A Generalized Grid-Based Fast Multipole Method for Integrating Helmholtz Kernels

A grid-based fast multipole method (GB-FMM) for optimizing three-dimensional (3D) numerical molecular orbitals in the bubbles and cube double basis has been developed and implemented. The present GB-FMM method is a generalization of our recently published GB-FMM approach for numerically calculating electrostatic potentials and two-electron interaction energies. The orbital optimization is performed by integrating the Helmholtz kernel in the double basis. The steep part of the functions in the vicinity of the nuclei is represented by one-center bubbles functions, whereas the remaining cube part is expanded on an equidistant 3D grid The integration of the bubbles part is treated by using one-center expansions of the Helmholtz kernel in spherical harmonics multiplied with modified spherical Bessel functions of the first and second kind, analogously to the numerical inward and outward integration approach for calculating two-electron interaction potentials in atomic structure calculations. The expressions and algorithms for massively parallel calculations on general purpose graphics processing units (GPGPU) are described. The accuracy and the correctness of the implementation has been checked by performing Hartree-Fock self-consistent-field calculations (HF-SCF) on H-2, H2O, and CO. Our calculations show that an accuracy of 10(-4) to 10(-7) E-h can be reached in HF-SCF calculations on general molecules.Peer reviewe

A finite difference Hartree–Fock program for atoms and diatomic molecules

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018) Abstract The newest version of the two-dimensional finite difference Hartree–Fock program for atoms and diatomic molecules is presented. This is an updated and extended version of the program published in this journal in 1996. It can be used to obtain reference, Hartree–Fock limit values of total energies and multipole moments for a wide range of diatomic molecules and their ions in order to calibrate existing and develop new basis sets, calculate (hyper)polarizabilities ( α z z , β z z z , γ z z z z ... Title of program: 2dhf Catalogue Id: ADEB_v2_0 Nature of problem The program finds virtually exact solutions of the Hartree- Fock and density functional theory type equations for atoms, diatomic molecules and their ions. The lowest energy eigenstates of a given irreducible representation and spin can be obtained. The program can be used to perform one-particle calculations with (smooth) Coulomb and Krammers-Henneberger potentials and also DFT-type calculations using LDA or B88 exchange functionals and LYP or VWN correlations ones or the Self-Consistent Multip ... Versions of this program held in the CPC repository in Mendeley Data ADEB_v1_0; 2dhf; 10.1016/0010-4655(96)00098-7 ADEB_v2_0; 2dhf; 10.1016/j.cpc.2012.09.03

A finite difference Hartree–Fock program for atoms and diatomic molecules

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018) Abstract The newest version of the two-dimensional finite difference Hartree–Fock program for atoms and diatomic molecules is presented. This is an updated and extended version of the program published in this journal in 1996. It can be used to obtain reference, Hartree–Fock limit values of total energies and multipole moments for a wide range of diatomic molecules and their ions in order to calibrate existing and develop new basis sets, calculate (hyper)polarizabilities ( α z z , β z z z , γ z z z z ... Title of program: 2dhf Catalogue Id: ADEB_v2_0 Nature of problem The program finds virtually exact solutions of the Hartree- Fock and density functional theory type equations for atoms, diatomic molecules and their ions. The lowest energy eigenstates of a given irreducible representation and spin can be obtained. The program can be used to perform one-particle calculations with (smooth) Coulomb and Krammers-Henneberger potentials and also DFT-type calculations using LDA or B88 exchange functionals and LYP or VWN correlations ones or the Self-Consistent Multip ... Versions of this program held in the CPC repository in Mendeley Data ADEB_v1_0; 2dhf; 10.1016/0010-4655(96)00098-7 ADEB_v2_0; 2dhf; 10.1016/j.cpc.2012.09.03