Hartree-Fock Program Research Articles

Impact of carbon number and atom number on cc-pVTZ Hartree-Fock Energy and program runtime of alkanes

Impact of carbon number and atom number on cc-pVTZ Hartree-Fock Energy and program runtime of alkanes

Atomic Mean-Field Approach within Exact Two-Component Theory Based on the Dirac–Coulomb–Breit Hamiltonian

An extension of the exact two-component theory with atomic mean-field integrals (the X2CAMF scheme) to the treatment of the Breit term together with efficient implementation using an atomic Dirac-Coulomb-Breit Hartree-Fock program is reported. The accuracy of the X2CAMF scheme for treating the contributions from the Breit term to the molecular properties is demonstrated using benchmark calculations of equilibrium bond lengths, harmonic frequencies, and dipole moments for molecules containing elements across the periodic table. Calculations of the properties for molecules containing period four elements aiming at high accuracy as well as for Th- and U-containing molecules are also presented and compared with experimental results to demonstrate the usefulness of the X2CAMF scheme in combination with accurate treatments of electron correlation by the coupled-cluster (CC) methods. The combination of CC methods and the X2CAMF scheme shows potential to extend the accuracy of CC calculations to heavy elements, e.g., to computational heavy-element thermochemistry.

Development of the numerical Hartree-Fock method for screened atoms with Debye-Hückel potential

SynopsisThe difficulties in developing the numerical Hartree-Fock programs for atoms interacting with screened Coulomb potential have been overcome. The binding energies of atoms for various screening parameters are obtained in high accuracy. C4+ ion is investigated to demonstrate the validity of our program.

Accurate computation of screened Coulomb potential integrals in numerical Hartree–Fock programs

The frequently-used Zk and Yk functions in the framework of numerical Hartree–Fock method are formulated for atomic systems embedded in weakly-coupled plasmas modeled by Debye–Hückel potential. The Gegenbauer expansion is used to decompose the screened interelectronic Coulomb potential. Two numerical methods, the integration and differentiation ones, are developed to accurately and efficiently calculate the Zk and Yk integrals with each one showing special advantages in the implementation of numerical Hartree–Fock programs. Comparing to the analytical results specialized for Slater-type radial functions, it is generally concluded that the integration method possesses more accuracy and robustness than the differentiation one. Calculations on the two-electron C4+ ion in three different screening models are performed to demonstrate the applicability and stability of present methods in a wider range of screening parameters than existing Hartree–Fock calculations. With benchmark Hartree–Fock energies obtained in this work and accurate non-relativistic energies calculated based on Hylleraas-CI basis functions, it is found that the correlation energies are smallest in the fully screening model.

The argon nuclear quadrupole moments

ABSTRACTNew standard values -116(2) mb and 76(3) mb are suggested for the nuclear quadrupole moments (Q) of the 39Ar and 37Ar nuclei, respectively. The Q values were obtained by combining optical measurements of the quadrupole coupling constant (B or eqQ/h) of the 3s23p54s[3/2]2 (3Po) and 3s23p54p[5/2]3 (3De) states of argon with large scale numerical complete active space self-consistent field and restricted active space self-consistent field calculations of the electric field gradient at the nucleus (q) using the LUCAS code, which is a finite-element based multiconfiguration Hartree–Fock program for atomic structure calculations.

Experimental and theoretical oscillator strengths of Mg i for accurate abundance analysis

Context. With the aid of stellar abundance analysis, it is possible to study the galactic formation and evolution. Magnesium is an important element to trace the alpha-element evolution in our Galaxy. For chemical abundance analysis, such as magnesium abundance, accurate and complete atomic data are essential. Inaccurate atomic data lead to uncertain abundances and prevent discrimination between different evolution models. Aims. We study the spectrum of neutral magnesium from laboratory measurements and theoretical calculations. Our aim is to improve the oscillator strengths ( f -values) of Mg I lines and to create a complete set of accurate atomic data, particularly for the near-IR region. Methods. We derived oscillator strengths by combining the experimental branching fractions with radiative lifetimes reported in the literature and computed in this work. A hollow cathode discharge lamp was used to produce free atoms in the plasma and a Fourier transform spectrometer recorded the intensity-calibrated high-resolution spectra. In addition, we performed theoretical calculations using the multiconfiguration Hartree-Fock program ATSP2K. Results. This project provides a set of experimental and theoretical oscillator strengths. We derived 34 experimental oscillator strengths. Except from the Mg I optical triplet lines (3p 3^P^o_0,1,2 - 4s 3^S_1), these oscillator strengths are measured for the first time. The theoretical oscillator strengths are in very good agreement with the experimental data and complement the missing transitions of the experimental data up to n = 7 from even and odd parity terms. We present an evaluated set of oscillator strengths, gf, with uncertainties as small as 5%. The new values of the Mg I optical triplet line (3p 3^P^o_0,1,2 - 4s 3^S_1) oscillator strength values are ~0.08 dex larger than the previous measurements.

Parallel and Low-Order Scaling Implementation of Hartree-Fock Exchange Using Local Density Fitting.

Calculations using modern linear-scaling electron-correlation methods are often much faster than the necessary reference Hartree-Fock (HF) calculations. We report a newly implemented HF program that speeds up the most time-consuming step, namely, the evaluation of the exchange contributions to the Fock matrix. Using localized orbitals and their sparsity, local density fitting (LDF), and atomic orbital domains, we demonstrate that the calculation of the exchange matrix scales asymptotically linearly with molecular size. The remaining parts of the HF calculation scale cubically but become dominant only for very large molecular sizes or with many processing cores. The method is well parallelized, and the speedup scales well with up to about 100CPU cores on multiple compute nodes. The effect of the local approximations on the accuracy of computed HF and local second-order Møller-Plesset perturbation theory energies is systematically investigated, and default values are established for the parameters that determine the domain sizes. Using these values, calculations for molecules with hundreds of atoms in combination with triple-ζ basis sets can be carried out in less than 1 h, with just a few compute nodes. The method can also be used to speed up density functional theory calculations with hybrid functionals that contain HF exchange.

DBSR_HF: A B-spline Dirac–Hartree–Fock program

A B-spline version of a general Dirac–Hartree–Fock program is described. The usual differential equations are replaced by a set of generalized eigenvalue problems of the form (Ha−εaB)Pa=0, where Ha and B are the Hamiltonian and overlap matrices, respectively, and Pa is the two-component relativistic orbit in the B-spline basis. A default universal grid allows for flexible adjustment to different nuclear models. When two orthogonal orbitals are both varied, the energy must also be stationary with respect to orthonormal transformations. At such a stationary point the off-diagonal Lagrange multipliers may be eliminated through projection operators. The self-consistent field procedure exhibits excellent convergence. Several atomic states can be considered simultaneously, including some configuration-interaction calculations. The program provides several options for the treatment of Breit interaction and QED corrections. The information about atoms up to Z=104 is stored by the program. Along with a simple interface through command-line arguments, this information allows the user to run the program with minimal initial preparations. Program summaryProgram title: DBSR_HFCatalogue identifier: AEZK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEZK_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 22643No. of bytes in distributed program, including test data, etc.: 354629Distribution format: tar.gzProgramming language: Fortran 95.Computer: No specific requirements to the computer.Operating system: Any system with a Fortran 95 compiler.Classification: 2.1.External routines: LAPACK (http://www.netlib.org/lapack/)Nature of problem:Relativistic Dirac–Hartree–Fock wavefunctions are determined for atoms in a bound state. These wavefunctions may be used to predict a variety of atomic properties.Solution method:The radial functions for large and small components of the one-electron spinor are expanded in B-spline bases. The variational principle applied to an energy functional that includes Lagrange multipliers for orthonormal constraints defines the Dirac–Hartree–Fock matrix for each orbital. Orthonormal transformations for a stationary solution were applied and Lagrange multipliers eliminated through projection operators.Restrictions:There is no restriction on calculations for the average or specific term energy of any atomic configuration with shells whose angular momenta are less than or equal to 9/2.Unusual features:The program allows the consideration of a few atomic states simultaneously. A simple interface through the command-line arguments allows the user to run the program with minimal initial preparations.Running time:From a few seconds to a few minutes depending on the atom under consideration.

DMTDHF: A full dimensional time-dependent Hartree–Fock program for diatomic molecules in strong laser fields

We present the DMTDHF package, which investigates the non-perturbative electronic dynamics of diatomic molecules subjected to strong external laser fields by the fully propagated time-dependent Hartree–Fock theory. The package uses the prolate spheroidal coordinates, together with the finite-element method and discrete-variable representation, while short iterative Lanczos algorithm is employed for the time propagation. This package can be applied to diatomic molecules with many electrons, and is implemented to allow easy extensions for additional capabilities. Program summaryProgram title: DMTDHFCatalogue identifier: AEWN_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEWN_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 702996No. of bytes in distributed program, including test data, etc.: 7336872Distribution format: tar.gzProgramming language: Fortran 2003.Computer: All computers with a Fortran compiler supporting at least Fortran 2003.Operating system: All operating systems with such a compiler. The makefile depends on a Unix-like system and needs modification under Windows.Has the code been vectorized or parallelized?: The program is able to run both in sequential and parallel mode. For parallel running, the number of processors can be arbitrary.RAM: Several GBs, depends on the size of the molecules and the number of DVR basis functions.Classification: 16.1, 16.2, 16.6.External routines: BLAS, LAPACK, FFTW3, MPINature of problem: The investigation of molecules interacting with intense laser pulses requires non-perturbative theoretical treatment. It has been evidenced that multiorbital and multipole effects come into play for strong-field physics, while the direct numerical integration of TDSE is computationally prohibitive for systems with more than two electrons. TDHF goes beyond the SAE approach and includes the response to the field of all electrons, which is helpful to resolve the multielectron effects from the collective response of electrons.Solution method: The package uses the prolate spheroidal coordinates, together with the finite-elements method and discrete-variable representation, while short iterative Lanczos algorithm is employed for the time propagation.Restrictions: Currently, the spin-restricted form of TDHF is implemented, which can be applied to closed-shell molecules. However, the extension to spin-unrestricted form is straight forward.Unusual features: Due to the prolate spheroidal coordinates, the Coulomb potential is treated accurately. The calculations can converge with only a mild number of basis functions and are highly efficient due to the nature of DVR functions in calculation of the two-electron integrals.Running time: The running time depends on the size of the molecules, the number of basis functions, the duration of laser pulses, and the number of processors used. Depending on these factors, it can vary between a few hours and weeks.

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

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 (αzz, βzzz, γzzzz, Az,zz, Bzz,zz) of atoms, homonuclear and heteronuclear diatomic molecules and their ions via the finite field method, perform DFT-type calculations using LDA or B88 exchange functionals and LYP or VWN correlations ones or the self-consistent multiplicative constant method, perform one-particle calculations with (smooth) Coulomb and Krammers–Henneberger potentials and take account of finite nucleus models. The program is easy to install and compile (tarball+configure+make) and can be used to perform calculations within double- or quadruple-precision arithmetic. Program summaryProgram title: 2dhfCatalogue identifier: ADEB_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADEB_v2_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License version 2No. of lines in distributed program, including test data, etc.: 171196No. of bytes in distributed program, including test data, etc.: 9481802Distribution format: tar.gzProgramming language: Fortran 77, C.Computer: any 32- or 64-bit platform.Operating system: Unix/Linux.RAM: Case dependent, from few MB to many GBClassification: 16.1.Catalogue identifier of previous version: ADEB_v1_0Journal reference of previous version: Comput. Phys. Comm. 98(1996)346Does the new version supersede the previous version?: YesNature 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 multiplicative constant method.Solution method: Single-particle two-dimensional numerical functions (orbitals) are used to construct an antisymmetric many-electron wave function of the restricted open-shell Hartree–Fock model. The orbitals are obtained by solving the Hartree–Fock equations as coupled two-dimensional second-order (elliptic) partial differential equations (PDEs). The Coulomb and exchange potentials are obtained as solutions of the corresponding Poisson equations. The PDEs are discretized by the eighth-order central difference stencil on a two-dimensional single grid, and the resulting large and sparse system of linear equations is solved by the (multicolour) successive overrelaxation ((MC)SOR) method. The self-consistent-field iterations are interwoven with the (MC)SOR ones and orbital energies and normalization factors are used to monitor the convergence. The accuracy of solutions depends mainly on the grid and the system under consideration, which means that within double precision arithmetic one can obtain orbitals and energies having up to 12 significant figures. If more accurate results are needed, quadruple-precision floating-point arithmetic can be used.Reasons for new version: Additional features, many modifications and corrections, improved convergence rate, overhauled code and documentation.Summary of revisions: see ChangeLog found in tar.gz archiveRestrictions: The present version of the program is restricted to 60 orbitals. The maximum grid size is determined at compilation time.Unusual features: The program uses two C routines for allocating and deallocating memory. Several BLAS (Basic Linear Algebra System) routines are emulated by the program. When possible they should be replaced by their library equivalents.Additional comments: automake and autoconf tools are required to build and compile the program; checked with f77, gfortran and ifort compilersRunning time: Very case dependent — from a few CPU seconds for the H2 defined on a small grid up to several weeks for the Hartree–Fock-limit calculations for 40–50 electron molecules.

A Fortran 90 Hartree–Fock program for one-dimensional periodic π-conjugated systems using Pariser–Parr–Pople model

Pariser–Parr–Pople (P-P-P) model Hamiltonian is employed frequently to study the electronic structure and optical properties of π-conjugated systems. In this paper we describe a Fortran 90 computer program which uses the P-P-P model Hamiltonian to solve the Hartree–Fock (HF) equation for infinitely long, one-dimensional, periodic, π-electron systems. The code is capable of computing the band structure, as also the linear optical absorption spectrum, by using the tight-binding and the HF methods. Furthermore, using our program the user can solve the HF equation in the presence of a finite external electric field, thereby, allowing the simulation of gated systems. We apply our code to compute various properties of polymers such as trans-polyacetylene, poly- para-phenylene, and armchair and zigzag graphene nanoribbons, in the infinite length limit. Program summary Program title: ppp_bulk.x Catalogue identifier: AEKW_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEKW_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 87 464 No. of bytes in distributed program, including test data, etc.: 2 046 933 Distribution format: tar.gz Programming language: Fortran 90 Computer: PCs and workstations Operating system: Linux, Code was developed and tested on various recent versions of 64-bit Fedora including Fedora 14 (kernel version 2.6.35.12-90). Classification: 7.3 External routines: This program needs to link with LAPACK/BLAS libraries compiled with the same compiler as the program. For the Intel Fortran Compiler we used the ACML library version 4.4.0, while for the gfortran compiler we used the libraries supplied with the Fedora distribution. Nature of problem: The electronic structure of one-dimensional periodic π-conjugated systems is an intense area of research at present because of the tremendous interest in the physics of conjugated polymers and graphene nanoribbons. The computer program described in this paper provides an efficient way of solving the Hartree–Fock equations for such systems within the P-P-P model. In addition to the Bloch orbitals, band structure, and the density of states, the program can also compute quantities such as the linear absorption spectrum, and the electro-absorption spectrum of these systems. Solution method: For a one-dimensional periodic π-conjugated system lying in the xy-plane, the single-particle Bloch orbitals are expressed as linear combinations of p z -orbitals of individual atoms. Then using various parameters defining the P-P-P Hamiltonian, the Hartree–Fock equations are set up as a matrix eigenvalue problem in the k-space. Thereby, its solutions are obtained in a self-consistent manner, using the iterative diagonalizing technique at several k points. The band structure and the corresponding Bloch orbitals thus obtained are used to perform a variety of calculations such as the density of states, linear optical absorption spectrum, electro-absorption spectrum, etc. Running time: Most of the examples provided take only a few seconds to run. For a large system, however, depending on the system size, the run time may be a few minutes to a few hours.

Björn O. Roos: 1937–2010. Mentor, colleague, innovator

Björn O. Roos: 1937–2010. Mentor, colleague, innovator

A B-spline Hartree–Fock program

A B-spline version of a Hartree–Fock program is described. The usual differential equations are replaced by systems of non-linear equations and generalized eigenvalue problems of the form ( H a − ε a a B ) P a = 0 , where a designates the orbital. When orbital a is required to be orthogonal to a fixed orbital, this form assumes that a projection operator has been applied to eliminate the Lagrange multiplier. When two orthogonal orbitals are both varied, the energy must also be stationary with respect to orthogonal transformations. At such a stationary point, the matrix of Lagrange multipliers, ε a b = ( P b | H a | P a ) , is symmetric and the off-diagonal Lagrange multipliers may again be eliminated through projection operators. For multiply occupied shells, convergence problems are avoided by the use of a single-orbital Newton–Raphson method. A self-consistent field procedure based on these two possibilities exhibits excellent convergence. A Newton–Raphson method for updating all orbitals simultaneously has better numerical properties and a more rapid rate of convergence but requires more computer processing time. Both ground and excited states may be computed using a default universal grid. Output from a calculation for Al 3 s 2 3 p P 2 shows the improvement in accuracy that can be achieved by mapping results from low-order splines on a coarse grid to splines of higher order onto a refined grid. The program distribution contains output from additional test cases. Program summary Program title: SPHF version 1.00 Catalogue identifier: AEIJ_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEIJ_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 13 925 No. of bytes in distributed program, including test data, etc.: 714 254 Distribution format: tar.gz Programming language: Fortran 95 Computer: Any system with a Fortran 95 compiler. Tested on Intel Xeon CPU X5355, 2.66 GHz Operating system: Any system with a Fortran 95 compiler Classification: 2.1 External routines: LAPACK ( http://www.netlib.org/lapack/) Nature of problem: Non-relativistic Hartree–Fock wavefunctions are determined for atoms in a bound state that may be used to predict a variety atomic properties. Solution method: The radial functions are expanded in a B-spline basis [1]. The variational principle applied to an energy functional that includes Lagrange multipliers for orthonormal constraints defines the Hartree–Fock matrix for each orbital. Orthogonal transformations symmetrize the matrix of Lagrange multipliers and projection operators eliminate the off-diagonal Lagrange multipliers to yield a generalized eigenvalue problem. For multiply occupied shells, a single-orbital Newton–Raphson (NR) method is used to speed convergence with very little extra computation effort. In a final step, all orbitals are updated simultaneously by a Newton–Raphson method to improve numerical accuracy. Restrictions: There is no restriction on calculations for the average energy of a configuration. As in the earlier HF96 program [2], only one or two open shells are allowed when results are required for a specific LS coupling. These include: 1. ( nl ) N n ′ s , where l = 0 , 1 , 2 , 3 2. ( np ) N n ′ l , where l = 0 , 1 , 2 , 3 , … 3. ( nd ) ( n ′ f ) Unusual features: Unlike HF96, the present program is a Fortran 90/95 program without the use of COMMON. It is assumed that Lapack libraries are available. Running time: For Ac 7 s 2 7 p P 2 the execution time varied from 6.9 s to 9.1 s depending on the iteration method.

A Quasirelativistic Two-component Density Functional and Hartree-Fock Program

Abstract This work describes the implementation of an efficient two-component quasirelativistic density functional and Hartree-Fock program. The fact that the basis functions are real can be exploited if a special internal representation of operators and density matrices is used. This also leads to a considerable reduction of the effort in the closed shell case. While in most applications to open shell molecules, the noncollinear approach to define a relativistic spin density is preferable, the collinear approach finds its application in the calculation of magnetic anisotropy energies. Linear algebra steps in the SCF procedure have a higher relative weight compared to the nonrelativistic case, therefore some care was necessary to make them fast when parallelizing the code. The quasirelativistic Hamiltonians that have been implemented are the ´zeroth-order regular approximation´ (ZORA) Hamiltonian, the Douglas-Kroll-Hess Hamiltonian up to the sixth order, together with an accurate approximation to treat the picture change effect of the electron interaction, and effective core potential (ECP) matrix elements. Geometry gradients are available for the ZORA and ECP methods.

Beyond a Hartree–Fock description of crystalline solids: the case of lithium hydride

It is shown that a local MP2 approach can be conveniently adopted as a first step towards the post-Hartree–Fock description of crystalline solids. The relation of a new periodic MP2 code (CRYSCOR) to a classical Hartree–Fock program (CRYSTAL) is outlined. As an illustration, the case of LiH, a prototypical ionic crystal, is treated in some detail by analyzing the effect of the perturbative correction on equilibrium geometry, lattice energy and electron distribution (X-ray structure factors, directional Compton profiles), with reference to experimental data.

Two-component relativistic density-functional calculations of the dimers of the halogens from bromine through element 117 using effective core potential and all-electron methods

A two-component quasirelativistic Hamiltonian based on spin-dependent effective core potentials is used to calculate ionization energies and electron affinities of the heavy halogen atom bromine through the superheavy element 117 (eka-astatine) as well as spectroscopic constants of the homonuclear dimers of these atoms. We describe a two-component Hartree-Fock and density-functional program that treats spin-orbit coupling self-consistently within the orbital optimization procedure. A comparison with results from high-order Douglas-Kroll calculations--for the superheavy systems also with zeroth-order regular approximation and four-component Dirac results--demonstrates the validity of the pseudopotential approximation. The density-functional (but not the Hartree-Fock) results show very satisfactory agreement with theoretical coupled cluster as well as experimental data where available, such that the theoretical results can serve as an estimate for the hitherto unknown properties of astatine, element 117, and their dimers.

Further theoretical analyses (2D and 3D) of Ni 1/4TiS 2 probed by XPS/STM studies

The surface of Ni 1/4TiS 2 was investigated by X-ray photoelectron spectroscopy (XPS) and scanning tunneling microscopy (STM). Electronic calculations were performed using the ab initio Hartree–Fock program crystal. The XPS results (chemical shift of core peaks) are satisfactorily accounted for through a Mulliken population analysis. Concerning the STM results, we imaged the top sulfur plane (0 0 1) and interpret the data on the basis of the partial electron density of a slab which consist of seven (0 0 1) Ni 1/4TiS 2 layers. It was found that the bright spots in experimental STM images correspond to sulfur atoms in a single metallic environment (Ti atoms). Beside higher electronic density, these atoms are highlighted because of their proximity to the tip compared with sulfur atoms in a double environment (Ti and Ni).

A new implementation of four-component relativistic density functional method for heavy-atom polyatomic systems

A new four-component Dirac–Kohn–Sham (DKS) method is presented. The method provides a computationally efficient way to perform fully relativistic and correlated ground state calculations on heavy-atom molecular systems with reliable accuracy. The DKS routine has been implemented in the four-component Dirac–Hartree–Fock program system REL4D. Two-component generally contracted, kinetically balanced Gaussian-type spinors (GTSs) are used as basis spinors. The one-electron and Coulomb integrals are computed analytically, and exchange-correlation potentials are calculated with a numerical grid-quadrature routine. An approximation scheme is presented to reduce the evaluation time of the two-electron repulsion integrals over full sets of small-component GTSs, (SS|SS). Benchmark calculations for the ground states of the group IB hydrides, MH, and dimers, M2 (M=Cu, Ag, and Au), by the DKS method are presented.

VOH center in magnesium oxide: an ab initio supercell study

The V OH trapped-electron-hole center in magnesium oxide is studied with the periodic ab initio Hartree–Fock program crystal by using the supercell scheme. The H atom that formally is substituted for a Mg atom at its lattice position migrates towards one of the neighboring O atoms, forming a strong covalent bond with it, whereas the hole localizes at the opposite O atom completely. The electronic structure of the defect is discussed in terms of electron charge and spin density maps and band structure. The isotropic and anisotropic components of the hyperfine coupling constant between the H nucleus and the unpaired electron are calculated and are in quite good agreement with ENDOR results.

Performance Analysis, PVM and MPI Implementation of a DSCF Hartree Fock Program

A new Direct SCF-Hartree Fock program (DSCF) has been improved by the method of DIIS. (17), (18) General performance measurement tools, as provided on the SGIPower Challenge/R10000 (194 MHz) running IRIX 6.2, which are the shell-commands perfex -a a.out and ssrun -(pcsampl, ideal, usertime) a.out, have been used for profiling the code. The main cpu-time-consuming subroutine was detected and parallel versions for PVM 3.3 as well as MPI have been deduced. An additional module for the purpose of achieving load-balancewas introduced and obtained speed-up parameters are presented and compared.