Page 59 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

44 O. PARISEL AND Y. ELLINGER
F can be advantageously taken as the following effective operator [39] in which orbital
occupancies are explicitely considered :

If we define the orbital energies by :

are easily expressed as :

More generally, given a set of orbitals and their corresponding energies with respect to
some one-electron operator, it is always possible to define a (non local) one-electron
operator having these orbitals and energies as eigenvectors and eigenvalues [40]. Such a
possibility which amounts to extending relations (12), (19), (20) and (22), will not be
developed further here, but allows us to use various level of correlated orbitals in the
calculations [34,41,42] and gives the opportunity to circumvent the problem of the
invariance of the perturbation energy correction relative to any arbitrary rotations of the
orbitals when those are not unambiguously defined . Furthermore, in the implementation
used here, and contrary to the CASPT2 approach [22,31,43], the zeroth-order
wavefunction is not necessarily supposed to ensure the Generalized Brillouin Theorem
[44].

3. The "Chemical" choice of the zeroth-order wavefunction
There is no general way to choose the "best" zeroth-order wavefunction to be used.
However, to avoid large variational expansions or to be sure not to miss some important
effects by a too drastic truncation, it may be wise to keep some rules in mind.

3.1. DESIGNING A "GOOD" ZEROTH-ORDER WAVEFUNCTION
First of all, the wavefunction has to contain the necessary ingredients to properly describe
the phenomenon under investigation: for example, when dealing with electronic spectra, it
thus has to contain every CSFs needed to account at least qualitatively for the description of
the excited states. The zeroth-order wavefunction has then to include a number of
monoexcitations from the ground state occupied orbitals to some virtual orbitals. In that
sense, the choice of a Single CI type of wavefunction as proposed by Foresman et al.
[45,46] in their treatment of electronic spectra represents the minimum zeroth-order space
that can be considered.
However, the restriction of this space to monoexcited configurations wrongly sweeps away
the complexity of excited state wavefunctions [22]. In particular, such a truncated space
lacks all the CSFs that account for non-dynamical correlation effects. These effects are
poorly recovered by any subsequent second-order perturbation while being essential in the
description of excited states or potential energy surfaces. In those cases, a wavefunction
generated by a specific configuration interaction is necessary. The structure of the
corresponding multiconfiguration reference space must however be carefully designed if
one does not want to handle large expansions that might include useless CSFs. The