势谐函数展开方法下的快速收敛研究

势谐函数展开方法下的快速收敛研究王沂轩,邓从豪（山东大学化学院,济南,２５０１００）关键词超球坐标,势谐函数,广义Ｌａｇｕｅｒｒｅ函数（ＧＬＦ）超球坐标表象中的势谐（ＰＨ）展开方法是减少超球径耦合微分方程的数目和广义本征矩阵的维数,以解决高维超球谐（...     

原子Schrǒdinger方程直接求解的相关函数-势谐-广义Laguerre函数方法

引入相关函数,将势谐-广义Laguerre函数(PHGLF)方法发展为相关函数-势谐-广义Laguerre函数(CFPHGLF)方法,应用于He,H~-,Li~+和Be~(2+)等三体体系的n~1S(n=1～4)态.得到了比由PHGLF方法更精确的激发态n~1S(n=2～4)本征能量,且从n=2至4,与Hylleraas组态相互作用(HCI)能量愈来愈近,如He原子的3个激发态的本征能与最精确的HCI之差分别为0.001 827,0.000 666,0.000 376(a. u.);但基态的能量本征值逊于PHGLF方法.结果表明,非势谐函数对基态波函数尚有较显著的贡献,对激发态波函数的贡献较小;在势谐方案下,对基态(1~1S)应考虑电子间的相关,对于激发态重要的是消除电子与核间的歧点.     

类氦离子Schrdinger方程直接求解的精确势谐方法

给出了一种直接求解三体原子Schrdinger方程的完整势谐展开方法,包括联立的超球径耦合微分方程和广义本征能方程;将其应用于类氦离子,得到了非常精确的基态和低躺激发态的本征能.     

超球坐标下相关函数对锂原子基态本征能收敛行为的影响

在超球坐标下,由3个对称相关函数exp[-α(r₁+r₂+r₃)](α分别为,√-2E/3,2.76和核电荷数z),利用相关函数-超球谐-广义Laguerre函数方法(CFHHGLF)直接求解Li原子的Schrdinger方程,计算基态本征能。从数值来看,α=z结果最好,其次是α=2.76,变参数α较差;而从径向的收敛速度来看,变参数α收敛最快,α=2.76收敛较慢,α=z时本征能只有当对称基超过100时才呈现收敛趋势。结果表明,在超球谐展开方案下只有α=z的相关函数才能得到高精度的本征能量。     

一些密度泛函方法预测电子亲和势

选取了杂化泛函B3LYP, B3PW91, O3LYP, PBE0, 以及与之相对应的GGA泛函BLYP, BPW91, OLYP和PBE, 还选取了能更好地兼顾强相互作用和弱相互作用的X3LYP泛函和在预测NMR的化学位移有较好表现的OPBE泛函, 以及两种meta-GGA泛函VSXC和TPSS, 共12种泛函, 详细地考察了这些泛函在预测EA方面的准确性.     

三电子原子的超球坐标分析和基态能态计算

用超球坐标表示多电子原子的薛定谔方程,从符合Pauli原理的全反称波函数出发,推导出相应的超球径耦合微分方程,其形式与双电子原子的相似。以九维超球谐为投影函数构造S₃群不可约表示的对称基,将超球谐-广义Laguerre展开法(HHGL)推广到Li原子,首次对其Schrdinger方程的精确求解进行了研究,基态能量的计算值与实验值接近。最后,还从波函数出发对提高计算的精度进行了讨论。     

超球坐标下Li原子^4S态Schrodinger方程的直接解

以九维超球谐为投影函数, 构造置换群S3一维不可约表示的全反称基函数。应用HHGLF和CFHHGLF方法直接求解Li原子^4S态的Schrodinger方程。由HHGLF方法得到的本征能量与精确变分数值相差较远; CFHHGLF方法给出了与变分值相近的结果。     

Rg-HX分子间势的精确从头计算研究

在用非迭代的三重激发项来校正CCSD的CCSD(T)理论水平下,采用aug cc pVQZ基函数对He HF的分子间势进行了系统的研究.结果表明：He HF以线型结构存在.在极限基的情况下,复合物两种线型极小点结构He H F和He F H势阱深分别为46.614 cm－1和25.026 cm－1,对应He原子到HF分子质心的距离Rm分别为0.3149 nm和0.3012 nm.讨论了不同的基函数和理论方法在研究此类弱束缚态复合物的分子间势时的可靠性及其对结果的影响,并研究了HF分子中H－F键长的改变对势能的影响,同时也给出了势函数的解析形式.     

超球坐标下Li原子~4S化态Schrdinger方程的直接解

以九维超球谐为投影函数,构造置换群S_3一维不可约表示的全反称基函数.应用HHGLF和CFHHGLF方法直接求解Li原子~4S态的Schrodinger方程.由HHGLF方法得到的本征能量与精确变分数值相差较远;CFHHGLF方法给出了与变分值相近的结果.     

处理量子反应散射的负虚数势方法

处理量子反应散射的负虚数势方法蔡宇民，胡旭光，李前树（西安石油学院化学工程系．西安，７１００６１）（吉林大学理论化学研究所，长春，１３００２３）关键词反应散射，反应几率，光学势近年来，处理反应散射问题的各种严格的和近似的量子力学方法发展迅速［１～５］...     

The eigenenergies for ~3S excited states of the helium atom with CFPHGLF method

The matrix elements of the correlation function between symmetric potential harmonics were first simplified into the analytical summation of the grand angular momentum. The correlation-function potential-harmonic and generalized Laguerre function method (CFPHGLF) proposed by us recently was then applied to directly solve the Schrodinger equation for n3S(n=2-5) excited states of the helium atom. With only 12 PHs, the convergent eigenenergies of 23S, 33S, 43S and 53S states were 2.17427, 2.06849, 2.03644, 2.02257 Eh, respectively. The errors only were 0.00096, 0.00020, 0.00007, 0.00005 Eh, when compared with the exact Hylleraas variational results respectively.     

A potential harmonic method for the three-body coulomb problem

A potential harmonic method that is suitable for the three-body coulomb systems is presented. This method is applied to solve the three-body Schroedinger equations for He and e ⁺ e ⁻ e ⁺ directly, and the calculations yield very good results for the energy. For example, we obtain a ground-state energy of −0.26181 hartrees for e ⁺ e ⁻ e ⁺, and −2.90300 hartrees for He with finite nuclear mass, in good agreement with the exact values of −0.26200 hartrees and −2.90330 hartrees. Compared with the full-set calculations, the errors in the total energy for ground and excited states of e ⁺ e ⁻ e ⁺ are very small, around −0.0001 hartrees. We conclude that the present method is one of the best PH methods for the three-body coulomb problem. Received: 5 September 1996 / Accepted: 14 July 1997     

Harmonic analysis and discrete polynomials. From semiclassical angular momentum theory to the hyperquantization algorithm

Orthogonal polynomials of a discrete variable have been widely investigated as fundamental tools of numerical analysis. This work aims to propose the extension of their use to quantum mechanical problems. By exploiting both their connection with coupling and recoupling coefficients of angular momentum theory and their asymptotic relationships (semiclassical limit) with spherical and hyperspherical harmonics, a discretization procedure, the hyperquantization algorithm, has been developed and applied to the study of anisotropic interactions and of reactive scattering. One of the most appealing features of this method turns out to be a drastic reduction of memory requirements and computing time for extensive dynamical calculations. Examples of the application of this technique to stereodirected dynamics via an exact representation for the S matrix as well as to the characterization of molecular beam polarization are also illustrated. Received: 17 September 1999 / Accepted: 3 February 2000 / Published online: 5 June 2000     

超球坐标下原子、分子体系的变分计算：—氦原子和氢负离子基态

应用超球会标表示氦原子和氢负离子的薛定谔方程，将二电子原子在三维空间中的运动转化为单电子原子在六维空间中受广义库仑力作用的运动，我们给出了六维空间广义角动量算符的本征值与本征函数，并以此本征函数微基构造超球波函数，得到超球径微分方程，以广义Laguerre 多项式表示超球径波函数，运用密度矩阵和线性变分法得到非正交基下超球径波函数满足的久期方程，最后求得能量和波函数，计算结果与精确的计算符合良好。     

Overlap Integrals Between Irregular Solid Harmonics and STOs Via the Fourier Transform Methods

In this paper, a unified analytical and numerical treatment of overlap integrals between Slater type orbitals (STOs) and irregular Solid Harmonics (ISH) with different screening parameters is presented via the Fourier transform method. Fourier transform of STOs is probably the simplest to express of overlap integrals. Consequently, it is relatively easy to express the Fourier integral representations of the overlap integrals as finite sums and infinite series of STOs, ISHs, Gegenbauer, and Gaunt coefficients. The another mathematical tools except for Fourier transform have used partial-fraction decomposition and Taylor expansions of rational functions. Our approach leads to considerable simplification of the derivation of the previously known analytical representations for the overlap integrals between STOs and ISHs with different screening parameters. These overlap integrals have also been calculated for extremely large quantum numbers using Gegenbauer, Clebsch-Gordan and Binomial coefficients. The accuracy of the numerical results is quite high for the quantum numbers of Slater functions, irregular solid harmonic functions and for arbitrary values of internuclear distances and screening parameters of atomic orbitals.     

电位滴定法研究3,5-二甲基-DL-酪氨酸与3,5-二碘-L-酪氨酸去质子化特性

本文采用pH电位滴定法测定了3,5-二甲基-DL-酪氨酸(DL-Dmtyr)的酸解离常数。通过与碘基取代酪氨酸解离常数相对比,发现甲基对邻位酚羟基解离的影响明显小于碘基。     

控制电位滴定法的误差分析

研究了影响控制电位滴定法测定结果准确度的因素,得到的结论是:第一,电位的控制误差及滴定剂体积的测定误差是影响控制电位滴定法测定结果准确度的主要因素.计算模型中的比例系数越大,滴定曲线的变化率越大,这种影响越小.第二,多组分体系的测定误差,与组分在计算模型中比例系数的相对大小有关.比例系数越大,测定误差越小.第三,不同浓度(或不同浓度比)待测溶液滴定曲线的差异越大,对控制电位滴定法的测定越有利.