Calculations of the FC overlap integral with matrix elements are basic problems in molecular physics [15-21].
Franck-Condon Overlap Integral Based on Harmonic Oscillator Wave Function
Substituting (5) into (6), we obtain the following equation for the FC overlap integral:
Substituting Equation (9) into Equation (7), we obtain the following formula for the FC overlap integral:
where [R.sub.0] is the Forster radius, [[phi].sub.0] is the quantum yield of donor, n is the refractive index of the medium, J is the normalized overlap integral
of the donor and the acceptor spectra, and k is the orientation of the dipoles.
When the output waveguide is of single-mode, the spectral response for a certain output channel can be approximated with the following overlap integral,
where c is the velocity of the light in vacuum, and [PHI] is the phase response determined by the overlap integral [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Mamedov, "On the accurate evaluation of overlap integrals
over slater type orbitals using analytical and recurrence relations," Zeitschrift fur Naturforschung, vol.
We noticed that the SF three-center nuclear attraction integrals are expressed in terms of two-center overlap integrals and two-center nuclear attraction integrals over NISTOs.
For the evaluation of [mathematical expression not reproducible] overlap integrals we use the formula defined in terms of [Q.sup.q.sub.ns] auxiliary functions .
As can be seen from (7) and (9), by the use of Guseinov one-range addition theorems, the SF three-center nuclear attraction integrals are expressed through the two-center overlap integrals, gamma functions, auxiliary functions, and coefficients.
We believe that a common storage scheme for the [F.sub.m] (n) and [[omega].sup.l.sub.nn'], coefficients and [mathematical expression not reproducible] overlap integrals with the same selection rule, as proposed in this study, will give important contributions in reducing requirements of computer time for computation of multicenter integrals which arise in the HartreeFock-Roothaan and Hylleraas approaches.