Page 237 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

220 J. WEBER ET AL.

set (when possible), total energies [6]. It is of course impossible to implement such a
procedure using the DFT methodology, as there is no equivalent to the Hartree-Fock
energy. In other words, one extracts from such a calculation a total energy which contains
"some" correlation contribution, without the possibility to separate it from the SCF energy.
To elucidate this point, one has therefore to compare molecular properties calculated using
the DFT formalism with their values predicted by ab initio computations performed at
various levels of approximation.
It has been recently pointed out that DFT models are in general adequate to describe to a
good extent, through the standard exchange-correlation potentials generally used, the
correlated movement of electrons at short interelectronic distance, i.e. the so-called dynamic
correlation [5]. This is even possible in the simple formalism of the local density
approximation (LDA) [7], using a potential such as that of Vosko, Wilk and Nusair (VWN)
which is now commonly employed for many DFT applications [8]. It has indeed been
shown that such calculations incorporate dynamic correlation effects at least to the same
extent as second-order Moller-Plesset (MP2) MBPT [9], which represents now a standard
for post-Hartree-Fock ab initio calculations. However, there is a second category of
correlation, known as static or long-range correlation, which accounts for near-degeneracy
effects in the wavefunction [10]. Whereas it can be accounted for in ab initio calculations
through the MCSCF procedure, it is more difficult to describe in DFT as it requires the use
of involved exchange-correlation potentials, with the risk of a double counting of
correlation corrections [11]. Alternatively, long-range correlation can be introduced in the
DF formalism by combining CI or MCSCF with DF through a scaling of the electron
density by a factor depending on Hartree-Fock and CI (or MCSCF) two-electron density
matrices calculated in the same one-electron basis set [12].

In the present work, we shall investigate the problem of the amount of correlation
accounted for in the DF formalism by comparing the molecular electrostatic potentials
(MEPs) and dipole moments of CO and calculated by DF and ab initio methods. It is
indeed well known that the calculated dipole moment of these compounds is critically
dependent on the level of theory implemented and, in particular, that introduction of
correlation is essential for an accurate prediction [13,14]. As the MEP property reflects
reliably the partial charges distribution on the atoms of the molecule, it is expected that the
MEP will exhibit a similar dependence and that its gross features correlate with the changes
in the value of dipole moment when switching from one level of theory to the other. Such a
behavior has indeed been reported recently by Luque et al. [15], but their study is limited to
the ab initio method and we found it worthwhile to extend it to the DF formalism. Finally,
the proton affinity and the site of protonation of as calculated by both DF and ab initio
methods, will be reported.

2. Computational Details
For the DFT calculations, the linear combination of Gaussian - type orbitals - density
functional (LCGTO-DF) method and its corresponding deMon program package [16] have
been used. In all calculations, the VWN exchange-correlation potential was employed [8]
and all the core and valence electrons were explicitly taken into account. To enable a
meaningful comparison with the ab initio results, the same one-electron basis set has been
used in all the calculations, i.e. which has been recently found
adequate for calculating the dipole moment of CO and N 2O [14]. The auxiliary basis sets
required by the LCGTO-DF model to fit the electron density and the exchange-correlation