Husimi representation for stationary states

This paper considers a Husimi representation of quantum mechanics in which the (stationary) state of a system or ensemble is described by a Husimi function and an observable is described by a phase space function or distribution such that the expectation value of the observable is given by an integral over phase space of the product of that function or distribution and the Husimi function. The density matrix, Wigner function, and Husimi function are considered to be alternative ways of describing the state of a system or ensemble, and methods of recovering the Wigner function or density matrix from the Husimi function are discussed. The classical limits of the Wigner and Husimi functions and of the relationship between them are considered. © 1993 John Wiley & Sons, Inc.     

Solving the Schrödinger equation of helium and its isoelectronic ions with the exponential integral (Ei) function in the free iterative complement interaction method

We introduce here the exponential integral (Ei) function for variationally solving the Schr?dinger equation of helium and its isoelectronic ions with the free iterative complement interaction (ICI) method. In our previous study [J. Chem. Phys., 2007, 127, 224104], we could calculate very accurate energies of these atoms by using the logarithmic function as the starting function of the free ICI calculation. The Ei function has a weak singularity at the origin, similarly to the logarithmic function, which is important for accurately describing the three-particle coalescence region. The logarithmic function, however, has a node and a maximum along the radial coordinate which may be physically meaningless. In contrast, the Ei function does not have such unphysical behaviors and so would provide an improvement over the logarithmic function. Actually, using the Ei function, instead of the logarithmic function, we obtained the energy, E= -2.903 724 377 034 119 598 311 159 245 194 404 446 696 924 865 a.u. for the helium ground state with 21 035 functions, which is a slight improvement over our previous result (the bold face shows the digits that are believed to have converged). This result supports the suggestion that the Ei function is better than the logarithmic function for describing the three-particle coalescence region.     

一个广泛适用的聚合度分布函数

本文提出了一个新的聚合度分布函数,该分布函数包括三个参数a、b、P_0。当a等于1时,该分布函数为Schulz分布。通过十一种聚合物的应用考查,都比较适用。得到了该分布函数的数均聚合度、重均聚合度、Z均聚合度和粘均聚合度的解析表达式。     

Comparison among four different ways to condense the Fukui function

Four different ways to condense the Fukui function are compared. Three of them perform a numerical integration over different basins to define the condensed Fukui function, and the other one is the most traditional Fukui function using Mulliken population analysis. The basins are chosen to be the basins of the electron density (AIM), the basins of the electron localization function (ELF), and the basins of the Fukui function itself. The use of the last two basins is new and presented for the first time here. It is found that the last three methods yield results which are stable against a change in the basis set. The condensed Fukui function using the basins of the ELF is not able to give information on the reactivity of an acceptor molecule. In general, the condensed Fukui function using the basins of the density or the basins of the Fukui function describe the reactivity trends well. The latter is preferred, because it only contains information about the Fukui function itself and it gives the right information for donor as well as acceptor centers.     

The unvalidity of Kohlrausch' regulating function for Svensson's isoelectric focusing and stationary electrolysis at steady state

Kohlrausch' regulating function is of important significance in the field of electrophoresis. In this paper, the relative regulating function is defined from Kohlrausch' regulating function. The relative values, including the limited values, of the regulating function for the stationary electrolysis of salt, on which the classic isoelectric focusing (IEF) is based, are computed and compared with the computer program of the QBASIC written by us. The results directly demonstrate that, (1) in a few cases the regulating function is valid for the stationary electrolysis and IEF, whereas (2) the function is, in most of cases, not valid for the stationary electrolysis and IEF at steady-state. Those findings may be useful for the studies on the relationships between Kohlrausch' regulating function and IEF and for the classification of numerous electrophoretic techniques.     

Liquid structure of vanadium tetrachloride from neutron diffraction study

Assuming the separation of the intermolecular scattering function into the radial and angular parts and using Egelstaffet al’s orientational model for tetrachlorides, the structure of liquid vanadium tetrachloride has been studied. It has been observed that such a separation is approximate for this liquid and the introduction of a third correction term is required to account for the molecular structure function. The chlorine-chlorine partial structure and effective angleaveraged intermolecular chlorine-chlorine potential in the liquid has been evaluated. Without taking the third correction term, introduced to generate theoretically the molecular structure function, the centre structure function has been obtained in an approximate way from the experimentally observed molecular structure function and from it the centre radial distribution function, centre direct correlation function and the angle-averaged vanadium-vanadium effective potential has been evaluated.     

On the Applicability of Mathematical Constants and Sequences in Intermolecular Potential Energy Functions

Six intermolecular potential energy functions incorporating mathematical functions such as the Golden ratio, Euler number and Pi, and three consecutive numbers in the Half Square, Lucas and Fibonacci sequences are proposed herein. It is shown that the Lucas potential function exhibits reasonable agreement with the Lennard-Jones(12-10) function, whilst the Golden ratio potential function describes the argon gas potential energy and the Lennard-Jones(14-7) function excellently. Both the Euler and Pi potential functions agree well with the Lennard-Jones(12-6) function, whilst the Fibonacci potential function exhibits very good correlation with the Lennard-Jones(9-6) function. The relatedness of the mathematical constants and sequences examined in this paper with application to intermolecular potential functions suggests their additional significance in the field of chemistry.     

New approach to the correlation problem: Electron interaction potential as a variable in solving the many-particle Schrödinger equation

The many-electron wave function is represented as the product of the wave function of the independent particles and the function that depends only on the value of the interelectron interaction potential. The function defines the electron correlation effects; a standard linear differential equation was derived to define the function. The equation depends on the functions of independent particles; a generalization of the Hartree-Fock equations including electron correlation was obtained for these functions. The total energy calculation of two-electron ions shows that even solving an ordinary differential equation for the function of independent particles represented by the functions of noninteracting electrons leads to higher accuracy than the one achieved in the Hartree-Fock theory.     

Rapid evaluation of the Voigt function and its use for interpreting X-ray photoelectron spectroscopic data

While the Voigt function is recognized as the best function to represent the photoelectron spectroscopic process, it is less frequently used because it cannot be represented as an analytical function and thus has to be evaluated numerically. This paper shows how the true Voigt function can be calculated rapidly with approximately the same speed as pseudo-Voigt functions by using approaches that have been used by the astronomical sciences community. The Voigt function is calculated using code previously published by Wells. The paper describes a method for calculating the function to generate photoelectron peaks for curve fitting X-ray photoelectron spectroscopic data. An appendix is provided with the listing of a Fortran 90 program which uses the subroutine HUMDEV published by Wells. Examples of using this approach for the fitting of experimental core X-ray photoelectron spectroscopic data are presented, and the fits compared with fits using a pseudo Voigt product function. The use of the true Voigt function in the calculation of spectra in the core and valence band region is also described and illustrated by comparing the calculated spectra with experimental spectra.     

A note on generalized Green functions

A partial-wave expansion in terms of Jost function is obtained for the sngle-particle generalized Green function. Each partial-wave generalized Green function so obtained is in closed form. The results apply at least to Jost function treatable potentials.     

Electron pair localization function: a practical tool to visualize electron localization in molecules from quantum Monte Carlo data

In this work we introduce an electron localization function describing the pairing of electrons in a molecular system. This function, called "electron pair localization function," is constructed to be particularly simple to evaluate within a quantum Monte Carlo framework. Two major advantages of this function are the following: (i) the simplicity and generality of its definition; and (ii) the possibility of calculating it with quantum Monte Carlo at various levels of accuracy (Hartree-Fock, multiconfigurational wave functions, valence bond, density functional theory, variational Monte Carlo with explicitly correlated trial wave functions, fixed-node diffusion Monte Carlo, etc). A number of applications of the electron pair localization function to simple atomic and molecular systems are presented and systematic comparisons with the more standard electron localization function of Becke and Edgecombe are done. Results illustrate that the electron pair localization function is a simple and practical tool for visualizing electronic localization in molecular systems.     

A vibrational molecular force field of model compounds with biological interest. I. Harmonic dynamics of crystalline urea at 123 K

Normal coordinate calculations have been performed for urea and deuterated urea in the crystalline state. We have used the modified Urey–Bradley–Shimanouchi intramolecular potential energy function and a rather sophisticated intermolecular energy function to reproduce I.R. and Raman frequencies with an average error of 2 cm^–1. The general agreement between the calculation and experiment suggests that intermolecular interactions must be taken into account to determine reliable intramolecular parameters of the potential energy function, mainly the barrier to internal rotation around the C? N bond. The intermolecular energy function, which consists of the Buckingham function and an explicit harmonic function for hydrogen-bonding, then has the merit to reproduce quite well the observed frequencies of lattice vibrations.     

Extracting the time scales of conformational dynamics from single-molecule single-photon fluorescence statistics

The quenching rate of a fluorophore attached to a macromolecule can be rather sensitive to its conformational state. The decay of the corresponding fluorescence lifetime autocorrelation function can therefore provide unique information on the time scales of conformational dynamics. The conventional way of measuring the fluorescence lifetime autocorrelation function involves evaluating it from the distribution of delay times between photoexcitation and photon emission. However, the time resolution of this procedure is limited by the time window required for collecting enough photons in order to establish this distribution with sufficient signal-to-noise ratio. Yang and Xie have recently proposed an approach for improving the time resolution, which is based on the argument that the autocorrelation function of the delay time between photoexcitation and photon emission is proportional to the autocorrelation function of the square of the fluorescence lifetime [Yang, H.; Xie, X. S. J. Chem. Phys. 2002, 117, 10965]. In this paper, we show that the delay-time autocorrelation function is equal to the autocorrelation function of the square of the fluorescence lifetime divided by the autocorrelation function of the fluorescence lifetime. We examine the conditions under which the delay-time autocorrelation function is approximately proportional to the autocorrelation function of the square of the fluorescence lifetime. We also investigate the correlation between the decay of the delay-time autocorrelation function and the time scales of conformational dynamics. The results are demonstrated via applications to a two-state model and an off-lattice model of a polypeptide.     

剩余函数量子Monte Carlo方法

为量子Ｍｏｎｔｅ Ｃａｒｌｏ方法提出一条新途径－剩余函数法,引入了Ｓｃｈｒｏｅｄｉｎｇｅｒ方程剩余函数的概念,利用剩余函数将一种新的有明显物理意义的试探函数应用到量子Ｍｏｎｔｅ Ｃａｒｌｏ过程中,这种试探函数是通过一种迭进式的方式确定的,它不需要在Ｍｏｎｔｅ Ｃａｒｌｏ过程中优化参数。文中我们将给出这种试探函数的具体形式,证明由这种试探函数求出的能量期望值收敛于体系真实的能量值;文中还给出这种试探     

子的配分函数——物理意义与作用

讨论怎样理解子的配分函数的物理意义,以及它和系统的配分函数在计算热力学函数中的作用,指出它既不是系统的广延性质,也不是系统的强度性质,只是联系系统热力学函数与微观信息的纽带。     

A Green's function approach to the nonrelativistic radial wave equation of hydrogen atom

We report an efficient and consistent method for the solution of Schrödinger wave equation using the Green's function technique and its successful application to the nonrelativistic radial wave equation of hydrogen atom. For the radial wave equation, the Green's function is worked out analytically by means of Laplace transform method and the wave function is proposed under the boundary conditions. Computationally the product of potential term, the proposed wave function and the Green's function are integrated iteratively to get the nonrelativistic radial wave function. The resultant wave after each iteration is normalized and plotted against the standard nonrelativistic radial wave function. The solution converges to the standard wave with the increasing number of iterations. Results are verified for the first 15 states of hydrogen atom. The method adopted here can be extended to many‐body problem and hope that it can enhance our knowledge about complex systems.     

最大熵原理推导自由结合链末端距的径向分布函数

将自由结合链看成一个微观系统,应用最大熵原理推导出自由结合链末端距的径向分布函数,进而证明自由结合链的末端距符合高斯分布。     

Binding energies of on-axis hydrogenic and nonhydrogenic donors in GaAs/Ga1−x Al x As

In a previous work [Phys. Rev. B43(1991)9262], the binding energies of hydrogenic and nonhydrogenic on-axis donors in GaAs/Ga_1?x A1 _X As quantum-well wires of circular cross section have been calculated as functions of the radius of the quantum-well wire. In both the hydrogenic and nonhydrogenic cases, a variational trial wave function was chosen that could be written as the product of an “envelope function”, and a function containing the variational parameter. It was assumed in these calculations that the potential barrier that exists at the surface of the GaAs cylinder and the surrounding Ga_1?x A1 _X As matrix is infinite. For the envelope function, an ordinary Bessel function of the first kind and of order zero was chosen. This envelope function satisfies the boundary condition, the vanishing of the trial function at the surface of the quantum-well wire. The question arises: how sensitive are the calculated binding energies to the choice of the envelope function? In the present work, we attempt to provide a partial answer to this question by choosing another envelope function, a spherical Bessel function of order zero. This function also satisfies the boundary condition and makes the trial wave function vanish at the interface between the GaAs cylinder and the Ga_1?x A1 _X As matrix. Our calculations show that the binding energies of both the hydrogenic and the nonhydrogenic on-axis donors depend on the choice of the envelope function.     

高分子链相关函数与液体小分子速度/应力-时间相关函数的可类比性

通过标度关系,给出了良溶剂和熔体或θ溶剂中真实高分子链相关函数的幂率衰减关系.这一问题的物理背景,与液体中小分子速度和应力的时间相关函数的长时间拖尾现象,具有可类比的物理图像,但是由于高分子系统的复杂性,高分子的链相关函数表现出更复杂和丰富的可能形式.