Direct method for optimized effective potentials in density-functional theory

The conventional optimized effective potential method is based on a difficult-to-solve integral equation. In the new method, this potential is constructed as a sum of a fixed potential and a linear combination of basis functions. The energy derivatives with respect to the coefficients of the linear combination are obtained. This enables calculations by optimization methods. Accurate atomic and molecular calculations with Gaussian basis sets are presented for exact exchange functionals. This efficient and accurate method for the optimized effective potential should play an important role in the development and application of density functionals.     

Feynman path integral with underlying noncommutative “geometry” and quantum mechanics in external field

Noncommutative algebra of translations as a deforming commutative algebra induces a linear vector potential in the plane. This potential perturbs the generators of translations. Such potential we can identify, for example, with constant magnetic or with homogeneous electric fields. This potential introduces an extra phase factor in the Feynman formulation of quantum mechanic.Presented at the Colloquium on the Quantum Groups, Prague, 18–20 June 1992.     

Large binding due to dispersive screening and bloch function interference in many-valley semiconductors

We derive here a generalization of the effective mass equation which includes the intervalley mixing for many-valley semiconductors. This equation is numerically solved with a model impurity potential for donors in silicon. The results show an extreme sensitivity to the short-range impurity potential and a shallow-deep instability. The combined effect of dispersive screening and many-valley interference gives a deep ground state. This seem to be in agreement with the experimental situation for hydrogen and muonium impurities, to which the chosen model potential applies.     

Dynamic oscillations of coupled domain walls

In domain wall (DW) excitation experiments, nonlinearity (NL) intrinsic to the DW dynamics is often hard to distinguish from perturbation due to the confining potential or DW distortion. Here we numerically investigate the dynamic oscillations of magnetostatically coupled DWs: a system well understood in the quasistatic limit. NL is observed, even for a harmonic potential, due to the intrinsic DW motion. This behavior is principally dependent on terms normally associated with the DW canonical momentum and is in contrast with a NL restoring potential. This NL is not observable in quasistatic measurements, relatively insensitive to the confining potential, and may be tuned by the nanowire parameters. The shown NLs are present in any DW restoring potential and must be accounted for when probing DW potential landscapes.     

A new representation of the heavy ion Coulomb potential

The Coulomb potential between two heavy ions at their interpretation condition has been represented in terms of two point charges with reduced effective charge, dependent on overlap volume. This representation enables visualization of the dynamic development of the deformations of the colliding nuclei as a function of the degree of overlap. The potential has been compared with well known potentials for heavy-ion collisions. This Coulomb potential gave good agreement in reproducing excitation functions for fusion for a large number of heavy-ion systems.     

The Darboux Transformation for the One-Dimensional Stationary Dirac Equation with a Scalar Potential

This paper deals with the Darboux transformation for the Dirac equation with a scalar-type potential. Formulas are derived for the potential difference and for the solutions of the transformed equations. The relationship between the Darboux transforms for Dirac and Schrödinger equations is analyzed. New transparent potentials and a potential with a Coulomb asymptotics are obtained as examples.     

Molecular dynamics simulation of thermal accommodation coefficients for laser-induced incandescence sizing of nickel particles

Extending time-resolved laser-induced incandescence (TiRe-LII), a diagnostic traditionally used to characterize soot and other carbonaceous particles, into a tool for measuring metal nanoparticles requires knowledge of the thermal accommodation coefficient for those systems. This parameter can be calculated using molecular dynamics (MD) simulations provided the interatomic potential is known between the gas molecule and surface atoms, but this is not often the case for many gas/surface combinations. In this instance, researchers often resort to the Lorentz–Berthelot combination rules to estimate the gas/surface potential using parameters derived for homogeneous systems. This paper compares this methodology with a more accurate approach based on ab initio derived potentials to estimate the thermal accommodation coefficient for laser-energized nickel nanoparticles in argon. Results show that the Lorentz–Berthelot combining rules overestimate the true potential well depth by an order of magnitude, resulting in perfect thermal accommodation, whereas the more accurate ab initio derived potential predicts an accommodation coefficient in excellent agreement with experimentally-determined values for other metal nanoparticle aerosols. This result highlights the importance of accurately characterizing the gas/surface potential when using MD to estimate thermal accommodation coefficients for TiRe-LII.     

He-NO体系一种拟合的各向异性相互作用势

根据MS(Maitland Smith)势模型拟合出了He -NO系统一种形式简单的各向异性相互作用势 ,利用拟合的势能计算了基态氦原子和NO分子碰撞的散射截面 ,计算结果表明拟合势能较好的描写了He -NO系统相互作用的特征。     

Absolute spectroscopic determination of cross-membrane potential

Spectroscopic determination of the cross-membrane electric potential has been used for more than 20 years. This method, which usually employs absorption or fluorescence measurements, allows for a rapid and noninvasive study of the electrical properties of the membranes of cells and liposomes. However, the usual fluorescence techniques preferably allow monitoring changes in the potential on triggerable or excitable membranes, and not the absolute value of the potential. They also do not provide means for measuring the potential on single cells. This paper reviews three methods that solve these issues. Nernstian dyes which partition between intra-and extracompartmental volumes enable a fluorescence microscopic determination of a single cell and even a single organelle. Dual-wavelength ratiometric recording from membrane-staining dyes also provides means for measuring the field on a single cell. Resonance Raman probes provide a spectroscopic method with a natural internal standard for the absolute measurement of membrane potential.     

Exact solutions of a Fokker-Planck equation

Exact explicit solutions are given for a one-dimensional Fokker-Planck equation with a particular potential form involving hyperbolic functions. This potential contains four arbitrary parameters that can be chosen so that the potential is bistable. The solutions also contain parameters that can be chosen so that the initial distribution is approximately Gaussian, centered either at the unstable potential maximum or in the neighborhood of the secondary minimum. The use of the solutions to approximate solutions for other potentials is considered.     

双原子分子激发态势能的自旋相关局域Hartree-Fock密度泛函理论方法

基于自旋相关局域Hartree-Fock (SLHF)势函数,本文提出了一种计算双原子分子激发态势能的密度泛函理论(DFT)方法,并将该方法应用于和的激发态势能曲线的计算。在只考虑交换能的情况下,本文的DFT计算结果与文献中精确方法和Hartree-Fock (HF)方法的结果符合的非常好,说明采用SLHF势函数作为交换势的DFT方法是一个很好的计算激发态势能的方法。本文还计算和探讨了电子的关联势函数和关联能,发现传统的近似方法在较大核间距的情况下大大低估了电子的关联能.     

大气中HCO~+与COH~+ 分子体系的分析势能函数

在从头算的基础上,对HCO+和COH+的全势能表面用多体项展式方法进行优化,确定了分析势能函数,并且正确地再现了HCO+和COH+的结构与能量,预测了HCO+与COH+异构化的角形鞍点     

Non-equilibrium 2PI potential and its possible application to evaluation of bulk viscosity

Within non-equilibrium Green’s function technique on the real-time contour and the two-particle irreducible Φ-functional method, a non-equilibrium potential is introduced. It naturally generalizes the conventional thermodynamic potential with which it coincides in thermal equilibrium. Variations of the non-equilibrium potential over respective parameters result in the same quantities as those of the thermodynamic potential but in arbitrary non-equilibrium. In particular, for slightly non-equilibrium inhomogeneous configurations a variation of the non-equilibrium potential over volume is associated with the trace of the non-equilibrium stress tensor. The latter is related to the bulk viscosity. This provides a novel way for evaluation of the bulk viscosity.     

Modified Kramers formulas for the decay rate in agreement with dynamical modeling

Accuracy of the Kramers approximate formulas for the thermal decay rate of the metastable state is studied for the anharmonic shapes of the potential pocket and the barrier. This is done by the comparison with the quasistationary rate resulting from the dynamical modeling. Disagreement between the Kramers rate and the dynamical one is shown to reach 15% in the cases when much better agreement is expected. Corrections to the Kramers formulas accounting for the higher derivatives of the potential are obtained. The small parameters are the ratios of the thermal energy to the stiffnesses at the extremes of the potential. The distance between the potential barrier and the absorptive border is accounted for as well. This corrected Kramers rate is demonstrated to agree with the dynamical rate typically within 2%. Probably the most interesting result is that despite the corrections are derived in the case of the overdamped Brownian motion, the above 2% agreement holds even in the case of medium friction.     

An investigation of the scaled modified oscillator potential

In the second volume of their book Nuclear structure, Bohr and Mottelson propose that in the modified oscillator potential the spin-orbit term and the l² term should be scaled according to the deformation of the potential. This scaling has been studied in detail, and some of its more general consequences are discussed. The single-particle parameters κ and μ have been fitted for nuclei in the rare earth region, for lead and for actinides. The scaled potential has been used for a detailed investigation of the nuclei in the actinide region, including calculations of potential energy surfaces, fission barriers and ground-state masses. Both symmetric and reflection asymmetric deformations have been considered and the results thus obtained with the scaled potential have been compared to those obtained with the modified oscillator potential and the folded-Yukawa potential.     

Single-electron charging spectra: from natural to artificial atoms

We present a theoretical study of the charging spectra in natural and artificial atoms. We apply a model electrostatic potential created by a homogenously charged sphere. This model potential allows for a continuous passage from the Coulomb potential of the nucleus to parabolic confinement potential of quantum dots. We consider electron systems with N=1,…,10 electrons with the use of the Hartree–Fock method. We discuss the qualitative similarities and differences between the chemical potential spectrum of electron systems bound to nucleus and confined in quantum dots.     

Brownian motion in fluctuating periodic potentials

This work deals with the overdamped motion of a particle in a fluctuating one-dimensional periodic potential. If the potential has no inversion symmetry and its fluctuations are asymmetric and correlated in time, a net flow can be generated at finite temperatures. We present results for the stationary current for the case of a piecewise linear potential, especially for potentials being close to the case with inversion symmetry. The aim is to study the stationary current as a function of the potential. Depending on the form of the potential, the current changes sign once or even twice as a function of the correlation time of the potential fluctuations. To explain these current reversals, several mechanisms are proposed. Finally, we discuss to what extent the model is useful to understand the motion of biomolecular motors.     

Nernst voltage losses in planar fuel cells caused by changes in chemical composition: effects of operating parameters

Conventionally, the reversible potential at inlet conditions is considered to be the ideal voltage for a fuel cell. However, the reversible potential in planar cells varies along the cell length due to changes in gas composition caused by consumption of fuel and oxidant. This contributes to voltage losses, referred to as Nernst losses, compared to the reversible potential at the inlet of the cell. In the conventional breakdown of cell voltage losses, the variation of reversible potential is not accounted for. To estimate the “true” losses, this needs to be accounted for by employing calculations of the reversible potential with changing composition. This paper quantifies such losses in the context of solid oxide fuel cells (SOFCs) for which they are found to contribute significantly, in the range of 25 to 33% of the total voltage losses. The Nernst equation for fuel cell operation is analyzed and analytical expressions for Nernst losses are derived. The latter allows prediction of the effects of operating parameters which are later verified with an isothermal model of the SOFC.     

Determination of the potential distribution of electron optical systems by agent-based simulation

We demonstrate that the potential distribution of electron optical systems can be quickly determined by agent-based simulation with relatively high accuracy. There is no need for the solution of large systems of algebraic equations. This method is especially useful for quick analysis of potential distributions and demonstration purposes.