Hiickel Calculations Using a Programmable Pocket Calculator
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The recent introduction of moderatelv oriced nromammable calculators allows the direct calculation of simole r" molecular orhitnla of the Huckel or Mulliken-Wolfsher~-Helmholz type. These ralculatorr. are capable of handling iterative method* that are necmary to solve the characteristic equations and obtaining solutions of linear systems ofequat~ons,thus greatly reducing the amount of time involved in these ralrulations. Several programs for the Hewlett-Packard HP-25 calculator capable of determining the real roots of polynomials using the Newton-Raphson method have been written. The first of these programs calculates the roots ofx4 a l x 3 + aZx2 + a y or = 0 to a determined accuracy. This program can be easily adopted to solve third degree equations. A slightly different program capable of finding the roots of a fifth degree equation such asx5 + alx4 + nzx3 + a s Z+ a@ 0 5 = 0 has been written. Due to the limited number of steps available, this program is not iterative but it can be cycled by adding a few steps manually after each iteration. A program capable of calculating x,+, = x, - P. (x,)lP.' (x,) where P,, (x,) is a nth degree characteristic equation and P,,' (x,) is its first derivative,has also been written. In each iterative cycle one must enter all the ewficients. This pmgram offers two alternative ways of checking the convergence. The usual cofador method for determining the coefficients of the atomic orbitals is very tedious when done by hand. In order to save time. a Droeram for determining the value of the determinant of a 3 X 3 matrix has also been written. Copies of these programs are available from the author.
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Departmento de Fisica Universidad de Oriente Cumana. Estado Sucre. Venezuela
J u a n Murgich
Volume 54, Number 7, July 1977 1 421
