从头计算法分子轨道绘图程序

在前文中,我们报道了以Slater函数(STO)和类氢函数为原子轨道基组的分子轨道绘图程序,文介绍以Gauss函数(GTO)为基组的从头计算分子轨道绘图程序,该程序可绘制各类型(s,p,d等)GTO表示的原子轨道和以STO-GTO系基组构成的各种分子轨道ψ或|ψ|²的截面立体图及等值图,利用从头计算的结果,所绘制的图形能很好的反映从头计算法本身的特点。     

吡啶甲酸分子平衡构型的ab initio理论研究

本文用能量梯度法TEXAS从头计算程序,选取4-21G(,N原子含极化d轨道)基组,对α-,β-吡啶甲酸分子的平衡几何构型进行了全优化计算,二套基组的理论优化表明,三个吡啶甲酸分子都具有平面的平衡构型,其计算键长经4-21G 基组的标准经验校正值校正后,所得的理论预测平衡几何构型与X射线单晶衍射实验结果有很好的一致性.对部分键长以及羧基与吡啶华平面的二面角中出现的差异进行了讨论.     

含三重键有机小分子定域分子轨道的理论研究

为了能够应用定域分子轨道(LMO)模型计算链状有机大分子的光电子能谱,我们已做了一系列工作。本文是用STO-3G基组和Foster-Boys LMO程序,采用文中的计算方法,对含H、C、N和O原子及单,双和叁键的近20个有机小分子进行研究,得到了它们     

NMR偶合常数的从头算级别自然杂化轨道研究

为了研究自然杂化轨道计算结果与核自旋偶合常数的相关性,本文进行了从头算级别的自然杂化轨道计算。采用STO－3G基组,利用Lowdin正交化原子轨道基组下的密度矩阵,得到了分子中各原子的杂化轨道、净电荷与^13C-H、^13C-^13C键自旋偶合常数^1Jcn和^1Jcc之间关系式。利用这些式子计算得到的结果与实验数据非常一致。     

链烃,环状烃和多面体烃的定域分子轨道研究

采用GAUSSAN 80程序对一系列直链烷烃、环状烃和多面体烷烃进行STO-3G基组下的曲initio计算,在所得非定域分子轨道自洽场结果的基础上,利用Boys方法进行定域化,进而研究了这些分子的定域分子轨道的键弯曲性质、轨道能量和集居数与几何结构之间的关系,用上述结果对一些典型分子的稳定性进行了讨论。     

三氧化硫分子杂化轨道的探讨

分别选用量子化学从头算MP2、QCISD、CCSD法和密度泛函B3LYP方法,在6-311++G(3df,3pd)基组水平下对SO_3分子的结构进行了优化比较,结果显示QCISD/6-311++G(3df,3pd)条件下的计算结果最优。在此条件下,用自然键轨道理论(NBO)对SO_3分子的杂化轨道、杂化方式、离域π键进行了研究。结果表明S原子采取sp~2等性杂化,杂化后形成含3对电子的sp~2轨道和1个空的3p_z轨道,O原子采取sp~3不等性杂化。S与O原子之间的σ键为S→O配位键,3个O原子各1对2p_z孤对电子与S原子的3p_z空轨道形成π_4~6离域π键。Mayer键级显示S=O键级为1.77,呈现明显的双键特性。     

分子轨道图形理论应用于单环共轭分子中的一个教学问题

对于单环共轭分子,简单分子轨道理论只处理π电子,把平面内的σ电子系统连同核和内层电子看作刚性的分子实,单电子薛定谔方程为Hψ=Eψ(1) 其中H是哈密顿算符,ψ是π电子分子轨道,E是能级·分子轨道近似用原子轨道的线性组合来表示.     

键能的分子轨道理论研究Ⅱ.键能与Mulliken布居对键强度的判断的比较

用键能EAB和Mulliken布居对化学键强度的判别进行了分析比较.结果表明,键能判据比Mulliken布居判据所得结论更符合实际情况.作为衡量原子间化学键强度的尺度,不仅应考虑原子轨道间的布居因素,还应考虑分子轨道(或原子轨道)的能量因素.     

键能的分子轨道理论研究2: 键能与Mulliken布居对键强度的 判断的比较

用键能E~A~B和Mulliken布居对化学键强度的判别进行了分析比较。结果表明,键能判据比Mulliken布居判据所得结论更符合实际情况。作为衡量原子间化学键强度的尺度,不仅应考虑原子轨道间的布居因素,还应考虑分子轨道(或原子轨道)的能量因素。     

键能的分子轨道理论研究2: 键能与Mulliken布居对键强度的 判断的比较

用键能E~A~B和Mulliken布居对化学键强度的判别进行了分析比较。结果表明,键能判据比Mulliken布居判据所得结论更符合实际情况。作为衡量原子间化学键强度的尺度,不仅应考虑原子轨道间的布居因素,还应考虑分子轨道(或原子轨道)的能量因素。     

生物热动力学研究——大肠杆菌生长速率和激活能

大肠杆菌生长的全热谱已被测定,再进一步根据其指数生长期的热谱信息,确定了它的生长速率和激活能。在指数生长期,细菌数按指数规律增加,可用下式表示:n_t=n_0e~(kt)(1)式中:t为指数生长期开始后的某一时间,n_0,n_t分别为指数生长期开始时和t时的细菌数,k为生长速率常数。因此,同期细菌输出的热功率也是按指数规律同步增长。可表示为:     

Molecular calculations for HeH<Superscript>+</Superscript> with two-center correlated orbitals

A two-center correlated orbital approach was used to calculate the electronic ground state energy for the HeH⁺ molecular ion. The wavefunctions were constructed from the exact solution of the Schrödinger equation for the HeH⁺⁺ problem in prolate-spheroidal coordinates taken together with a Hylleraas type correlation factor. With a simple single term wavefunction, we obtained ground state energy of ?2.95308691 hartree without any variational parameters in the calculation. When a two-configuration-state wavefunction was used and effective charges were allowed to be adjusted, we found an energy of ?2.97384868 hartree, which is to be compared with ?2.97869074 hartree obtained by an 83 term configuration interaction wavefunction or ?2.97364338 hartree by an ab initio calculation (at the MP4(SDQ)/6-311++G(3df, 3dp) level) using the well-known “canned” code.     

Correlation energy extrapolation by intrinsic scaling. V. Electronic energy, atomization energy, and enthalpy of formation of water

The method of correlation energy extrapolation by intrinsic scaling, recently introduced to obtain accurate molecular electronic energies, is used to calculate the total nonrelativistic electronic ground state energy of the water molecule. Accurate approximations to the full configuration interaction energies are determined for Dunning's [J. Chem. Phys. 90, 1007 (1989)] correlation-consistent double-, triple- and quadruple-zeta basis sets and then extrapolated to the complete basis set limit. The approach yields the total nonrelativistic energy -76.4390+/-0.0004 hartree, which compares very well with the value of -76.4389 hartree derived from experiment. The energy of atomization is recovered within 0.1 mh. The enthalpy of formation, which is obtained in conjunction with our previous calculation of the dissociation energy of the oxygen molecule, is recovered within 0.05 mh.     

Gaussian-type function set without prolapse 1H through 83Bi for the Dirac-Fock-Roothaan equation

We have developed prolapse free Gaussian basis sets which can be used for 1H to 83Bi, imposing the condition that the Dirac-Fock-Roothaan (DFR) total energy (TE) decreases monotonically toward the numerical DF (NDF) TE as the expansion term increases. An even-tempered basis set was assumed. The resulting sets gave |TE(DFR) - TE(NDF)| < or = 1 x 10(-6) hartree for any atoms less or equal to 83Bi; TE(NDF) = -21 565.638 345, and TE(DFR) = -21,565.638 345 +/- 0.000 001 hartree for Bi when the expansion terms are in the range (58, 58, 58, 36, 36, 36, and 36) and (72, 72, 72, 36, 36, 36, and 36) for (s+, p-, p+, d-, d+, f-, and f+) symmetries, respectively. A practical set with 44, 44, 44, 36, 36, 32, and 32 for the respective symmetries is also proposed where |TE(DFR) - TE(NDF)| < or = 4 x 10(-5).     

Gaussian-type function set without prolapse for the Dirac-Fock-Roothaan equation (II): 80Hg through 103Lr

We present prolapse-free universal Gaussian-type basis sets for 80Hg through 103Lr. The basis set is determined so that the Dirac-Fock-Roothaan total energy should decrease monotonically toward the numerical Dirac-Fock total energy. The difference between the Dirac-Fock-Roothaan total energy and the numerical Dirac-Fock total energy is less than 3 x 10(-6) hartree for 1H through 102No, and less than 5 x 10(-6) hartree for 103Lr. The exponents of the present sets are determined in an even-tempered manner, aiming to give total energy closer to the numerical Dirac-Fock value as the expansion term increases. The recommended set is expanded by (64, 64, 64, 46, 46, 46, 46) terms for (s+, p-, p+, d-, d+, f-, f+) symmetries, respectively. A practical set with (56, 48, 48, 36, 36, 36, 36) terms is also presented.     

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.     

A path from I(h) to C1 symmetry for C20 cage molecule

The symmetry of the C20 cage is studied based on the intrinsical relationship among point groups (Bradley, C. J.; Cracknell, A. P. The Mathematical Theory of Symmetry in Solids; Claredon Press: Oxford, 1972). The structure of the C20 cage with I(h) symmetry is constructed, as are eight other structures with subgroup symmetry. A path from I(h) symmetry to C1 symmetry is obtained for the closed-shell electronic state, and the structure with D2h symmetry is the most stable on this path. Using the D2h structure the correlation energy correction is studied on the condition of restricted excitation space at the CCSD(T) level. We obtain curves on the relation between the orbital numbers and the total energy at the CCSD(T), CCSD, and MP2 level, respectively. The results of these curves obtained from MP2 and CCSD(T) methods have the same tendency, while the results of CCSD gradually diverge with an increase in orbital numbers. When the orbitals used in the calculation reach 460, the total energy is -759.644 hartree at MP2 level and is -759.721 hartree by the CCSD(T) method. From the calculation results, we find that a large basis set can improve the reliability of the MP2 method, and to restrict excitation space is necessary when using the CCSD(T) method.     

Gaussian-type function set without prolapse for the Dirac-Fock-Roothaan equation

A Gaussian-type function (GTF) set without a prolapse (variation collapse) is generated for the Dirac-Fock-Roothaan (DFR) equation. The test atom was mercury. The number of primitive GTFs used is between 7 and 62 (abbreviated as 7-62), 6-62, 6-62, 4-36, 4-36, 3-36, and 3-36 for s(+), p(-), p(+), d(-), d(+), f(-), and f(+) symmetries. The respective exponent parameters were determined with even-tempered manner, which requires the minimum and maximum exponents for the respective symmetries. We prepared several sets of these. The total energy (TE) given by the numerical DF (NDF) is -19648.849250 hartree; one of the present sets with largest number of expansion terms gave -19648.849251 hartree. The error (deltaTE) relative to the NDR TE is quite small. We then applied this set to the inert gas atoms Ne (10), Ar (18), Kr (36), Xe (54), Rn (86), and No (102), and also to Es (99) as the representative of the open shell atoms. The absolute values of deltaTE were at most 2.8 x 10(-6) hartree, showing the potential of this set as a universal set.     

Simultaneous analytical optimization of variational parameters in Gaussian-type functions with full configuration interaction of multicomponent molecular orbital method by elimination of translational and rotational motions: application to isotopomers of the hydrogen molecule

We have extended the multicomponent molecular orbital (MCMO) method to the full-configuration interaction (full-CI) fully variational molecular orbital method by elimination of translational and rotational motion components from total Hamiltonian. In the MCMO scheme, the quantum effects of protons and deuterons as well as electrons can be directly taken into account. All variational parameters in the full-CI scheme, i.e., exponents and centers (alpha and R) in the Gaussian-type function (GTF) basis set as well as the CI coefficients, are simultaneously optimized by using their analytical gradients. The total energy of the H(2) molecule calculated using the electronic [6s3p2d1f] and nuclear [1s1p1d1f] GTFs is -1.161 726 hartree, which can be compared to the energy of -1.164 025 hartree reported using a 512 term-explicitly correlated GTF calculation. Although the d- and f-type nuclear GTFs contribute to the improvement of energy convergence, the convergence of electron-nucleus correlation energy is slower than that of electron-electron one. The nuclear wave functions are delocalized due to the electron-nucleus correlation effect compared to the result of Hartree-Fock level of MCMO method. In addition, the average internuclear distances of all diatomic molecules are within 0.001 A of the previously reported experimental results. The dipole moment of the HD molecule estimated by our method is 8.4 x 10(-4) D, which is in excellent agreement with the experimental result of (8-10) x 10(-4) D.     

化学反应位能面LEPS法的改进

In this paper we gave an improvement of the LEPS method for the reaction potential energy surface, in which the coulomb energy Q and exchange energy J include the overlap integral S with the parameter v: J=S~vD_e{[1-e~(-β(r-r_0))]~2-1} Q=(1-S~v)D_e{[1-e~(-β(r-r_o)]-1} By this modified LEPS method we have calculated five reaction potential energy surfaces, of which the transition state parameters have been shown in the table: Reaction Energy barrier Internuclear separation E≠/kcal mol~(-1) H_2+H=H+H_2 9.746 R≠H...