Prasanjit Samal

Exploring foundations of time-independent density functional theory for excited states

Based on the work of Gorling and that of Levy and Nagy, a density-functional formalism for many fermionic excited states is explored through a careful and rigorous analysis of the excited-state density to external potential mapping. It is shown that knowledge of the ground-state density is a must to fix the mapping from an excited-state density to an external potential. This is the excited-state counterpart of the Hohenberg–Kohn theorem, where instead of the ground-state density the density of the excited state gives the true many-body wavefunctions of the system. Further, the excited-state Kohn–Sham system is defined by comparing its non-interacting kinetic energy with the true kinetic energy. The theory is demonstrated by studying a large number of atomic systems.

Time-independent excited-state density functional theory: study of 1s22p3(4S) and 1s22p3(2D) states of the boron isoelectronic series up to Ne5+

Using accurate Monte Carlo densities for excited states of the boron isoelectronic series, we construct the Kohn–Sham systems for these excited states. The Kohn–Sham system is that for which the non-interacting kinetic energy is closest to the true kinetic energy. Within the exchange-only approximation we also demonstrate the accuracy of a newly constructed exchange-energy functional for these excited states.

Assessing the performance of the Tao-Mo semilocal density functional in the projector-augmented-wave method

We assess the performance of the recently proposed Tao-Mo (TM) semilocal exchange-correlation functional [J. Tao and Y. Mo, Phys. Rev. Lett. 117, 073001 (2016)] using the projector-augmented-wave method with the plane wave basis set. The meta-generalized gradient approximation level semilocal functional constructed by Tao-Mo is an all-purpose exchange-correlation functional for the quantum chemistry and solid-state physics. The exchange of the TM functional is based on the density matrix expansion technique together with the slowly varying fourth order gradient expansion. The correlation functional corresponding to the exchange is based on the one-electron self-interaction-free Tao-Perdew-Staroverov-Scuseria functional. Our test includes solid-state lattice constants, bulk moduli, bandgaps, cohesive energies, magnetic moments and vacancy-formation energies of transition metals. It is observed that in the plane wave basis, the TM functional performs accurately in predicting all the solid state properties at the semilocal level.

Local-density approximation for the exchange energy functional in excited-state density functional theory

An exchange energy functional is proposed and tested for obtaining a class of excited-state energies using density functional formalism. The functional is the excited-state counterpart of the local-density approximation functional for the ground state. It takes care of the state dependence of the energy functional and leads to highly accurate excitation energies.

Semilocal Exchange Energy Functional for Two-Dimensional Quantum Systems: A Step Beyond Generalized Gradient Approximations

Semilocal density functionals for the exchange-correlation energy of electrons are extensively used as they produce realistic and accurate results for finite and extended systems. The choice of techniques plays a crucial role in constructing such functionals of improved accuracy and efficiency. An accurate and efficient semilocal exchange energy functional in two dimensions is constructed by making use of the corresponding hole which is derived 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 accuracy of results obtained by using the newly constructed functional is quite remarkable as it substantially reduces the errors present in the local and nonempirical exchange functionals proposed so far for two-dimensional quantum systems. The underlying principles involved in the functional construction are physically appealing and hold promise for developing range separated and nonlocal exchange functionals in two dimensions.

Excited-state density functional theory

Starting with a brief introduction to excited-state density functional theory, we present our method of constructing modified local density approximated (MLDA) energy functionals for the excited states. We show that these functionals give accurate results for kinetic energy and exchange energy compared to the ground state LDA functionals. Further, with the inclusion of GGA correction, highly accurate total energies for excited states are obtained. We conclude with a brief discussion on the further direction of research that include the construction of correlation energy functional and exchange potential for excited states.

A local-density approximation for the exchange energy functional for excited states: The band-gap problem

We present excited-state density functional theory (DFT) to calculate band gap for semiconductors and insulators. For the excited-state exchange-correlation functional, we use a simple local-density approximation (LDA) like functional and it gives the result which is very close to experimental results. The linear muffin-tin potential is used to solve the self-consistent Kohn-Sham equation.

Time‐Independent Excited‐State Density Functional Theory

We review the current status of time‐independent density‐functional theory for an individual excited‐state. The theory is built upon generalized constrained‐search formulation that maps a given excited‐state density ρ(r) to the corresponding many‐body wavefunction. This process obtains the wavefunction Ψ[ρ;ρ0] as a bi‐functional of the excited‐state desnity ρ(r) and the ground‐state density ρ0(r). However, the important issues in excited‐state density‐functional theory are whether an accurate exchange‐correlation functional can be constructed to get excited‐state energy and whether a unique Kohn‐Sham system can be constructed for a given excited‐state. In this paper we show that the answer to both the questions is in the affirmative. The existence of excited‐state Kohn‐Sham system is demonstrated by constructing it for the excited‐states of some members of Boron isoelectronic series. In connection with the excited‐state functional, we present recently constructed exchnage energy fucntional for excited‐sta...

A Parameter-Free Semilocal Exchange Energy Functional for Two-Dimensional Quantum Systems

The method of constructing semilocal density functional for exchange in two dimensions using one of the premier approaches, i.e., density matrix expansion, is revisited, and an accurate functional is constructed. The form of the functional is quite simple and includes no adjustable semiempirical parameters. In it, the kinetic energy dependent momentum is used to compensate nonlocal effects of the system. The functional is then examined by considering the very well-known semiconductor quantum dot systems. And despite its very simple form, the results obtained for quantum dots containing a higher number of electrons agrees pretty well with that of the standard exact exchange theory. Some of the desired properties relevant for the two-dimensional exchange functional and the lower bound associated with it are also discussed. It is observed that the above parameter-free semilocal exchange functional satisfies most of the discussed conditions.

Inhomogeneity induced and appropriately parameterized semilocal exchange and correlation energy functionals in two-dimensions

The construction of meta generalized gradient approximations based on the density matrix expansion (DME) is considered as one of the most accurate techniques to design semilocal exchange energy functionals in two-dimensional density functional formalism. The exchange holes modeled using DME possess unique features that make it a superior entity. Parameterized semilocal exchange energy functionals based on the DME are proposed. The use of different forms of the momentum and flexible parameters is to subsume the non-uniform effects of the density in the newly constructed semilocal functionals. In addition to the exchange functionals, a suitable correlation functional is also constructed by working upon the local correlation functional developed for 2D homogeneous electron gas. The non-local effects are induced into the correlation functional by a parametric form of one of the newly constructed exchange energy functionals. The proposed functionals are applied to the parabolic quantum dots with a varying number of confined electrons and the confinement strength. The results obtained with the aforementioned functionals are quite satisfactory, which indicates why these are suitable for two-dimensional quantum systems.