利用基于直接动力学的轨线面跳跃方法处理非绝热过程

势能面交叉引起的非绝热过程广泛存在于光化学和光物理中。对这一过程进行描述是理论化学的重要挑战之一。非绝热过程涉及原子核与电子之间的耦合运动,因此量子化学的基本假设之一"玻恩-奥本海默"近似被打破,所以对其进行描述需要发展新的动力学理论方法。在这些方法中,Tully发展的最少轨线面跳跃方法凭借易于程序化、便于计算等优点已经发展成为处理非绝热问题的主要动力学方法之一。其中原子核以经典的方式在单一势能面上进行演化,电子以量子的方式沿着同一轨线进行演化。在整个演化过程中,非绝热跃迁通过轨线在不同势能面间的跃迁来描述,其中跳跃发生的几率与电子的演化有关。如果将该方法与从头算直接动力学相结合,可以在全原子水平上研究实际分子体系的非绝热动力学,给出其激发态寿命、非绝热动力学中分子的主要运动方式、反应通道以及分支比等重要信息。本文旨在讨论最少面跳跃直接动力学方法研究非绝热问题的一些进展,包括动力学基本理论,特别关注将最少面跳跃方法和直接动力学结合的数值实现细节,同时讨论该方法在研究实际体系当中的一些应用,并对轨线面跳跃方法下一步发展的一些方向进行合理的展望。     

化学动力学中的非绝热过程及其理论研究

伴随着原子核的运动出现的电子态之间的跃迁,被称为非绝热过程.近年来,实验结果表明,非绝热过程广泛存在于多种化学体系中.从理论上理解这一过程极具挑战性,因为该过程中电子和原子核的运动耦合在一起,量子化学的基本假设"波恩-奥本海默近似"被打破.本文介绍通过理论化学方法模拟非绝热过程的现状,讨论所涉及的非绝热动力学(量子和半经典动力学)和量子化学计算方法(高精度电子相关方法、半经验方法和TDDFT方法),同时也介绍一些典型的非绝热过程(生物分子的光稳定性、光异构化、自旋翻转、激发态电子和能量转移).尽管目前非绝热动力学领域已经取得了很大进展,但处理复杂体系仍然面临诸多挑战.解决这一问题需要动力学理论、量子化学方法和计算机技术等领域的共同发展.     

改进的半经典动力学模拟二苯乙烯光致顺反异构化反应

发展了一种改进的半经典动力学模拟方法, 并将其程序化用于气相二苯乙烯光致顺反异构化反应的机理研究.新的方法不仅采用e 指数模型改进了原有Zhu-Nakamura 理论中计算电子非绝热跃迁几率的计算方法, 而且将约束哈密顿方法用于限制性分子动力学模拟过程中. 计算结果表明, 采用此方法得到的统计平均的量子产率及反应机理与以前的实验与理论结果吻合较好, 从而可以应用于全量子动力学方法无法进行的大分子体系的动力学研究.     

混合量子-经典方法计算电荷转移速率及其在实际体系中的应用(英文)

混合量子-经典方法在复杂分子体系动力学过程的模拟方面有重要应用.我们采用Ehrenfest方法、surfacehopping方法和混合量子经典Liouville方程计算了在非绝热极限下的电荷转移速率.然后将这三种方法应用于有机半导体材料电荷转移速率的计算.研究结果发现,Ehrenfest方法和surface hopping方法可能严重偏离正确的结果.偏离的原因是这两种方法没有正确处理相干项的运动,而且这种偏离在涉及到高频模式时显得更加严重.     

非绝热量子散射动力学

综述了非绝热化学过程的研究,着重介绍了含时波包非绝热量子动力学方法,以及在化学反应中的非绝热动力学、光解非绝热动力学及非绝热传能过程的应用.     

含时密度矩阵重正化群的理论与应用

密度矩阵重正化群(DMRG)作为计算低维强关联体系强有力的方法为人熟知, 在量子化学电子结构计算中得到广泛应用. 最近几年, 含时密度矩阵重正化群(TD-DMRG)的理论取得较快发展, TD-DMRG逐渐成为复杂体系量子动力学理论模拟的重要新兴方法之一. 本文综述了基于矩阵乘积态(MPS) 和矩阵乘积算符(MPO)的DMRG基本理论, 并重点介绍了若干最常见的TD-DMRG时间演化算法, 包括基于演化再压缩(P&C) 的算法、 基于含时变分原理(TDVP)的算法和时间步瞄准(TST)算法; 还对利用TD-DMRG模拟有限温体系的纯化(Purification)算法和最小纠缠典型量子热态(METTS)算法进行了介绍. 最后, 对近年TD-DMRG在复杂体系量子动力学中的应用进行了总结.     

耗散对受激拉曼绝热转移过程的影响

应用最近发展的量子耗散理论,研究了耗散对简单三能级体系的受激拉曼绝热转移过程的影响,并与pump-dump过程比较.计算结果表明,受激拉曼绝热转移的机制能很好地抑制中间态的弛豫与涨落的影响.数值结果也表明了新的量子耗散理论可以正确地描述场与耗散相互耦合的动力学问题.     

PBFC-PI量子动力学方法及应用

对多原子体系的量子动力学计算非常重要, 然而, 对含六原子以上的分子体系进行精确量子动力学计算仍具挑战性. 面向过程的基函数定制(PBFC)-并行迭代(PI)方法是一种高效的量子动力学方法, 已应用于对含九原子的丙二醛异构体系的氢迁移速率的精确量子计算. 本综述首先阐明了PBFC的基本思想, 之后重点回顾了PBFC-PI方法的具体内容、 该方法与其它方法的结合及其应用方面的新进展. 应用这些方法实现了对单氢迁移、 协同双氢迁移和分步双氢迁移3种类型基准体系的大规模并行计算, 有助于获得对氢迁移过程的新认识.     

量子耗散与量子输运的级联方程组方法

级联方程已成为研究量子开放系统的稳态性质和动力学过程的重要方法。本文旨在系统综述量子耗散和量子输运的级联方程组方法的建立、发展以及在理论、算法和应用方面的一些最新进展。级联方程形式理论的建立以影响泛函路径积分为基础,并具有数值上的高效性和应用上的灵活性,可用于研究分子体系的复杂动力学过程以及强关联电子体系中的量子输运。其级联耦合结构以非微扰的方式揭示了多体相互作用、体系-环境耦合、非马尔可夫记忆等的综合效应。作为应用示例,我们采用级联方程模拟了生物光富集体系的二维相干动力学光谱以及含时电子输运过程中的动态近藤效应。     

H+H2(v=0,1)→H2(v′)+H反应截面的电子非绝热三维量子散射近似计算

本文把电子非绝热一维量子散射反应几率和三维量子散射反应截面的近似公式结合起来, 对于反应物分子(H_2)不同的量子振动态(v=0, 1) 分别计算了H+H_2(v=0)→H_2(v′=0, 1)+H和H+H_2(v=1)→H_2(v′=0, 1)+H的平均反应截面σ_0和σ_1, 并同文献上用电子绝热理论计算的结果作了比较, 表明对这类中性原予-分子反应碰撞的过程, 特别是当反应物分子处于振动激发态时, 电子非绝热效应是存在的。     

Fully adaptive propagation of the quantum-classical Liouville equation

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The TRAIL (trapezoidal rule for adaptive integration of Liouville dynamics) scheme [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for nonadiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac deltalike trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-type trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multidimensional problems with deterministic treatment of nonadiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Nonadiabatic effects occurring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results.     

Nonadiabatic quantum dynamics in O(3P)+H2→OH+H: a revisited study

To investigate the extent of nonadiabatic effects in the title reaction, quasi-classical trajectory and nonadiabatic quantum scattering as well as the nonadiabatic quantum-classical trajectory calculations were performed on the accurate ab initio benchmark potential energy surfaces of the lowest (3)A' and (3)A" electronic states [Rogers et al., J Phys Chem A 2000, 104, 2308], together with the spin-orbit coupling matrix [Maiti and Schatz, J Chem Phys 2003, 119, 12360] and the lowest singlet (1) A' potential energy surface [Dobby and Knowles, Faraday Discuss 1998, 110, 247]. Comparison of the calculated total cross sections from both adiabatic and nonadiabatic calculations has demonstrated that for adiabatic channels including (3)A'→(3)A' and (3)A"→(3)A", difference does exist between the two kinds of adiabatic and nonadiabatic calculations, showing nonadiabatic effects to some extent. Such nonadiabatic effects tend to become more conspicuous at high collision energies and are found to be more pronounced with trajectories/quantum wave packet initiated on (3)A' than on (3)A". Furthermore, the present study also showed that nonadiabatic effects can bring the component of forward-scattering in the product angular distributions.     

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.     

Algorithmic decoherence time for decay-of-mixing non-Born-Oppenheimer dynamics

The performance of an analytical expression for algorithmic decoherence time is investigated for non-Born-Oppenheimer molecular dynamics. There are two terms in the function that represents the dependence of the decoherence time on the system parameters; one represents decoherence due to the quantum time-energy uncertainty principle and the other represents a back reaction from the decoherent force on the classical trajectory. We particularly examine the question of whether the first term should dominate. Five one-dimensional two-state model systems that represent limits of multidimensional nonadiabatic dynamics are designed for testing mixed quantum-classical methods and for comparing semiclassical calculations with exact quantum calculations. Simulations are carried out with the semiclassical Ehrenfest method (SE), Tully's fewest switch version (TFS) of the trajectory surface hopping method, and the decay-of-mixing method with natural switching, coherent switching (CSDM), and coherent switching with reinitiation (CSDM-D). The CSDM method is demonstrated to be the most accurate method, and it has several desirable features: (i) It behaves like the representation-independent SE method in the strong nonadiabatic coupling regions; (ii) it behaves physically like the TFS method in noninteractive region; and (iii) the trajectories are continuous with continuous momenta. The CSDM method is also demonstrated to balance coherence well with decoherence, and the results are nearly independent of whether one uses the adiabatic or diabatic representation. The present results provide new insight into the formulation of a physically correct decoherence time to be used with the CSDM method for non-Born-Oppenheimer molecular dynamic simulations.     

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.     

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.     

Libra: An open‐Source “methodology discovery” library for quantum and classical dynamics simulations

The “methodology discovery” library for quantum and classical dynamics simulations is presented. One of the major foci of the code is on nonadiabatic molecular dynamics simulations with model and atomistic Hamiltonians treated on the same footing. The essential aspects of the methodology, design philosophy, and implementation are discussed. The code capabilities are demonstrated on a number of model and atomistic test cases. It is demonstrated how the library can be used to study methodologies for quantum and classical dynamics, as well as a tool for performing detailed atomistic studies of nonadiabatic processes in molecular systems. The source code and additional information are available on the Web at http://www.acsu.buffalo.edu/~alexeyak/libra/index.html . © 2016 Wiley Periodicals, Inc.