π和σ体系彻底分离的高度定域的键轨道基组的建立

高度定域的、对称的、键轨道基组的建立是一个多步的计算程序：(1)以定域片断轨道[φk,φi,φj]为基,对分子作有条件的RHF运算,算得FUL和DSI°态的片断分子轨道[Φ°l',Φ°n,Φ°m]和[Φl,Φn,Φm]。在基组[φk,φi,φj]中,φi∈双占据和空σ片断分子轨道(FMOs)组,φj∈πFMO组,φk∈单占据σFMO组,它们都精确地定域在各自的片断内;(2)利用Φ°l'与Φ°l间的重叠积分值(Sl'l>0.5),可以从DSI°态中,自动地选出Ns个对称的、由单占据轨道线性组合而成的分子轨道Φ°l'=Σakl'φk(k=1,2,…,Ns),接着,用Φ°l'取代FUL态中同类的、非对称轨道组Φl=Σaklφk(k=1,2,…,Ns);(3)以上述新的轨道组[Φ°l',Φn,Φm]为基(其中,Φ°l'∈DSI°态,它们离域于整个分子;双占据及空σFMO组Φm和πFMO组Φm属于FUL态),按FUL态的条件,再次对分子作有条件的RHF运算,从中得到一组对称的、闭壳层正则FMOs,而且每一个FMO均有正确的电子占据数;(4)利用Perkin原理,将第3步所得的正则FMO组定域成一个对称的键轨道基组[Φl',Φn',Φm']。在这个基组中,π体系Φm'与σ构架Φn'是彻底分离的,而且这两个轨道组始终精确地定域在各自的片断内。     

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     

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.     

用微扰分子轨道法研究饱和有机化合物的成环反应

在饱和有机化合物的成环反应中,五员环和六员环最易形成,这一事实通常是用环的张力和空间因素来解释的。但有些实验结果表明,五员环比六员环容易生成,三员环比四员环容易生成。这些事实用张力和空间因素都不能圆满解释。我们采用微扰分子轨道(PMO)法来计算成环反应中体系能量的变化。所得的计算结果可以较好地说明上述实验事实。     

多面体碳烷的分子轨道方法研究

利用INDO自洽场方法和Edmiston-Ruedenberg定域化方法,计算了多面体碳烷C_2nH_2n(n=2,3,4,5和10)及其骨架C_2n,讨论了它们的电子结构、稳定性和化学键性质。     

邻近C-H键对中心金属原子的配位作用—[Fe(PH3)3(C8H13)]+的定域分子轨道研究

采用INDO方法计算了{Fe[P(OMe)_3]_3(C_8H_(13))}~+的简化离子[Fe(PH_3)_3(C_8H_(13))]~+,将正则分子轨道用Edmiston-Ruedenberg定域化方法变换为定域分子轨道,结果表明:在对应C_1-H_(1A)键的定域分子轨道中,明显包含有铁原子轨道成分(7.8％),Fe-H_(1A)和Fe—C_1键级分别为0.190和0.302。指出C_1-H_(1A)键是以一对成键σ电子配位到铁原子上的。C_8H_(13)环以包含三个碳原子的η~4—共轭体系与铁原子相互作用。铁以二价(d~6-Fe(Ⅱ)的形式存在于该离子中。C_1-H_(1A)键的配位满足了文献[15]提出的Fe(Ⅱ)的共价12价。     

Hickel分子轨道计算的割键法则及其应用

Tang Ao-qing et al. have put forward graph theory method for determining the Huckel molecular orbits and the calculation of energy levels for conjugated molecules. Based on the work of the forerunners, the bond-break rule for determining the molecular orbits is presented in this paper. The general concept of the bond ratio is first introduced. The calculation of orbital coefficients and of energy levels are transformed into a calculation of bond ratio and of energy levels. Following the rules governing bond-breaking established in this paper to break some bonds in the structural diagram of molecules and at the same time modify the Coulomb's integration of atoms, it becomes possible to use a group of mutually independent sub-diagrams to replace the complicated structural diagram of molecules. The secular determinants of each sub-diagram must all equal zero. Thereby series of equations (called series of equations of bond ratio) can be established with the energy level and the bond ratio as the unkowns. When this is solved, the energy level and bond ratio are obtained. Because of the simplicity of the construction of the sub-diagrams, the calculation is greatly simplified when this method is used. Futhermore, this method can be widely applied to all kinds of complicated conjugated molecules. In this paper the authors have gone through some calculations for molecules with heteropoly-radicals.     

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.     

π-σ轨道作用能分解法和限制π轨道作用的几何优化*

简要地介绍能量分解法的发展历史,强调能量分解的特点是给量子化学的计算提供明确的化学意义,介绍本实验室建立的能量分解法和限制轨道作用的几何优化法。 在这两个方法的基础上,论证了π-电子离域是失稳定的;颠倒了经典有机结构理论中基本的因果关系——共轭效应和构象之间的因果关系;为芳香能的计算提供了一个新的模型和新的方法,表明芳香能的计算不再需要参考分子;定量地区别静电作用和电子离域在化学键形成中的作用;定量地讨论取代基效应和张力芳环的扭曲驱动力。     

A comparison of quantum chemical models for calculating NMR shielding parameters in peptides: mixed basis set and ONIOM methods combined with a complete basis set extrapolation

This article compares several quantum mechanical approaches to the computation of chemical shielding tensors in peptide fragments. First, we describe the effects of basis set quality up to the complete basis set (CBS) limit and level of theory (HF, MP2, and DFT) for four different atoms in trans N-methylacetamide. For both isotropic shielding and shielding anisotropy, the MP2 results in the CBS limit show the best agreement with experiment. The HF values show quite a different tendency to MP2, and even in the CBS limit they are far from experiment for not only the isotropic shielding of carbonyl carbon but also most shielding anisotropies. In most cases, the DFT values differ systematically from MP2, and small basis-set (double- or triple-zeta) results are often fortuitously in better agreement with the experiment than the CBS ones. Second, we compare the mixed basis set and ONIOM methods, combined with CBS extrapolation, for chemical shielding calculations at a DFT level using various model peptides. From the results, it is shown that the mixed basis set method provides better results than ONIOM, compared to CBS calculations using the nonpartitioned full systems. The information studied here will be useful in guiding the selection of proper quantum chemical models, which are in a tradeoff between accuracy and cost, for shielding studies of peptides and proteins.     

Effects of different basis sets and donor‐acceptor groups on linear and second‐order nonlinear optical properties and molecular frontier orbital energies

The calculation of molecular hyperpolarizability, molecular frontier orbital energies of some donor‐acceptor oxadiazoles ( 5a – f , 8a – f , and 9a – f ) have been investigated using ab initio methods and different basis sets. Ab initio optimizations were performed at the Hartree–Fock (HF) and density functional (Beckee‐3–Lee–Yang–Parr; B3LYP) levels of theory with 6‐31G basis set. The polarizability (<α>), anisotropy of polarizability (Δα), and ground‐state dipole moment (μ), first hyperpolarizability (β), and molecular frontier orbital (HOMO, highest occupied molecular orbital and LUMO, lowest unoccupied molecular orbital) energies of 5a – f , 8a – f , and 9a – f have been calculated at the HF and B3LYP methods with 6‐31G, 6‐31G(d), 6‐31+G(d), 6‐31++G(d,p), 6‐311G, 6‐311G(d), 6‐311+G(d), and 6‐311++G(d,p) basis sets. Also, the molecular hardness (η) and electronegativity (χ) parameters have been obtained using molecular frontier orbital energies. The <α>, Δα, μ, β, HOMO, LUMO energies, η and χ parameters have been investigated as dependence on the choice of method and basis set. The variation graphics of <α>, Δα, μ, β, η, and χ parameters using HF and B3LYP methods with different basis sets are presented. We have examined the frontier molecular orbital pictures of 5a – f , 8a – f , and 9a – f using B3LYP/6‐31++G(d,p) level. The 5a – f , 8a – f , and 9a – f display significant linear, second‐order molecular nonlinearity, and molecular parameters and provide the basis for future design of efficient nonlinear optical materials having the 1,3,4‐oxadiazole core. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011