分子轨道图形理论的新进展

1977年,本刊发表了分子轨道图形理论一文,用切割图的边及除去图片断的观点,统一地讨论简单分子轨道理论(HMO)中能级与波函数的计算。十多年来,化学图论迅速发展,不局限于HMO传统模式,从微观上讨论分子行     

分子轨道图形理论中对称面定理的扩展

对唐敖庆教授和江元生教授建立的对称面定理做了一定的扩展，引进了原子轨道对称性的概念，扩展后的对称面定理可以应用于包含过渡金属和非相邻相互作用等较为复杂的体系中     

键能的分子轨道理论研究 1: 理论公式

从LCAO-MO出发, 给出了一个计算键能的近似方法, 即EAB(i)-∑∑CaiSabCbiεi为第i个占据分子轨道(MO)中的一对电子对A-B键键能的贡献。对所有分子轨道求和即为该键的键能: EAB=∑EAB(i)。按该方法, 不仅可以计算各种不同分子中每两个相键连原子间的键能, 还可以从MO及AO角度分析每一具体键, 如σ, π, δ键的键能以及各AO对键能的贡献。该方法虽有别于求键焓和平衡离解能De, 但计算结果和De的实验值甚相符合。通过对键能的分析研究, 能较好地揭示原子间的相互作用关系及化学键的强弱, 从而可进一步探讨化学反应活性, 反应速率等化学性质。     

含重复单元共轭分子本征方程的约化定理

在唐敖庆教授和江元生教授等人建立的分子轨道图形理论的基础上提出和发展了弯键思想 ,并相继利用对称面和对称轴投影算符 ,得到了含重复单元链状共轭分子本征方程的约化定理 .该定理形式直观 ,而且只要反复应用弯链思想 ,可以推广应用于二维和三维含重复单元共轭分子体系 ,但为了保证精确度 ,应使镜面只包含 1个原子[1～ 5] .1　基本思想虽然链状共轭分子不具有Ｃｎ 轴 ,也不构成平移群 ,不能直接利用对称轴或平移群投影算符来得到其本征方程的约化定理 ,但可以将链状共轭分子弯成半圆形 ,使之通过一个位于半圆处的镜面的反映来得到另一个…     

键能的分子轨道理论研究 1: 理论公式

从LCAO-MO出发, 给出了一个计算键能的近似方法, 即EAB(i)-∑∑CaiSabCbiεi为第i个占据分子轨道(MO)中的一对电子对A-B键键能的贡献。对所有分子轨道求和即为该键的键能: EAB=∑EAB(i)。按该方法, 不仅可以计算各种不同分子中每两个相键连原子间的键能, 还可以从MO及AO角度分析每一具体键, 如σ, π, δ键的键能以及各AO对键能的贡献。该方法虽有别于求键焓和平衡离解能De, 但计算结果和De的实验值甚相符合。通过对键能的分析研究, 能较好地揭示原子间的相互作用关系及化学键的强弱, 从而可进一步探讨化学反应活性, 反应速率等化学性质。     

分子轨道理论奠基人之一:约翰·爱德华·兰纳-琼斯

约翰·爱德华·兰纳-琼斯(1894—1954)是英国杰出的理论化学家。兰纳-琼斯因其在分子结构、原子价和分子间力等方面的研究而闻名,其中最重要的是提出了表达中性原子或分子之间的相互作用的一个简单的数学模型,这个模型被称为兰纳-琼斯势函数(也称L-J势函数或6～12势函数);他是第一个以目前普遍使用的方式使用原子轨道的线性组合来定量描述分子轨道(LCAO MO理论)的人,被称为分子轨道理论的奠基人之一。本文介绍了约翰·爱德华·兰纳-琼斯的生平,并对兰纳-琼斯提出兰纳-琼斯势函数和建立分子轨道的原子轨道线性组合法的过程进行了详细论述。     

分子轨道图形理论的应用——求a_k的断键公式

本文应用分子轨道图形理论公式,推导出求HMO本征多项式系数a_k的图形公式。应用该公式,求出了常见同系列共轭分子a_k的封闭公式。     

π电子自洽场分子轨道理论及其应用

本文对π电子自洽场分子轨道理论 (PPP)方法及其应用进行了评述。表明PPP半经验分子轨道方法在研究有机共轭大分子光物理性质和预示新型材料方面起着积极重要的作用。     

分子轨道图形理论的应用（Ⅲ）—估算Eπ的断键法

分子轨道图形理论的应用（Ⅲ）──估算Ｅ_π的断键法赵洪刚，杨开海，王长生，张继才，曹阳（辽宁师范大学化学系，大连，１１６０２２）（苏州大学化学系，苏州）关键词π电子总能量，矩，分子拓扑在分子轨道图形理论中，对一般的应用，π电子总能量Ｅπ的近似表达式就?..     

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     

Implementation of molecular symmetry in valence bond calculation

A novel strategy for the construction of many-electron symmetry-adapted wave function is proposed for ab initio valence bond (VB) calculations and is implemented for valence bond self-consistent filed (VBSCF) and breathing orbital valence bond (BOVB) methods with various orbital optimization algorithms. Symmetry-adapted VB functions are constructed by the projection operator of symmetry group. The many-electron symmetry-adapted wave function is expressed in terms of symmetry-adapted VB functions, and thus the VB calculations can be performed with the molecular symmetry restriction. Test results show that molecular symmetry reduces the computational cost of both the iteration numbers and CPU time. Furthermore, excited states with specific symmetry can be conveniently obtained in VB calculations by using symmetry-adapted VB functions.     

Use of unsymmetrical one-range addition theorems of Slater type orbitals in molecular electronic structure determination

In this work, the applicability of the unsymmetrical one-range addition theorems obtained from the use of complete orthonormal sets of Ψ^α-exponential type orbitals (Ψ^α-ETOs, where α = 1, 0, − 1, − 2, ...) to the study of electronic structure of molecules is demonstrated using minimal basis sets of Slater type orbitals (STOs). As an example of application of unsymmetrical one-range addition expansion method to evaluate the multicenter electronic integrals, the calculation has been performed for the ground state of BH ₃ molecule. The results of computer calculations for the orbital and total energies, and linear combination coefficients of symmetrized molecular orbitals are presented.     

Generation of the eigenvectors of the topological matrix from graph theory

The technique of describing the characteristic polynomial of a graph is here extended to construction of the eigenvectors. Recurrence relations and path tracing are combined to generate eigenvector coefficients as polynomial functions of the eigenvalues. The polynomials are expressed as linear functions of Chebyshev polynomials in order to simplify the computational effort. Particular applications to the Hückel MO theory, including heteroatom effects, are shown.     

Classification of polymer structures by graph theory

Compact polymers such as proteins obtain their unique conformation by appropriate nonbonded interactions among their monomer residues. Innumerable nonnative compact conformations are also possible, and it is essential to distinguish the native from the nonnative conformations. Toward this goal we have used graph‐theoretic methods to classify polymer structures formed by noncovalent interactions. All compact structures on a 4×4 two‐dimensional lattice and a few conformations on 3×3×3 cubic lattice have been investigated. The 69 compact conformations in 4×4 two‐dimensional lattice are classified into 12 groups based on the highest eigenvalue and eigenvector. The complex graphs obtained for polymers in a 3×3×3 lattice space are analyzed. Their eigenvalues and eigenvector components are correlated with the branching structure and the center of the graph. The method has application in classifying real polymers such as proteins into their substructures, cluster, and domains. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 349–356, 1999     

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     

Exploiting space‐group symmetry in fragment‐based molecular crystal calculations

Recent developments in fragment‐based methods make it increasingly feasible to use high‐level ab initio electronic structure techniques to molecular crystals. Such studies remain computationally demanding, however. Here, we describe a straightforward algorithm for exploiting space‐group symmetry in fragment‐based methods which often provides computational speed‐ups of several fold or more. This algorithm does not require a priori specification of the space group or symmetry operators. Rather, the symmetrically equivalent fragments are identified automatically by aligning the individual fragments along their principle axes of inertia and testing for equivalence with other fragments. The symmetry operators relating equivalent fragments can then be worked out easily. Implementation of this algorithm for computing energies, nuclear gradients with respect to both atomic coordinates and lattice parameters, and the nuclear hessian is described. © 2014 Wiley Periodicals, Inc.     

The delocalisation energy of benzene and the non-empirical MO theory

Algebraic expressions for the vertical Delocalisation Energy (DE) of benzene are derived from non-empirical MO theory. For comparison with early work in the π-electron approximation, and ultimately with Hückel theory, the results are formulated in terms of a core resonance integral,β, and π-electronic repulsion integrals. All integral values are inferred from the results ofab initio SCF calculations. Two expressions are derived, which refer to two ways of forming the localised π MOs: one where three pairs of adjacent atomic orbitals are selected from a set of six orthogonalised orbitals; and another where a non-orthogonal set of atomic orbitals is used. The first expression is formally similar to an expression originally derived by Pople from a different point of view and with many approximations. This expression gives too large a magnitude for DE when used with anab initio value ofβ. The second expression gives a result much closer to an empirical value of DE and shows that the main reason for DE being about 50% of 2β rather than 2β is the stabilising effect of overlap in the localised structure, and that the less important factor is the inclusion of electronic repulsion.     

Applications of fourier transforms in molecular orbital theory. Calculation of optical properties and tables of two-center one-electron integrals

Fourier transform methods initiated by Geller and Harris are applied to the calculation of optical properties of molecules. Tables of one-electron two-center integrals needed for the accurate computation of molecular absorption and optical activity are calculated by the Fourier transform method. A general theorem is derived which allows the angular part of the integrals to be treated by means of projection operators. The radial parts of the integrals are treated by the methods of Harris. The results are obtained in a simple closed form which avoids the usual transformation to local coordinates. The two-center integrals evaluated include matrix elements of the momentum operator, the dipole moment operator, the tensor operator , the quadrupole moment operator, and the angular momentum operator. These are evaluated between 1s, 2s, and 2p Slater-type atomic orbitals located on different atoms. The results are expressed as functions of the Slater exponents and of the relative coordinates of the two atoms.