Electronic wave functions - The evaluation of the general vector-coupling coefficients by automatic computation

Boys, Samuel Francis; Sahni, R. C.

doi:10.1098/rsta.1954.0005

Cited by 13 publications

(5 citation statements)

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“…In parallel, the influence of Lennard-Jones in Cambridge ensured that the interest in computational chemistry was high. After the war, Hartree and Maurice Wilkes were ensconced in Cambridge and a thriving computational chemistry group developed, with the first publications also appearing in the mid-1950s [338][339][340][341][342][343][344][345][346]. Boys had identified the need for computational methods in a 1950 paper where he wrote with considerable perspicacity: "It is shown that the only obstacle to the evaluation of wave functions of any required degree of accuracy is the labour of computation" [347].…”

Section: When Calculation Moved From Pen and Paper To Machinesmentioning

confidence: 99%

Chemical Bonding: The Journey from Miniature Hooks to Density Functional Theory

Constable

Housecroft

2020

Molecules

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Our modern understanding of chemistry is predicated upon bonding interactions between atoms and ions resulting in the assembly of all of the forms of matter that we encounter in our daily life. It was not always so. This review article traces the development of our understanding of bonding from prehistory, through the debates in the 19th century C.E. bearing on valence, to modern quantum chemical models and beyond.

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Section: When Calculation Moved From Pen and Paper To Machinesmentioning

confidence: 99%

Chemical Bonding: The Journey from Miniature Hooks to Density Functional Theory

Constable

Housecroft

2020

Molecules

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“…This work was continued at Cambridge, where he returned as a lecturer in theoretical chemistry in 1948. There he published his landmark series of 12 papers − under the overall title of “Electronic wave functions”, which included the work he had done in London as well as later work, including research with a number of graduate students, at Cambridge.…”

Section: Early Historymentioning

confidence: 99%

“…XI in his “Electronic wave functions” series, with Vector E. Price, on Cl, Cl - , S, and S - , for which it “was found possible to adapt several sections of the calculation to the automatic calculating machine, the EDSAC, which has performed a considerable amount of the computations. In the next paper, with R. C. Sahni, concerned with the evaluation of vector coupling coefficients for atomic configuration interaction calculations, he states that it has been “found possible to develop a method of calculation which can be performed purely automatically by the EDSAC, proceeding from the lowest argument values indefinitely through all higher values.” By the time molecular electronic structure calculations were begun in Boys's group in the early 1950s (as discussed later in this review), all the computational steps and formula derivations were being completely automated.…”

Section: Computers At Cambridgementioning

confidence: 99%

“…He proceeded to work out various details of the application of CI, − concentrating initially on application to atoms. In this context the problem of vector coupling, i.e., the construction of co-detors adapted to spherical symmetry, looms large, and much of the “Electronic wave functions” series is devoted to dealing with this problem and with the reduction of matrix elements of the Hamiltonian between vector-coupled co-detors to linear combinations of one- and two-electron integrals over the orbitals. − , He called this latter process “projective reduction” and devoted considerable effort to designing efficient algorithms for its implementation. He also introduced a simple iterative method for the solution of the matrix eigenvalue problem …”

Section: Researchmentioning

confidence: 99%

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Samuel Francis Boys

1996

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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.

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“…(1.6) provides a suitable computing algorithm. Such a method has been described in some detail by Boys and SAHNI (1953) of only 30 cards for the computation of individual 3-j coefficients. A copy is available on request.…”

Section: Numerical Workmentioning

confidence: 99%

Evaluation of geomagnetic dynamo integrals.

Winch

1974

J. geomagn. geoelec

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Electronic wave functions - The evaluation of the general vector-coupling coefficients by automatic computation

Cited by 13 publications

References 1 publication

Chemical Bonding: The Journey from Miniature Hooks to Density Functional Theory

Chemical Bonding: The Journey from Miniature Hooks to Density Functional Theory

Samuel Francis Boys

Evaluation of geomagnetic dynamo integrals.

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