A Monte Carlo method for an objective Bayesian procedure

This paper describes a method for an objective selection of the optimal prior distribution, or for adjusting its hyper-parameter, among the competing priors for a variety of Bayesian models. In order to implement this method, the integration of very high dimensional functions is required to get the normalizing constants of the posterior and even of the prior distribution. The logarithm of the high dimensional integral is reduced to the one-dimensional integration of a cerain function with respect to the scalar parameter over the range of the unit interval. Having decided the prior, the Bayes estimate or the posterior mean is used mainly here in addition to the posterior mode. All of these are based on the simulation of Gibbs distributions such as Metropolis' Monte Carlo algorithm. The improvement of the integration's accuracy is substantial in comparison with the conventional crude Monte Carlo integration. In the present method, we have essentially no practical restrictions in modeling the prior and the likelihood. Illustrative artificial data of the lattice system are given to show the practicability of the present procedure.     

Intrinsic field theory of chemical reactions

An intrinsic principle of least action is presented for the intrinsic dynamism of chemical reactions. Then, as the stationary trajectory, a meta-IRC (intrinsic reaction coordinate) draws a geodesic curve in a rigged Riemannian space. This establishes a geodesic law for the intrinsic dynamism. Moreover, a diagrammatic perturbation theory is formulated for the intrinsic dynamism, and a dynamical interaction between a chemically reacting system and a background system is investigated. Then, the structural stability of the system is discussed using a new concept of the dynamical potential field. An example is given in order to elucidate the present theory.Dedicated to Prof. Hermann Hartmann on the occasion of his 65th birthday.     

Determination of the correlation effects in molecules using the complete error potential

Summary The complete error potential is used for the study of the correlation of molecules. The correlation can be seen as a relaxation of the electrons and a relaxation of the nuclei. From the Fermi sea, the electronic relaxation gives rise to a partial excitation of each orbital which collectively generates a linear, a surface or a volume pressure; the resulting forces acting on the nuclei are defined in a general theory of the intramolecular forces. H₃, H ₃ ⁺ , the diatoms and the hydrid of the first nine elements are taken as examples.     

Electrical Potential Distribution around a Charged Colloidal Particle: Nonlinear Integral Equation

多电解质溶液中带电胶体粒子的电势分布由球形Ｐｏｉｓｓｏｎ－Ｂｏｌｔｚｍａｎｎ方程（ＰＢＥ）描述．ＰＢＥ是一个非线性的微分方程，且难以求得其解析解．本文采用非线性Ｐ－Ｂ积分方程，计算电势分布的数值解．首先，根据静电场和热力学系统中的物理定理，导出描述电势分布的Ｐ－Ｂ积分方程（ＰＢＩＥ）；其次，用迭代方法求ＰＢＩＥ的数值解．最后，计算了在３－１型电解液中无量纲半径κａ分别为０．１２和０．２２，无量纲表面电势ξ分别为１，２，４，６时球形胶体粒子外部的电势值．为了检验数值解的精度，计算了表面电荷密度，并与Ｌｏｅｂ（１９６１）和Ｏｓｈｉｍａ（１９９５）等人的结果比较，本文结果的相对误差小于１％，优于Ｏｓｈｉｍａ的结果．     

Ab initio study of the complexes of halogen-containing molecules RX (X=Cl, Br, and I) and NH3: towards understanding the nature of halogen bonding and the electron-accepting propensities of covalently bonded halogen atoms

Ab initio calculations have been performed on a series of complexes formed between halogen-containing molecules and ammonia to gain a deeper insight into the nature of halogen bonding. It appears that the dihalogen molecules form the strongest halogen-bonded complexes with ammonia, followed by HOX; the charge-transfer-type contribution has been demonstrated to dominate the halogen bonding in these complexes. For the complexes involving carbon-bound halogen molecules, our calculations clearly indicate that electrostatic interactions are mainly responsible for their binding energies. Whereas the halogen-bond strength is significantly enhanced by progressive fluorine substitution, the substitution of a hydrogen atom by a methyl group in the CH(3)X...NH(3) complex weakened the halogen bonding. Moreover, remote substituent effects have also been noted in the complexes of halobenzenes with different para substituents. The influence of the hybridization state of the carbon atom bonded to the halogen atom has also been examined and the results reveal that halogen-bond strengths decrease in the order HC triple bond CX > H(2)C=CHX approximately O=CHX approximately C(6)H(5)X > CH(3)X. In addition, several excellent linear correlations have been established between the interaction energies and both the amount of charge transfer and the electrostatic potentials corresponding to an electron density of 0.002 au along the R-X axis; these correlations provide good models with which to evaluate the electron-accepting abilities of the covalently bonded halogen atoms. Finally, some positively charged halogen-bonded systems have been investigated and the effect of the charge has been discussed.     

Preparation of solutions of amidomagnesium chlorides in poly(ethylene oxide) and their characterization by conductivity measurements

Polymer electrolyte systems were prepared for the first time by dissolution of amidomagnesium chlorides in poly(ethylene oxide), (PEO). For the preparation, solutions of (hexamethyldisilylamido)magnesium chloride, (dimethylpyrrolyl)magnesium chloride, (diisopropylamido)magnesium chloride, piperidinomagnesium chloride and morpholinomagnesium chloride were chosen. The composition of these polymer electrolyte systems corresponds to the general formula R₂NMgCl·P(EO)_n·THF. Most work has been done with the system (hexamethyldisilylamido)magnesium chloride in PEO, (Me₃Si)₂NMgCl·P(EO)_n·THF, with n= 3, 4, 5, or 7. The electrolytes have a soft rubber-like consistency. At 30 °C, electrical conductivities of 10⁻⁶–10⁻⁵ S/cm were found. The conductivities were measured in the temperature range 20–60 °C. Within this temperature range a linear dependence of the logarithms of the conductivity on the inverse temperature was found and activation energies for the conducting process of 30–60 kJ/mol were calculated. Using those polymer electrolytes with a high content of the amidomagnesium compound, a reversible magnesium deposition takes place by cathodic reduction at potentials below −1.9 V vs. a Ag/AgCl reference electrode. These polymer electrolytes were found to be stable against oxidation up to about −0.3 V vs. Ag/AgCl. Electronic Publication     

Simple evaluation of Franck–Condon factors and non‐Condon effects in the Morse potential

The calculation of Franck–Condon factors between different 1‐D Morse potential eigenstates using a formula derived from the Wigner function is discussed. Our numerical calculations using a simple program written in Mathematica are compared with other calculations. We show that our results have a similar accuracy as those calculations performed with more sophisticated methods. We discuss the extension of our method to include non‐Condon effects in the calculation. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 88: 280–295, 2002     

APPLICATION OF MSW-X_α METHOD WITH OVERLAPPING ATOMIC-SPHERE TO IONIZATION POTENTIALS FOR SOME PLANAR ORGANIC MOLECULES

Application of multiple scattered-wave X_α method with overlapping atomic-sphere to ionization potentials is reported for benzene, pyridine, pyrazine, pyrrole and imidazole. The calculated results show that the orbital charges in the intersphere region are non-negative and the energy levels get improvements in orderings.     

分子筛模型中非骨架离子位置的研究

从理论上研究了非骨架阳离子可能的分布位置．计算了分子筛晶体基本结构单元在整个空间的静电势分布，找出空间中静电势的各个极小点．在静电势最低点逐个放置钠离子，优化，重新计算模型分子筛的电势分布．研究了阳离子放置过程中静电势变化的趋势．