Bound states of a more general exponential screened Coulomb potential

An alternative approximation scheme has been used in solving the Schr?dinger equation to the more general case of exponential screened Coulomb potential, V(r) = −(a/r)[1 + (1 + br)e ^−2br ]. The bound state energies of the 1s, 2s and 3s-states, together with the ground state wave function are obtained analytically upto the second perturbation term.      

Approximating the Pauli Potential in Bound Coulomb Systems

It is shown that the Pauli potential in bound Coulomb systems can in good approximation be composed from the corresponding atomic fragments. This provides a simple and fast procedure how to generate the Pauli potential in bound systems, which is needed to perform an orbital‐free density functional calculation. The method is applicable to molecules and solids. © 2016 Wiley Periodicals, Inc.     

Sampling Potential Energy Surfaces in the Condensed Phase with Many-Body Electronic Structure Methods

Sampling potential energy surfaces (PES) is pivotal for understanding chemical structure, energetics and reactivity and is of special importance for complex condensed-phase systems. Until recently such simulations based on electronic structure theory have been performed only by density functional theory and semiempirical methods. Many-body electronic structure methods, almost routinely used for molecules, have been practically unavailable for sampling PES in the condensed-phase. This has changed during the last few years, as efficient algorithms and software implementations for the evaluation of electronic energies and forces on atoms have been developed, allowing for geometry optimization, molecular dynamics and Monte-Carlo simulations, which was previously unthinkable. Herein, we introduce the theory and software developments and overview the applications in the field, the most encouraging results being obtained for aqueous chemistry. Requiring state-of-the-art computer resources PES sampling with many-body electronic structure methods in the condensed phase provides high-quality benchmarks and will gradually become more available due to fast progress in reduced scaling algorithms and computational technologies.     

Matrix elements of the Coulomb Green function between Slater orbitals

Analytic expressions are given for integrals of the Coulomb Green function with Slater type atomic orbitals. The results involve hypergeometric functions.Supported by the National Institutes of Health, Grant No. GM23223.     

关于最弱受约束电子势模型理论中势函数物理意义的讨论

从屏蔽、贯穿和极化作用考虑,对最弱受约束电子势模型理论(简称WBEPM理论)的势函数进行了讨论.通过一系列推导、论证,得出WBEPM理论的有效势的物理意义为:势函数中的第一项表示最弱受约束电子在有效核电荷+Z＇e中心场中的势能;第二项代表最弱受约束电子对非最弱受约束电子和核组成的"实”的极化作用所引起的偶极子场中的势能.     

Parallel DFT gradients using the Fourier Transform Coulomb method

The recently described Fourier Transform Coulomb (FTC) algorithm for fast and accurate calculation of Density Functional Theory (DFT) gradients (Füsti-Molnar, J Chem Phys 2003, 119, 11080) has been parallelized. We present several calculations showing the speed and accuracy of our new parallel FTC gradient code, comparing its performance with our standard DFT code. For that part of the total derivative Coulomb potential that can be evaluated in plane wave space, the current parallel FTC gradient algorithm is up to 200 times faster in total than our classical all-integral algorithm, depending on the system size and basis set, with essentially no loss in accuracy. Proposed modifications should further improve the overall performance relative to the classical algorithm.     

Thinking inside the box: Novel linear scaling algorithm for Coulomb potential evaluation

Beginning with the Poisson equation, and expanding the electronic potential in terms of sine functions, the natural orbitals for describing the particle‐in‐a‐box problem, we find that simple analytic forms can be found for the evaluation of the Coulomb energy for both the interacting and non‐interacting system of N‐electrons in a box. This method is reminiscent of fast‐Fourier transform and scales linearly. To improve the usefulness of this result, we generalize the idea by considering a molecular system, embedded in a box, within which we determine the electrostatic potential, in the same manner as that described for our model systems. Within this general formalism, we consider both periodic and aperiodic recipes with specific application to systems described using Gaussian orbitals; although in principle the method is seen to be completely general. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Near-Diagonal Behaviour of First-order Density Matrix for N Closed Shells in a Bare Coulomb Field

Abstract

When the first order density matrix is expanded to lowest order, it is shown that the lowest order term is characterized by a functionf(r) whose derivative can be expressed in terms of the diagonal electron density and the nuclear charge, for the case of N closed shells in a bare Coulomb field.     

Normalization and Fermi–Coulomb and Coulomb hole sum rules for approximate wave functions

For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

A new estimate on the indirect Coulomb energy

Here we prove a new lower bound on the indirect Coulomb energy in quantum mechanics, in terms of the single particle density of the system. The new universal lower bound is an alternative to the classical Lieb–Oxford bound (with a smaller constant, C = 1.45 < C_LO = 1.68) but involving an additive kinetic energy term of the single particle density as well. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

The antiparallel electron correlation coefficient and Coulomb hole structure

Based on the charge density functional theory, a simple method is proposed to calculate the antiparallel electron correlation coefficient, correlation charge, and correlation energy. In contrast to the result stated in the literature, our analysis reveals that the Coulomb hole has a fine structure. To our knowledge, this is the first time it has been proven that the electrons obey the curve correlation law in an intermediate separation range but the electrons obey the linear correlation law in small and large separation ranges. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 1–6, 1999     

An improvement of the resolution of the identity approximation for the formation of the Coulomb matrix

A straightforward modification of the resolution of the identity (RI) approximation to the Coulomb interaction is described. In the limit of basis sets that are dominated by high angular momentum functions the observed speedups in realistic test systems reach a factor of 2 compared to the standard RI algorithm, and a factor of up to 300 compared to the standard algorithm to form the Coulomb matrix. More moderate savings on the order of 0-20% are obtained for the more commonly used smaller basis sets. A series of test calculations is reported to illustrate the efficiency of the algorithm.     

The topology of the Coulomb potential density. A comparison with the electron density,the virial energy density,and the Ehrenfest force density

The topology of the Coulomb potential density has been studied within the context of the theory of Atoms in Molecules and has been compared with the topologies of the electron density, the virial energy density and the Ehrenfest force density. The Coulomb potential density is found to be mainly structurally homeomorphic with the electron density. The Coulomb potential density reproduces the non‐nuclear attractor which is observed experimentally in the molecular graph of the electron density of a Mg dimer, thus, for the first time ever providing an alternative and energetic foundation for the existence of this critical point. © 2017 Wiley Periodicals, Inc.     

Pauli potential functional for spherical inhomogeneous electron liquids generated by a bare Coulomb field

Making use of the spatial generalisation of Kato's theorem, the Pauli potential functional is derived for spherical inhomogeneous electron liquids generated by a bare Coulomb field.     

Ion Co-storage in Porous Organic Frameworks through On-site Coulomb Interactions for High Energy and Power Density Batteries

Fast and continuous ion insertion is blocked in the common electrodes operating with widely accepted single-ion storage mechanism, primarily due to Coulomb repulsion between the same ions. It results in an irreconcilable conflict between capacity and rate performance. Herein, we designed a porous organic framework with novel multiple-ion co-storage modes, including PF₆⁻/Li⁺, OTF⁻/Mg²⁺, and OTF⁻/Zn²⁺ co-storage. The Coulomb interactions between cationic and anionic carriers in the framework can significantly promote electrode kinetics, by rejuvenating fast ion carrier migration toward framework interior. Consequently, the framework via PF₆⁻/Li⁺ co-storage mode shows a high energy density of 878 Wh kg⁻¹ cycled more than 20 000 cycles, with an excellent power density of 28 kW kg⁻¹ that is already comparable to commercial supercapacitors. The both greatly improved energy and power densities via the co-storage mode may pave a way for exploring new electrodes that are not available from common single-ion electrodes.     

基态PuOH分子的多体展式分析势能函数

Using the density functional method B3LYP with relativistic effective core potential(RECP)for Pu atom,thelow-lying excited states(~4Σ~ ,~6Σ~ ,~8Σ~ )for three structures of PuOH molecule were optimized.The results showthat the ground state is X~6Σ~ of the linear Pu-O-H(C_(∞v)),its corresponding equilibrium geometry and dissociationenergy are R_(Pu-O)=0.20595 nm,R_(O-H)=0.09581 nm and —8.68 eV,respectively.At the same time,two other me-tastable structures [PuOH(C_s)and H-Pu-O(C_(∞v)] were found.The analytical potential energy function has alsobeen derived for whole range using the many-body expansion method.This potential energy function represents theconsiderable topographical features of PuOH molecule in detail,which is adequately accurate in the whole potentialsurface and can be used for the molecular reaction dynamics research.     

Critical parameters and spherical confinement of H atom in screened Coulomb potential

Critical parameters in three screened potentials, namely, Hulthén, Yukawa, and exponential cosine screened Coulomb potential are reported. Accurate estimates of these parameters are given for each of these potentials, for all states having . Comparison with literature results is made, wherever possible. Present values compare excellently with reference values; for higher n, ?, our results are slightly better. Some of these are presented for first time. Further, we investigate the spherical confinement of H atom embedded in a dense plasma modeled by an exponential cosine screened potential. Accurate energies along with their variation with respect to box size and screening parameter are calculated and compared with reference results in literature. Sample dipole polarizabilities are also provided in this case. The generalized pseudospectral method is used for accurate determination of eigenvalues and eigenfunctions for all calculations. © 2016 Wiley Periodicals, Inc.     

最弱受约束电子势模型理论下使用双广义拉盖尔多项式计算氦原子基态能量

计算了在最弱受约束电子势模型理论下使用双广义拉盖尔多项式的氦原子基态能量. 给出了氦原子基态能量期望值的表达式. 通过搜索它的极小, 找到了氦原子基态能量的极小值. 将我们的结果与双灼(zeta)函数的Hartree-Fock(HF)方法的结果进行比较后发现, 我们的结果略优于双灼(zeta)函数的Hartree-Fock(HF)方法的结果. 如此表明线性组合技术可以应用在最弱受约束电子势模型理论中.     

两体扰动势构造CO_2通道反应三原子体系解析势

应用两体扰动势，成功地构造了线性三原分子CO_2平衡态及通道反应的三原子 体系相互作用解析热。势函数不但定量地描述了CO_2平衡态的临界特性，而且势能 面正确的描述了O(~1D)+CO(X~1∑+)→CO_2→C(~3P)+O_2(X~3∑-_g)通道反应的性 质。理论分析与实验推测结果非常吻合。