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277. CEXCH: Two-Center Exchange Integral between
Linear Combinations of Slater-Type Atomic Orbitals
Using the Method of Mehler and Ruedenberg
by B. Hejda and J. Malek, Institute of Physics, Czechoslovak Academy of Science, Prague, Czechoslovakia The method of calculation is due to E. L. Mehler and K. Ruedenberg, J. Chem. Phys., 50 2575 (1969). (Errata: J. Chem. Phys., 57, No. 8 (1972)). The authors of the program have verified all formulae in this paper and have corrected some mistakes. In the paper, the formula for calculation of the two-center exchange integral between Slater-type atomic orbitals (STAOs) has been developed. It is possible to calculate the integral between linear combinations of STAOs by direct combination of the Mehler and Ruedenberg formula. It would result in computation time increasing as the product of the lengths of the four linear combinations:
Instead, the program combines the stored values: Wlm(i(1) ,i(2)) (t) , Wlm(i(3) ,i(4)) (t) (See Mehler and Ruedenberg's paper for definition of the function Wlm(t). The computation of Wlm(t) takes the main amount of time which is proportional to respectively and they are not computed more times than necessary. The subprogram uses Gauss-Legendre quadrature. It is sufficient to integrate over 12 points, and this number of points is fixed in the program. Also, the summation in the final Mehler and Ruedenberg formula may be limited by the number l = 20. Usually, the necessary precision is reached for l < 20, and the program cuts off the summation sooner. FORTRAN IV (IBM 360/370) Lines of Code: 560 Recommended Citation: B. Hejda and J. Malek, QCPE 11, 277 (1975). |