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Coulomb Potential (coulomb + potential)
Selected AbstractsGrid-based density functional calculations of many-electron systemsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2008Amlan K. RoyArticle first published online: 10 DEC 200 Abstract Exploratory variational pseudopotential density functional calculations are performed for the electronic properties of many-electron systems in the 3D cartesian coordinate grid (CCG). The atom-centered localized gaussian basis set, electronic density, and the two-body potentials are set up in the 3D cubic box. The classical Hartree potential is calculated accurately and efficiently through a Fourier convolution technique. As a first step, simple local density functionals of homogeneous electron gas are used for the exchange-correlation potential, while Hay-Wadt-type effective core potentials are employed to eliminate the core electrons. No auxiliary basis set is invoked. Preliminary illustrative calculations on total energies, individual energy components, eigenvalues, potential energy curves, ionization energies, and atomization energies of a set of 12 molecules show excellent agreement with the corresponding reference values of atom-centered grid as well as the grid-free calculation. Results for three atoms are also given. Combination of CCG and the convolution procedure used for classical Coulomb potential can provide reasonably accurate and reliable results for many-electron systems. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source] Application of the asymptotic iteration method to the exponential cosine screened Coulomb potentialINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2007O. Bayrak Abstract We present the iterative solutions of the radial Schrödinger equation for the exponential cosine screened Coulomb (ECSC) potential for any n and l quantum states by applying the asymptotic iteration method (AIM). We show that it is possible to obtain the solution as accurate as the other methods without any perturbation. Furthermore, there are no tedious mathematical difficulties and restrictions on finding the energy eigenvalues for any n and l quantum numbers. Our results are in excellent agreement with the ones published in the literature. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source] Studies on some singular potentials in quantum mechanicsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 6 2005Amlan K. RoyArticle first published online: 10 MAY 200 Abstract A simple methodology is suggested for the efficient calculation of certain central potentials having singularities. The generalized pseudospectral method used in this work facilitates nonuniform and optimal spatial discretization. Applications have been made to calculate the energies, densities, and expectation values for two singular potentials of physical interest, viz., (i) the harmonic potential plus inverse quartic and sextic perturbation and (ii) the Coulomb potential with a linear and quadratic term for a broad range of parameters. The first 10 states belonging to a maximum of ,, = 8 and 5 for (i) and (ii) have been computed with good accuracy and compared with the most accurate available literature data. The calculated results are in excellent agreement, especially in light of the difficulties encountered in these potentials. Some new states are reported here for the first time. This offers a general and efficient scheme for calculating these and other similar potentials of physical and mathematical interest in quantum mechanics accurately. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source] Linear augmented Slater-type orbital method for free standing clustersJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 8 2009K. S. Kang Abstract We have developed a Scalable Linear Augmented Slater-Type Orbital (LASTO) method for electronic-structure calculations on free-standing atomic clusters. As with other linear methods we solve the Schrödinger equation using a mixed basis set consisting of numerical functions inside atom-centered spheres and matched onto tail functions outside. The tail functions are Slater-type orbitals, which are localized, exponentially decaying functions. To solve the Poisson equation between spheres, we use a finite difference method replacing the rapidly varying charge density inside the spheres with a smoothed density with the same multipole moments. We use multigrid techniques on the mesh, which yields the Coulomb potential on the spheres and in turn defines the potential inside via a Dirichlet problem. To solve the linear eigen-problem, we use ScaLAPACK, a well-developed package to solve large eigensystems with dense matrices. We have tested the method on small clusters of palladium. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009 [source] Two-electron integral evaluation on the graphics processor unitJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 3 2008Koji Yasuda Abstract We propose the algorithm to evaluate the Coulomb potential in the ab initio density functional calculation on the graphics processor unit (GPU). The numerical accuracy required for the algorithm is investigated in detail. It is shown that GPU, which supports only the single-precision floating number natively, can take part in the major computational tasks. Because of the limited size of the working memory, the Gauss-Rys quadrature to evaluate the electron repulsion integrals (ERIs) is investigated in detail. The error analysis of the quadrature is performed. New interpolation formula of the roots and weights is presented, which is suitable for the processor of the single-instruction multiple-data type. It is proposed to calculate only small ERIs on GPU. ERIs can be classified efficiently with the upper-bound formula. The algorithm is implemented on NVIDIA GeForce 8800 GTX and the Gaussian 03 program suite. It is applied to the test molecules Taxol and Valinomycin. The total energies calculated are essentially the same as the reference ones. The preliminary results show the considerable speedup over the commodity microprocessor. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008 [source] Spontaneous bremsstrahlung effect in the nonrelativistic electron scattering by a nucleus in the field of pulsed light waveLASER PHYSICS LETTERS, Issue 6 2009A.A. Lebed' Abstract The theory of nonresonant spontaneous bremsstrahlung by a nonrelativistic electron scattered by a nucleus in the field of a pulsed light wave is developed. The electron interaction with a Coulomb potential of a nucleus is considered in the first order of perturbation theory (the Born approximation), and the interaction with an external pulsed field is taken into account accurately. The approximation is examined when the pulsewidth is considerably greater than the characteristic time of wave oscillations. For the range of moderately strong fields the analytic expression for the nonresonant differential cross-section was obtained, which has the form of a sum over partial differential crosssections. It is shown, that in the case of nonrelativistic electron energy the partial cross-section is not factorable on the crosssection of electron-nucleus spontaneous bremsstrahlung in the absence of the external field and the emission-absorption probability of a certain number of wave photons. It is concluded, that the total cross-section of spontaneous bremsstrahlung of an electron scattered by a nucleus in the field of pulsed light wave summing over all possible partial processes differs essentially from the cross-section of electron-nucleus spontaneous bremsstrahlung in the absence of the external field. (© 2009 by Astro Ltd., Published exclusively by WILEY-VCH Verlag GmbH & Co. KGaA) [source] 3D Monte Carlo simulation including full Coulomb interaction under high electron concentration regimesPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 1 2008Tadayoshi Uechi Abstract We construct 3D Monte Carlo (MC) simulations including the full Coulomb interaction as accurately as possible. In order to achieve this goal, the usual strategy for the MC approach is employed; the Coulomb potential is split into the long-range and the short-range parts. The long-range part of the Coulomb potential is taken into account by solving the Poisson equation, in which the simulation parameters such as mesh size, charged-particle size, time step etc are carefully optimized by performing the particle simulations with turning off artificially all short-ranged scatterings. The short-range part of the Coulomb potential is incorporated into the MC simulations as scattering processes by developing a new scattering model, in which the impurities are localized in real space. It is shown that the present 3D MC simulations successfully explain the entire regime of the electron mobility as a function of impurity concentrations. In addition, it is found for the first time that the plasma frequency is modulated due to localization of the background impurities. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] From quantum chemistry and the classical theory of polar liquids to continuum approximations in molecular mechanics calculations,INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2005Sergio A. Hassan Abstract Biological macromolecules and other polymers belong to the class of mesoscopic systems, with characteristic length scale of the order of a nanometer. Although microscopic models would be the preferred choice in theoretical calculations, their use in computer simulations becomes prohibitive for large systems or long simulation times. On the other hand, the use of purely macroscopic models in the mesoscopic domain may introduce artifacts, with effects that are difficult to assess and that may compromise the reliability of the calculations. Here is proposed an approach with the aim of minimizing the empirical nature of continuum approximations of solvent effects within the scope of molecular mechanics (MM) approximations in mesoscopic systems. Using quantum chemical methods, the potential generated by the molecular electron density is first decomposed in a multicenter-multipole expansion around predetermined centers. The monopole and dipole terms of the expansion at each site create electric fields that polarize the surrounding aqueous medium whose dielectric properties can be described by the classical theory of polar liquids. Debye's theory allows a derivation of the dielectric profiles created around isolated point charges and dipoles that can incorporate Onsager reaction field corrections. A superposition of screened Coulomb potentials obtained from this theory makes possible a simple derivation of a formal expression for the total electrostatic energy and the polar component of the solvation energy of the system. A discussion is presented on the physical meaning of the model parameters, their transferability, and their convergence to calculable quantities in the limit of simple systems. The performance of this continuum approximation in computer calculations of amino acids in the context of an atomistic force field is discussed. Applications of a continuum model based on screened Coulomb potentials in multinanosecond simulations of peptides and proteins are briefly reviewed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source] Hartree,Fock exchange fitting basis sets for H to Rn ,JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 2 2008Florian Weigend Abstract For elements H to Rn (except Lanthanides), a series of auxiliary basis sets fitting exchange and also Coulomb potentials in Hartree,Fock treatments (RI-JK-HF) is presented. A large set of small molecules representing nearly each element in all its common oxidation states was used to assess the quality of these auxiliary bases. For orbital basis sets of triple zeta valence and quadruple zeta valence quality, errors in total energies arising from the RI-JK approximation are below ,1 meV per atom in molecular compounds. Accuracy of RI-JK-approximated HF wave functions is sufficient for being used for post-HF treatments like Møller,Plesset perturbation theory, MP2. Compared to nonapproximated treatments, RI-JK-HF leads to large computational savings for quadruple zeta valence orbital bases and, in case of small to midsize systems, to significant savings for triple zeta valence bases. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008 [source] Liouville and Fokker,Planck dynamics for classical plasmas and radiationANNALEN DER PHYSIK, Issue 6 2006R.F. Alvarez-Estrada Abstract We consider a nonequilibrium statistical system formed by many classical non-relativistic particles of opposite electric charges (plasma) and by the classical dynamical electromagnetic (EM) field. The charges interact with one another directly through instantaneous Coulomb potentials and with the dynamical degrees of freedom of the transverse EM field. The system may also be subject to external influences of: i) either static, but spatially inhomogeneous, electric and magnetic fields (case 1)), or ii) weak distributions of electric charges and currents (case 2)). The particles and the dynamical EM field are described, for any time t > 0, by the classical phase-space probability distribution functional (CPSPDF) f and, at the initial time (t = 0), by the initial CPSPDF fin. The CPSPDF f and fin, multiplied by suitable Hermite polynomials (for particles and field) and integrated over all canonical momenta, yield new moments. The Liouville equation and fin imply a new nonequilibrium linear infinite hierarchy for the moments. In case 1), fin describes local equilibrium but global nonequilibrium, and we propose a long-time approximation in the hierarchy, which introduces irreversibility and relaxation towards global thermal equilibrium. In case 2), the statistical system, having been at global thermal equilibrium, without external influences, for t , 0, is subject to weak external charge-current distributions: then, new hierarchies for moments and their long-time behaviours are discussed in outline. As examples, approximate mean-field (Vlasov) approximations are treated for both cases 1) and 2). [source] | |||||||||||||