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.     

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.     

自优化剩余函数量子Monte Carlo方法

提出剩余函数量子Monte Carlo的一个新算法，这是一个自优化和自改善的过程.与以前的算法相比，本算法中的试探函数的优化是在剩余函数方法中同步进行的，而不是在变分Monte Carlo计算之前.为了优化试探函数，使用一种改进了的速降法，这是一个步长能够自动调节，超线性收敛的优化技术.在这个算法中,还使用了一种新的相关函数，它满足电子与电子以及电子与核奇点条件.此方法已被用于计算H2、LiH、Li2、H2O分子的基态以及CH2的X 3B1态、1 1A1态和2 1A1态的能量值.     

聚合物链构象的研究 Ⅰ.1,2-聚丁二烯的构象分析

本文应用Flory的链分子统计理论研究1,2-聚丁二烯的链构象,选择固定键长和键角的分子模型,计算构象能,构成势能面图,并由势能面的构型积分,得到了表征1,2-聚丁二烯链构象特征的统计权重矩阵.     

聚合物链构象的研究I: 1,2-聚丁二烯的构象分析

本文应用Flory的链分子统计理论研究1,2-聚丁二烯的链构象,选择固定键长和键角的分子模型,计算构象能,构成势能面图,并由势能面的构型积分,得到了表征1,2-聚丁二烯链构象特征的统计权重矩阵.     

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。     

用神经网络方法拟合的反应体系H＋CH4←→H2＋CH3的一个全域势能面

利用神经网络力法,基于47783个高精度从头算能量点构建了反应体系H＋CH4←→H2＋CH3的一个全域势能面．通过大最的准经典轨线以及量子散射计算测试了势能面的收敛性质．这个势能面对于拟合过程以及从头算点的数目都已经完全收敛,拟合误差很小县比Shepard插值的势能面计算速度更快,代表了此标志性多原子反应体系最好的势能面．     

无辐射跃迁理论进展

在本文中,我们将介绍运用第一性原理计算包含非谐效应或势能面锥形交叉情况下内转换速率的最新工作。我们同时计算了包含非谐效应的分子吸收和发射光谱,以检验量子化学方法计算得到势能面的准确性。势能面的锥形交叉对内转换过程的影响是学界广泛关注的焦点。本文将介绍如何在内转换速率计算的过程中考虑势能面锥形交叉的影响,并将之运用于吡嗪分子。本文运用绝热近似理论处理了另外一个重要的无辐射过程,分子的振动驰豫过程,并将这个理论应用于水二聚体和苯胺的振动弛豫速率的计算。     

计算机模拟分子束实验——准经典轨线法

本文以Cl+H_2的经典轨线计算为例,介绍了准经典轨线法的原理,即LEPS势能面的选取,运动方程的建立以及初始条件的选择.应用Monte Carlo方法大量随机选择变量的初始条件,所计算的轨线可分为非反应和反应的两大类.通过轨线计算可以得到反应截面积和分子反应的其他有关信息.     

Differential diffusion quantum Monte Carlo method: determination of potential energy surfaces of molecules

A differential approach for self-optimizing diffusion Monte Carlo calculation was proposed in this paper, which is a new algorithm combining three techniques such as optimizing, diffusion and correlation sampling. This method can be used to directly compute the energy differential between two systems in the diffusion process, making the statistical error of calculation be reduced to order of 10-5 hartree, and recover about more than 80% of the correlation energy. We employed this approach to set up a potential energy surface of a molecule, used a "rigid move" model, and utilized Jacobi transformation to make energy calculation for two configurations of a molecule having good positive correlation. So, an accurate energy differential could be obtained, and the potential energy surface with good quality can be depicted. In calculation, a technique called "post-equilibrium remaining sample was set up firstly, which can save about 50% of computation expense. This novel algorithm was used to study the potenti     

Gamma distribution model to provide a direct assessment of the overall quality of quantum Monte Carlo-generated electron distributions

Our objective is to assess the accuracy of simulated quantum Monte Carlo electron distributions of atoms and molecules. Our approach is first to model the exact electron distribution by a linear combination of gamma distribution functions, with parameters chosen to exactly reproduce highly accurate literature values for a number of selected moments for the system of interest. In application to the ground-state electron distributions of helium and dihydrogen, a high level of accuracy of the model was confirmed upon comparing its predicted moments, not used in the model's parametrization, to those calculated from high-level theory. Next, we generated electron-electron and electron-nucleus distributions for dihydrogen from electron positions outputted from a variety of quantum Monte Carlo algorithms. Upon juxtaposition of the simulated distributions with the putatively exact one that we derived from the model, we quantified the error in simulated distributions. The most accurate distributions were obtained from no-compromise reptation quantum Monte Carlo, a recently developed algorithm designed to ameliorate the distributions' time-step bias. Marginally less accurate distributions were generated from fixed-node diffusion Monte Carlo with descendant counting and detailed balance.     

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…     

A diffusion quantum Monte Carlo study on the lowest singlet and triplet electronic states of BN molecule

Ab initio calculation of both the lowest singlet and triplet electronic states of BN has been performed by the fixed-node Ornstein-Uhlenbeck diffusion quantum Monte Carlo method with the floating spherical Gaussian orbitals and spherical Gaussian geminals. The Monte Carlo calculation gives equilibrium bond lengths and equilibrium harmonic frequencies of 1.3317(7) A and 1529(7) cm(-1), respectively, for the lowest triplet state and 1.2751(7) A and 1709(8) cm(-1), respectively, for the lowest singlet state. Also, the Monte Carlo calculation reports an energy separation of 178(83) cm(-1) between the two electronic states and recommends the ground state is the lowest triplet state.     

剩余函数量子Monte Carlo方法

为量子Ｍｏｎｔｅ Ｃａｒｌｏ方法提出一条新途径－剩余函数法,引入了Ｓｃｈｒｏｅｄｉｎｇｅｒ方程剩余函数的概念,利用剩余函数将一种新的有明显物理意义的试探函数应用到量子Ｍｏｎｔｅ Ｃａｒｌｏ过程中,这种试探函数是通过一种迭进式的方式确定的,它不需要在Ｍｏｎｔｅ Ｃａｒｌｏ过程中优化参数。文中我们将给出这种试探函数的具体形式,证明由这种试探函数求出的能量期望值收敛于体系真实的能量值;文中还给出这种试探     

Theoretical study of transition state structure and reaction enthalpy of the F + H2-->HF + H reaction by a diffusion quantum Monte Carlo approach

Ab initio calculations of transition state structure and reaction enthalpy of the F + H2-->HF + H reaction has been carried out by the fixed-node diffusion quantum Monte Carlo method in this study. The Monte Carlo sampling is based on the Ornstein-Uhlenbeck random walks guided by a trial wave function constructed from the floating spherical Gaussian orbitals and spherical Gaussian geminals. The Monte Carlo calculated barrier height of 1.09(16) kcal/mol is consistent with the experimental values, 0.86(10)/1.18(10) kcal/mol, and the calculated value from the multireference-type coupled-cluster (MRCC) calculation with the aug-cc-pVQZ(F)/cc-pVQZ(H) basis set, 1.11 kcal/mol. The Monte Carlo-based calculation also gives a similar value of the reaction enthalpy, -32.00(4) kcal/mol, compared with the experimental value, -32.06(17) kcal/mol, and the calculated value from a MRCC/aug-cc-pVQZ(F)/cc-pVQZ(H) calculation, -31.94 kcal/mol. This study clearly indicates a further application of the random-walk-based approach in the field of quantum chemical calculation.     

Towards accurate all-electron quantum Monte Carlo calculations of transition-metal systems: spectroscopy of the copper atom

In this work we present all-electron fixed-node diffusion Monte Carlo (FN-DMC) calculations of the low-lying electronic states of the copper atom and its cation. The states considered are those which are the most relevant for the organometallic chemistry of copper-containing systems, namely, the (2)S, (2)D, and (2)P electronic states of Cu and the (1)S ground state of Cu(+). We systematically compare our FN-DMC results to CCSD(T) calculations using very large atomic-natural-orbital-type all-electron basis sets. The FN-DMC results presented in this work provide, to the best of our knowledge, the most accurate nonrelativistic all-electron correlation energies for the lowest-lying states of copper and its cation. To compare our results to experimental data we include the relativistic contributions for all states through numerical Dirac-Fock calculations, which for copper (Z=29) provide almost the entire relativistic effects. It is found that the fixed-node errors using Hartree-Fock nodes for the lowest transition energies of copper and the first ionization potential of the atom cancel out within statistical fluctuations. The overall accuracy achieved with quantum Monte Carlo for the nonrelativistic correlation energy (statistical fluctuations of about 1600 cm(-1) and near cancelation of fixed-node errors) is good enough to reproduce the experimental spectrum when relativistic effects are included. These results illustrate that, despite the presence of the large statistical fluctuations associated with core electrons, accurate all-electron FN-DMC calculations for transition metals are nowadays feasible using extensive but accessible computer resources.