Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics

Abstract

We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. We present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.

Nonadiabatic quantum transition-state theory in the golden-rule limit. I. Theory and application to model systems

“…117 An isomorphic Hamiltonian can be used to include quantum nuclear effects in nonadiabatic trajectory simulations. 118 It is expected that in an accurate nonadiabatic RPMD simulation, the ring polymer will pass through transitionstate configurations similar to those sampled in the GR-QTST ensemble. We therefore expect that our study of GR-QTST will be of use in understanding and improving the dynamical methods discussed above.…”

On the identity of the identity operator in nonadiabatic linearized semiclassical dynamics

“…Despite progress in methodology relying, in part, on classical trajectories, 9,10 more approximate semiclassical techniques are generally required in the condensed phase. [11][12][13][14][15][16][17] Their favourable, linear scaling with system size allows insight into realistic processes to be gained without incurring extreme computational costs.…”

An analysis of isomorphic RPMD in the golden rule limit

“…In fact, the accuracy of iso-RPMD has already been demonstrated in such a situation by Tao et al in their calculation of state-resolved reaction rates for a one-dimensional two-state model of the F + H 2 reaction. 1,2 Application of the method to similar but more complex systems will no doubt provide physical insight in the future.…”

“…To set the scene for this investigation, let us begin by introducing the iso-RPMD formalism. 1,2 Although this formalism is in principle applicable to systems with many electronic states, it will be sufficient for our purposes to consider just a two level system, for which the Hamiltonian can be written in the diabatic representation aŝ…”