Carlos F. Bunge

Selected configuration interaction with truncation energy error and application to the Ne atom

Selected configuration interaction (SCI) for atomic and molecular electronic structure calculations is reformulated in a general framework encompassing all CI methods. The linked cluster expansion is used as an intermediate device to approximate CI coefficients B(K) of disconnected configurations (those that can be expressed as products of combinations of singly and doubly excited ones) in terms of CI coefficients of lower-excited configurations where each K is a linear combination of configuration-state-functions (CSFs) over all degenerate elements of K. Disconnected configurations up to sextuply excited ones are selected by Browns energy formula, Delta E(K) = (E-H(KK))B(K)2/(1-B(K)2), with B(K) determined from coefficients of singly and doubly excited configurations. The truncation energy error from disconnected configurations, Delta E(dis), is approximated by the sum of Delta E(K)s of all discarded Ks. The remaining (connected) configurations are selected by thresholds based on natural orbital concepts. Given a model CI space M, a usual upper bound E(S) is computed by CI in a selected space S, and E(M) = E(S) + Delta E(dis) + delta E, where delta E is a residual error which can be calculated by well-defined sensitivity analyses. An SCI calculation on Ne ground state featuring 1077 orbitals is presented. Convergence to within near spectroscopic accuracy (0.5 cm(-1)) is achieved in a model space M of 1.4 x 10(9) CSFs (1.1 x 10(12) determinants) containing up to quadruply excited CSFs. Accurate energy contributions of quintuples and sextuples in a model space of 6.5 x 10(12) CSFs are obtained. The impact of SCI on various orbital methods is discussed. Since Delta E(dis) can readily be calculated for very large basis sets without the need of a CI calculation, it can be used to estimate the orbital basis incompleteness error. A method for precise and efficient evaluation of E(S) is taken up in a companion paper.

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.

Transition Probabilities for Hydrogen-Like Atoms

E1, M1, E2, M2, E3, and M3 transition probabilities for hydrogen-like atoms are calculated with point-nucleus Dirac eigenfunctions for Z=1–118 and up to large quantum numbers l=25 and n=26, increasing existing data more than a thousandfold. A critical evaluation of the accuracy shows a higher reliability with respect to previous works. Tables for hydrogen containing a subset of the results are given explicitly, listing the states involved in each transition, wavelength, term energies, statistical weights, transition probabilities, oscillator strengths, and line strengths. The complete results, including 1 863 574 distinct transition probabilities, lifetimes, and branching fractions are available at http://www.fisica.unam.mx/research/tables/spectra/1el

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.

Eigenfunctions of spin and orbital angular momentum by the projection operator technique

A computer program has been written in Fortran IV to produce eigenfunctions of spin and orbital angular momentum (LS functions) by the projection operator technique. The projection operator acts on a Slater determinant built up from symmetry-adapted spinorbitals. When degeneracies exist, it is easy to provide a set of determinants whose projections span the whole degenerate space. In such cases, the LS functions are Schmidt orthonormalized. These functions provide natural partitions of degenerate LS spaces which are useful in the simplification and systematization of atomic calculations. Some representative examples are discussed.

Systematic search of excited states of negative ions lying above the ground state of the neutral atom

Abstract Nonrelativistic fixed-core valence-shell configuration interaction calculations are carried out for excited states of atomic negative ions in the range H through Ca, in an effort to identify the ones which are metastable against autoionization. Approximate relativistic corrections are included in some cases. From Be onwards, all (Core)n(n+1)sq(n+1)pr neutrals appear to bind an extra electron into a bound ( Core ) n (n+1) s q (n+1) p r+1 2S+1 L negative ion, in all cases where the 2S+1L continuum starts at the corresponding neutral atom state. Similarly as in the recently discussed case of Li−, alkali-earths (Be−, Mg−, Ca−), Zn−, B−, Al−, C−, Si−, Ar−, and possibly S−, have two bound excited states connected by an E1 transition in regions extending from infrared to vacuum ultraviolet. Negative neon is found to decay by E1 radiation into a continuum, thus Ne− beams are unlikely to be made in the future. However, there exists a metastable [Ne]3p54s4p 4S state of negative argon, making possible the production of Ar− beams.

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.

The Present Limits of Accuracy in Atomic Calculations of Small Systems

From the point of view of a dedicated configuration interaction practitioner, and for a given amount of available computer resources, the current limitations in the accuracy of atomic energy calculations are assumed to be: (i) an inadequate theoretical knowledge regarding the proper handling of slowly convergent radial and harmonic expansions in electron-pair functions, (ii) insufficient experience regarding the quantitative implications of possible systematic simplifications in the Hamiltonian matrix, (iii) tedious and empirical procedures to account for three-excited linked clusters, (iv) quantitatively uncertain methods to predict the effect of four and higher-excited unlinked clusters, and (v) a limited conceptual versatility in available computer programs. These problems are discussed vis-a-vis energy errors in contemporary calculations and new ideas to attempt increased accuracy.