# [molpro-user] Calculation of the properties of the outermost electron of an atom

sasha medvedev vinsanity305 at mail.ru
Thu Mar 6 11:32:41 GMT 2014

 Hello, molpro users.

Is there any possibility to calculate the root mean square (r.m.s.)
distance of the outermost electron of a particular atom with the help of molpro2010 package?
I faced several problems, when I tried to do it. Here they are:

1) How can one get the wave function of the outermost electron?
Is it possible in molpro to extract a wave function of a particular electron from the wave function of the atom?
In other words, can I take in molpro2010 one-electron wave function (with the desired set of quantum numbers n,l,m)
from a Slater determinant after restricted/unrestricted-HF routine for an atom?

2) So, I should calculate the diagonal matrix element of the x^2+y^2+z^2=r^2 one-electron operator,
using a wave function of the outermost electron (i.e. <nlm|r^2|nlm>, where n,l,m - quantum numbers of the outermost electron).
Molpro provides me with the second moment (SM) operator ( http://www.molpro.net/info/2012.1/doc/manual/node68.html ).
But it contains summation over all electrons in a system (i.e. SM_{XX} = \sum_{i=1}^{N} x_{i}^{2}, where x_{i} is the x coordinate of the i^{th} electron,
N - total number of electrons in the system).
Will this sum reduce to 1 electron (i.e. SM_{XX}= x_{1}^{2}), when I ask molpro to calculate the expectation value of the
SM operator using wave function of the outermost electron?

I'm interested in it, because I want to calculate the Le Roy radius ( http://leroy.uwaterloo.ca/leroy_radius.html ).

Alexander Medvedev,
student of the 5th course,
Chemistry department,
Chair of laser chemistry,
MSU
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