screened (Yukawa type) Coulomb potential
Dear all,
I'm formulating the SCF using screened Coulomb potential
(Yukawa potential). In calculating matrix elements, I must
evaluate the integral such as:
int[0-1] t^{2m}*exp(-A*t^{2}-B*t^{-2}) dt
(A,B are given constants)
in which only difference between usual Coulomb potential case
is the factor exp(-B*t^{-2}) (and that the constant A may be complex,
because I use gaussian and plane-wave as basis sets).
This factor is due to using screened Coulomb potential
(Yukawa potential) exp(-lambda * r)/r instead of 1/r
(lambda is screening constant). It looks like to be calculated by
N-point quadrature, but I don't know the abscissas and weight
factors for weight function exp(A*t^{2}-B*t^{-2}) with interval
[0,1]. Do I have to generate them myself, by the method in ,
for example, "Numerical Recipes in Fortran", or can I find
them in some early works or references ?
Any references are wellcome.
Thanks in advance,
Yosinobu
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Akinaga Yoshinobu
Department of Applied Chemistry, Graduate School of Engineering,
University of Tokyo,
Tokyo 113-8656, Japan
tel : 03-3812-2111(7252), E-mail : akinaga "-at-" qcl.t.u-tokyo.ac.jp
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