Subrata Jana — Page 3

arXiv2017

Semi-local Exchange Energy Functional For Two-Dimensional Quantum Systems: A Step Beyond Generalized Gradient Approximations

Semi-local density functionals for the exchange-correlation energy of electrons are extensively used as it produce realistic and accurate results for finite and extended systems. The choice of techniques play crucial role in constructing such functionals of improved accuracy and efficiency. An accurate and efficient semi-local exchange energy functional in two dimensions is constructed by making use of the corresponding hole based on the density matrix expansion. The exchange hole involved is localized under the generalized coordinate transformation and satisfies all the relevant constraints. Comprehensive testing and excellent performance of the functional is demonstrated versus exact exchange results. The functional also achieves remarkable accuracy by substantially reducing the errors present in the local and non-empirical density functionals proposed so far for two dimensional systems. The underlying principles involved in the functional construction are physically appealing and practically useful for developing range separated and non-local functionals in two dimensions.

cond-mat.mtrl-sci↗

arXiv2015

Excited-State Density-Functional Theory Revisited: on the Uniqueness, Existence, and Construction of the Density-to-Potential Mapping

The generalized constrained search formalism is used to address the issues concerning density-to-potential mapping for excited states in time-independent density-functional theory. The multiplicity of potentials for any given density and the uniqueness in density-to-potential mapping are explained within the framework of unified constrained search formalism for excited-states due to Görling, Levy-Nagy, Samal-Harbola and Ayers-Levy. The extensions of Samal-Harbola criteria and it's link to the generalized constrained search formalism are revealed in the context of existence and unique construction of the density-to-potential mapping. The close connections between the proposed criteria and the generalized adiabatic connection are further elaborated so as to keep the desired mapping intact at the strictly correlated regime. Exemplification of the unified constrained search formalism is done through model systems in order to demonstrate that the seemingly contradictory results reported so far are neither the true confirmation of lack of Hohenberg-Kohn theorem nor valid representation of violation of Gunnarsson-Lundqvist theorem for excited states. Hence the misleading interpretation of subtle differences between the ground and excited state density functional formalism are exemplified.

cond-mat.mtrl-sci↗