量子Monte Carlo处理激发态

提出了用于电子激发态的剩余函数变分量子ＭｏｎｔｅＣａｒｌｏ（ＳＦＶＭＣ）方法,已经证明：若激发态的初始波函数与基态的初始波函数属于对称性不同的不可约表示时,该激发态的ＳＦＶＭＣ方法与基态的ＳＦＶＭＣ方法完全相同;若激发态的初始波函数与基态的初始波函数有相同的对称性时,只要对激发态的初始波函数作正交性修正,则其态的ＳＦＶＭＣ方法亦可推到该激发态的情况。文章导出了这第二类激发态的ＳＦＶＭＣ方法的详细计     

用变分Monte Carlo方法处理分子

对变分量子Ｍｏｎｔｅ Ｃａｒｔｏ方法提出了一种种算法：将传统的Ｈａｒｔｒｅｅ－Ｆｏｅｋ方法与量子Ｍｏｎｔｅ Ｃａｒｌｏ方法有机结合在一起；导出了“局部能”的解析式；使用了一种新的相关函数和随机数发生器。我们用这个新算法计算了Ｈ２、ＬｉＨ、Ｌｉ２、Ｈ２Ｏ、Ｆ２分子的基态和ＣＨ２分子的＾３Ｂ１、＾１Ａ１态的能量。计算结果表明，这个新算法在精度和统计误差两个方面比一般ＶＭＣ过程都要好得多。     

固定节面量子Monte Carlo的一个新算法

提出了一个固定节面量子Monte Carlo的新算法,与前人的算法相比,其“指导函数”的优化不是在扩散前,而是在扩散过程中同步进行;这不仅在机时上是节省的,更重要的是优化与扩散两者按相同的取样方式进行,达到互相改善的目的;这一优化方案是超线性收敛的,它能加快粒子的扩散;在扩散过程中,“指导函数”的节面不断发生改变,这有利于减小“固定节面误差”.这一新算法已被运用到CH_2的X~3B_1态和a~1A_1态,以及NH_2的π-X~2B_1态和σ-A~2A_1态总能量的计算,由此算出了CH_2单一三重态的“劈开”能△E_(s-T)=(45.542±1.840)kJ/mol和NH_2的σ-π“劈开”能△E_(σ-π)=(141.644±1.589)kJ/mol.计算结果表明这一新算法在精度、统计误差和计算量方面比一般固定节面量子Monte Carlo方法都要优越得多.     

高分子单链热力学量的Monte Carlo模拟

提出了一种Monte Carlo模拟方法,可以计算高分子链的热力学量.该方法采用简单立方格子上的自避行走链和紧邻相互作用模型,计算了链长200以内的链在无量纲相互作用参数△_ε/(?)T不同数值下的构象熵和Helmholtz自由能,其中△_ε为一次接触的能量,(?)为Boltzmann常数,T为绝对温度.模拟结果和直接计数法的准确结果显示出较好的一致性 并且得到排除体积和相互作用效应互相抵消的(?)条件下的参数△_ε/(?)T之值大约为-0.6且与链长无关.     

两亲性梳形聚合物胶束行为的Monte Carlo模拟

采用二维和三维格子模型用Monte Carlo法模拟两亲性梳形聚合物的胶束行 为. 模拟时采用动态算法结合链的reptation运动并且编制了三维结构显示程序及获得了体系的Monte Carlo自由能. 结果表明: 约化相互作用能的选取对胶束及乳液体系的形态结构有重大影响; 三维模拟可以得到体系形态结构更为直观的结果; 亲油主链亲水侧链型梳形聚合物在水相中的胶束比在油相的胶束有更低的能量.     

流体熵相关性质的Monte Carlo模拟新方法

提出了用于计算实际体系熵相关性质的Monte Carlo 多级取样分子模拟方法.应用这一方法,对硬球流体的化学势及Helmholtz 自由能进行了估算,得到了满意的结果.计算化学势时,不存在通常试验粒子方法所遇到的高密度问题.该方法特别适合规律性的系统研究,较之普通模拟方法要有效得多.模拟得到的硬球体系无限稀释组份的超额化学势与对比直径的关系,在相变区域为一条双凹曲线;无论是在相变区还是在单相区,Carnahan-Starling 公式对这一关系的描述均有较大偏差.     

共聚合多分散体系的Monte Carlo仿真算法及应用

在凝胶色谱(GPC)测试高聚物分子量和分子量分布的实验基础上, 建立了一个共聚合多分散体系的Monte Carlo计算机仿真算法, 模拟共聚合过程中每个单体链节的形成, 记录每条长度不等的高分子链的链节结构和微观序列分布. 应用于2,2-二甲基三亚甲基环碳酸酯(DTC)和e-己内酯(ε-CL)开环共聚合的高分子链链节结构研究中, 模拟结果较好地重现了实验数据, 并提供了三元组分布、均聚链链节长度等难于从实验测定的微观信息. 本算法为研究复杂机理的多链共聚合体系提出了仿真框架.     

流体熵相关性质的Monte Carlo模拟新方法

提出了用于计算实际体系熵相关性质的Monte Carlo多级取样分子模拟方法. 应用这一方法, 对硬球流体的化学势及Helmholtz自由能进行了估算, 得到了满意的结果. 计算化学势时, 不存在通常试验粒子方法所遇到的高密度问题. 该方法特别适合规律性的系统研究, 较之普通模拟方法要有效得多. 模拟得到的硬球体系无限稀释组份的超额化学势与对比直径的关系, 在相变区域为一条双凹曲线; 无论是在相变区还是在单相区, Carnahan-Starling公式对这一关系的描述均有较大偏差.     

应用Monte Carlo方法计算He原子包含电子相关作用的基态能量

应用Monte Carlo方法计算He原子包含电子相关波函数的基态能量,获得了与精确值非常接近的结果．实践表明,应用Monte Carlo方法有可能在多电子体系中直接采用包含任意2个电子间距离ry的函数作为变分函数来考虑电子相关作用．     

甲醇在超临界环已烷中形成簇团的Monte Carlo初探

用Ｍｏｎｔｅ Ｃａｒｌｏ方法研究了甲醇－环己烷体系的微观结构随压力（密度）的变化情况，结果表明，在临界区域甲醇分子的聚集最为明显，形成的甲醇团簇尺寸最大，溶剂分子在甲醇周围的局部密度则在低于临界区或亚临界区较大。     

A Novel Exact Fixed-node Quantum Monte Carlo Algorithm

In this paper we proposed a novel exact fixed-node quantum Monte Carlo (EFNQMC)algorithm,which is a self-optimizing and self-improving procedure,In contrast to the previous EFNQMC method,the trial function is optimized synchronistically in the diffusion procedure,but not before the beginning of EFNQMC computation.In order to optimize the trial function,the improved steepest descent technique is used,in which the step size is automatically adjustable.The procedure is quasi-Newton and converges super linearly.We also use a novel trial function,which has correct electron-electron and electron-nucleus cusp conditions.The novel EFNQMC algorithm and the novel trial function are employed to calculate the energies of 1^1A1 state of CH2,^1Ag state of C8 and the ground-states of H2,LiH,Li2,H2O,respectively.The test results show that both the novel algorithm and the trial function proposed in the present paper are very excellent.     

A Novel Method for Fixed‐node Quantum Monte Carlo

In this paper, a novel method for fixed‐node quantum Monte Carlo is given. By comparing this method with the traditional fixed‐node one, this novel method can be applied to calculate molecular energy more exactly. An expansion of the eigenvalue of the energy for a system has been derived. It is proved that the value of the energy calculated using the traditional fixed‐node method is only the zeroth order approximation of the eigenvalue of the energy. But when using this novel method, in the case of only increasing less computing amounts ( < 1%), the first order approximation, the second order approximation, and so on can be obtained conveniently with the detailed equations and steps in the practical calculation to calculate the values of the zeroth, first and second approximation of the energies of 1 ¹A, state of CH₂, ¹A₂(C_4h, acet) state of C₈ and the ground‐states of H₂, LiH, Li₂, and H₂O The results indicate that for these states it needs only the second order approximation to obtain over 97% of electronic correlation energy, which demonstrates that this novel method is very excellent in both the computing accuracy and the amount of calculation required.     

Fixed—node Quantum Monte Carlo：A Novel Approach

The fixed-node quantum Monte Carlo (FNQMC)1,2 method has made it possible to calculate the electronic structure of relatively large molecular systems. These large systems range from positron complexes [NH2, Ps] with ～10 electrons to C20 isomers with 120 electrons, silicon crystal structures of 250 atoms and 1000 valence electrons. In the practical calculation for FNQMC method, in general, a minimal basis set of Slater-type atomic orbital (STO) and Jastrow functions are taken to cons…     

精确固定节面量子Monte Carlo差值法

提出了精确固定节面量子Monte Carlo差值法, 这个新算法能够在精确固定节面量子Monte Carlo方法的基础上直接计算两个体系之间的能量差, 且使计算结果的统计误差达到10-5 hartree 数量级, 获得电子相关能90%以上. 我们把这个新算法应用于分子势能面的研究中, 使用一个“刚性移动”模型, 利用Jacobi变换使分子两个几何构型的能量计算具有很好的正相关性, 因而能得到准确的能量差值, 由此就可以得到精确的分子势能面.     

自优化扩散量子Monte Carlo差值法

提出了自优化扩散量子MonteCarlo差值法,这是一个集优化、扩散和相关取样三项技术于一身的MonteCarlo新算法.这个算法能够在扩散过程中直接计算两个体系之间的能量差,且使计算结果的统计误差达到10^-5hartree数量级,获得相关能达80%以上.应用该方法研究分子势能面,使用"刚性移动"模型,利用Jacobi变换使分子两个几何构型的能量计算具有很好的正相关性,因而能得到准确的能量差值和分子势能面.另外,我们还首创了"平衡后留样"技术,可节省50%以上的计算量.该算法还可应用于分子光谱、化学反应能量变化值等领域的研究.     

Exact Fixed-node Quantum Monte Carlo： Self-optimizing Procedure

In this paper, a novel exact fixed-node quantum Monte Carlo (EFNQMC) algorithm was proposed, which is a self-optimizing and self-improving procedure. In contrast to the previous EFN-QMC method, the importance function of this method is optimized synchronistically in the diffusion procedure, but not be-fore beginning the EFNQMC computation. In order to optimize the importance function, the improved steepest descent tech-nique is used, in which the step size is automatically adjustable.The procedure is quasi-Newton type and converges super linear-ly. The present method also uses a novel trial function, which has correct electron-electron and electron-nucleus cusp condi-tious. The novel EFNQMC algorithm and the novel trial func-tion are employed to calculate the energies of 1 ^1A1 state of CH2, ^1Ag state of Cs and the ground-states of H2, LiH, Li2 and H2O.     

Linear expansions of correlated functions: Variational Monte Carlo case study

The relative performance of trial wave functions expressed as linear combination of correlated exponentials has been tested on a variety of systems. The results are compared against other correlated functions commonly used in the literature to assess the capabilities of the proposed ansatz. A possible departure from the simple exponential functional form used in previous works is discussed, along with its advantages and drawbacks. We also discuss how to implement an efficient optimization procedure for this correlated basis set. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 23–33, 1999     

一种高效的优化量子Monte Carlo波函数的新方法

提出了一个优化量子MonteCarlo波函数的新方法，与前人的方法相比，它不使用变分原理而是极小化Schrodinger方程的剩余量；不按Ψ2取样而是按Ψ2（EL－E）2取样；不用差分而是用分析导数；不使用传统的速降法而是使用一个步长自动调节的下降法，它具有拟牛顿性质，因而是超线性收敛的．由于这四项新技术的使用，使得波函数的优化快速、准确，收敛速度比前人提出的方法快3～5倍．     

Self-optimizing Diffusion Quantum Monte Carlo Calculation: the Potential Energy Curve of C_2

11NTRODUCTIONDiffusionquantumMonteCarlo(DMC)isoneofthesimplestofthevariousMonteCarlotechniquesavailabletosolvetheSchrodingerequation,forarecentre-viewofDMC(seeRef[1i).Foravarietyofsmallatomsandmolecules,DMChasbeenshowntobecapableofprovidinganestimateoftheground-state(nonrelativistic)energywithanaccuracycomparabletogoodqualityClcalculations,evenwhenarelativelysimpletrialwavefunctionisemployed.However,todate,thereareseveralobstaclesinaDMCcalculation:(1)BeforetheDMCcomputation,thepar…