[molpro-user] occupation numbers and orbital energies in multi

[H.-J. Werner]

Dear Molpro users,

following questions of a Molpro user I would like to clarify
the definition of the orbital energies and occupation numbers
printed by multi.

With NATORB the density matrix is diagonalized in the active
space. The effective Fock matrix is transformed accordingly,
and the printed "orbital energies" are the diagonal values of
the transformed Fock matrix (i.e. in the natural orbital basis).
This means that in this case  the "orbital energies" have no or
limited physical meaning, since the Fock matrix is not diagonal
in the natural orbital basis.

With CANONICAL, the effective Fock matrix is diagonalized in the
active space, and the printed orbital energies are then the
eigenvalues. In this case the "occupation numbers" are the
diagonal elements of the density matrix in the basis of the
canonical orbitals. Since the density matrix is not diagonal
in this basis, the occupation numbers are of limited value.

In any case, the inactive and virtual blocks of the Fock matrix
are diagonalized, and the printed orbital energies for these
spaces are the eigenvalues corresponding the resulting (pseudo)
canonical orbitals.

In summary, the "occupation numbers" are always the diagonal elements 
of the density matrix and the "orbital energies" the diagonal elements
of the Fock matrix, in whatever orbital basis one has created.

-- 
Prof. Hans-Joachim Werner
Institute for Theoretical Chemistry
University of Stuttgart
Pfaffenwaldring 55
D-70569 Stuttgart, Germany
Tel.: (0049) 711 / 685 64400
Fax.: (0049) 711 / 685 64442
e-mail: werner at theochem.uni-stuttgart.de