An Interactive Computer Program for Solving Secular Equations We have developed a eomputer program which permits the user, with no knowledge of computer languages, to solve secular equations. The APL program is interactive, requires minimal effort to input data, and presents the results immediatelv. .. These advantares should he of suecial interest to those who have not vet mastered the details of computer programmmg or cannut spend the rime nerersar).lur such provommtng. Thesecular pqn. ( I ) ir s particular form of the wave equation which arises in rhe LCAO.MOapproximation. ~~
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+ all
a21
all X+ann
.. .alm ... 02,
awi.
aw2
...x + aww
X
=0
(1)
The elements (atj) of the determinant are energy parameters, and the x's are related to the eigenvalues, E, by the expression X = r* - EIB; where in a simple Hiiekel approximation by convention a = H, digital computer. The program allows the elements (arj) to be entered simply as a vector, i.e., the determinant of eqn. (1) neet not be manually expanded and translated to a computer language. Through the use of a control vector, the user determines the maximum number of iterations for each root, the maximum absolute error allowed for each root, and the number af subintervals to be used to study the function behavior. Check statements, throughout the program, prevent erron in data input and syntax. The program provides the user with the options of studying locus behavior and/or solving for roats. Roots are approximated to the level of accuracy desired. The program includes perhaps the mast practical method for determining the multiplicities of roats. Those interested in obtaining copies of the program may write to either one of us. Syracuse University Syracuse, New York 13210
494
/ Journal of Chemical Education
John R. Potts Daniel J. Maeero
