Transport properties of quantum-classical systems

Correlation function expressions for calculating transport coefficients for quantum-classical systems are derived. The results are obtained by starting with quantum transport coefficient expressions and replacing the quantum time evolution with quantum-classical Liouville evolution, while retaining the full quantum equilibrium structure through the spectral density function. The method provides a variety of routes for simulating transport coefficients of mixed quantum-classical systems, composed of a quantum subsystem and a classical bath, by selecting different but equivalent time evolution schemes of any operator or the spectral density. The structure of the spectral density is examined for a single harmonic oscillator where exact analytical results can be obtained. The utility of the formulation is illustrated by considering the rate constant of an activated quantum transfer process that can be described by a many-body bath reaction coordinate.     

Quantum-classical Liouville dynamics of nonadiabatic proton transfer

A proton transfer reaction in a linear hydrogen-bonded complex dissolved in a polar solvent is studied using mixed quantum-classical Liouville dynamics. In this system, the proton is treated quantum mechanically and the remainder of the degrees of freedom is treated classically. The rates and mechanisms of the reaction are investigated using both adiabatic and nonadiabatic molecular dynamics. We use a nonadiabatic dynamics algorithm which allows the system to evolve on single adiabatic surfaces and on coherently coupled pairs of adiabatic surfaces. Reactive-flux correlation function expressions are used to compute the rate coefficients and the role of the dynamics on the coherently coupled surfaces is elucidated.     

Analysis of kinetic isotope effects for nonadiabatic reactions

Factors influencing the rates of quantum mechanical particle transfer reactions in many-body systems are discussed. The investigations are carried out on a simple model for a proton transfer reaction that captures generic features seen in more realistic models of condensed phase systems. The model involves a bistable quantum oscillator coupled to a one-dimensional double-well reaction coordinate, which is in turn coupled to a bath of harmonic oscillators. Reactive-flux correlation functions that involve quantum-classical Liouville dynamics for chemical species operators and quantum equilibrium sampling are used to estimate the reaction rates. Approximate analytical expressions for the quantum equilibrium structure are derived. Reaction rates are shown to be influenced significantly by both the quantum equilibrium structure and nonadiabatic dynamics. Nonadiabatic dynamical effects are found to play the major role in determining the magnitude of the kinetic isotope effect for the model transfer reaction.     

Quantum-classical Liouville dynamics of proton and deuteron transfer rates in a solvated hydrogen-bonded complex

Proton and deuteron transfer reactions in a hydrogen-bonded complex dissolved in a polar solution are studied using quantum-classical Liouville dynamics. Reactive-flux correlation functions that involve quantum-classical Liouville dynamics for species operators and quantum equilibrium sampling are used to calculate the rate constants. Adiabatic and nonadiabatic reaction rates are computed, compared, and analyzed. Large variations of the kinetic isotope effect (KIE) for this reaction have been observed in the literature, which depend on the nature of the approximate calculation used to estimate the proton and deuteron transfer rates. Our estimate of the KIE lies at the low end of the range of previously observed values, suggesting a rather small KIE for this reaction.     

Mixed quantum-classical description of spectroscopy of dissipative systems

Mixed quantum-classical statistical mechanics is employed to calculate dipole moment correlation function and linear absorption spectra. A quantum two-level subsystem interacting with quantum vibrations (primary oscillators) which in turn are coupled to a classical bath composed of infinite set of harmonic oscillators is used as a dissipative system. Starting with mixed quantum-classical Liouville equation for the evaluation of the mixed quantum-classical dipole moment correlation function and using coherent states and the inverse of Baker-Campbell-Hausdorf formula to evaluate the trace over the primary oscillators, whereby, a closed analytical expression for the electronic dipole moment correlation function is obtained. Illustrations of several absorption spectra at different temperatures are provided. An approximate optical four-point correlation is obtained in the high temperature limit. A strategy for deriving an exact optical four-point correlation is suggested.     

Quantum equilibrium structure for strong nonadiabatic coupling: Reaction rate enhancement

The quantum reactive flux correlation function is computed for a two-level system using an expression for the quantum equilibrium structure appropriate for strong nonadiabatic coupling, in conjunction with quantum–classical Liouville dynamics. The magnitude of the quantum mechanical enhancement of the reaction rate as a result of strong nonadiabatic coupling is studied. The reaction rate is found to increase strongly with an increase in the nonadiabatic coupling strength as well as with a decrease in the temperature. Equilibrium quantum effects increase the ground-state contribution to the rate constant but these effects decrease the excited-state contribution.     

Quantum wavepacket ab initio molecular dynamics: an approach for computing dynamically averaged vibrational spectra including critical nuclear quantum effects

We have introduced a computational methodology to study vibrational spectroscopy in clusters inclusive of critical nuclear quantum effects. This approach is based on the recently developed quantum wavepacket ab initio molecular dynamics method that combines quantum wavepacket dynamics with ab initio molecular dynamics. The computational efficiency of the dynamical procedure is drastically improved (by several orders of magnitude) through the utilization of wavelet-based techniques combined with the previously introduced time-dependent deterministic sampling procedure measure to achieve stable, picosecond length, quantum-classical dynamics of electrons and nuclei in clusters. The dynamical information is employed to construct a novel cumulative flux/velocity correlation function, where the wavepacket flux from the quantized particle is combined with classical nuclear velocities to obtain the vibrational density of states. The approach is demonstrated by computing the vibrational density of states of [Cl-H-Cl]-, inclusive of critical quantum nuclear effects, and our results are in good agreement with experiment. A general hierarchical procedure is also provided, based on electronic structure harmonic frequencies, classical ab initio molecular dynamics, computation of nuclear quantum-mechanical eigenstates, and employing quantum wavepacket ab initio dynamics to understand vibrational spectroscopy in hydrogen-bonded clusters that display large degrees of anharmonicities.     

多原子体系非绝热动力学的近似理论方法

非绝热动力学普遍存在于光物理和光化学过程中。描述非绝热跃迁需要处理电子-原子核间的相互耦合运动。由于计算量随体系尺度增大剧烈增长,准确的量子动力学计算目前只适用于描述小分子体系。为了研究多原子分子体系的非绝热过程,近年来发展了一些基于量子-经典动力学近似方法。本文将对典型的这类方法包括经典Ehrenfest方法、面跳跃方法、基于Wigner表示的混合量子-经典方法进行简要的介绍,并讨论如何将量子-经典动力学方法与电子结构从头算手段相结合,模拟非绝热过程。重点阐明各种方法的基本思想和优缺点,并对该领域的发展进行展望。     

Proton transfer in nanoconfined polar solvents. II. Adiabatic proton transfer dynamics

The reaction dynamics for a model phenol-amine proton transfer system in a confined methyl chloride solvent have been simulated by mixed quantum-classical molecular dynamics. In this approach, the proton vibration is treated quantum mechanically (and adiabatically), while the rest of the system is described classically. Nonequilibrium trajectories are used to determine the proton transfer reaction rate constant. The reaction complex and methyl chloride solvent are confined in a smooth, hydrophobic spherical cavity, and radii of 10, 12, and 15 A have been considered. The effects of the cavity radius and the heavy atom (hydrogen bond) distance on the reaction dynamics are considered, and the mechanism of the proton transfer is examined in detail by analysis of the trajectories.     

Finite temperature application of the corrected propagator method to reactive dynamics in a condensed-phase environment

The recently proposed mixed quantum-classical method is extended to applications at finite temperatures. The method is designed to treat complex systems consisting of a low-dimensional quantum part (the primary system) coupled to a dissipative bath described classically. The method is based on a formalism showing how to systematically correct the approximate zeroth-order evolution rule. The corrections are defined in terms of the total quantum Hamiltonian and are taken to the classical limit by introducing the frozen Gaussian approximation for the bath degrees of freedom. The evolution of the primary system is governed by the corrected propagator yielding the exact quantum dynamics. The method has been tested on a standard model system describing proton transfer in a condensed-phase environment: a symmetric double-well potential bilinearly coupled to a bath of harmonic oscillators. Flux correlation functions and thermal rate constants have been calculated at two different temperatures for a range of coupling strengths. The results have been compared to the fully quantum simulations of Topaler and Makri [J. Chem. Phys. 101, 7500 (1994)] with the real path integral method.     

Optical linear response function with linear and diagonal quadratic electron-vibration coupling in mixed quantum-classical systems

Optical linear response function of linearly and quadratically coupled mixed quantum-classical condensed phase systems is derived. The linear response function is derived using Kapral's formalism of statistical mechanics in mixed quantum-classical systems. Our mixed quantum-classical linear dipole moment correlation function J(t) is compared with the full quantum J(t) [Y. J. Yan and S. Mukamel, J. Chem. Phys. 85, 5908 (1986)] in the high temperature limit. Model calculations and discussion of our results are presented. Various formulas of Franck-Condon factors for both linear and quadratic coupling are discussed.     

Quantum-classical dynamics of wave fields

An approach to the quantum-classical mechanics of phase space dependent operators, which has been proposed recently, is remodeled as a formalism for wave fields. Such wave fields obey a system of coupled nonlinear equations that can be written by means of a suitable non-Hamiltonian bracket. As an example, the theory is applied to the relaxation dynamics of the spin-boson model. In the adiabatic limit, a good agreement with calculations performed by the operator approach is obtained. Moreover, the theory proposed in this paper can take nonadiabatic effects into account without resorting to surface-hopping approximations. Hence, the results obtained follow qualitatively those of previous surface-hopping calculations and increase by a factor of (at least) 2, the time length over which nonadiabatic dynamics can be propagated with small statistical errors. Moreover, it is worth to note that the dynamics of quantum-classical wave fields proposed here is a straightforward non-Hamiltonian generalization of the formalism for nonlinear quantum mechanics that Weinberg introduced recently.     

Non-adiabatic molecular dynamics with quantum solvent effects

Three novel approaches extending quantum-classical non-adiabatic (NA) molecular dynamics (MD) to include quantum effects of solvent environments are described. In a standard NA-MD the solute subsystem is treated quantum mechanically, while the larger solvent part of a system is treated classically. The three novel approaches presented here are based on the Bohmian formulation of quantum mechanics, the stochastic Schrödinger equation for the evolution of open quantum systems and the quantized Hamilton dynamics generalization of classical mechanics. The approaches extend the standard NA-MD to incorporate the following quantum effects of the solvent. (1) Branching, i.e. the ability of solvent quantum wave packets to split and follow asymptotically diverging trajectories correlated with different quantum states of the solute. (2) Decoherence, i.e. loss of quantum interference within the solute subsystem induced by the diverging solvent trajectories. (3) Zero point energy that contributes to NA coupling and must be preserved during the energy exchange between solvent and solute degrees of freedom. The Bohmian quantum-classical mechanics, stochastic mean-field and quantized mean-field approximations incorporate the quantum solvent effects into the standard quantum-classical NA-MD in a straightforward and efficient way that can be easily applied to quantum dynamics of condensed phase chemical systems.