Determination of the Coefficients of Hiickel Molecular Orbital Wave Functions: A Computer Program in the Basic Language A Basic computer program for solving sets of up to ten simultaneous equations is readily available to most owners of small computers. Such a program, SIMEQN' has been modified to allow its use in the determination of the coefficients of Hiickel moleeularorhital wave functions of the form2 @ = CZXI+ CzXz + . . . C,X,. In the absence of the normalization requirement (Cia + CzZ+ . . . Cn2 = 1) the set of simultaneous equations used to determine the coefficients of a wave function has no unique solution. The user of SIMEQN will obtain the trivial solution C1 = Cz = . = Cn = 0.In many cases, one can force a unique solution by assigning some value to one of the coefficients, such as C1 = 1. This equation may he added to any one of the simultaneous equations in the set and a unique solution will often be obtained. If these results are then normalized (dividing each by J R + ~ Rz2 + . . . + RnZ, where the R's are the solutions to the set of equations) proper results are obtained. The modified SIMEQN program, HMOCOEF, has the following features: (1) complete instructions for setting up the simultaneous equations and adjusting them so that a unique solution is obtained, (2) a normalization routine, (3) an additional loop which allows the simultaneous equations t o be entered as data once and used repeatedly. Each time the program is run, an input statement calls for a root of the secular equation and the program computes the eoefficients of the corresponding wave function. The program is limited to nondegenerate wave functions and some caution must be exercised in choosing a coeEcient to set equal t o one. For linear compounds, coefficients of p-orbitals on terminal carbons may be safely set equal to one since these coefficients are always nonzero. In cyclic or branched compounds, the chosen coefficient should not correspond to an atom which lies on a two-fold symmetry axis (e.g., for pyrrole choose C2 = 1). The program has been used to obtain coefficients of wave functions far the fallowing compounds: linear hydroearbons up to Ce, benzene (*I and * B only), pyrrole, furan, the carbanyl group, enolates, unsaturated enolates, the nitmxyl radical and others. A listing of the program in the Basic language is available from the author.
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'Hewlett Packard, "BASIC Program Library Handbook" Program tA314-36026A. Hewlett-Packard Company, Cupertino, California, 1972. 2Liberles, Amo, "Introduction to Maleeular Orbital Theory," Holt, Rinehert and Winston, Inc. New York, 1966, p. 118.
W. Gale Rhodes Lvnn Brown Maryville College M a m i l l e , Tennessee 37801
Volume 51, Number 9, September 1974
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