Stephen Wilson

Universal basis sets for electronic structure calculations

The concept of a ’’universal’’ basis set for electronic structure calculations is explored by presenting energy results obtained when basis sets are transferred from one atom to another. The calculations are performed using the diagrammatic techniques of many‐body perturbation theory. A single universal basis set is shown to give uniformly accurate descriptions of the matrix Hartree–Fock and correlation energies of the He, Be, and Ne atoms.

Triple and quadruple excitations and the valence correlation energies of small molecules

Abstract The contribution of triply-excited states and quadruply-excited states to the valence correlation energy is investigated for a number of atoms and molecules using the diagrammatic many-body perturbation theory. The importance of triple excitations in accurate calculations is demonstrated.

Diagrammatic perturbation theory: An application to the nitrogen, carbon monoxide, and boron fluoride molecules using a universal even‐tempered basis set

Diagrammatic many‐body perturbation theory is applied to the nitrogen, carbon monoxide, and boron fluoride molecules. The same universal even‐tempered basis set of Slater functions is used to parameterize the single particle state functions in each of the molecules. Calculations are performed at nuclear separations of 1.75, 2.00, 2.25, and 2.50 bohr. Approximately 83.7%, 82.7%, and 77.1% of the correlation energy is recovered in N2, CO, and BF at their respective equilibrium internuclear distances.

Effect of basis-set completeness on the relative importance of triply and quadruply excited configurations in correlation energy calculations

Abstract It is demonstrated, using the ground state of the water molecule, that the contribution of triply excited configurations to electron correlation energies in closed-shell systems is more sensitive to the degree of completeness of the basis set than the component associated with quadruply excited configurations. The relative importance of the triply excited states increases more rapidly than that of the quadruple excitations, as the quality of the basis set is improved.

Universal basis sets in molecular calculations

Abstract The concept of a universal basis set for electronic structure calculations is illustrated in molecular calculations. Matrix Hartree—Fock calculations are reported for the nitrogen, carbon monoxide and boron fluoride molecules at various nuclear geometries. The results are in good agreement with previous calculations which have used basis sets specifically designed for the corresponding molecule.

Diagrammatic perturbation theory: evaluation of fourth-order energy terms involving quadruply-excited states for closed-shell systems

The energy terms involving quadruply-excited states that arise in fourth order in the many-body perturbation series are discussed in detail. Both linked-diagram and unlinked-diagram components are calculated for the nitrogen molecule. The unlinked diagram components, which are required to correct for the unphysical terms included in configuration interaction calculations that are restricted to double excitations, are calculated for some closed-shell diatomic hydrides at their respective equilibrium separations and for the hydrogen fluoride molecule as a function of internuclear distance.

Universal systematic sequence of even-tempered Gaussian primitive functions in electronic correlation studies

The possibility of developing a universal systematic sequence of eventempered Gaussian primitive functions for atomic and molecular electronic structure studies is examined. The radial beryllium-like ions are used to demonstrate this approach both within the Hartree-Fock model and by including correlation effects. Correlation energies are computed using the diagrammatic many-body perturbation theory. The Hartree extrapolation procedure is used to obtain empirical upper bounds to the basis set limit and the procedure of Schmidt and Ruedenberg is employed to obtain empirical lower bounds for the basis set limit. The convergence properties of the calculations with respect to the size of the basis set are examined.

Systematic Sequences of Even-tempered Gaussian Primitives in Electron Correlation Studies Using Many-Body Perturbation Theory

The use of systematic sequences of even-tempered Gaussian primitive functions in electron correlation studies using diagrammatic many-body perturbation theory is examined. The “s limit” electronic energy of the Be atom and the ‘sp limit” energy of the Ne atom have been computed as examples. The use of the Hartree extrapolation procedure to obtain empirical upper bounds for the basis set limit is investigated. The empirical lower bound for the basis set limit suggested by Schmidt and Ruedenberg is examined for calculations which include electron correlation.

On the contribution of higher-order excitations to correlation energies: The ground state of the water molecule

Using the results of a configuration interaction calculation reported by Rosenberg and Shavitt, we derive an approximation to the correlation energy which may be associated with the sum to infinite order of all linked diagrams involving singly- and doubly-excited states. This result is compared with that obtained by calculation of the energy through third-order. The fourth-order linked diagrams involving quadruply-excited states are computed. It is shown that there is a considerable degree of cancellation between the fourth-order linked diagram energy terms involving doubly-excited intermediate states only and those which contain quadruply-excited states.

Scaling in second-order electron correlation calculations using systematic sequences of even-tempered basis sets

Improved results can often be obtained from second-order Rayleigh-Schrödinger perturbation calculations of electron correlation energies using large basis sets by introducing a scaling factor in the zero-order Hamiltonian. The scaling parameter may be determined from full third-order calculations using a smaller basis set. This scaling procedure can be applied in a systematic fashion by employing a sequence of even-tempered basis sets. Calculations illustrating this approach for the beryllium atom and the neon atom are presented. The scaling procedure is also employed in conjunction with a universal systematic sequence of basis functions. Calculations illustrating this Correlation energy — Mang-body perturbation theory.