[molpro-user] Expectation of second moment and kinetic energy
Peter Knowles
KnowlesPJ at cardiff.ac.uk
Mon Mar 3 07:29:54 GMT 2014
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
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