Subject: Re:CCL:CCL:Multideterminantal DFT

From: Juan Carlos Sancho <[email-masked]>
Date: Fri, 04 Sep 1998 18:28:26 +0200

In DFT the electron density is the key function because the HK theorem
establishes that the ground state exact energy is provided through an
universal functional. KS theory makes practicable DFT affording its
calculation using a single Slater determinant subject to the condition
of providing the exact density. Posteriorly the need to include the
on-top pair density has always appeared in situations when
quasi-degenerations are present. In these cases the density functional
deficiencies have been solved using this on-top density constructed from
a minimal number of Slater determinant neccesary to take into account
this degeneracy. As a possible solution it has been proposed years ago,
to write the density as a sum of terms with a non-integer occupation
number associated with the KS orbitals. A funtional like this was used
for the first time in DFT by Lie and Clementi (1974).

If we select, for the Ks partition of the energy, an exchange potential
similar to the HF one, we have an unique way of defining the remaining
term (correlation potential) and most of the published correlation
potentials have been obtained using the above definition of the exchange
potential. We can look for correlation functionals depending of the
polarization concept (Perdew 86) or not (Lee-Yang-Parr) but, in all
cases, the potential energy curves are not reproduced although the
correct dissociation limit is reached in an unrestricted KS calculation.
And, why this potentials provide good results whenever the wavefunction
is well approximated by just one Slater determinant?. I think that, when
the exact energy requires a many-determinant wavefunction, a partition
of the energy must be made with the many-determinant contribution
completely included into the exchange-correlation term. The DFT
potentials published so far have not been obtained considering this
depedence. Certainly the deficiency appears in significative systems.
For instance, in the PEC of fluorine molecule we can see how UKS does
not provide the shape of the curve at intermediate distance. If we use a
two-determinant wavefunction (GVB with perfect pairing) and evaluating
later the correlation energy by means of the Colle-Salvetti functional,
using the GVB two-body density matrix previously obtained, we recover
the shape of the curve and the results improves greatly the UKS one !.
What comes out from this analysis ?, How we can recognize the non-local
corrections needed for the functionals ?, Dynamical vs. non-dynamical
correlation ? ...

        It would be a great pleasure to find answers to this questions
between
all, mixing experiences and opinions. Thanks,

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        J.C. Sancho-Garcia
        Dpto. Quimica-Fisica
        Universidad de Alicante
        Apartado 99, 03080 Alicante
        SPAIN

        [email-masked]

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