定域分子轨道对称性

提出了利用定域分子轨道重心确定分子轨道的对称性。确定了线型的、非线型的、环状的分子定域分子轨道对称性。结果表明非线型分子和其中双中心键具有相同对称性,但含孤对或三中心键的分子则存在一些差别。还讨论了定域分子轨道的特征。     

Quantifying the symmetry content of the electronic structure of molecules: molecular orbitals and the wave function

A scheme to quantify the symmetry content of the electronic wave function and molecular orbitals for arbitrary molecules is developed within the formalism of Continuous Symmetry Measures (CSMs). After defining the symmetry operation expectation values (SOEVs) as the key quantity to gauge the symmetry content of molecular wavefunctions, we present the working equations to be implemented in order to carry out real calculations using standard quantum chemistry software. The potentialities of a symmetry analysis using this new method are shown by means of some illustrative examples such as the changes induced in the molecular orbitals of a diatomic molecule by an electronegativity perturbation, the breaking of orbital symmetry along the dissociation path of the H(2) molecule, the changes in the molecular orbitals upon a geometrical distortion of the benzene molecule, and the inversion symmetry content in the different spin states of the [Fe(CH(3))(4)](2-) complex.     

Symmetry measures of the electron density

In this communication we define electronic symmetry operation and symmetry group measures, eSOM and eSGM, respectively, develop the basic algorithms to obtain them, and give some examples of the possible applications of these new computational tools. These new symmetry measures based on the electron density have been tested in an analysis of (a) the inversion symmetry for heteronuclear diatomic molecules, for the eclipsed and staggered conformations of ethane and tetrafluoroethane, and for a series of octahedral sulfur halides; (b) the reflection symmetry of three different conformers of tetrafluoroethene; and (c) the loss of C₆ symmetry along the B_2u distortion mode of benzene and an analysis of rotational symmetry for different six‐member ring heterocycles. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Symmetry in the design of NMR multiple-pulse sequences

The symmetry principles of NMR pulse-sequence design are summarized. The discussion is guided by an analogy with tiling schemes in the decorative arts. The symmetry operations for NMR pulse sequences are discussed in terms of excitation field modifiers and temporal modifiers. The quantum operators which describe the effect of these modifiers on the excitation field spin Hamiltonian are provided. The symmetry transformations of spin propagators, and the different types of pulse-sequence elements are discussed. The common types of symmetry expansion are treated using the propagator transformations and the Euler angles for the excitation field propagators. The selection rules associated with symmetrical pulse sequences are discussed using average Hamiltonian theory.     

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     

The consequences of neglecting permutation symmetry in the description of many-electrons systems

The consequences of neglecting the permutation symmetry of the Hamiltonian of many-electrons system are examined. From the comparison of wave functions based on methods, which take (generalized valence bond [GVB]) and do not take (Hartree-Fock) the permutation symmetry into account, it is shown that neglecting the permutation symmetry leads to false concepts, misinterpretations, and unjustifiable approximations when dealing with many-electrons systems, atoms, and molecules. In particular, it is shown that how the double occupancy of atomic and molecular orbitals, the exchange integral, the correlation energy, and the so-called “nondynamic” correlation energy are related to neglecting the permutation symmetry.     

New developments in the symmetry-adapted algorithm of the Polarizable Continuum Model

We present recent developments in the symmetry implementation of the Polarizable Continuum Model (PCM). The structure of the matrix, which defines the PCM solvent response, is examined, and we demonstrate how this matrix can be transformed to a block diagonal form where each block belongs to different irreducible representations of the molecular point group. This development is especially important at the Multi-configurational Self-Consistent Field (MCSCF) level where symmetry is needed to avoid problems with symmetry breaking in the wave function and facilitate the optimization of electronic excited states. Moreover, although only the totally symmetric part of the solvent interaction is needed for energy calculations, in response or perturbation theory calculations of molecular properties, other irreps play an important role and the classification of solvent interaction terms by irrep is, therefore, desirable. In addition, the use of symmetry reduces the computational cost. The implementation presented here is illustrated with a series of calculations of absorption and emission processes in solution on the diazines pyrazine, pyrimidine, and pyridazine. These calculations allow us to illustrate both formal aspects of the implementation such as the choice of active spaces based on orbital symmetry as well as practical aspects such as the speed-up of the calculation.     

A multiconfigurational approach of the symmetry breaking problem in the cyclic C3H radical

The ground state of the cyclic C₃H radical is prone to symmetry breaking due to a peculiar structure that require to distribute three electrons on two centers which are equivalent by symmetry. A pseudo Jahn–Teller effect is also observed due to the non-adiabatic interaction with the first excited state. The multiconfigurational self-consistent-field method is used to calculate wavefunctions free from symmetry breaking. The weakening of the pseudo Jahn–Teller effect is observed when the correlation energy is increased. The equilibrium geometry and harmonic vibrational frequencies are calculated with the multireference configuration interaction method and a good agreement with experimental results is obtained. The present work confirms that the ground state of the cyclic C₃H has the C_2v symmetry.     

Continuity in symmetry and in distinguishability of states: the symmetry numbers of nonrigid molecules

We establish a connection between the concept of distinguishability of quantum states and the concept of continuity in geometric symmetry. For this purpose, we employ the continuous symmetry measure and the nuclear wave functions of a molecule, and evaluate the physical effects of deviation from geometric symmetry. We apply this tool in presenting a unified approach to assigning symmetry numbers to rigid and nonrigid molecules, and readdress, as a specific example, the evaluation of the temperature dependence of the entropy of cyclobutane and cyclohexane. We believe we show that the concept of continuity in geometric symmetry provides a more natural and practical approach to the inherent link between symmetry and entropy, compared with the classical approach.     

C64H6的结构和光谱的理论研究

本文用INDO系列方法研究了C64H6的结构与光谱, 表明C64H6有C2v和Cs两种稳定构型, 其中C2v构型能量较低, 讨论其加成及环加成产物对称性的规律并与13C NMR谱的实验结果相结合。计算了两种构型的电子光谱, 对电子跃迁进行了理论指认,并讨论了C64H6谱带红移的原因, 理论计算结果与实验事实基本吻合。     

The dependence of the fluorescence properties, laser properties and photochemical stability of aromatic compounds on the molecular symmetry

It is known that the spectral properties of organic compounds are, to a large extent, determined by the molecular symmetry. Numerous articles and monographs have been devoted to this problem. However, the influence of the molecular symmetry on fluorescence and, hence, laser parameters has not been fully investigated. In this paper, the fluorescence and laser properties of 20 aromatic compounds are experimentally studied at room temperature. The compounds studied are arranged in family-related pi-structure pairs. In each pair, even-numbered compounds belong to a higher symmetry group than odd-numbered compounds due to symmetrical substitution. All main fluorescence parameters such as quantum yield, gamma, decay time, tauf, fluorescence rate constant, k(f) (Einstein coefficient, A), and intersystem crossing rate constant, kST, are measured or calculated. It has been found that for most of the symmetrically substituted molecules, the value of kST decreases, sometimes very significantly. For example, the transition from 9-phenylanthracene (C2 symmetry) to 9,10-diphenylanthracene (D2 symmetry) is accompanied by an 18-fold decrease in the value of kST. This phenomenon is explained by the fact that, in a molecule of higher symmetry, not all triplet states mix with the fluorescing S1 state. It is also found that the symmetry of a molecule greatly affects laser parameters such as the threshold of laser action and the photochemical stability of a laser solution. It is observed that the threshold for even-numbered compounds is much lower and the photochemical stability, in most cases, is much higher than for odd-numbered compounds. These phenomena are discussed and explained.     

原子构造原理与过渡元素原子的价电子组态

众所周知,元素周期系过渡元素基态原子价电子组态的多样化是已往的原子构造理论无论是从定性还是从定量方面都是迄今难以给出圆满理论解释的原子构造现象之一^[1-11]。本文介绍新近提出的原子构造的对称性原理以及依据这一原理对上述原子构造现象所作的系统理论解释。     

DFT Study on the Heterofullerene C48O12 with Rare Th Symmetry

The molecule with T_h symmetry is rare. A novel C60-like molecule C48O12 with rare Th symmetry has been studied at the B3LYP/6-31G(d) level of theory. Its structural, electronic, vibrational, NMR, and thermodynamic properties have been calculated at the B3LYP/6-31G(d) level of theory. Vibrational modes have been assigned according to their symmetry. There are 73 independent vibrational modes: 22 IR-active modes with T u symmetry and 37 Raman-active modes with Ag , Eg and Tg symmetry, respectively. The heat of formation has been calculated by using isodesmic reactions, 765.7 kJ mol-1 . According to the heat of formation and the HOMO-LUMO gap, C48O12 with rare Th symmetry is more stable than C60 .     

On the use of symmetry in the ab initio quantum mechanical simulation of nanotubes and related materials

Nanotubes can be characterized by a very high point symmetry, comparable or even larger than the one of the most symmetric crystalline systems (cubic, 48 point symmetry operators). For example, N = 2n rototranslation symmetry operators connect the atoms of the (n,0) nanotubes. This symmetry is fully exploited in the CRYSTAL code. As a result, ab initio quantum mechanical large basis set calculations of carbon nanotubes containing more than 150 atoms in the unit cell become very cheap, because the irreducible part of the unit cell reduces to two atoms only. The nanotube symmetry is exploited at three levels in the present implementation. First, for the automatic generation of the nanotube structure (and then of the input file for the SCF calculation) starting from a two‐dimensional structure (in the specific case, graphene). Second, the nanotube symmetry is used for the calculation of the mono‐ and bi‐electronic integrals that enter into the Fock (Kohn‐Sham) matrix definition. Only the irreducible wedge of the Fock matrix is computed, with a saving factor close to N. Finally, the symmetry is exploited for the diagonalization, where each irreducible representation is separately treated. When M atomic orbitals per carbon atom are used, the diagonalization computing time is close to Nt, where t is the time required for the diagonalization of each 2M × 2M matrix. The efficiency and accuracy of the computational scheme is documented. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Wigner crystals of Na+ ions at the surface of a silica hydrosol

The symmetry of the surface of an electrolyte solution can be anisotropic, regardless of the bulk's isotropic symmetry, because of spatial correlations between adsorbed ions. The author used x-ray grazing-incidence diffraction to measure the spatial correlations between sodium ions in "classical one-component plasma" adsorbed with Bjerrum's density at the surface of a monodispersed 22 nm particle colloidal silica solution stabilized by NaOH with a total bulk concentration approximately 0.05 mol/L. The authors findings show that the surface compact layer is in a two-dimensional crystalline state (symmetry p2), with four sodium ions forming the unit cell and a approximately 30 A translational correlation length between the ions.     

应用双相角结构不变量概率值分辨相角双银问题

分析了Harker作图法中在几何上不可分辨的双解的对称性, 将衍射的物理性质(双相角结构不变量的概率性质)附加到对称的双解上时, 发现它具有可能分辨的彩色对称性。因此, 把Hauptman 1982年的概率式同Harker作图法相结合, 得到了蛋白细胞色素C550的大约1000个相角的估计值, 并对误差来源及其影响做了计算。     

An algorithm for the use of symmetry in molecular self-consistent-field calculations

The application of a simple relationship between atomic orbital integrals and symmetry orbital integrals is described in connection with traditional uses of symmetry. The simple modifications for implementation in the POLYATOM molecular self-consistent-field programs are given and discussed. Examples of the effectiveness of these modifications are included.     

C62O3的结构和光谱的理论研究

用ＩＮＤＯ法研究了Ｃ６２Ｏ３的结构与光谱，结果表明，Ｃ６２Ｏ３有Ｃ２０和Ｃ５两种种稳定构型，其中Ｃ２０构型能量较低。利用Ｃ６０的碎片拓扑图讨论基加成及环加成产物对称性的规律，理论计算与＾１３ＣＮＭＲ谱的实验结果相符合。     

Theoretical Study of Structural Symmetry in Ternary Clusters

The geometrical symmetry presents an intriguing theoretical problem in many kinds of clusters. The diversity of geometrical structures is associated with cluster sizes, different model functions and potential parameters, and ternary clusters are investigated to study the relationship between geometrical symmetry and homotopic symmetry. Ternary Lennard-Jones model potential is studied with different parameters, and the putative global minimum structures of A₁₃B₃₀C₁₂ clusters are optimized using an adaptive immune optimization algorithm. The results show that there mainly exist five geometrical symmetry structures, i.e., Mackay icosahedral, fivefold partial Mackay icosahedral, sixfold pancake, partial double Mackay icosahedral, and amorphous structures. Furthermore, the number of bonds is used to distinguish the geometrical symmetry. The importance of geometrical symmetry and homotopic symmetry determined by potential parameters is discussed. It was found that in the optimization it is more important to generate geometrical symmetry than to optimize homotopic symmetry.