[molpro-user] Expectation of second moment and kinetic energy

[Peter Knowles]

Dear Yannis,

On 1 Mar 2014, at 06:23, Yannis Petousis <petousis at stanford.edu> wrote:
> 
> I still have one question about the second moment.
> I am looking to calculate the terms: <ψ|x^2|ψ> and <ψ|x|ψ> however, I believe I mistakenly thought that SM would give me the value of the first of the 2 terms. I looked for a mathematical definition of the operators but could not find one.

The SM should indeed give you sum_i q_i <x_i^2> but you have to remember that the sum is over all charged particles i, both nuclei and electrons; q_i is the charge. The same definition is used for the dipole, and other multipole, moments.

> If I am right, is it possible to calculate the above quantities in molpro either directly or indirectly by extracting the wavefunction and position operator?

I am not sure I understand this question, since extracting an operator implies getting it in some representation. In the end what you can really calculate are (approximations to) the expectation values of operators.

--
Prof. Peter J. Knowles             
School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, UK
Telephone +44 29 208 79182 Email KnowlesPJ at Cardiff.ac.uk 
WWW http://www.cardiff.ac.uk/chemy/contactsandpeople/academicstaff/knowles.html