Subsystem formulation of density functional theory.
One of our principal interests concerns the subsystem formulation of density functional theory [P. Cortona Phys. Rev. B 44 (1991) 8455]. Similarly to the conventional Kohn-Sham formalism, the subsystem formulation is based on Hohenberg-Kohn theorems. However, opposite to the Kohn-Sham formalism, the total electron density is not construct by means of one set of orthogonal one-electron functions (orbitals) but it is represented as a sum of electron densities of several subsystems. For each subsystem, a set of one-elecron functions (embedded orbitals) is used to construct the corresponding electron density. The embedded orbitals in each subsystem are obtained as solutions of Kohn-Sham-like one electron equations.
Obtaining embedded oritals as well as the evaluation of the total energy as an explicit functional of these orbitals hinges on approximations to two types of explicit functionals of the electron density: i) exchange-correlation and ii) non-additive kinetic energy. One of our major interest concerns development of approximations for the latter quantity.
We developed the first numerical implementation of the subsystem based formalism applicable for molecular systems [Wesolowski, Weber, Chem. Phys. Lett., 248 (1996) 71] based on the code deMon. This code was used principally to work on development/testing approximations to the functionals needed in this formalism but also for some applications (for summary, see [Wesolowski, Tran, J. Chem. Phys., 118 (2003) 2072]). A more applications oriented numerical implementation was developped recently [Wesolowski, Dulak, Intl. J. Quant. Chem., 101 (2005) 243]. This implementation was used to introduce an efficient algorithm to perform geometry optimisation which is based on a particular sequence of partial minimisations of the total energy with respect to either electron density or nuclear coordinates for each subsystem [Dulak et al., J. Chem. Theory and Comput. 3 (2007) 735].
The generalisation of the subsystem formulation of density functial theory to excited stats uses the Linear-Response Time-Dependent Density-Finctional-Theory stategy. The working equations are given in [Casida and Wesolowski, Intl. J. Quant. Chem. ., 96, (2004) 577].
Our activities concerning the subsystem formulation of density functional thery are closely related to another of our principal interests concerning the orbital-free embedding formalism [Wesolowski and Warshel, J. Phys. Chem., 97, (1993) 8050]. In the orbital-free embedding strategy, only one subsystem is described at the orbital resolution whereas electron density of other subsystems is subject to additional approximations. In practice, calculations following subsystem formulation of density functional theory are performed to estimate the effects of these additional approximations.