Page 55 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

40 O. PARISEL AND Y. ELLINGER
is no method currently avalaible to perform efficient MPn calculations on open-shell
systems described by a spin-clean single ROHF determinant (Restricted Open Hartree-
Fock) [14]; when dealing with unpaired electrons, UHF orbitals are used instead,
sometimes leading to the well-known drawbacks of spin contamination (for an extreme
example, see reference [15] or poor convergence [16,17] and even to dramatic failures [18-
21].
The advantages of MPn perturbation treatments are however clear on both the theoretical
and computational points of view. For example, size-consistency is ensured, analytical
gradients and Hessians are avalaible, parallelization of the codes is feasable.

Most of the previous advantages are lost in the variational approaches: getting upper-bound
energies has to be paid for and despite numerous and ingenious implementations using a
large variety of algorithms, large-scale CI are not easily tractable. The cost-effectiveness
argument leads either to carefully design a CI space or to truncate it in order to
accommodate the storage limitations of modern computers, whatever the method used. The
single-reference SDCI (Singles and Doubles Configuration Interaction) approach is an
example of such a truncation which is known to give an unbalanced description of the
correlation energy between excited states [22]. Even the extension to the SDTQ CI appears
to be insufficient [23], especially as soon as the single reference does not dominate the
exact wavefunction by a large margin. Also the lack of size-consistency of such
dramatically truncated CIs [24-26] makes them too flimsy to accurately deal with
correlation problems. Major improvements in variational methods have been reached using
MRCI (Multi-Reference CI) [27,28]: however, a careful choice of the reference
configurations has to be made in order to avoid both the inflation of the CI expansion and
the lack for some potentially important configurations needed for a proper description of the
phenomenon under investigation. Even carefully truncated MRCI may lead to deceptive
results when one deals with excited states.

It is seen that neither the MBPT nor the CI approaches are the panacea.

1.2. THE COUPLING OF VARIATION AND PERTURBATION TREATMENTS

The idea of coupling variational and perturbational methods is nowadays gaining wider and
wider acceptance in the quantum chemistry community. The background philosophy is to
realize the best blend of a well-defined theoretical plateau provided by the application of the
variational principle coupled to the computational efficiency of the perturbation
techniques.[29-34]. In that sense, the aim of these approaches is to improve a limited
Configuration Interaction (CI) wavefunction by a perturbation treatment.

One of the first attempts was done more than 20 years ago and led to the so-called 'CIPSI'
method whose basic idea is to progressively include the most important correlation terms in
the variational space to be improved by a forthcoming second-order perturbation treatment
[35]. The selection of the terms to be included in the variational zeroth-order space is made
according to a user-fixed numerical threshold based either on the contribution of these
terms to the perturbed wavefunction, as in the original CIPSI approaches [35,36], or on
their energetic contribution to the total energy [37,38]. The pitfalls to avoid when using
such iterative algorithms are now well-established, although often forgotten: in particular,
extreme caution must be taken to ensure an homogeneous treatment of correlation energies
along a reaction path or between excited states.