A new two-step Uncontracted Determinantal SO-CI method
Christian Teichteil
Laboratoire de Physique Quantique - IRSAMC, Universite Paul Sabatier,
118, route de Narbonne, 31062 Toulouse Cedex 04, France
The main question about SO-CI methods is the
leadership between electrostatic and magnetic interactions. If the spin-orbit
interaction can be considered as a perturbation compared to the electronic
correlation contributions, it is well founded to treat it after the
CI process. This is generally the case for light atoms for which a "two-step"
method, where the spin-orbit coupling is handled after the CI process in a scalar
relativistic approximation with usual efficient CI codes, is naturally well
adapted and gives accurate results. The question of the leading contribution
(electrostatic or magnetic) can be eluded with a simultaneous treatment of
electronic correlation and spin-orbit coupling, defining here a "one-step"
method. When spin-orbit terms are included in the Hamiltonian, we have to
deal with a Double Group Configuration Interaction (DGCI) process, with in
general a complex representation of the Hamiltonian on the basis of
determinants or double group adapted functions.
The breakdown of the non relativistic symmetries in the CI process makes
high correlated treatments very difficult and expensive, increasing the
limitations of such methods.
We propose a new SO-CI treatment taking advantage of both
"two-step" and "one-step" methods.
We keep the "two-step" efficiency for correlation, where usual
sophisticated configuration interaction calculations are carried out in the
first step, within a scalar relativistic approximation. The energies of
these high correlated states are then used in the second step, in a
Bloch-type effective Hamiltonian. In the second step, unlike the usual
"two-step" methods using a contracted wavefunction, we
propose an uncontracted treatment taking into account the repolarisation
of the correlated wavefunction by the spin-orbit operator, which is the
main characteristic of "one-step" methods. The most important
feature of this approach being the inclusion of polarisation effects,
all the excited configurations which have a non-zero spin-orbit interaction
with a pre-defined small set of generators are created. The main contributions
are kept for a diagonalisation procedure, and the remaining configurations
can be treated up to the second order of perturbation.
Atomic and molecular tests calculations involving heavy atoms are presented,
and compared with usual SO-CI treatments.