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To: chemistry@www.ccl.net
Subject: screened (Yukawa type) Coulomb potential
Date: Sun, 18 Apr 1999 17:27:59 +0900
From: AKINAGA Yoshinobu <akinaga@qcl.t.u-tokyo.ac.jp>

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 

===============================================================
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@qcl.t.u-tokyo.ac.jp
===============================================================