Hartree-Fock与密度泛函混合处理中的电子自相关和自旋平行相关问题

电子气近似中的电子相关能与量子化学中的Hartree-Fock相关能在定义上不相互等同 作者从假想的、含N个电子的“有限电子气”出发,通过比较这类体系与无限电子气在物理模型上的差异,合理地把电子气相关能定量地分解为单电子自相关、电子自旋平行相关以及Hartree-Fock相关三个部分,并阐明了各组分的构成随N的变化规律在此基础上建立的Hartree-Fock与密函混合处理方案,无须借助任何经验参数,仅通过简捷的计算即可实现原子和分子的相关能校正平均误差为4.2%,优于CI—SD和MP_4等Hartree—Fock处理的结果.     

Cl,Cl-和MCl(M=H,Li9 Na,K)对内对间相关能的规律性

通过对内对间相关能的计算,发现Cl, Cl-及其化合物中的K电子层的对内相关能基本上是一常数,而且Cl的K,L层电子层内相关能和它们之间的层间相关能也变化很小.另外,所研究的MCI系列化合物中Cl价电子对相关能的贡献是跟MCI的离子性有关,即随着化合物离子性的增加而增加,但其相关能最大不大于Cl-离子的,最小不小于Cl原子的.这些规律对人们考虑一些化合物的相关能,以至化学反应能量很有参考意义.     

Cl,Cl-和MCl(M=H,Li,Na,K)对内对间相关能的规律性

通过对内对间相关能的计算,发现Cl,Cl^-及其化合物中的K电子层的对内相关能基本上是一常数,而且Cl的K,L层电子层内相关能和它们之间的层间相关能也变化很小.另外,所研究的MCl系列化合物中Cl价电子对相关能的贡献是跟MCl的离子性有关,即随着化合物离子性的增加而增加,但其相关能最大不大于Cl^-离子的,最小不小于Cl原子的.这些规律对人们考虑一些化合物的相关能,以至化学反应能量很有参考意义.     

密度泛函理论与Hartree-Fock方法混合处理中的稳态相关能校正

本文分析了通常的Hartree-Fock(HF)相关能定义和密度泛函理论(DFT)中的相关能定义的等价性条件。认为在参考电子密度与真实密度相差很大时两种定义是不等价的, 严格的DFT相关能比HF相关能(绝对值)要大。而在DFT与HF混合处理中得到的相关能比HF相关能(绝对值)要小, 两者之差相当于稳态相关能。实际计算表明, 通过合理地选择组态, 采用有限CI可以求得这一差值。本文描绘了双原子分子H2(X^1∑g^+), HF(X^1∑^+), N2(X^1∑g^+)的势能曲线, 结果比完全CISD和MP4的曲线还要好。H2的离解能是0.17a.u., 逼近实验值0.1747a.u..。     

Cl,Cl~-和MCl(M=H,Li,Na,K)对内对间相关能的规律性

通过对内对间相关能的计算,发现Ｃｌ,Ｃｌ－及其化合物中的Ｋ电子层的对内相关能基本上是一常数,而且Ｃｌ的Ｋ,Ｌ层电子层内相关能和它们之间的层间相关能也变化很小．另外,所研究的ＭＣｌ系列化合物中Ｃｌ价电子对相关能的贡献是跟ＭＣｌ的离子性有关,即随着化合物离子性的增加而增加,但其相关能最大不大于Ｃｌ离子的,最小不小于Ｃｌ原子的．这些规律对人们考虑一些化合物的相关能,以至化学反应能量很有参考意义．     

HF,Ne等电子体系对内对间电子相关能的比较研究

采用MELD程序ROHF－OPT1方法在MP2/6-311++G(d)水平上,计算了HF分子基态1^∑和Ne原子基态1^S的对内对间电子相关能,并对两等电子体系的对相关能进行了分析和比较,深入研究两等电子体系对内对间相关能所具有的共同规律和存在的差异性,通过比较说明分子内的化学键是影响电子相关能的重要因素之一。HF分子和Ne原子两体系三重激发和四重激发对体系电子相关能的贡献的计算结果表明高激发项对电子相关能的贡献在精确量子化学计算中是不可以忽略的。     

HF,Ne等电子体系对内对间电子相关能的比较研究

采用MELD程序ROHF－OPT1方法在MP2/6-311++G(d)水平上,计算了HF分子基态1^∑和Ne原子基态1^S的对内对间电子相关能,并对两等电子体系的对相关能进行了分析和比较,深入研究两等电子体系对内对间相关能所具有的共同规律和存在的差异性,通过比较说明分子内的化学键是影响电子相关能的重要因素之一。HF分子和Ne原子两体系三重激发和四重激发对体系电子相关能的贡献的计算结果表明高激发项对电子相关能的贡献在精确量子化学计算中是不可以忽略的。     

密度泛函理论和从头算方法对富勒烯分子静电势的比较研究

分别在Hartree-Fock和密度泛函B3LYP理论下,用6-31G*基组研究了C60和C70分子的静电势,比较了这方法计算得到上述分子静电势值的大小,静电势图形和静电势差值曲线,分析了富勒烯的电子相关效应.     

一维函数方法求解原子和分子薛定谔方程

对薛定谔方程的严格数值求解, 尤其是发展标准方法之外的、 包含新功能的解法, 一直是物理学研究的基本关注点. 本文介绍一种近些年发展的一维函数近似解方法, 该方法通过对波函数的不同坐标分量进行处理来求解原子和分子体系的薛定谔方程. 电子的试探波函数被离散化到实空间均匀格点上, 因此可以通过残差矢量校正的方法对其进行改进. 一维函数方法本身的特征决定其非常利于数值积分, 避免了很多由常规的多电子、 多中心势分子积分所带来的问题. 计算中, 最终能量是从严格的能量上限逐渐收敛所获得, 计算出的两电子薛定谔波函数呈现出常规单电子近似方法所含有的电子关联效应. 不同于密度泛函理论及Hartree-Fock的单电子解法, 本方法对电子-电子排斥能的多体效应的处理更加精确.     

移动窗口二维相关光谱技术

移动窗口二维相关光谱是一种新的二维相关分析方法,它将移动窗口的概念和二维相关分析方法有效地结合在了一起,利用移动窗口将庞大的光谱数据按矩阵分割成若干个便于操作的子矩阵,用二维相关光谱分别处理,将得到的结果综合分析,用以光谱变量和扰动变量为坐标的等高图表现出来,从中可以非常直观地观察出光谱强度在扰动变量方向上的变化,进而找出引起光谱强度突变的特征扰动点。本文主要介绍了移动窗口二维相关光谱的计算方法、基本特征、影响因素和实际应用,同时还详细介绍了以它为基础改进得到的扰动相关移动窗口二维相关光谱。扰动相关移动窗口二维相关光谱包括同步图和异步图,它不仅能很好地反映出引起光谱强度突变的特征扰动,还能详尽地描述出光谱强度在扰动过程中的变化情况。     

Bond alternation in infinite polyene: Peierls distortion reduced by electron correlation

The formation of the bond-alternating structure in polyene is investigated both within the one-particle (Hartree-Fock) picture and including electron correlation effects by perturbation theory. An off-diagonal charge-density wave of the equi-distant structure is identified at the Hartree-Fock level as precursor of the bond-alternate state which is found by subsequent lattice optimization. The valence-shell correlation energy is calculated by using second-order Møller-Plesset perturbation theory. It is found to be finite also in the metallic one-dimensional chain and a comparison with results obtained for the acetylene unit shows that this method recovers ~-70–75% of the total valence-shell correlation. Correlation effects are shown to reduce the Peierls distortion and the corresponding energy barrier but the bond alternation persists also if the results are extrapolated to the case of full correlation.     

Cohesive properties of CeN and LaN from first principles

The effect of electron-correlation on the ground-state properties of CeN and LaN is studied by ab initio quantum-chemical methods. The approach which is used combines two separate steps: (1) the ground-state Hartree-Fock calculations for the crystal; (2) application of the method of increments to the studied system, which allows an expansion of bulk properties using the information from quantum-chemical calculations performed for finite clusters. As can be expected, for CeN correlation plays a significant role: with Hartree-Fock method only 49% of the experimental cohesive energy has been recovered, whereas after correlation corrections (coupled-cluster approach) the ground-state properties were found to be in good agreement with the experimental data found in literature. Thus, we obtained about 90% of the expected cohesive energy; the computed lattice constants and bulk moduli also agree well with the experimental values. For comparison, the equivalent treatment has been performed for LaN, where no f orbital is occupied. There the HF contribution to the ground-state properties is larger and hence the correlation effects weaker.     

Solvent effects on the vibronic one-photon absorption profiles of dioxaborine heterocycles

The vibronic profiles of one-photon absorption spectra of dioxaborine heterocycles in gas phase and solution have been calculated at the Hartree-Fock and density-functional-theory levels. The polarizable continuum model has been applied to simulate the solvent effect, while the linear coupling model is used to compute the Franck-Condon and Herzberg-Teller contributions. It is found that a good agreement between theory and experiment can be achieved when the solvent effect and electron correlation are taken into account simultaneously. For the first excited charge-transfer state, the maximum of its Herzberg-Teller profile is blueshifted from that of the Franck-Condon profile. The shifted energy is found to be around 0.2 eV, which agrees well with the measured energy difference between two- and one-photon absorptions of the first excited state.     

Static dipole polarizability and binding energy of sodium clusters Nan (n=1-10): A critical assessment of all-electron based post Hartree-Fock and density functional methods

A systematic all electron post Hartree-Fock as well as density functional theory (DFT) based calculations for the polarizability and binding energy of sodium metal clusters have been performed and an in-depth analysis of the discrepancy between the experimental and theoretical results is presented. A systematic investigation for the assessment of different DFT exchange-correlation functionals in predicting the polarizability values has also been reported. All the pure DFT functionals have been found to considerably underestimate the calculated polarizability values as compared to the MP2 results. DFT calculations using the full Hartree-Fock exchange along with one-parameter progressive correlation functional have, however, been shown to yield results in good agreement with the MP2 and experimental results. The possible sources of error present in the experimental measurements as well as in the different theoretical methods have also been analyzed. One of the most important conclusions of the present study is that the effect of electron correlation plays a significant role in determining the polarizability of the clusters and the MP2 method can be considered to be one of the most reliable methods for their prediction. It has also been noted that the polarizability value of the lower member clusters (Na2 and Na4) calculated by highly sophisticated methods such as, CCSD and CCSD(T) are found to be very close to the corresponding MP2 values. The polarizability and the binding energy of the clusters are found to be inversely related to each other and their correlation is rationalized by invoking the minimum polarizability principle. A good linear correlation between the polarizability and volume of the cluster has also been found to exist.     

Hartree-Fock soft Coulomb hole to estimate correlation energies in atoms, molecules and polymers

We have shown that the empirical correction introduced into the Hartree-Fock method to calculate correlation energies for atoms and therefore to remove the error caused by the so-called Coulomb hole can be extended from atoms to molecules and polymers. A reformulation was required of the necessary parameter representation. The reparametrization has been performed staying as close as possible to the original expressions for atoms reported by Chakravorty and Clementi (S.J. Chakravorty and E. Clementi, Phys. Rev. A, 39 (1989) 2290). In addition to their work, where the correlation energy has been calculated with the self-consistent Hartree-Fock wavefunction and the correction integrals, we have performed investigations, including the perturbation operator in the Fock operator, so that the total energy also contains the correlation energy. The applications of this approach to atoms and molecules show that the total electron correlation energies and ionization potentials calculated as differences of total energies can be obtained very satisfactorily. On the basis of the reported calculations it turns out that one obtains better agreement with reference values of more sophisticated calculations when the correction integrals are used to build up the Fock matrix. Furthermore we have found that the magnitude of the correlation energy depends only weakly on the size of the basis sets, which makes this empirical method very attractive for its application to large molecular and polymeric systems.     

Towards benchmark second-order correlation energies for large atoms: Zn2+ revisited

To provide very accurate reference results for the second-order M?ller-Plesset (MP2) energy and its various components for Zn(2+), which plays for 3d-electron systems a similar role as Ne for smaller atoms and molecules, we have performed extensive calculation by two completely different implementations of the MP2 method: the finite element method (FEM) and the variation-perturbation (VP) method. The FEM and VP calculations yield partial wave contributions up to l(max)=45 and 12, respectively. Detailed comparison of all FEM and VP energy components for l(max)=12 has disclosed an extraordinary similarity, which justifies using the present results as benchmarks. The present correlation energies are compared with other works. The dependability of an earlier version of FEM, already applied to very large closed-shell atoms, is confirmed. It has been found that for larger atoms the accuracy of the analytical Hartree-Fock results has an impact on the accuracy of the MP2 energies greater than for smaller atoms. Fields of applications of the present results in studies of various electron correlation effects in 3d-electron atoms and molecules are indicated.     

A family of intracules, a conjecture and the electron correlation problem

We present a radical approach to the calculation of electron correlation energies. Unlike conventional methods based on Hartree-Fock or density functional theory, it is based on the two-electron phase-space information in the Omega intracule, a three-dimensional function derived from the Wigner distribution. Our formula for the correlation energy is isomorphic to the Hartree-Fock energy expression but requires a new type of four-index integral. Preliminary results, obtained using a model that is based on the known correlation energies of small atoms, are encouraging.     

A finite B-spline basis set for accurate diatomic molecule calculations

A finite basis set particularly adapted for solving the Hartree-Fock equation for diatomic molecules in prolate spheroidal coordinates has been constructed. These basis functions have been devised as products of B-splines times associated Legendre polynomials. Due to the large number of B-splines, the resulting set of eigenfunctions is amply distributed over excited states. This gives the possibility of using these basis sets to calculate sums over excited states, appearing in various orders of perturbation theory. As an illustration, the second-order corrections to the ground-state energy of some atoms and diatomic molecules with closed electron shells have been calculated.     

Exchange energy gradients with respect to atomic positions and cell parameters within the Hartree-Fock Gamma-point approximation

Recently, linear scaling construction of the periodic exact Hartree-Fock exchange matrix within the Gamma-point approximation has been introduced [J. Chem. Phys. 122, 124105 (2005)]. In this article, a formalism for evaluation of analytical Hartree-Fock exchange energy gradients with respect to atomic positions and cell parameters at the Gamma-point approximation is presented. While the evaluation of exchange gradients with respect to atomic positions is similar to those in the gas phase limit, the gradients with respect to cell parameters involve the accumulation of atomic gradients multiplied by appropriate factors and a modified electron repulsion integral (ERI). This latter integral arises from use of the minimum image convention in the definition of the Gamma-point Hartree-Fock approximation. We demonstrate how this new ERI can be computed with the help of a modified vertical recurrence relation in the frame of the Obara-Saika and Head-Gordon-Pople algorithm. As an illustration, the analytical gradients have been used in conjunction with the QUICCA algorithm [K. Nemeth and M. Challacombe, J. Chem. Phys. 121, 2877 (2004)] to optimize periodic systems at the Hartree-Fock level of theory.