Determination of atomic valence indices from population analyses at correlated level

This work carries out a study of atomic valences within molecular systems based on Mulliken and topological population analyses at correlated level. The use of the unpaired electron densities leads to suitable relationships between valences, free valence indices, and bond indices, which turn out to be quite useful for computational purposes. The results arising from both methods at correlated and uncorrelated levels are compared in a large series of chemical compounds. Several interesting conclusions are drawn out and analyzed in detail.     

IDENTIFICATION OF PARTIAL MUTATIONAL SITES IN HUMAN MITOCHONDRIAL DNA IN THE CHINESE AND ITS SIGNIFICANCE

A simple method for the identification of mutational sites in human mitochondrial DNA (mtDNA) was described. It was based on the human Cambridge sequence as a relative standard sequence and a single base pair substitution in mtDNA as a unique mutational form. The partial mutational sites can be determined using this method which was characterized by combining the restriction mapping with the analysis for the table of human mtDNA potential mutational sites with rapidity and simplicity. In the meanwhile, six mtDNA mutational sites found in Chinese population were identified by means of this method.     

Theoretical study of 3d‐metal mononitrides using DFT method

3d‐Metal mononitrides are studied using the density functional theory method. The lowest spin state for these dimers is obtained using the B3LYP hybrid functional with the 6‐311+G* basis set. The equilibrium geometries, vibrational frequencies, binding energies, Mulliken, and natural orbital population analysis charges, natural orbital electronic configuration, electron affinity, and ionization potential are obtained. Mulliken as well as natural orbital population analysis charges indicate that for all dimers, in cations most of the positive charge localized on the transition metal atom where in anions most of the negative charge localized on nitrogen atom. The binding energies for 3d‐metal mononitrides are higher than those for monocarbides and monoxides. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

On guaranteed stability of uncertain linear systems via linear control

This paper addresses the problem of stabilizing an uncertain linear system. The uncertaintyq(·) which enters the dynamics is nonstistical in nature. That is, noa priori statistics forq(·) are assumed; only boundsQ on the admissible variations ofq(·) are taken as given. The results given here applied to so-called matched systems differ from previous results in two ways. Firstly, the stabilizing control in this paper is linear; for this same class of problems, many of the existing results would require a nonlinear control. Furthermore, those results which do in fact yield linear controls are only valid when a certain matrix (q) (formed using the given data) is negative definite for allq Q. In contrast, the theory given here only requires compactness of the bounding setQ. Secondly, we show that the so-called matching conditions (used in earlier work) can be generalized so as to encompass a larger class of dynamical systems.This research was supported by the US Department of Energy under Contract No. ET-78-S-01-3390.     

A central limit theorem for age- and density-dependent population processes

Consider a population consisting of one type of individual living in a fixed region with area A. In [8], we constructed a stochastic population model in which the death rate is affected by the age of the individual and the birth rate is affected by the population density P_A(t), i.e., the population size divided by the area A of the given region. In [8], we proposed a continuous deterministic model which in general is a nonlinear Volterra type integral equation and proved that under appropriate conditions the sequence P_A(t) would converge to the solution P(t) of our integral equation in the sense that

$\text{lim}\text{→∞}\text{P}\text{sup}\text{0?s?t}\text{|P}{}_{\mathrm{A}}\text{(s) ? P(s)|>ε}\text{=0}\text{for every}\text{ε > 0}$

.In this paper, we obtain a “central limit theorem” for the random element √A(P_A(t)?P(t)). We prove that under appropriate conditions √A(P_A(t)?P(t)) will converge to a Gaussian process. (See Theorem 3.4 for the explicit formula of this Gaussian process.)     

邻位吡啶自由基多通道分解反应的动力学和反应机理研究

Utilizing Gaussian94 program package, all species involved in decomposition reactions of o-pyridyl radical were optimized fully at B3LYP/6-311＋＋G^＊＊ level. Intrinsic reaction coordinate calculations were employed to confirm the connections of the transition states and products, and transition states were ascertained by the number of imaginary frequency （0 or 1）. The reaction mechanism was elucidated by the vibrational mode analysis and electronic population analysis, and the reaction rate constants were calculated with transition state theory.     

A theoretical investigation into the conformational changes of dibenzo-p-dioxin, thianthrene, and selenanthrene

Theoretical ab initio calculations using the HF and B3LYP methods have been carried out to investigate the conformational differences of three cyclic rings, dibenzo-p-dioxin (DPD), thianthrene (THT), and selenanthrene (SET). The physical origin for the conformational preference of each molecule has been studied using the natural bond orbital (NBO) analysis. The NBO results indicate that DPD exists in a planar form due to strong electron delocalization caused by the specific orbital interaction, around the X atom. On the other hand, THT and SET exist as puckered forms with high inversion barriers due to less effective electron delocalization. The NBO analysis also shows that the conformational stabilization in DPD is caused by a more effective overlap of the orbitals, compared with the overlap of the orbitals in THT.     

Analysis of B3LYP and MP2 conformational population distributions in trans‐nicotine,acetylcholine, and ABT‐594

This work presents an analysis of the equivalence of MP2 and DFT (B3LYP functional) conformational populations. As a test case, we select three cholinergic agents (trans‐nicotine, acetylcholine, and the nicotinic analgesic ABT‐594), where the minima on the conformational energy hypersurfaces expand a large range of energies (～0–30 kJ mol^?1). From energetic and structural data obtained in vacuo at the MP2 and B3LYP/cc‐pVDZ levels, we build conformational partition functions, including the effect of the conformational kinetic energy and the rotovibrational coupling. Our results at a physiological temperature (37°C) show qualitative agreement in all cases. Quantitative agreement, however, is only found for trans‐nicotine and ABT‐594. In the first case, energy minima differ by <0.2 kJ mol^?1. Therefore, the equivalence of structural results translates in the equivalence of the conformational distribution. For ABT‐594, the minima are separated by as much as 8.0 kJ mol^?1, and the conformational energy determines the conformational distribution. In this case, the slight relative variation of conformational energy, between B3LYP and MP2, does not affect the population, since the secondary minima are high in energy and very low in population. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Estimating reaction parameters in mechanism-enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach

In order to quantitatively predict nano- as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth. The Bayesian approach addresses the question of “how well do we know our parameters, along with their uncertainties?.” The results reveal that Bayesian inversion statistical analysis on an example, prototype nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. The paper can also be seen as a tutorial with the additional goal of achieving a “Gold Standard” Bayesian inversion ME-PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems.     

Properties of the random search in global optimization

From theorems which we prove about the behavior of gaps in a set ofN uniformly random points on the interval [0, 1], we determine properties of the random search procedure in one-dimensional global optimization. In particular, we show that the uniform grid search is better than the random search when the optimum is chosen using the deterministic strategy, that a significant proportion of large gaps are contained in the uniformly random search, and that the error in the determination of the point at which the optimum occurs, assuming that it is unique, will on the average be twice as large using the uniformly random search compared with the uniform grid. In addition, some of the properties of the largest gap are verified numerically, and some extensions to higher dimensions are discussed. The latter show that not all of the conclusions derived concerning the inadequacies of the one-dimensional random search extend to higher dimensions, and thaton average the random search is better than the uniform grid for dimensions greater than 6.This paper is based on work started in the Statistics Department of Princeton University when the first author was visiting as a Research Associate. Part of this research was supported by the Office of Naval Research, Contract No. 0014-67-A-0151-0017, and by the US Army Research Office—Durham, Contract No. DA-31-124-ARO-D-215.2 The authors wish to thank B. Omodei for his careful work in preparing the programs for the results of Figs. 1–2 and Table 1. The computations were performed on the IBM 360/50 of the Australian National University's Computer Centre. Thanks are also due to R. Miles for suggestions regarding the extension of the results to multidimensional regions, and to P. A. P. Moran and R. Brent for suggestions regarding the evaluation of the integral ₀ ¹ ... ^0/1 (x ₁ ² + ... +x _n ^/2 )^1/2 dx ₁ ...dx _n.