Samuel Francis Boys

Abstract

The development most often associated with the name of S. F. Boys in quantum chemistry is the introduction of Gaussian basis functions in electronic structure calculations. Interestingly, while Boys was fascinated with the integrability properties of products of Gaussians on different centers, and used them in other applications, including approximation schemes for multicenter integrals over Slater-type orbitals, he did not pursue their use as basis functions in their own right in his own molecular calculations. It was the work of his student, Colin M. Reeves, and the latter's student, Malcolm C. Harrison, which revived interest in Boys's original proposal and started the wide-scale application of Gaussian basis functions in this field. The major interest of Boys in the 1950s was the development of the formalism and algorithmic tools needed for configuration interaction calculations on atoms and molecules. His earlier work concentrated on atoms and atomic ions and initially employed desk calculators, but he soon realized the potential of the electronic computer, not only for the arithmetic calculations but also for the formal manipulations required in the derivation of formulas and the overall organization of the calculations. He devoted much effort to vector coupling, the construction of symmetry- and spin-adapted linear combinations of Slater determinants (“co-detors” in his terminology), and the development of practical procedures for “projective reduction”, the reduction of matrix elements of the Hamiltonian between co-detors to linear combinations of one- and two-electron integrals. The computer was used to develop the formulas for the various basis set integrals and for the projective reduction formulas, and the formal and numerical parts of the work were integrated on the computer to reduce the need for human intervention and minimize the opportunities for mistakes. On turning his attention to molecules, he developed and tested a variety of schemes for calculation of the multicenter integrals over Slater-type orbitals and made several pioneering applications of his ideas, notably including the first correct prediction of the geometry of the methylene ground state and a landmark calculation on formaldehyde. In later years, concerned about the slow convergence of the configuration interaction expansion, he focused on schemes for the incorporation of interelectronic distances directly into the trial wave function, leading to the development of the “transcorrelated” method. Other interests included the convergence of nonsymmetric secular equations, studies of basis set superposition error, and the calculation of ro-vibrational energy levels.

Molecular Structures and Vibrational Frequencies of Iron Carbonyls: Fe(CO)5, Fe2(CO)9, and Fe3(CO)12

“…Its trigonal-bipyramidal structure (Figure ) was determined by Ewens in 1939 . Relative to Fe 2 (CO) 9 , and Fe 3 (CO) 12 , the mononuclear complex Fe(CO) 5 has been studied more thoroughly both experimentally , and theoretically. ,,− Among the previous theoretical studies of Fe(CO) 5 , however, many early DFT studies were plagued by systematic and/or nonsystematic errors due to lack of precision in the numerical integration procedures . Perhaps the first truly reliable comprehensive study of monometal carbonyls was the 1995 study of Jonas and Thiel .…”

Theoretical methods for small-molecule ro-vibrational spectroscopy

“…The result of this very steep scaling is that for most systems CISD is the only computationally feasible CI level of treatment. Unfortunately CISD energies, even when the reference Hartree-Fock wavefunction is a good approximation, are not particularly accurate [204] as higherorder excitations (in particular, quadruple excitations) give a significant contribution [208].…”

Variational transcorrelated method

“…18 The lack of variational bounds is regarded as a severe problem, which has discouraged further investigations of the TC method. 24 In recent years, Ten-no and collaborators [25][26][27] use the transcorrelated Hamiltonian in the perturbation and the coupled electron-pair approximations. In this approach the correlation factor is kept fixed and is used to speed up the basis set convergence for conventional many-particle methods.…”