville equation (QCLE), leading to a unique prescription for momentum rescaling and frustrated hops. Hence, a quantum-jump procedure can in principle be used to systematically converge the accuracy of the results to that of the QCLE. This jump procedure also provides a rigorous framework for deriving approximate decoherence corrections similar to those proposed for FSSH. We apply MASH to simulate the nonadiabatic dynamics in various model systems and show that it consistently produces more accurate results than FSSH at a comparable computational cost.

Which Algorithm Best Propagates the Meyer–Miller–Stock–Thoss Mapping Hamiltonian for Non-Adiabatic Dynamics?

“…Many methods exist to incorporate discrete quantum DoF into classical frameworks including Ehrenfest dynamics, approximations to the quantum-classical Liouville equation, − the symmetrical quasi-classical windowing method, surface hopping, , and mapping methods such as methods inspired by the Meyer–Miller–Stock–Thoss (MMST) mapping − and spin-mapping, , including the mapping approach to surface hopping (MASH) . The simplest nonadiabatic method, proposed by Mott (1931), evaluates the quantum electronic dynamics along the classical path of the nuclei, known as the “classical path” approach. ,,, However, this does not include the “back reaction” on the nuclei .…”

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

“…Importantly, MASH has the additional property that its decoherence corrections can be rigorously derived. Because MASH is an exact short-time approximation of the QCLE, it can be systematically improved toward the full QCLE result by application of so-called “quantum jumps” . These jumps differ from decoherence corrections in that they cannot be applied too often (i.e., no quantum Zeno effect).…”

“…Recently, an alternative to FSSH has been derived known as the mapping approach to surface hopping (MASH) . MASH was designed to offer the best of both worlds between surface hopping and mapping approaches, such as the Meyer–Miller–Stock–Thoss mapping , and spin mapping. , Unlike FSSH, which was proposed heuristically, MASH can be rigorously derived from the quantum–classical Liouville equation (QCLE). − Tests against exact results for the Tully models, a series of spin-boson models, as well as 3-mode and 24-mode vibronic models of pyrazine have shown that the results of MASH are generally as good as or better than those of FSSH for an equivalent computational cost . Perhaps most interesting are the results for the spin-boson model, where the system crosses the coupling region many times during the dynamics.…”

How Quantum is the Resonance Behavior in Vibrational Polariton Chemistry?

“…In any case, if it turns out that the reactions studied in experiment are indeed in the energy-diffusion-limited regime, then our results demonstrate that quantum dynamics is vital for capturing the single-molecule resonance behavior correctly (as the lion’s share of molecular vibrations are “high frequency” in the context of vibrational energy transfer), and one cannot get away with doing classical molecular dynamics (as in refs and ) or even RPMD, as this will yield qualitatively different results. However, not all is lost: one may for example still be able to cut computational costs by only treating important molecular and cavity degrees of freedom quantum-mechanically in a mixed quantum–classical scheme. − This is another exciting avenue for further exploration.…”