Charlotte Froese Fischer

Average-energy-of-configuration Hartree-Fock results for the atoms helium to radon charlotte froese fischer

Numerical Hartree-Fock results for the average energy of ground-state or near-ground-state configurations of the neutral atoms helium to radon are reported. Tables of various useful parameters and of radial wavefunctions are presented, also plots of the wavefunctions and radial density functions.

General Hartree-Fock program

Abstract Title of program : HF86 Catalogue number : AATK Program obtainable from : CPC Program Library, Queens University of Belfast, N. Ireland (see application from in this issue) Computer : Vax 11/780; Installation : Vanderbilt University, Nashville, TN 37235, USA Operation system : VMS Version 4.4 Programming language used : FORTRAN 77 Virtual memory : 526 kbytes No. of bits in a word : 32 Peripherals used : disk, printer, terminal No. of lines in combined program and test deck : 4167

The MCHF atomic-structure package

The programs, as described in Computational Atomic Structure: An MCHF Approach (C. Froese Fischer, T. Brage, and P. Jonsson, Institute of Physics (Bristol, 1997)) are collected into an atomic structure package. Included with the package are test examples with complete output of results. Also included are executable binaries for the Intel Linux operating system. The programs have previously been published separately except for a simple continuum CMCHF program with one continuum channel and associated photoionization program that are unpublished.

A Davidson program for finding a few selected extreme eigenpairs of a large, sparse, real, symmetric matrix

Abstract A program is presented for determining a few selected eigenvalues and their eigenvectors on either end of the spectrum of a large, real, symmetric matrix. Based on the Davidson method, which is extensively used in quantum chemistry/physics, the current implementation improves the power of the original algorithm by adopting several extensions. The matrix-vector multiplication routine that it requires is to be provided by the user. Different matrix formats and optimizations are thus feasible. Examples of an efficient sparse matrix representation and a matrix-vector multiplication are given. Some comparisons with the Lanczos method demonstrate the efficiency of the program.

Extension of the HF program to partially filled f-subshells

A new version of a Hartree-Fock program is presented that includes extensions for partially filled f subshells. The program allows the calculation of term dependent Hartree-Fock orbitals and energies in LS coupling for configurations with no more than two open subshells, including f subshells.

A general program for computing angular integrals of the Breit-Pauli Hamiltonian

Abstract The MCHF_BREIT program performs the angular integrations necessary for expressing the matrix elements of the Breit-Pauli Hamiltonian (except for the orbit-orbit operator) as linear combinations of radial integrals. All matrix elements for a given list of configuration states may be evaluated or selected subsets. An orthonormal set of orbitals is assumed.

An MCHF atomic-structure package for large-scale calculations

Abstract An MCHF atomic-structure package is presented based on dynamic memory allocation, sparse matrix methods, and a recently developed angular library. It is meant for large-scale calculations in a basis of orthogonal orbitals for groups of LS terms of arbitrary parity. For Breit–Pauli calculations, all operators—spin–orbit, spin–other orbit, spin–spin, and orbit–orbit—may be included. For transition probabilities the orbitals of the initial and final state need not be orthogonal. A bi-orthogonal transformation is used for the evaluation of matrix elements in such cases. In addition to transition rates of all types, isotope shifts and hyperfine constants can be computed as well as g J factors. New version summary Title of program: atsp 2K Version number: 1.00 Catalogue identifier: ADLY_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADLY_v2_0 Program obtainable from: CPC Program Library, Queens University of Belfast, N. Ireland Computer: Pentium III 500 MHz Installations: Vanderbilt University, Nashville, TN 37235, USA Operating systems under which the present version has been tested: Red Hat 8 Programming language used in the present version: FORTRAN 90 Memory required to execute with typical data: 256 Mbytes words No. of bits in a word: 32 Supplementary material: User manuals for the program atsp 2k and for the Spin-Angular library are available No. of lines in distributed program, including test data, etc.: 209 992 No. of bytes in distributed package, including test data, etc.: 1 740 883 Distribution format: tar.gz CPC Program Library subprograms used: none Does the new version supersede the previous version?: Yes Nature of physical problem: This program determines energy levels and associated wave functions for states of atoms and ions in the MCHF ( LS ) or Breit–Pauli ( LSJ ) approximation. Given the wave function, various atomic properties can be computed such as electric (E k ) and magnetic (M k ) multipole radiative transition probabilities ( k max = 10 ) between LS or LSJ states, isotope shift constants, hyperfine parameters, and g J factors. Method of solution: The new version of the program closely follows the design and structure of the previous one [C. Froese Fischer, Comput. Phys. Comm. 128 (2000) 635], except that a simultaneous optimization scheme has been introduced. This program uses the angular methodology of [G. Gaigalas, Lithuanian J. Phys. 41 (2000) 39] and has been extended to include partially filled f -subshells in wavefunction expansions but assumes all orbitals are orthonormal. The bi-orthogonal transformation method is used to deal with the non-orthogonality of orbitals between initial and final states of an electromagnetic radiative transition. Reasons for new version: The previous version of the MCHF atomic structure package [C. Froese Fischer, Comput. Phys. Comm. 128 (2000) 635] was intended for small calculations, ideal for someone not familiar with the code, producing extensive print-out of intermediate results. The codes for the calculation of spin-angular coefficients were often not the most efficient and could only treat configurations with open f -subshells containing at most two electrons or an almost filled shell with one hole. The present version is designed for large-scale computation using algorithms for angular integration that have been shown to be faster, and include the case of arbitrarily filled f -shells. In addition, the MCHF program has been modified to include optimization on an energy functional that is a weighted average of energy functionals for expansions of wavefunctions for different LS terms or parity, thus facilitating Breit–Pauli calculations for complex atomic systems and for computing targets in collision calculations. Summary of revisions: Programs have been modified to take advantage of the newly developed angular library [G. Gaigalas, Lithuanian J. Phys. 41 (2000) 39], extended to arbitrarily filled f -shells. New programs have been developed for simultaneous optimization and for the efficient calculation of atomic spectra and transition rates for an iso-electronic sequence. All applications now take advantage of dynamic memory allocation and sparse matrix methods. Restrictions on the complexity of the problem: All orbitals in a wave function expansion are assumed to be orthonormal. Configuration states are restricted to at most eight (8) subshells in addition to the closed shells common to all configuration states. The maximum size is limited by the available memory and disk space. Typical running time: Included with the code are scripts for calculating E2 and M1 transitions between levels of 3 s 2 3 p 2 for Si and P + . This calculation has two stages: LS and LSJ . The calculation of the former required 21 minutes for the LS calculation and 36.5 minutes for the Breit–Pauli configuration interaction calculation that determines the mixing of the terms. Unusual features of the program: The programming style is essentially F77 with extensions for the POINTER data type and associated memory allocation. These have been available on workstations for more than a decade but their implementations are compiler dependent. The present serial code has been installed and tested extensively using both the Portland Group, pgf90, compiler and the IBM SP2, xlf90, compiler. The former is compatible also with the Intel Fortran90 compiler. The MPI codes are included for completeness though testing has not been as extensive. Additional comments: Parallel versions (MPI) of the following programs are included in the distribution. Use of these is optional but can speed up the angular integration processing. Serial Parallel nonh nonh_mpi mchf mchf_mpi bp_ang, bp_mat, bp_eiv bp_ang_mpi, bp_mat_ang, bp_eiv_mpi biotr_ang, biotr_tr biotr_ang_mpi, biotr_tr_mpi

An efficient approach for spin-angular integrations in atomic structure calculations

A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional parentage nor unit tensors. It is based on the combination of second quantization in the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin), and a generalized graphical technique. The latter allows us to graphically calculate the irreducible tensorial products of the second-quantization operators and their commutators, and to formulate additional rules for operations with diagrams. The additional rules allow us to graphically find the normal form of the complicated tensorial products of the operators. All matrix elements (diagonal and non-diagonal with respect to configurations) differ only by the values of the projections of the quasispin momenta of separate shells and are expressed in terms of completely reduced matrix elements (in all three spaces) of the second-quantization operators. As a result, it allows us to use standard quantities uniformly for both diagonal and off-diagonal matrix elements.

Multiconfiguration Hartree-Fock Results with Breit-Pauli Corrections for Transitions in the Carbon Sequence

The Multiconfiguration Hartree-Fock method, extended to include relativistic effects in the Breit-Pauli approximation (MCHF + BP), has been used to determine wavefunctions for the different LSJ states of the 2s22p2 ground and the 2s2p3 excited configurations of the carbon iso-electronic sequence for nuclear charges, Z, up to thirty. Term energies and fine-structure splitting have been predicted from these wavefunctions, as well as transition probabilities. The latter include the forbidden transitions, electric quadrupole (E2) and magnetic dipole (M1), between the levels of the ground configuration, as well as the allowed 2s22p2-2s2p3 transitions. In this paper our results are reported and typical transitions compared with those from other theories as well as those from observation, as available. For Z up to about 20, our energy levels are generally in better agreement with observation than those from other theories.

The use of basis splines and non-orthogonal orbitals in R-matrix calculations: application to Li photoionization

We present a new extended version of the R -matrix method for the calculation of continuum properties in which non-orthogonal orbitals are extensively used for describing both the target states and the R -matrix basis functions. In particular, a B -spline basis is used for the description of continuum states in the inner region and the target states may be obtained from independent calculations. This leads to a generalized eigenvalue problem but has the advantage of requiring much smaller bases for accurate representation of target wavefunctions and to achieve convergence in the close-coupling expansion. The present approach and its code are both applicable to a general atom and their efficiency for low-energy scattering processes is demonstrated by calculating the photoionization of Li. A detailed analysis of the resonance structure is given. Very good agreement with experimental data has been obtained, and considerable improvement in the description of resonances has been achieved in comparison with the standard R -matrix calculations.