频域空间密度矩阵重正化群的研究进展

密度矩阵重正化群(DMRG)作为低维强关联体系中电子结构计算的强有力方法被广泛熟知,并被迅速地应用于量子化学,不仅在电子结构计算中发挥重要作用,同时也在近几年迅速地成为复杂体系量子动力学计算的重要方法.在DMRG框架中,衍生出了一系列计算动态响应性质的有效方法,并得到了广泛应用.本文简述了DMRG的基本理论,其矩阵乘积态(MPS)表示有效地扩展了该方法的应用范围.重点介绍了基于线性响应理论的动态DMRG,在频率空间求解系统在零温以及有限温度下响应性质的算法,并介绍其在电子关联问题和电子-声子关联问题中的应用,最后展望了该领域的未来发展方向.     

密度矩阵重正化群计算电子激发态的算法比较研究

激发态电子结构计算是理论与计算化学领域中的重要问题.本文测试了密度矩阵重正化群理论的state specific激发态算法,并在Pariser-Parr-Pople(PPP)模型下以并苯体系和聚乙炔体系为例对state specific算法和传统的态平均激发态算法进行了比较.计算结果表明,state specific算法可以正确地跟踪较低的激发态,并能得到比态平均算法更精确的能量本征值;在高激发态的计算过程中,state specific算法可能出现收敛于错误本征态的问题.     

液态RbCl的态密度

给出了在分子动力学模拟基础上Fumi-Tosi势离子液体的正则模式分析方法,用Fumi-Tosi势(包括长程势)代替Lennard-Jones势,并且用等效Coulomb势处理长程Coulomb作用.讨论了Hessian矩阵元的计算方法和Hessian矩阵特征值的计算方法.计算实践表明，取用余误差函数形式的等效库仑势,可以合理地得到Hessian矩阵和态密度.液态RbCl中构型平均态密度的数值结果表明，液态RbCl的态密度表现出与Lennard-Jones液体的态密度相仿的特点.     

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.     

PBFC-PI量子动力学方法及应用（英文）

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.     

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.     

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。     

用动力学Lie代数方法研究H2在Ni(100)面离解吸附量子动力学

用动力学Lie代数方法处理H2 在一个光滑金属表面上离解吸附量子动力学 .用一个修正LEPS势能面描述H2 与Ni( 1 0 0 )表面相互作用 ,得到了H2 初态确定的离解几率的初始动能和时间依赖的解析表示 ,并与实验和其他理论计算做了比较 .这个方法能有效地用于描述表面反应散射动力学 .     

取代苯体系的二阶非线性光学性质:动力学李代数方法

提出了一种动力学李代数方法来研究取代苯体系的非线性光学性质. 对于给定的PPP模型(Pariser-Parr-Pople)哈密顿量, 生成了一个动力学李代数. 依据这些代数元构造出演化算子作为群参数的函数, 通过求解一组非线性微分方程能够得到这些群参数. 再按照统计力学中的密度算子公式给出取代苯分子体系偶极矩的统计平均值. 于是导出二阶极化率的表达式. 与其他量子力学计算结果比较, 表明这种动力学李代数方法在预言有机共轭分子的非线性光学性质上同样有用.     

离子对生成反应截面的量子散射理论研究

将Miller的S-矩阵变分法推广到离子对生成反应动力学的研究。M＋X~2→M^+＋X~2^-反应体系包括共价态(M＋X~2)和离子态(M^+＋X~2^-)两个势能面及其交叉效应,本文在此两态模型下导出了生成截面公式。在矩阵元计算中,平动波函数采用分布Gauss基作展开。作为上述公式的应用,对Cs＋O~2→Cs^+＋O~2^-反应体系作了数值计算并取得了满意结果。     

Density matrix renormalisation group Lagrangians

We introduce a Lagrangian formulation of the density matrix renormalisation group (DMRG). We present Lagrangians which, when minimised, yield the optimal DMRG wavefunction in a variational sense, both within the general matrix product ansatz and within the canonical form of the matrix product that is constructed within the DMRG sweep algorithm. Some of the results obtained are similar to elementary expressions in Hartree-Fock theory, and we draw attention to such analogies. The Lagrangians introduced here will be useful in developing theories of analytic response and derivatives in the DMRG.     

Time-Dependent Density Matrix Renormalization Group Coupled with n-Mode Representation Potentials for the Excited State Radiationless Decay Rate: Formalism and Application to Azulene?

We propose a method for calculating the nonradiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface (PES) in the Franck-Condon region. The method combines the n-mode representation method to construct the ab initio PES and the nearly exact time-dependent density matrix renormalization group method (TD-DMRG) to simulate quantum dynamics. In addition, in the framework of TD-DMRG, we further develop an algorithm to calculate the final-state-resolved rate coefficient which is very useful to analyze the contribution from each vibrational mode to the transition process. We use this method to study the internal conversion (IC) process of azulene after taking into account the anharmonicity of the ground state PES. The results show that even for this semi-rigid molecule, the intramode anharmonicity enhances the IC rate significantly, and after considering the two-mode coupling effect, the rate increases even further. The reason is that the anharmonicity enables the C-H vibrations to receive electronic energy while C-H vibrations do not contribute on the harmonic PES as the Huang-Rhys factor is close to 0.     

Spin-adapted density matrix renormalization group algorithms for quantum chemistry

We extend the spin-adapted density matrix renormalization group (DMRG) algorithm of McCulloch and Gulacsi [Europhys. Lett. 57, 852 (2002)] to quantum chemical Hamiltonians. This involves using a quasi-density matrix, to ensure that the renormalized DMRG states are eigenfunctions of S?(2), and the Wigner-Eckart theorem, to reduce overall storage and computational costs. We argue that the spin-adapted DMRG algorithm is most advantageous for low spin states. Consequently, we also implement a singlet-embedding strategy due to Tatsuaki [Phys. Rev. E 61, 3199 (2000)] where we target high spin states as a component of a larger fictitious singlet system. Finally, we present an efficient algorithm to calculate one- and two-body reduced density matrices from the spin-adapted wavefunctions. We evaluate our developments with benchmark calculations on transition metal system active space models. These include the Fe(2)S(2), [Fe(2)S(2)(SCH(3))(4)](2-), and Cr(2) systems. In the case of Fe(2)S(2), the spin-ladder spacing is on the microHartree scale, and here we show that we can target such very closely spaced states. In [Fe(2)S(2)(SCH(3))(4)](2-), we calculate particle and spin correlation functions, to examine the role of sulfur bridging orbitals in the electronic structure. In Cr(2) we demonstrate that spin-adaptation with the Wigner-Eckart theorem and using singlet embedding can yield up to an order of magnitude increase in computational efficiency. Overall, these calculations demonstrate the potential of using spin-adaptation to extend the range of DMRG calculations in complex transition metal problems.     

多原子反应体系的高精度拟合势能面

本文介绍了近几年来我们组构建多原子反应体系的高精度拟合势能面的进展。我们基于神经网络(NN)方法,成功构建了多原子气相分子体系和气相分子在金属表面解离的一系列势能面。这些势能面的拟合精度相当高,并且经过了严格的量子动力学测试,能广泛应用到动力学研究中。我们还提出了一种新的置换不变势能面的拟合方法,即基本不变量神经网络方法(FI-NN)。基本不变量的使用极大地减少了神经网络输入层多项式的个数,有效提高了势能面的计算速度。     

The role of theory in the laboratory control of quantum dynamics phenomena

Interest in the control of quantum dynamics phenomena has grown in recent years, with laboratory studies showing increasing successes. The role of theory in the control of quantum phenomena encompasses the design of laser controls, the development of algorithms to guide the laboratory studies, and the means to analyze the ensuing dynamics observations. Laboratory laser control instrumentation has the special capability of performing massive numbers of experiments in a short period of time, to rapidly search for controls that meet the objectives. This unique laboratory feature needs to be factored in when considering how to best utilize theoretical analyses. The present paper reviews the role that theory is playing, as well as suggests some future avenues for theory in the laser control of quantum phenomena. Received: 8 June 2002 / Accepted: 7 October 2002 / Published online: 10 March 2003 Acknowledgements. The author acknowledges support from the National Science Fund and the US Department of Defense.     

Molecular dynamics with quantum statistics: time correlation functions and weakly bound nano-clusters

An account of recent developments in the study of molecular dynamics with the inclusion of quantum exchange effects is presented. Approaches for quantum dynamical calculations are reviewed and the determination of time correlation functions is a special point of focus. It is shown that the exact basis set techniques can be used to perform highly accurate calculations but are restricted to relatively small systems since computational cost scales exponentially with system size. Alternate formulations can be introduced to circumvent this problem, and semi-classical initial value representation and Feynman path centroid approaches are considered. It is then showed that from a practical point of view, for complex bosonic systems such as doped helium clusters, Quantum Monte Carlo techniques can currently be used for the calculation of quantities of experimental interest. A perspective on future prospects for the calculation of real time correlation functions of bosonic nano-scale systems is presented     

基元化学反应态态动力学研究

化学反应动力学是化学领域最基础的学科之一,量子态分辨的基元化学反应动力学在最为基本的原子与分子的层次上对化学反应的机制提供深刻的理解。该领域的科学家们通过精心设计的实验和高精度的理论计算,使得态态反应动力学在过去的半个多世纪中取得了长足的进步,实验和理论的相互结合极大地促进了我们对化学反应本质的认识。本文从实验研究的角度,通过对实验技术的发展和对H₂O光解离、H+H₂、F+H₂、Cl+H₂、OH+H₂、F+CH₄等具体实例的态态动力学研究的简介,概况介绍了过去二十年里态态化学反应动力学研究所取得的进展,希望借此为读者提供对化学反应动力学领域的一个概略认识。     

Simulating quantum dynamics in classical environments

Methods for simulating the dynamics of composite systems, where part of the system is treated quantum mechanically and its environment is treated classically, are discussed. Such quantum–classical systems arise in many physical contexts where certain degrees of freedom have an essential quantum character while the other degrees of freedom to which they are coupled may be treated classically to a good approximation. The dynamics of these composite systems are governed by a quantum–classical Liouville equation for either the density matrix or the dynamical variables which are operators in the Hilbert space of the quantum subsystem and functions of the classical phase space variables of the classical environment. Solutions of the evolution equations may be formulated in terms of surface-hopping dynamics involving ensembles of trajectory segments interspersed with quantum transitions. The surface-hopping schemes incorporate quantum coherence and account for energy exchanges between the quantum and classical degrees of freedom. Various simulation algorithms are discussed and illustrated with calculations on simple spin-boson models but the methods described here are applicable to realistic many-body environments.