Gerardo Cisneros

Symmetry-eigenfunctions for many-electron atoms and molecules: A unified and friendly approach for frontier research and student training

Abstract Atomic and molecular many-electron symmetry-eigenfunctions are obtained by means of a FORTRAN program based on projection operators and ordered Slater determinants. When degeneracies exist, Schmidt orthonormalization of a conveniently ordered manifold allows for the construction of a hierarchy of interacting spaces, unattainable through Racah algebra or group-theoretical methods, but necessary for compact many-electron theories and calculations beyond Hartree-Fock. Through a strict modular organization, this program offers a variety of concurrent evolution pathways covering all kinds of symmetry-eigenfunctions. Also, the results it generates can be fed into other modules for the general and efficient calculation of many-electron wave functions, or for symbolic evaluation of selected many-electron matrix elements of symmetry-operators such as the Hamiltonian. The program may be run interactively or in batch form to produce lists of configuration state functions for actual electronic structure calculations. In tutorial and interactive modes, help, status and overview commands can be invoked as an aid to gain working knowledge on many-electron symmetry-eigenfunctions. Standard FORTRAN 77 and full validation of array dimensions expressed in terms of parameters ensure widespread portability.

Spin eigenfunctions for many-electron calculations

Abstract We discuss a modular and efficient FORTRAN program which operating on a given linear combination of Slater determinants generates a spin eigenfunction by means of a symmetric, idempotent and hermtitian projection operator. In combination with other modules described in two previous and three further papers it may be used to generate all symmetry eigenfunctions needed in atomic and molecular electronic structure calculations. In particular, first-order and second-order interacting spaces are discussed.

Angular momentum eigenfunctions for many-electron calculations

Abstract We discuss a modular and efficient FORTRAN program to generate many-particle jj-JM and L 2 eigenfunctions obtained as projections of a single ordered Slater determinant built up from symmetry-adapted one-electron functions. Interacting spaces useful in calculations beyond Hartree-Fock are considered. In combination with other modules described in the previous and in four further papers this program can be used to generate all symmetry-eigenfunctions needed in atomic electronic structure calculations.

Molecular symmetry eigenfunctions for many-electron calculations

Abstract We discuss a modular FORTRAN program which operating on an ordered Slater determinant generates an eigenfunction spanning an irreducible representation of a given molecular symmetry group. The program is supported by a database of point group representation matrices. In combination with other modules described in two previous and two further papers it may be used to acquire a working knowledge about molecular symmetry eigenfunctions and to generate lists of many-electron symmetry-adapted configurations suitable for electronic structure calculations beyond Hartree-Fock.

DVDSON: A subroutine to evaluate selected sets of eigenvalues and eigenvectors of large symmetric matrices

Abstract Program HYMAT, originally written by Weber, Lacroix and Wanner, has been improved in efficiency and generalized to evaluate any selected set of eigenvalues and eigenvectors of large sparse real symmetric matrices. The time-consuming steps are expressed as calls to subroutines which may exploit a vector architecture. A novel way to improve speed of convergence is discussed.

New algorithm and FORTRAN module to carry out the four-index transformation of atomic and molecular physics wholly in central memory

Abstract This is the first of three companion papers describing a complete and modular library to carry out the four-index transformation of a block [( pq/mrs )] of two-electron integrals involving symmetry-adapted primitive orbitals p, q, r, s and a symmetry-related index m into a block [( ij/klm )] of integrals over symmetry-adapted orthonormal (orbitals i, j, k, l . The index m allows for the unified treatment of atomic and molecular, relativistic and nonrelativistic calculations. A new algorithm based on a generalization of a method by Saunders & van Lenthe [ Mol. Phys. 48, 923 (1983)] for non-symmetry orbitals has been developed. It is here implemented by means of a FORTRAN code, controlled by subroutine C4ITD, requiring all computed quantities to be held in central memory. A non-redundant set of integrals is used throughout. All pertinent sums run only over a limited range determined by a given symmetry. The rate determining steps may be carried out in parallel and are vectorizable within each possible concurrent processor. For 20 non-symmetry orbitals and with 64-bit precision on a VAX-11/780 computer, using a working set of 200 kbytes, subroutine C4ITD takes 48 CPU s. Ninety percent of this time is spent in steps dominated by vector-scalar-multiply-and-add (VSMA) operations carried out at 0.170 mega floating point operations per second, which is 91% of the performance achieved on the same computer by an equivalent mix of pure VSMA operations and vector sizes. C4ITD will be useful in atomic and molecular electronic structure calculations beyond Hartree-Fock.

The programming languages REC and convert

Two symbol manipulation languages are presented. REC (an acronym for Regular Expression Compiler) is a very compact language possessing a simple control structure. CONVERT is a pattern matching and substitution language well suited to problems whose solution may conveniently be expressed in terms of transformation rules. REC is useful when conciseness is required. such as for microcomputers with limited memory, interactive programming via the keyboard, and so on. Its present form was carefully chosen to facilitate the compilation of CONVERT programs while still preserving a universal appearance. In turn, CONVERT is a natural alternative to consider for an application which is already expressed in terms of transformation rules, as are many compilers, assemblers and symbol manipulation systems. This article primarily describes the appearance of these two languages, but some of the applications which they have been given are mentioned.

V4ITD: A portable and efficient FORTRAN implementation of the 4IT algorithm using virtual memory and an external storage device

Abstract V4ITD is a FORTRAN subroutine which does the four-index transformation of atomic and molecular physics by means of the 4IT algorithm described in the previous paper, and which requires enough virtual memory to store all intermediate quantities. Depending on the size of a given block of integrals and on the amount of central memory, an internal sort or a portable FORTRAN external sort library is used to carry out a localization of pertinent data sets. Since the number crunching steps involve the sequential use of virtual memory operating on localized data sets, for operations other than external sort V4ITD runs as efficiently as C4ITD from the previous paper. V4ITD is also more general than C4ITD: any number of blocks of integrals may optionally be read as incomplete dual lists of orbital indices and numerical values residing in an external file, in which case the final blocks of integrals are delivered also as dual lists into an external file. Furthermore, if the input integrals are not ordered as required by the 4IT algorithm, V4ITD will produce the correct ordering.

Modular libraries and literate programming in software for ab initio atomic and molecular electronic structure calculations

Abstract Modular libraries and literate programming in software for ab initio atomic and molecular electronic structure calculations are proposed as a short way out of a software crisis which is hindering innovation in the field.

E4ITD: A general FORTRAN implementation of the 4IT algorithm

Abstract E4ITD is a general FORTRAN implementation of the 4IT algorithm to carry out the four-index transformation of atomic and molecular physics. E4ITD makes intensive use of an external storage device to hold large arrays, replacing subroutine V4ITD from the previous paper whenever a four-index transformation cannot be carried out in a pre-allocated amount of central or virtual memory. Moreover, it operates upon arbitrarily truncated two-electron integral lists thus allowing implementations of efficient approximate ab initio methods. The number crunching steps are dominated by vector-scalar-multiply-and-add operations. On a VAX-11/780 computer they are carried out at 0.151 mega floating point operations per second, which is 82% of the performance achieved on the same computer by subroutine C4ITD running wholly in central memory but using complete integral lists.