Bessel, sine and cosine functions and extrapolation methods for computing molecular multi-center integrals
DOI10.1007/s11075-009-9326-8zbMath1190.65032OpenAlexW2007669205MaRDI QIDQ970592
Publication date: 19 May 2010
Published in: Numerical Algorithms (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11075-009-9326-8
convergencenumerical integrationnumerical examplesextrapolation methodsoscillatory integralsSlevinsky-Safouhi formulaemolecular electronic structure calculationmolecular multi-center integralsspherical Bessel integrals
Computation of special functions and constants, construction of tables (65D20) Other functions defined by series and integrals (33E20) Numerical quadrature and cubature formulas (65D32) Molecular physics (81V55) Numerical approximation and evaluation of special functions (33F05)
Related Items
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Computation of infinite integrals involving Bessel functions of arbitrary order by the \(\overline{D}\)-transformation
- New formulae for higher order derivatives and applications
- Numerical treatment of a twisted tail using extrapolation methods
- The numerical evaluation of a challenging integral
- An algorithm for a special case of a generalization of the Richardson extrapolation process
- Two new classes of nonlinear transformations for accelerating the convergence of infinite integrals and series
- Extrapolation methods theory and practice
- A convergent renormalized strong coupling perturbation expansion for the ground state energy of the quartic, sextic, and octic anharmonic oscillator
- Fast evaluation of Gaunt coefficients: Recursive approach
- A rational approximant for the digamma function
- Extrapolation methods for improving the convergence of oligomer calculations to the infinite chain limit of quasi-one-dimensional stereoregular polymers.
- Efficient and rapid numerical evaluation of the two-electron, four-center Coulomb integrals using nonlinear transformations and useful properties of sine and Bessel functions
- Extrapolation algorithms for filtering series of functions, and treating the Gibbs phenomenon
- Extrapolation methods for PageRank computations
- The properties of sine, spherical Bessel and reduced Bessel functions for improving convergence of semi-infinite very oscillatory integrals: the evaluation of three-centre nuclear attraction integrals overBfunctions
- On the eigenfunctions of many-particle systems in quantum mechanics
- The PageRank Vector: Properties, Computation, Approximation, and Acceleration
- Efficient evaluation of the Fourier transform over products of Slater-type orbitals on different centers
- Rational extrapolation for the PageRank vector
- Weakly convergent expansions of a plane wave and their use in Fourier integrals
- New representations for the spherical tensor gradient and the spherical delta function
- Some Properties of a Generalization of the Richardson Extrapolation Process
- Extrapolation Methods for Oscillatory Infinite Integrals
- A New Method for Approximating Improper Integrals
- Generating Functions for Spherical Harmonics Part I: Three-Dimensional Harmonics
- The three-dimensional convolution of reduced Bessel functions and other functions of physical interest
- The summation of the ordinary and renormalized perturbation series for the ground state energy of the quartic, sextic, and octic anharmonic oscillators using nonlinear sequence transformations
- Analytic Atomic Wave Functions
- Practical Extrapolation Methods
- An extremely efficient and rapid algorithm for numerical evaluation of three-centre nuclear attraction integrals over Slater-type functions
- Multicentre two-electron Coulomb and exchange integrals over Slater functions evaluated using a generalized algorithm based on nonlinear transformations
- A new algorithm for accurate and fast numerical evaluation of hybrid and three-centre two-electron Coulomb integrals over Slater-type functions
- The SIAM 100-Digit Challenge
- Development of non-linear transformations for improving convergence of sequences
- Two-Center Expansion for the Powers of the Distance Between Two Points
- Expansions in Spherical Harmonics. IV. Integral Form of the Radial Dependence
- Upon A Second Confluent Form of the Ɛ-Algorithm
- Generalization of Laplace's Expansion to Arbitrary Powers and Functions of the Distance between Two Points
- Three-Dimensional Addition Theorem for Arbitrary Functions Involving Expansions in Spherical Harmonics
- Electronic wave functions - I. A general method of calculation for the stationary states of any molecular system
- Electronic wave functions II. A calculation for the ground state of the beryllium atom
- Integrals Occurring in Problems of Molecular Structure
- CHA