University of Chicago Laboratory of Molecular Structure and Spectra Technical Report: 1952-1953, Part 2 Page: XX
xxiv, 359 p. : diagrams, graphs, ill. ; 28 cm.View a full description of this report.
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PROGRESS REPORTS
A method of dealing with the integrals has been developed which permitted an entirely
general solution of the problem. The treatment is based on a new type of auxiliary
functions, called C apy6, and it has been possible to express the two-center one-
electron integrals as well in terms of these auxiliary functions--with the only excep-
tion of the nuclear attraction integrals of the type j dVXaXl/rb, for which independent
formulas are given. Pilot computations are being started at present. It is antici-
pated that the final calculations will probably be carried out on an electronic digi-
tal computer; they shall furnish tables for one-electron integrals and tables for the
auxiliary functions occurring in the hybrid integrals.
4. Application of Machine Computing Techniques to Molecular Calculations
In view of the rapid improvements made in the last few years in the reliability
and power of electronic digital computers, it appears to be likely that future mole-
cular calculations will largely be carried out by means of such machines. Since the
techniques which are now being developed in the field of automatic machine computing
will therefore have to be considered in planning future work, a study of this new
field was initiated by Mr. P. Merryman, Dr. K. Ruedenberg, and Dr. C. C. J. Roothaan.
The possibilities of the new machines have also been recognized by other researchers;
pioneer work is being done in particular by Dr. S. F. Boys, who for several years has
been working with the EDSAC computer in Cambridge, England.
The most immediate consequence is, of course, that calculations whose complexity
makes them forbidding for hand computation are now within the range of possibility.
The most obvious examples are the integrals between the atomic orbitals. It may be
expected that codes can be prepared which will allow the evaluation of an integral of
this kind for a particular set of parameter values in a matter of minutes, so that it
may become possible to obtain a large number of them when required, e.g., if a diatomic
molecular problem is to be solved for many values of the interatomic distance in order
to construct a potential curve. Another important example is the solution of secular
equations of very high order; such equations up to the order forty are now being
solved, and it can be expected that equations of higher order will become soluble, by
automatic methods. This fact will facilitate the superposition of more atomic orbitals
to form molecular orbitals than appeared to be possible until now, and it will also
permit taking into account a greater amount of configurational interaction than was
hitherto feasible.xx
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University of Chicago. Laboratory of Molecular Structure and Spectra. University of Chicago Laboratory of Molecular Structure and Spectra Technical Report: 1952-1953, Part 2, report, 1953~; Chicago, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc228353/m1/22/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.