几种密度泛函理论公式用于镧系硫属化合物计算的比较

以镧系元素La、Gd、Lu的硫属化合物为对象,系统考察几种密度泛函理论公式对镧系化合物计算的适用情况,考虑了相对论效应的影响. 计算结果显示,相对论效应引起的键长变化在十2Pm到-3Pm之间,引起的键能减小为0. 4～0. 6eV,与采用的密度泛函公式关系不明显. 不同的密度泛函公式对键长的计算结果影响也不太大,但对键能有显著影响,其中LDA(VWN)＋PW86X公式给出最好结果. 交换能梯度校正明显改善键能计算结果,而相关能梯度校正反而使之变差. 简单的X_α公式给出相当好的键能计算结果. 在考虑相对论效应和梯度校正以后,密度泛函理论方法给出比较可靠的键长数值,键能则仍然偏高,但不超过20％.     

Algebraic Kekulé formulas for benzenoid hydrocarbons

By assigning two pi-electrons of CC double bonds in a Kekulé valence structure to a benzene ring if not shared by adjacent rings and one pi-electron if CC double bond is shared by two rings we arrived at numerical valence formulas for benzenoid hydrocarbons. We refer to numerical Kekulé formulas as algebraic Kekulé valence formulas to contrast them to the traditional geometrical Kekulé valences formulas. The average over all numerical Kekulé valence structures results in a single numerical structure when a benzenoid hydrocarbon molecule is considered. By ignoring numerical values the novel quantitative formula transforms into a qualitative one which can replace incorrectly used notation of pi-electron sextets to indicate aromatic benzenoids by placing inscribed circles in adjacent rings-which contradicts Clar's characterization of benzenoid hydrocarbons.     

镱硫属化合物的密度泛函理论研究

用密度泛函理论(DFT)研究镱硫属化合物的电子结构和性质,通过与实验比较考察了现有的几种近似密度泛函公式对镧系元素化合物的适用程度和相对论效应的影响.结果表明,用DFT计算的YbO键长对实验值的偏差约为0.002nm;但得到的键能即使在考虑梯度校正和相对论效应之后,仍比实验值高,在定域密度近似基础上引入交换梯度校正使键能计算值减小,其中PW86x使键能计算值减小稍多些,结果更接近实验值;相关梯度校正使键能计算值升高.相对论效应使键长缩短0.004～0.006nm,键能减小约0.5eV.计算结果的分析表明,Yb的5d轨道和配体的np轨道间形成σ键和π键.在所研究的分子体系中,配体原子从O到Te、Yb原子的5d轨道布后数依次减少,同键能减弱的顺序一致.相对论效应使键能减小的主要原因是在成键过程中发生了Yb的6s电子向5d轨道的转移,而相对论效应使该过程能量增加.偶极矩和电荷分布的计算表明,Yb-L键以共价性为主,相对论效应使共价性成份增加.     

A recipe for evaluating and differentiating cos ϕ expressions

We present a simple recipe for calculating and differentiating cosine of bond angle and dihedral angle expressions. The resulting formulas can be incorporated in a straightforward manner into the bond angle and dihedral angle components of potential energy functions. These formulas rely only on expressions and derivatives of dot products, and, in particular, they avoid cross products as well as excessive Fortran function references. Consequently, the expressions derived in this article can be written compactly and evaluated rapidly.     

A new three-center model for diatomic bonds based on the spherical Gaussian bonding function

A new three-center model for diatomic bonds is proposed based on the spherical Gaussian bonding function. The characteristics of the model are that the magnitude of effective bond-charge described by the function is different for different observation points, and that the position of the bond-charge on the bond axis satisfies the energy variation principle.

According to the model and two additional assumptions, some theoretical formulas for bond properties, such as the total energy of system, dissociation energy, dipole moment, force constant and field gradients at nuclei, are derived. The calculated results are basically in agreement with the observed ones.

In addition, a comparison between the new model and the electrostatic three-center model proposed in a previous paper is discussed in brief.     

Bond length features of linear carbon chains of finite to infinite size: Visual interpretation from Pauling bond orders

Schemes for Kekulé structure counting of linear carbon chains are suggested. Mathematical formulas, which calculate the Pauling bond order P(k, N) of a chemical bond numbered by k, are given for the carbon chain with N carbon atoms. By use of the least‐squares fitting of a linearity, relationships between Pauling bond orders and bond lengths are obtained, and such correlation of the Pauling bond order–bond length can be qualitatively extended to the excited states. The relative magnitudes of Pauling bond orders in unsaturated carbon chains dominate C–C bond lengths a well as the bond length feature with the chain size increasing. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 144–149, 2003     

C[bond]H- - -O hydrogen bonds in beta-sheetlike networks: combined X-ray crystallography and high-pressure infrared study

Close interactions of the C(alpha)[bond]H- - -O type have been analyzed via X-ray crystallography and high-pressure infrared spectroscopy. The results demonstrate that the C(alpha)[bond]H- - -O interactions can offer an additional stability to the beta-sheet formation. X-ray structural data suggest that while 1-acetamido-3-(2-pyrimidinyl)-imidazolium bromide exhibits a bilayer stacking, the PF(6)(-) salt reveals a beta-sheetlike pattern. The appearance of the free-NH infrared absorption indicates that the conventional N[bond]H- - -O or N[bond]H- - -N hydrogen bonds do not fully dominate the packing for the PF(6)(-) salt. The high-pressure infrared study suggests that the C(alpha)[bond]H- - -O hydrogen bonds are the important determinants for the stability of the PF(6)(-) salt. This study also verifies that the imidazolium C[bond]H stretching frequency shifts to a longer wavelength upon the formation of the C[bond]H- - -O hydrogen bonds.     

Remarks on the molecular mechanical calculations of functionalized hydrocarbons

Molecular mechanical calculations for hetero-substituted hydrocarbons present certain difficulties that are not encountered in dealing with hydrocarbons. Ways are proposed to overcome such difficulties, sometimes by two-step or iterative computation. The following topics are considered: fitting the force field by using data from studies in solution; ways to estimate atomic charges or, alternatively, bond moments; ways to account for field effects upon atomic charges and bond moments.     

Kirkwood factor for dipolar hard sphere fluids. hindered rotation model

Possibilities of using various physicochemical models of polar liquids for describing the dielectric properties of model systems (one-, two-, or threedimensional dipolar hard spheres) are analyzed. Simple analytical formulas for the Kirkwood factor of the model systems are derived using the generalized hindered rotation model in a nearest neighbor interaction approximation. In the onedimensional case, an exact formula is obtained. For two- and three-dimensional spheres, the formulas adequately reproduce the available data of computer simulations over a wide range of thermodynamic parameters. In the lowtemperature limit (highly polar fluid), the expressions for the Kirkwood factor coincide with those in Pople’s bent hydrogen bond model. The associated equilibrium model also adequately describes the available experimental data in this limit, but leads to nonphysical results at high temperatures. The worst results are obtained in Wertheim’s mediumsphere approximation. Translated fromZhumal Struktumoi Khimii, Vol. 39, No. 5, pp. 843–850, September–October, 1998.     

Bond strength and bond angles for hybrid orbitals composed of arbitrary sets of orbital angular momentum quantum number

According to the formulas obtained in the preceding paper, it may be used for all types of the hybridization with any set of azimuthal quantum numbers l, l = 0 through l = 5, and a complete theoretical data of bond angles and bond strengths are shown in this paper.     

诱导效应指数与XSiRxH3—x的标准生成热

诱导效应指数与ＸＳｉＲｘＨ３－ｘ的标准生成热张秀利（河北轻化工学院基础部石家庄０５００１８）关键词诱导效应指数标准生成热键裂能烷基硅衍生物对于含硅有机物的标准生成热大多未见报导［１－２］，本文将利用诱导效应指数Ｉ［３，４］，作为参数，建立一套简单而准...     

The importance of questioning scientific assumptions: some lessons from f element chemistry

As scientists, we know that we should constantly question the assumptions upon which our research is based. We also know that we do not do this often enough. The recent results in f element chemistry described here should serve to remind us not to take the traditional boundaries of any area of chemistry for granted including topics as fundamental as redox chemistry and bond-length generalizations. New ways of doing reductive chemistry in the f element area as well as the synthesis of "long bond organometallics" that have unconventional bond distances and reactivity demonstrate how the "rules" in this area, thought to be true for decades, have been recently overturned. The synthetic chemistry that made these advances possible has generated additional unexpected opportunities in f element chemistry that are also described here. Overall, these results should stimulate researchers in all areas to challenge their assumptions.     

密度泛函计算条件对结果精度的影响

通过对有代表性的分子BCl₃,SO₂,ZnO,TiCl₄,LuF₃的一系列计算,从三个方面考察密度泛函理论的Kohn-Sham方法中采用的计算条件对结果精度的影响.发现基组完备性对计算结果影响最大,数值积分取点数目对计算结果影响略小.电荷多极投影收敛较快.分子几何构型和振动基频对计算条件不太敏感,总能量和键能对计算结果较敏感.在计算键能时对分子及其组成原子采用相同的基组和积分布点方式可以减少误差.选择适当的计算条件,用较小的计算量可以得到与现有近似能量密度泛函精度相匹配的结果.     

Efficient treatment of out-of-plane bend and improper torsion interactions in MM2, MM3, and MM4 molecular mechanics calculations

Simple and very efficient formulas are presented for four-body out-of-plane bend (used in MM2 and MM3 force fields) and improper torsion (used in the MM4 force field) internal coordinates and their first and second derivatives. The use of a small set of bend and stretch intermediates allows for order of magnitude decreases in calculation time for potential energies and their first and second derivatives, which are required in molecular mechanics calculations. The formulas are eminently suitable for use in molecular simulations of systems with complicated bond networks. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1804–1811, 1997     

The bond order—bond length relationship

The difference in length between two bond orders was reported by Pauling to be essentially the same, regardless of the atoms that make up the bond. To a first approximation these differences hold not only for bond orders 1, 2 and 3 but also for six membered aromatic rings containing all carbon, carbon-nitrogen, nitrogen-nitrogen, carbon-phosphorous, carbon-arsenic, and carbon-antimony bonds. An equation was developed (based upon these differences) that relates bond order and bond length. The output of this equation was compared with those of Gordy and Pauling. Our equation as well as the Gordy equation (with revised constants) return a bond length of 1.4 Å for bond order 1.67 which is consistent with theory. (This bond order was not used in developing either the equation or the revised Gordy constants.)     

Relationships Among Potential-Energy Functions

We analyse recently proposed connection formulas between potential-energy functions for bond stretching, bond bending and molecular interactions, and propose more convenient and practical expressions. For example, our mathematical relationships between Morse and Murrel—Mottram potential parameters yield much closer agreement between such potential-energy functions.     

Insertion reactions of heterocumulene into metal-ligand bonds

Published and authors’ own data on the typical examples of behavior of organic iso(thio)cyanates and other unsaturated substrates in reactions with metal-heteroatom bonds-M-O, M-N, M-P, and M-Hal-are reviewed. A possibility of multiple insertion of heterocumulenes into the same M-L bond and their ability to undergo-sphere condensation with other ligands upon heteromolecular insertion as well as the cocyclization of inserted ligands upon complex will be discussed in this review. Factors that affect the direction of iso(thio)cyanate addition to upon metal-heteroatom bond as well as the possibility of different kinds of their combination for the formation of heterocyclic ligands or compounds are also. Most of the findings are based on the results of IR and NMR spectroscopical, as well as X-ray structural studies.     

Application of Coulson's Contour integral method to linear finite polymers

Coulson's contour integration method has been applied to calculate the charge and bond order matrices and total energies of conjugated systems composed of fragments whose Hückel secular equations have been solved. Integral formulas have been derived for the calculation of these quantities for two coupled conjugated systems and for linear polymers. A rapid method for the numerical evaluation of the integral formulas is presented and applied to a linear finite polyene.     

Hydrogen bond lifetime for water in classic and quantum molecular dynamics

The lifetime of hydrogen bonds in water at T = 298 K and p = 0.1 MPa is computed by means of classic molecular dynamics with eight different potentials of pair lifetime interaction and Car-Parinello molecular dynamics. The results obtained using various computational techniques for hydrogen bond life-times are compared. It is shown that they can differ from one another by several times. The dependence for the hydrogen bond lifetime computed in our numerical experiment upon the method of its determination is found.     

Numerical examination of performance of some exchange-correlation functionals for molecules containing heavy elements

The performance of 17 exchange-correlation functionals for molecules containing heavy elements are numerically examined through four-component relativistic density DFT calculations. The examined functionals show the similar accuracy as they do for the molecules containing light elements only except for bond lengths. LDA and OP86 produce good results for bond lengths and frequencies but bad bond energies. Different functionals do not show much different performance for bond energies except LDA. BP86 and GP86 produce results with average accuracy while LYP does not perform well. Although encouraging results are obtained with functional B97GGA-1, other heavily parameterized and meta-GGA functionals do not produce impressive results.