|
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).
| 
