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.     

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。     

类氦离子1,3P激发态Schrodinger方程的直接解

利用相关函数（CF）-超球谐（HH）-广义Laguerre(GLF)方法直接求解类氦离子n1,3P（n=1,2,3）低躺激发态的Schrodinger方程,得氦原子的本征能量分别为-2.13317Eh (13P),-2.12383Eh(11P),-2.05810Eh(23P),-2.05516Eh(21P),-2.03235Eh(33P)和-2.03109Eh(31P),它们与文献值在........第6位上很好地吻合。这说明CFHHGLF方法也适用于类氦离子1,3P激发态。还给出了总角动量L=1的对称超球谐基函数和有关矩阵元的解析式。     

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.     

超球谐展开的收敛行为He原子的^3S态

利用相关函数－超球谐－广义Ｌａｇｕｅｒｒｅ函数方法，研究Ｈｅ原子＾３Ｓ态波函数向超球谐函数展开的收敛行为。截止于ｌ＝０，１，２的超球谐函数给出的本征能分别与组态相互作用的ｓ－，ｓｐ－，ｓｐｄ－极限能一致。仅用４４个超球谐函数，便得到了与精确的ＨｙｌｌｅｒａａｓＣＩ变分能量小数点后第５位的２＾３Ｓ，３＾３Ｓ的４＾３Ｓ态本征能吻合。     

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（...     

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。     

包括电子间相关势谐函数的CFPHGLF方法

包括电子间相关势谐函数的ＣＦＰＨＧＬＦ方法王沂轩,邓从豪（山东大学化学院,济南,２５０１００）关键词超球坐标,势谐函数,快速收敛前文［１,２］吸收相关函数（ＣＦ）的思想,与势谐函数－广义Ｌａｇｕｅｒｒｅ函数（ＧＬＦ）方法（ＰＨＧＬＦ）［３,４］相结合...     

光谱法及热动力学法研究环糊精与四-N-正丙基吡啶基卟啉的作用

通过紫外吸收,荧光光谱,一维、二维核磁共振技术等光谱方法,确定了环糊精与四－N－正丙基吡啶基卟啉2：1型包合物的形成,分子模拟方法进一步证实了该包合物的形成;采用热动力学法研究了温度对包合反应的影响,计算得出包合过程的熵变、焓变及自由能变化,绘出了卟啉类化合物与环糊精包合物的熵焓补偿曲线,进而确定了包合反应的主 要驱动力是焓。     

含时变分S 矩阵解得一般形式

推导出含时S散射矩阵变分表达式经基函数展开并优化后的解的一般形式。     

PHGLF calculations of heliumlike three-body systems

By expanding the atomic wave function in potential harmonics (PH ) and generalized Laguerre functions (GLF ), we derived the recurrence relation of the expansion coefficients and then performed calculations for four He-like three-body systems. In comparison with the complete set calculation (HHGLF ), we find that the errors in eigenenergies introduced by the PHGLF scheme are approximately 0.00033, 0.00025, 0.00022, and 0.00021 au for the ground-state H⁻, He, Li⁺, and Be²⁺ systems, respectively, and that for excited states the error is slightly higher and decreases with the grand angular momentum. The present results indicate that the PHGLF scheme is such an efficient means to reduce the degeneracy of the hyperspherical harmonics (HH ) for three-body problems that it can give more satisfactory results than can the HHGLF method with much smaller eigenmatrices. © 1995 John Wiley & Sons, Inc.     

High precision variational calculations for the Born-Oppenheimer energies of the ground state of the hydrogen molecule

Born-Oppenheimer approximation Hylleraas variational calculations with up to 7034 expansion terms are reported for the 1sigma(g)+ ground state of neutral hydrogen at various internuclear distances. The nonrelativistic energy is calculated to be -1.174 475 714 220(1) hartree at R = 1.4 bohr, which is four orders of magnitude better than the best previous Hylleraas calculation, that of Wolniewicz [J. Chem. Phys. 103, 1792 (1995)]. This result agrees well with the best previous variational energy, -1.174 475 714 216 hartree, of Cencek (personal communication), obtained using explicitly correlated Gaussians (ECGs) [Cencek and Rychlewski, J. Chem. Phys. 98, 1252 (1993); Cencek et al., ibid. 95, 2572 (1995); Rychlewski, Adv. Quantum Chem. 31, 173 (1998)]. The uncertainty in our result is also discussed. The nonrelativistic energy is calculated to be -1.174 475 931 399(1) hartree at the equilibrium R = 1.4011 bohr distance. This result also agrees well with the best previous variational energy, -1.174 475 931 389 hartree, of Cencek and Rychlewski [Rychlewski, Handbook of Molecular Physics and Quantum Chemistry, edited by S. Wilson (Wiley, New York, 2003), Vol. 2, pp. 199-218; Rychlewski, Explicitly Correlated Wave Functions in Chemistry and Physics Theory and Applications, edited by J. Rychlewski (Kluwer Academic, Dordrecht, 2003), pp. 91-147.], obtained using ECGs.     

Variational calculations of the lowest 2S and 2P states of the Li atom

The lowest variational upper bounds to the lowest ²S state of ?7.478044 au and to the lowest ²P state of ?7.410097 au of the lithium atom are obtained.     

On the Dirac equation in the algebraic approximation

It is shown that the restrictive conditions of Wood et al. [1] are not necessary to reach the conclusion that the Dirac hamiltonian, projected onto the space of the large component, exhibits variational properties. The eigenvalue spectrum of matrix approximations to the partitioned hamiltonian (obtained by matrix partitioning) converges to the exact spectrum in the limit of infinite order (assuming completeness) but not necessarily from above as for true matrix representations (obtained from operator partitioning). Optimization of non-linear parameters is shown not to cause variational instabilities.Control Data Corporation PACER fellow 1984–1986     

Effect of different subsets on convergence patterns of hyperspherical harmonic expansion for the S states of the helium atom

Effects of different subsets on convergence patterns of hyperspherical harmonic (HH) expansions for the low-lying ¹S and ³S states of the helium atom have been investigated with the correlation-function-hyperspherical-harmonic-generalized-Laguerre-function (CFHHGLF) method by successively introducing HH subsets with the fixed three-dimensional angular momentums (l) into the atomic wave functions. The eigenenergies given by the HH subsets of l=0, 1, 2, and 3 are in good agreement with the best s-, sp-, spd-, and spdf limits of variational configuration interaction (CI) calculations, respectively. The final eigenenergies of the ground state as well as the examined low-lying excited ¹S and ³S states are quite close to the exact Hylleraas CI (HCI) values at the sixth decimal place. Moreover, l=0 and l≠0 expansion results also tell us that it is not necessary to take into account too many HHs at the given l, especially for higher l, and that the more the absolute electron correlation energies the bigger l it takes to obtain precise eigenenergies. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64 : 661–668, 1997     

Br+CH3S(O)CH3反应机理的直接动力学研究

采用直接动力学的方法，对多通道反应体系Br＋CH3S（O）CH3进行了理论研究．在BH＆H-LYP／6-311G（2d，2p）水平下获得了优化几何构型、频率及最小能量路径（MEP），能量信息的进一步确认在MC-QCISD（单点）水平下完成．利用正则变分过渡态理论，结合小曲率隧道效应校正（CVT／SCT）方法计算了该反应的两个可行的反应通道在200K～2000K温度范围内的速率常数．在整个反应区间内，生成HBr的反应通道与生成CHa的反应通道存在着竞争，前者是主反应通道，后者是次反应通道．变分效应和小曲率隧道效应对反应速率常数的计算影响都很小．理论计算得到的两个反应通道的反应速率常数与实验值符合得很好．