Related papers: On the Evaluation of the electron repulsion integr…
The influence of electron-electron Coulomb repulsion on nonsequential double ionization of rare-gas atoms is investigated. Several variants of the quantum-mechanical transition amplitude are evaluated that differ by the form of the…
A program for molecular calculations with B functions is reported and its performance is analyzed. All the one- and two-center integrals, and the three-center nuclear attraction integrals are computed by direct procedures, using previously…
This paper deals with the evaluation of some definite Euler-type integrals in terms of the Wright hypergeometric function. We obtain a theorem on the Wright hypergeometric function and then use this theorem to evaluate some definite…
We have developed a McMurchie-Davidson-like recursion formula for efficient evaluation of the Coulomb attraction and interaction matrix elements between two-dimensional primitive Cartesian Gaussian type orbitals. We also present recurrence…
We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring…
Ab initio GW calculations are a standard method for computing the spectroscopic properties of many materials. The most computationally expensive part in conventional implementations of the method is the generation and summation over the…
An alternative methodology to evaluate two-electron-repulsion integrals based on numerical approximation is proposed. Computational chemistry has branched into two major fields with methodologies based on quantum mechanics and classical…
Superintegrable systems are classical and quantum Hamiltonian systems which enjoy much symmetry and structure that permit their solubility via analytic and even, algebraic means. They include such well-known and important models as the…
Based on a method developed earlier for a finite-dimensional mechanical system, the problem of path integral reduction for scalar electrodynamics is considered. Using the Coulomb gauge, the stochastic differential equations for the reduced…
We present a general method for determining screened Coulomb parameters in molecular assemblies, in particular organic molecular crystals. This allows us to calculate the interaction parameters used in a generalized Hubbard model…
General elliptic hypergeometric functions are defined by elliptic hypergeometric integrals. They comprise the elliptic beta integral, elliptic analogues of the Euler-Gauss hypergeometric function and Selberg integral, as well as elliptic…
A relationship between two old mathematical subjects is observed: the theory of hypergeometric functions and the separability in classical mechanics. Separable potential perturbations of the integrable billiard systems and the Jacobi…
In this work, the transition matrix elements for inelastic electron--electron scattering are investigated. The angular part is given by spherical harmonics. For the weighted radial wave function overlap, analytic expressions are derived in…
We examine SERS from two perspectives: as a phenomenon described by the Laplace Equation (the electrostatic or Rayleigh limit) and by the Helmholtz Equation (electrodynamic or Mie limit). We formulate the problem in terms of the scalar…
Excited-state calculations, notably for quasiparticle band structures, are nowadays routinely performed within the GW approximation for the electronic self-energy. Nevertheless, certain numerical approximations and simplifications are still…
Superintegrable systems are a class of physical systems which possess more conserved quantities than their degrees of freedom. The study of these systems has a long history and continues to attract significant international attention. This…
Separating the Coulomb potential into short-range and long-range components enables the use of different electron repulsion integral algorithms for each component. The short-range part can be efficiently computed using the analytical…
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general cubic algebra and we present specific…
Formulas are presented for the recursive generation of four-body integrals in which the integrand consists of arbitrary integer powers (>= -1) of all the interparticle distances r_ij, multiplied by an exponential containing an arbitrary…
Ozdogan (Int. J. Quantum Chem., 92 (2003) 419) published formulas for evaluating the multielectron multicenter molecular integrals over Slater-type orbitals (STOs). It is demonstrated that the formulas presented in this work are not…