Mapping variable ring polymer molecular dynamics: A path-integral based method for nonadiabatic processes

We investigate the calculation of approximate non-equilibrium quantum time correlation functions (TCFs) using two popular path-integral-based molecular dynamics methods, ring-polymer molecular dynamics (RPMD) and centroid molecular dynamics (CMD). It is shown that for the cases of a sudden vertical excitation and an initial momentum impulse, both RPMD and CMD yield non-equilibrium TCFs for linear operators that are exact for high temperatures, in the t = 0 limit, and for harmonic potentials; the subset of these conditions that are preserved for non-equilibrium TCFs of non-linear operators is also discussed. Furthermore, it is shown that for these non-equilibrium initial conditions, both methods retain the connection to Matsubara dynamics that has previously been established for equilibrium initial conditions. Comparison of non-equilibrium TCFs from RPMD and CMD to Matsubara dynamics at short times reveals the orders in time to which the methods agree. Specifically, for the position-autocorrelation function associated with sudden vertical excitation, RPMD and CMD agree with Matsubara dynamics up to O(t4) and O(t1), respectively; for the position-autocorrelation function associated with an initial momentum impulse, RPMD and CMD agree with Matsubara dynamics up to O(t5) and O(t2), respectively. Numerical tests using model potentials for a wide range of non-equilibrium initial conditions show that RPMD and CMD yield non-equilibrium TCFs with an accuracy that is comparable to that for equilibrium TCFs. RPMD is also used to investigate excited-state proton transfer in a system-bath model, and it is compared to numerically exact calculations performed using a recently developed version of the Liouville space hierarchical equation of motion approach; again, similar accuracy is observed for non-equilibrium and equilibrium initial conditions.

Section: Discussionmentioning

confidence: 99%

Non-equilibrium dynamics from RPMD and CMD

Welsch

Song

Shi

et al. 2016

“…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%

“…It is obvious that in the adiabatic limit, where the Born-Oppenheimer approximation is valid, such a theory should reduce to something equivalent to classical rate theory, classical TST or ring-polymer TST, 51,52 which is known to be exact in the absence of recrossing. 53,54 In this limit, nonadiabatic dynamical approaches 40,41 can be applied to compute the small amount of dividing-surface recrossing due to nonadiabatic effects. However, this approach breaks down in the weak-coupling limit where the transmission coefficient is extremely small and therefore inefficient to calculate.…”

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.