# [molpro-user] Bug in calculation of expactation value of the potential energy operator (POT)

Gerald Knizia knizia at theochem.uni-stuttgart.de
Wed Mar 25 20:18:21 GMT 2009

On Wednesday 25 March 2009 16:02, Evgeniy Gromov wrote:
> Dear Developers and Users of Molpro,
>
> There seems to be bug in calculation of expectation
> value of the potential energy operator (POT). The
> value I get is not equal to <E_total>-<E_kinetic>.
> I mean it should be
>
> <E_potential>=<E_total>-<E_kinetic>
>
> shouldn't it?

There are still the nuclear repulsion energy and the two electron repulsion
energy. The total energy is:
E_tot = <t> + <v_nuc> + E_nuc + <2e-terms>
where:
t is the electronic kinetic energy
v_nuc is the energy due to the interaction of the atom cores
with the electrons
E_nuc = \sum_{a,b!=a} Z_a Z_b/||R_a-R_b|| is the electrostatic
repulsion of the atom cores amongst themselves.
2e-terms is the energy due to the interaction of the electrons with
each other
For RHF, the 2e-terms are again given by j + k, which are effective 1-particle
operators representing the mean field Coulomb potential due to the electrons
and Pauli repulsion (k=exchange operator). For general theories these
2e-terms look more complicated would require the 2-RDM for an exact
evaluation as general property expectation value.
--
Gerald Knizia