Computing the Kekulé structure count for alternant hydrocarbons

A fast computer algorithm brings computation of the permanents of sparse matrices, specifically, molecular adjacency matrices. Examples and results are presented, along with a discussion of the relationship of the permanent to the Kekulé structure count. A simple method is presented for determining the Kekulé structure count of alternant hydrocarbons. For these hydrocarbons, the square of the Kekulé structure count is equal to the permanent of the adjacency matrix. In addition, for alternant structures the adjacency matrix for N atoms can be written in such a way that only an N/2 × N/2 matrix need be evaluated. The Kekulé structure count correlates with topological indices. The inclusion of the number of cycles improves the fit. When comparing with previous results, the variance decreases 74%. The calculated standard heat of formation correlates with the logarithm of the Kekulé structure count. This heat increments 349 kJ/mol each time the Kekulé structure count increases by one order of magnitude. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

On the automatic restricted-step rational-function-optimization method

The rational function optimization algorithm is one of the widely used methods to search stationary points on surfaces. However, one of the drawbacks of this method is the step reduction procedure to deal with the overstepping problem. We present and comment on a method such that the step obtained from the solution of the rational function equations possesses the desired correct length. The analysis and discussion of the method is mainly centered on the location and optimization of transition states. Received: 18 June 1998 / Accepted: 17 September 1998 / Published online: 23 November 1998     

Modular design of icosahedral metal clusters

The concept of crystalline module, that is, an unambiguously isolated, repeated quasi-molecular element, is introduced. This concept is more general than the concept of crystal lattice. The generalized modular approach allows extension of the methods and principles of crystallography to quasi-crystals, clusters, amorphous solids, and periodic biological structures. Principles of construction of aperiodic, nonequilibrium regular modular structures are formulated. Limitations on the size of icosahedral clusters are due to the presence of spherical shells with non-Euclidean tetrahedral tiling in their structure. A parametric relationship between the structures of icosahedral fullerenes and metal clusters of the Chini series was found.     

Understanding the conformational dependence of spin-spin coupling constants: through-bond and through-space J(31P,31P) coupling in tetraphosphane-1,4-diides [M(L)x]2[P4R4

The characteristic dependence of J(31P,31P) spin-spin coupling constants of alkali metal tetraphosphane-1,4-diides on structure and composition has been analyzed by density functional methods. The computations confirm that the structure of the contact ion pairs is conserved in solution. Calculations on model systems M2P4H4, on naked P4H4(2-) anions, and on models including point charges, show that the role of the cations is mainly structural and to a smaller extent electrostatic. Three of the four J(P,P) coupling constants depend characteristically on the conformation of the anion, which in turn is determined by the substituents R and by cation-anion interactions. Several couplings exhibit a large through-space component and are thus strongly dependent on the relative orientation of nonbonding electron pairs on the phosphorus atoms involved. This is shown by visualization of coupling pathways using the recently introduced coupling energy density (CED), in combination with the electron localization function (ELF).     

多组分多出口稀土串级萃取静态优化设计研究(I)静态设计算法

研究了多组分、多出口稀土串级萃取体系静态优化设计过程的精确计算方法. 首先推导出串级萃取体系最重要的物料平衡和萃取平衡关系, 其次根据分离要求等条件确定了各出口的相对流量, 利用萃取平衡和物料平衡关系进行静态递推, 并在求解过程中根据物料平衡关系引入了校正参数, 通过对递推结果的迭代校正, 最终得到收敛的计算结果, 解决了静态设计算法的关键问题. 这一方法为多组分多出口稀土串级萃取过程的静态优化设计提供了精确算法.     

A Procedure for Transforming Impedance Spectra for the Determination of Mechanism of Electrochemical Reactions

Transformation of impedance spectra into relaxation time spectra (RTS) is used for determining contributions of individual processes of the oxygen electroreduction reaction (OER) to the polarization resistance of the electrochemical cell. The transformation technique involves the solution of the convolution equation found with the aid of a modified Van Cittert iteration algorithm checked on model impedance spectra. The technique, when used to analyze impedance spectra of electrochemical cells air|Pt|YSZ|YSZ + Pt|air, shows that the conversion of a globular structure of the YSZ + Pt cermet layer to a columnar one is accompanied by a change of peak amplitudes in RTS. The revealed RTS dynamics when heated to 750°C is compared with peculiarities of individual processes in OER.     

Comparative analysis of affine scaling algorithms based on simplifying assumptions

We analyze several affine potential reduction algorithms for linear programming based on simplifying assumptions. We show that, under a strong probabilistic assumption regarding the distribution of the data in an iteration, the decrease in the primal potential function will be with high probability, compared to the guaranteed(1). ( 2n is a parameter in the potential function andn is the number of variables.) Under the same assumption, we further show that the objective reduction rate of Dikin's affine scaling algorithm is with high probability, compared to no guaranteed convergence rate.Research supported in part by NSF Grant DDM-8922636.