Perturbatively corrected ring-polymer instanton theory for accurate tunneling splittings

Abstract

We introduce an approach for calculating perturbative corrections to the ring-polymer instanton approximation to tunneling splittings (RPI+PC), by computing higher-order terms in the asymptotic expansion in $\hslash$. The resulting method goes beyond standard instanton theory by using information on the third and fourth derivatives of the potential along the tunneling path to include additional anharmonic effects. This leads to significant improvements both in systems with low barriers and in systems with anharmonic modes. We demonstrate the applicability of RPI+PC to molecular systems by computing the tunneling splitting in full-dimensional malonaldehyde and a deuterated derivative. Comparing to both experiment and recent quantum-mechanical benchmark results, we find that our perturbative correction reduces the error from -11% to 2% for hydrogen transfer and performs even better for the deuterated case. This makes our approach more accurate than previous calculations using diffusion Monte Carlo and path-integral molecular dynamics, while being more computationally efficient.

arXiv comment18 pages, 4 figures

References in corpus (13)

• Direct simulation of electron transfer using ring polymer molecular dynamics: Comparison with semiclassical instanton theory and exact quantum methods
• Derivation of instanton rate theory from first principles
• Full- and reduced-dimensionality instanton calculations of the tunnelling splitting in the formic acid dimer
• Semiclassical Green's functions and an instanton formulation of electron-transfer rates in the nonadiabatic limit
• Path-integral dynamics of water using curvilinear centroids
• Instanton formulation of Fermi's golden rule in the Marcus inverted regime
• Quantum dynamics using path integral coarse-graining
• Fast quasi-centroid molecular dynamics
• Instanton theory of tunnelling in molecules with asymmetric isotopic substitutions
• Nonadiabatic instanton rate theory beyond the golden-rule limit
• Confirming the role of nuclear tunnelling in aqueous ferrous-ferric electron transfer
• Revisiting nuclear tunnelling in the aqueous ferrous-ferric electron transfer
• Exact tunneling splittings from symmetrized path integrals

Cited by in corpus (4)

• Semiclassical instanton theory for reaction rates at any temperature: How a rigorous real-time derivation solves the crossover temperature problem
• Evaluation of transition rates from nonequilibrium instantons
• Exact tunneling splittings from symmetrized path integrals
• Semiclassical Spin Exchange via Temperature-Dependent Transition States