关于构造合理非正交定域轨道问题的研究

与正交定域轨道相比, 非正交定域轨道更符合经典化学图像、更加紧缩从而更具有可移植性和更符合电子相关能计算和线性标度计算的要求. 非正交定域轨道应该尽可能紧缩而形状及空间分布又与传统化学图像一致. 研究结果表明, 非正交定域轨道组的延伸度是它的正交程度的单调下降函数, 随其正交程度的降低可以缩减到任意程度, 但在超过一定限度以后, 轨道的形状和空间分布不再符合传统化学图像, 最后趋向线性相关. 在没有正交条件约束下, 必须加上另外的限制条件, 优化轨道延伸度泛函才能获得合理的非正交定域轨道. 提出了一种在最小化轨道延伸度泛函的同时最大化轨道重心间距离的方法, 可以得到基本上符合要求的非正交定域轨道.     

定域分子轨道中的σ—π分离

对含重键的分子体系,分子轨道定域化会涉及到两种完全不同的重键描述,即等价的重键或“香蕉”键和不等价的σ和π键,文献曾利用杂化轨道法对此进行过讨论。对于定域分子轨道,具体得出哪种描述取决于所采用的定域准则及计算中采用的近似方法。对于从头算法的定域化研究,Boys定域准则强烈地趋向于等价重键描述;Ruedenberg定域准则只是对未共轭的重键体系有较强的等价重键描述倾向,对共轭的重键体系,这种倾向性明显减     

自然定域轨道方法研究

本文报导我们按自然定域轨道原理编制的NLMO程序以及对自然定域轨道计算方法的一些改进。用NLMO程序计算出七个具有不同成键特性分子(包括是否含有孤对或π键,是否含有多中心键等不同情况)的自然定域轨道,结果与用其它定域化方法得出的基本一致。由于自然定域轨道方法基本上具有内禀定域性质,而计算量明显小于其它定域化方法,可以认为它是有效和方便的。     

最佳定域分子轨道的新算法

本文提出了最佳群对称定域分子轨道（ＯＳＬＭＯＳ）的概念，报道了ＯＳＬＭＯｓ的生成方法。ＯＳＬＭＯｓ满足分子对称、等价与正交；同时最佳逅近经典的非正交价键型轨道，并可作为ＭＣＳＣＦ与ＣＩ方法中的单电子轨道。     

EHMO方法的分子轨道定域化

用Foster-Boys的定域化准则讨论了EHMO方法的分子轨道定域化问题,提出用双中心重叠积分近似计算双中心轨道偶极矩积分方法,得到的EHMO定域分子轨道与严格定域化结果接近,与从头计算方法的定域化结果定性一致。     

单占据片断轨道的组合式(Kost+Perkin)定域化

为了使开壳层片断轨道具有正确的集居数,正则轨道必须定域化.但是,在确保目标轨道Φ_sdan单占据性的同时,Kost定域化也破坏了Φ_s特定的对称性.实际计算表明,Perkin定域化可以弥补Kost程序的缺陷,将单占据的Φ_s转化成高度定域的、对称的片断轨道.在片断分子中,C-H_R键长r的选择和Kost定域化的方式对Perkin定域化的成败具有重大的影响.当Gaussian基组为STO-3G3-21G和4-31G时,r应为0.1nm;但在6-31G水平下,必须r=0.09nm.     

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。     

偶极积分与Boys法分子轨道定域化

定域分子轨道在分子体系的化学图象和物理图象之间充当重要的桥梁作用,它的产生依赖于定域化准则,其中最普遍使用的是Foster-Boys和Edmiston-Ruedenberg(E—R)提出的两种定域化准则。这两种定域化准则是等价的,因而结果也是一致的。但对于E—R定域化来说,由于涉及到大量的多中心积分的计算,计算极为费时,因而远不如Foster-Boys定     

C_4O_4~(m-)(m=0,1,2,3,4)的从头算研究——2.化学键、电离势和振动频率

在第1报优化的几何构型的基础上,用Boys定域化方法和QSU90程序计算了C_4O_4~(m-)(m=0,l,2,3,4)的定域化分子轨道,讨论了其成键特征和电离势.在6-31G水平用ad initio解析方法计算它们的谐振动频率.     

定域片断轨道基组的对称化

片断的UHF运算不能保证每个片断轨道具有确切的电子占据数,故Kost定域化是必需的.当片断产生于多键断裂时,在确保目标轨道单占据性的同时,Kost定域破坏了轨道基组的对称性.为此,在Kost定域化后,必须对单占据轨道作2×2对称化旋转后,再作有条件的RHF运算.以乙烯基片断CHCH(波二烯分子中的一个片断)为例,详述了对称化的方法、原理和计算程序.以C-H片断为例,细述三单键片断轨道基组对称化的特殊性.介绍C-HR参考键长选择的判据,探讨键长与选择Gaussian基组大小的关系.     

Study on the construction of satisfactory nonorthogonal localized molecular orbitals

Comparing to orthogonal localized molecular orbitals (OLMO), the nonorthogonal localized molecular orbitals (NOLMO) exhibit bonding pictures more accordant with those in the traditional chemistry. They are more contracted, so that they have a better transferability and better performances for the calculation of election correlation energies and for the linear scaling algorithms of large systems. The satisfactory NOLMOs should be as contracted as possible while their shapes and spatial distribution keep in accordance with the traditional chemical bonding picture. It is found that the spread of NOLMOs is a monotonic decreasing function of their orthogonality, and it may reduce to any extent as the orthogonality descends. However, when the orthogonality descends to some point, the shapes and spatial distribution of the NOLMOs deviate drastically from the traditional chemical bonding picture, and finally the NOLMOs tend to linear dependence. Without the requirement of orthogonalization, some other constrain     

An efficient method for constructing nonorthogonal localized molecular orbitals

A new method for constructing nonorthogonal localized molecular orbitals (NOLMOs) is presented. The set of highly localized NOLMOs is obtained by minimization of the spread functional starting from an initial set of canonical orthogonal molecular orbitals. To enhance the stability and efficiency, the centroids of the NOLMOs are constrained to be those of the corresponding orthogonal localized molecular orbitals (OLMOs), which are obtained with the Boys criterion in advance. In particular, these centroid constraints make the optimization for each NOLMO independent of the others, which is an attractive feature for application to large systems. The minimization with the constraints incorporated through the multiplier-penalty function method is stable and efficient in convergence. While exhibiting the classical bonding pattern in chemistry and sharing a spatial distribution similar to that of the corresponding OLMOs, the obtained NOLMOs are more compact than the corresponding OLMOs with about 10%-28% reduction in the value of the spread functional and devoid of the troublesome "orthogonalization tails."     

Extremely localized molecular orbitals (ELMO): a non-orthogonal Hartree-Fock method

A new optimization method for extremely localized molecular orbitals (ELMO) is derived in a non-orthogonal formalism. The method is based on a quasi Newton-Raphson algorithm in which an approximate diagonal-blocked Hessian matrix is calculated through the Fock matrix. The Hessian matrix inverse is updated at each iteration by a variable metric updating procedure to account for the intrinsically small coupling between the orbitals. The updated orbitals are obtained with approximately n ² operations. No n ³ processes such as matrix diagonalization, matrix multiplication or orbital orthogonalization are employed. The use of localized orbitals allows for the creation of high-quality initial “guess” orbitals from optimized molecular orbitals of small systems and thus reduces the number of iterations to converge. The delocalization effects are included by a Jacobi correction (JC) which allows the accurate calculation of the total energy with a limited number of operations. This extension, referred to as ELMO(JC), is a variational method that reproduces the Hartree-Fock (HF) energy with an error of less than 2 kcal/mol for a reduced total cost compared to standard HF methods. The small number of variables, even for a very large system, and the limited number of operations potentially makes ELMO a method of choice to study large systems. Received: 30 December 1996 / Accepted: 5 June 1997     

Localized orbitals for optimal decomposition of molecular properties

We present the procedure for transforming delocalized molecular orbitals into the localized property-optimized orbitals (LPOs) designed for building the most accurate, in the Frobenius norm sense, approximation to the first-order reduced density matrix in form of the sum of localized monoatomic and diatomic terms. In this way, a decomposition of molecular properties into contributions associated with individual atoms and the pairs of atoms is obtained with the a priori known upper bound for the decomposition accuracy. Additional algorithm is proposed for obtaining the set of “the Chemist's LPOs” (CLPOs) containing a single localized orbital, with nearly double occupancy, per a pair of electrons. CLPOs form an idealized Lewis structure optimized for the closest possible reproduction of one-electron properties derived from the original many-electron wavefunction. The computational algorithms for constructing LPOs and CLPOs from a general wavefunction are presented and their implementation within the open-source freeware program JANPA ( http://janpa.sourceforge.net /) is discussed. The performance of the proposed procedures is assessed using the test set of density matrices of 33 432 small molecules obtained at both Hartree-Fock and second-order Moller-Plesset theory levels and excellent agreement with the chemist's Lewis-structure picture is found.     

Localized orbitals based on the fermi hole

The Fermi hole provides a direct (non-iterative) method for tansforming canonical SCF molecular orbitals into localized orbitals. Except for simple overlap integrals required to maintain orthogonality, this method requires no integrals over orbitals or basis functions. This method is demonstrated by application to a furanone (C₄H₄O₂), methylacetylene, and boron trifluoride. The results of these calculations are compared to those determined by the orbital centroid criterion of localization.     

Determination of extremely localized molecular orbitals in the framework of density functional theory

Extremely localized molecular orbitals are rigorously localized on only a preselected set of atoms and do not have any tails outside the localization region. The importance of these orbitals lies in their ability to be transferred from one molecule to another one. A new algorithm to determine extremely localized molecular orbitals in the framework of the density functional theory method is presented. This could also be a valuable tool in the quantum mechanics/molecular mechanics methodology where localized molecular orbitals are used to describe covalent bonds across the frontier region. The present approach is used to build up the electron density of thymopentin, a polypeptide constituted by five residues, starting from extremely localized molecular orbitals determined on a set of model molecules. The results obtained confirm good transferability properties for these orbitals.Proceedings of the 11th International Congress of Quantum Chemistry satellite meeting in honor of Jean-Louis Rivail     

On the suitability of strictly localized orbitals for hybrid QM/MM calculations

In the QM/MM method we have developed (LSCF/MM), the QM and the MM parts are held together by means of strictly localized bonding orbitals (SLBOs). Generally these SLBOs are derived from localized bond orbitals (LBOs) that undergo tails deletion, resulting in a nonpredictable change of their properties. An alternative set of SLBOs is provided by the extremely localized molecular orbitals (ELMOs) approach, where the orbitals are rigorously localized on some prefixed atoms without tails on the other atoms of the molecule. A comparative study of SLBOs arising from various localization schemes and ELMOs is presented to test the reliability and the transferability of these functions within the Local Self-Consistent Field (LSCF) framework. Two types of chemical bonds were considered: C--C and C--O single bonds. The localized functions are obtained on the ethane and the methanol molecules, and are tested on beta-alanine and diethyl ether molecules. Moreover, the various protonation forms of beta-alanine have been investigated to illustrate how well the polarity variation of the chemical bond can be handled throughout a chemical process. At last, rotation energy profiles around C--C and C--O bonds are reproduced for butane and fluoromethanol. Energetic, geometric, as well as electronic factors all indicate that ELMO functions are much more transferable from one molecule to another, leading to results closer to the usual SCF reference than any other calculations involving any other localized orbitals. When the shape of the orbital is the most important factor then ELMO functions will perform as well as any other localized orbital.     

Optimal virtual orbitals to relax wave functions built up with transferred extremely localized molecular orbitals

Extremely localized molecular orbitals (ELMOs), namely orbitals strictly localized on molecular fragments, are easily transferable from one molecule to another one. Hence, they provide a natural way to set up the electronic structure of large molecules using a data base of orbitals obtained from model molecules. However, this procedure obviously increases the energy with respect to a traditional MO calculation. To gain accuracy, it is important to introduce a partial electron delocalization. This can be carried out by defining proper optimal virtual orbitals that supply an efficient set for nonorthogonal configurations to be employed in VB-like expansions.     

Quadratically convergent calculation of localized molecular orbitals

Two iterative procedures for the transformation of canonical self-consistent field molecular orbitals to intrinsic localized molecular orbitals are proposed. A first-order method based on a series of (n × n) unitary transformations may be applied to orbitals which are far from convergence. The second method, based on Newton's method, yields quadratic convergence. Numerical results based on Boys' criterion are presented for water, carbon monoxide, boron fluoride, nitric oxide, and methylacetylene. A composite method may be used to obtain rapid convergence for large molecules for which it is not practical to calculate the entire hessian matrix. The performance of the composite method is demonstrated by application to the dinitrogen tetroxide molecule. Highly converged localized molecular orbitals may be obtained for most molecules with five to eight first-order iterations followed by three or four iterations based on either the second-order or composite method.