Electronic Structure of Large Molecular Systems
Abstract
Computations of the electronic structure for molecules with more than 4 to 5 atoms have been traditionally based on semiempirical techniques. In this paper, a general computer program is described for computations of SelfConsistent FieldMolecular Orbital wave functions for molecules of any geometry and with a large number of nuclei and electrons. The molecular orbitals are linear expansions of symmetryadapted functions; the latter are linear combinations of socalled "contracted Gaussians." The "contracted Gaussian set" is a linear expansion of standard gaussian functions, with expansion coefficients obtained from atomic computation with Gaussian set. The use of "contracted Gaussians" decreases drastically the number of matrix elements over symmetry orbitals, and makes the size of the "contracted Gaussian set" comparable with the size of a Slatertype (exponential) basis set. Special provisions are included in the program for the elimination or approximation, or both, of integrals smaller than a preassigned threshold. With these innovations over traditional computations with standard Gaussian function, it is quite feasible to compute large molecular systems. The computer program, written as a preliminary version for the IBM 7094 computer (and now in process of conversion for the IBM System 360), can handle a maximum of 800 Gaussian functions distributed on 50 centers. Gaussian functions are restricted to s, p, d, and f type. In order to gain computer speed, s and p functions are computed with special formulas given in the Appendix. Average computational time for 4 center integrals over s Gaussian (uncontracted) functions is 0.6 milliseconds. This time increases for p type approximately to 2.6 milliseconds. For manycenter integrals involving d and f functions, the computing time is rather large, about 25 and 50 milliseconds, respectively. The computational time here quoted is somewhat higher than the time needed in standard computations, since no integral, however small, has been neglected or approximated in the time quoted above. The program has been used for problems involving no more than 44 × 10 ^{6} million twoelectron integrals. Larger computations can be done with our present program; however, one should consider the use of computers possibly with faster C.P.U. and certainly with larger core memory than the IBM 7094Mod. I. From our preliminary computations, and taking into account both the structure and limits of our present version of the program as well as newly announced highspeed computer specifications, we feel confident in stating that within the next 2 to 4 years "a priori" computations for molecules with about 100150 electrons and 520 atoms will be considered "routine" effort in theoretical chemistry.
 Publication:

Journal of Computational Physics
 Pub Date:
 November 1966
 DOI:
 10.1016/00219991(66)900040
 Bibcode:
 1966JCoPh...1..223C