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

Jacky LIEVIN jlievin at ulb.ac.be
Mon Mar 3 09:42:00 GMT 2014

```Dear Yannis,

Le 3 mars 2014 à 08:29, Peter Knowles <KnowlesPJ at cardiff.ac.uk> a écrit :

> 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.

{property
orbital,2105.2,state=1.1
density,2105.2,state=1.1
sm,1.0,0.0,0.0}

This set of commands gives the nuclear and electronic components of the second moment and their sum, and it also gives the orbital contributions.
It allows you to define the origin (here cartesian point 1,0,0) and also the state of interest in a multi-state calculation

Jacky

>
>> 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
>
>
>
>
>
>
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_____________________________________
Prof. Jacky Liévin
Service de Chimie Quantique et Photophysique
Université Libre de Bruxelles, CPi 160/09
50 av F.D. Roosevelt
B-1050 Bruxelles
Belgium
Tel: +32-2-650 4089
Fax: +32-2-650 4232
_____________________________________

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