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

Tatiana Korona tania at tiger.chem.uw.edu.pl
Thu Mar 6 20:51:38 GMT 2014

Hi, Alexander,

You can make these manipulations through matrop, i.e. load HF orbitals, zero
some of them, make a new "density matrix" and use it to calculate properties.
For the first part, see e.g.
http://www.molpro.net/pipermail/molpro-user/2012-December/005147.html
Other steps are described well in the manual.

Best wishes,

Tatiana

On Thu, 6 Mar 2014, sasha medvedev wrote:

> 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

Dr. Tatiana Korona http://tiger.chem.uw.edu.pl/staff/tania/index.html
Quantum Chemistry Laboratory
University of Warsaw
Pasteura 1, PL-02-093 Warsaw, POLAND

The man who makes no mistakes does not usually make anything.'
Edward John Phelps (1822-1900)
/-/...././ /--/.-/-./ /.--/..../---/ /--/.-/-.-/./.../ /-./---/ /--/../.../-/.-/-.-/./.../
/-../---/./.../ /-./---/-/ /..-/.../..-/.-/.-../.-../-.--/ /--/.-/-.-/./.../ /.-/-./-.--/-/..../../-./--./'
/./-../.--/.-/.-./-../ /.---/---/..../-./ /.--./...././.-../.--./.../
( /.----/---../..---/..---/ /.----/----./-----/-----/ )