A main direction
of our research focuses on the foundations of the reduced density matrix
functional theory (RDMFT). An alternative to DFT theory, RDMFT is an approach
to the problem of electronic correlations aiming to offer an improved
description of static correlations. Our group has made significant contribution
in the application of RDMFT to periodic systems. More specifically we
contributed to the development of new functionals, like the so-called Power
functional and their implementation/assessment for molecular and periodic
systems. Interestingly, such approximations were found describe well the
fundamental gaps of transition metal oxides, a promising result towards the
construction of a scheme to study strongly correlated systems. We have also
considered the enforcement of the generalized Pauli constraints in RDMFT aiming
to remedy inaccuracies of present functionals when applied to spin-systems. In
addition, we proposed necessary conditions for the one-body reduced density
matrix (1RDM) for the description of triplet states and studied consequences of
the generalized Pauli constraints in the structure of the 1RDM. Finally, we
have introduced quantitative criteria for the distinction of static and dynamic
electronic correlations in many electron systems.
A serious issue
in Kohn-Sham DFT is the actual value of the single particle Kohn-Sham (KS) orbitals
and their corresponding energy eigenvalues. In order to improve the quality of
the local KS potential, we proposed to replace it with the optimal one that
respects certain subsidiary conditions that enforce exact properties, like, for
instance, the correct asymptotic behavior of the potential. This method is
applicable to any density functional approximation and offers a significant
improvement in the local potential resulting in better single particle spectrum.
We applied the same recipe together with RDMFT functionals (local RDMFT), thus
combining the non-idempotency of RDMFT with a KS-like local potential, a combination
that potentially offers improved single particle spectral properties and decent
description of static correlations at the same time despite the fact that the
natural orbitals in RDMFT cannot be obtained by a local potential. In addition,
we proposed a method to invert any given density in order to obtain the
corresponding constrained local potential with predefined asymptotic behavior
and demonstrated its efficiency and quality of the resulting potentials.
Finally, based on the improvement of the constrained local potential method, we
are working on hybrid schemes that further improve the spectral properties.
