Exact quantum statistics for electronically nonadiabatic systems using continuous path variables

102

115

Powerful approximate methods for propagating the density matrix of complex systems that are conveniently described in terms of electronic subsystem states and nuclear degrees of freedom have recently been developed that involve linearizing the density matrix propagator in the difference between the forward and backward paths of the nuclear degrees of freedom while keeping the interference effects between the different forward and backward paths of the electronic subsystem described in terms of the mapping Hamiltonian formalism and semi-classical mechanics. Here we demonstrate that different approaches to developing the linearized approximation to the density matrix propagator can yield a mean-field like approximate propagator in which the nuclear variables evolve classically subject to Ehrenfest-like forces that involve an average over quantum subsystem states, and by adopting an alternative approach to linearizing we obtain an algorithm that involves classical like nuclear dynamics influenced by a quantum subsystem state dependent force reminiscent of trajectory surface hopping methods. We show how these different short time approximations can be implemented iteratively to achieve accurate, stable long time propagation and explore their implementation in different representations. The merits of the different approximate quantum dynamics methods that are thus consistently derived from the density matrix propagator starting point and different partial linearization approximations are explored in various model system studies of multi-state scattering problems and dissipative non-adiabatic relaxation in condensed phase environments that demonstrate the capabilities of these different types of approximations for treating non-adiabatic electronic relaxation, bifurcation of nuclear distributions, and the passage from nonequilibrium coherent dynamics at short times to long time thermal equilibration in the presence of a model dissipative environment.

“…35 Numerical implementation of Eq. (8) involves sampling initial nuclear DOF from (ρ) n 0 ,n 0 W (R 0 ,P 1 ), and mapping variables from the gaussian functions.…”

Section: A Meanmentioning

confidence: 99%

Consistent schemes for non-adiabatic dynamics derived from partial linearized density matrix propagation

Huo¹,

Coker²

2012

102

115

“…30,31 Approximations have been taken to treat the nonadiabatic dynamics from the resulting Hamiltonian classically, 32 semiclassically, 31,[33][34][35] using the linearized semiclassical approach, 36,37 or with centroidmolecular dynamics. 38 Recently, other methods based on the mapping approach have appeared for treating thermal initial states, 39 using a ring-polymer molecular dynamics (RPMD) Hamiltonian, 40,41 or in combination with partially linearized real-time path integrals. 42 Other dynamical approaches employ mean-field approximations, 43 multiple spawning, 44 the quantumclassical Liouville equation 45 or an exact factorization of the complete molecular Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory

Richardson

Thoss

2014

Quantum mechanical canonical rate theory: A new approach based on the reactive flux and numerical analytic continuation methods J. Chem. Phys. 112, 2605 (2000); 10.1063/1.480834Erratum: "A unified framework for quantum activated rate processes. II. The nonadiabatic limit" [J. Chem. Phys. 106, 1769 There is currently much interest in the development of improved trajectory-based methods for the simulation of nonadiabatic processes in complex systems. An important goal for such methods is the accurate calculation of the rate constant over a wide range of electronic coupling strengths and it is often the nonadiabatic, weak-coupling limit, which being far from the Born-Oppenheimer regime, provides the greatest challenge to current methods. We show that in this limit there is an inherent sign problem impeding further development which originates from the use of the usual quantum flux correlation functions, which can be very oscillatory at short times. From linear response theory, we derive a modified flux correlation function for the calculation of nonadiabatic reaction rates, which still rigorously gives the correct result in the long-time limit regardless of electronic coupling strength, but unlike the usual formalism is not oscillatory in the weak-coupling regime. In particular, a trajectory simulation of the modified correlation function is naturally initialized in a region localized about the crossing of the potential energy surfaces. In the weak-coupling limit, a simple link can be found between the dynamics initialized from this transition-state region and an generalized quantum goldenrule transition-state theory, which is equivalent to Marcus theory in the classical harmonic limit. This new correlation function formalism thus provides a platform on which a wide variety of dynamical simulation methods can be built aiding the development of accurate nonadiabatic rate theories applicable to complex systems. © 2014 AIP Publishing LLC. [http://dx

“…To apply methods like path-integral molecular dynamics (or dynamic extensions like ring-polymer molecular dynamics) to multilevel systems when the nonadiabatic effects cannot be neglected, a popular strategy is to use the mapping variable approach [18,19], see also the review article [2] and more recent developments in [20][21][22][23][24][25][26]. The idea is to replace the multi-level system by a single level system with higher dimension by mapping the discrete electronic states to continuous variables using uncoupled harmonic oscillators [19].…”

Section: Introductionmentioning

confidence: 99%

“…The idea is to replace the multi-level system by a single level system with higher dimension by mapping the discrete electronic states to continuous variables using uncoupled harmonic oscillators [19]. The ring polymer representation can then be applied to the mapped system [20][21][22][23]25].…”

Section: Introductionmentioning

confidence: 99%

Path integral molecular dynamics with surface hopping for thermal equilibrium sampling of nonadiabatic systems

Zhou

2017

In this work, a novel ring polymer representation for multi-level quantum system is proposed for thermal average calculations. The proposed representation keeps the discreteness of the electronic states: besides position and momentum, each bead in the ring polymer is also characterized by a surface index indicating the electronic energy surface. A path integral molecular dynamics with surface hopping (PIMD-SH) dynamics is also developed to sample the equilibrium distribution of ring polymer configurational space. The PIMD-SH sampling method is validated theoretically and by numerical examples.