[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>
	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

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