An accurate 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.Comment: 19 pages. 2 figures. Submitted to PR

A study of accurate exchange-correlation functionals through adiabatic connection

A systematic way of improving exchange-correlation energy functionals of density functional theory has been to make them satisfy more and more exact relations. Starting from the initial GGA functionals, this has culminated into the recently proposed SCAN(Strongly constrained and appropriately normed) functional that satisfies several known constraints and is appropriately normed. The ultimate test for the functionals developed is the accuracy of energy calculated by employing them. In this paper, we test these exchange-correlation functionals -the GGA hybrid functionals B3LYP and PBE0, and the meta-GGA functional SCAN- from a different perspective. We study how accurately these functionals reproduce the exchange-correlation energy when electron-electron interaction is scaled as scaling parameter times Vee with this parameter varying between 0 and 1. Our study reveals interesting comparison between these functionals and the associated difference Tc between the interacting and the non-interacting kinetic energy for the same density.Comment: 8 Pages, 3 Figures and 8 Table

A general penalty method for density-to-potential inversion

A general penalty method is presented for the construction of of Kohn-Sham system for given density through Levy's constrained-search. The method uses a functional $S[\rho]$ of one's choice. Different forms of $S[\rho]$ are employed to calculate the kinetic energy and exchange-correlation potential of atoms, jellium spheres, and Hookium and consistency among results obtained from them is shown

Hydrodynamic approach to TDDFT; response properties of metal clusters

Performing electronic structure calculations for large systems, such as nanoparticles or metal clusters, via orbital based Hartree-Fock or Kohn-Sham theories is computationaly demanding. To study such systems, therefore, we have taken recourse to the hydrodynaic approach to time-dependent density functonal theory. In this paper we develop variation-perturbation method within this theory in terms of the particle and the current densities of a system. We then apply this to study the linear and nnlinear resonse properties of alkali metal clusters within spherical jellium backgrond model.Comment: 28 pages and 5 figures in eps format, revised and new references and figures added. resubmitted to Journal of Chemical Physic

Comparison of van der Waals coefficient C6_{6} of sodium clusters obtained via spherical jellium background model and all-electron ab-initio method

In this paper we employ two distinct approaches - all-electron \textit{ab initio} method and the spherical jellium background model- within time dependent density functional theory to calculate the long range dipole-dipole dispersion coefficient (van der Waals coefficient) $C_{6}$ of sodium atom clusters containing even number of atoms ranging from 2 to 20 atoms. The dispersion coefficients are obtained via Casimir-Polder relation. All the calculations are carried out with local density approximation for exchange-correlation energy functional. These two sets of results are compared to assess the accuracy of jellium based results and to ascertain the effect of detail ionic structure of the clusters on the van der Waals coefficient.Comment: 15 pages including 2 figures. To be published in Journal of Computational Methods in Science and Engineerin

Accurate exchange energy and total energy for excited states: Inclusion of gradient correction

We present an approach for accurate calculation of exchange energy and total energy for excited states using time independent density functional formalism. This is done by inclusion of gradient correction into the excited state exchange energy functionals developed by us. We have incorporated Becke and Perdew Wang corrections into our functional and have studied various types of excited states having one and two gaps in occupation of orbitals

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

Local density approximation for the exchange energy is made for treatment of excited-states in density-functional theory. It is shown that taking care of the state-dependence of the LDA exchange energy functional leads to accurate excitation energies

Frequency dependent hyperpolarizabilities of atoms; calculations using density-functional theory

Using the orbitals generated by the van Leeuwen-Baerends potential, we calculate frequency dependent response properties of noble gas atoms of He, Ne and Ar and alkaline earth atoms Be and Mg, with particlar emphasis on their nonlinear polarizabilities. For this we employ time-dependent Kohn-Sham formalism with adiabatic local-density aproximation (ALDA) for exchange and correlation. We show that results thus obtained for frequency dependent polarizabilities of the inert gas atoms are highly acurate. On the other hand, polarizabilities of the alkaline earths are not given with the same accuracy. In light of this, we make an assessment of ALDA for obtaining linear and nonlinear response properties by employing time-dependent density-functional theory.Comment: 13 pages of text and 7 figure

Calculation of van der Walls coefficients of alkali metal clusters by hydrodynamic approach to time-dependent density-functional theory

In this paper we employ the hydrodynamic formulation of time-dependent density functional theory to obtain the van der Waal coefficients $C_{6}$ and $C_{8}$ of alkali-metal clusters of various sizes including very large clusters. Such calculation becomes computationally very demanding in the orbital-based Kohn-Sham formalism, but quite simple in the hydrodynamic approach. We show that for interactions between the clusters of same sizes, $C_{6}$ and $C_{8}$ sale as the sixth and the eighth power of the cluster radius rsepectively, and approach the respective classically predicted values for the large size clusters.Comment: 13 pages with two figures. Submitted to J. Phys. B: At. Mol. Opt. Phy

Study of adiabatic connection in density functional theory with an accurate wavefunction for 2-electron atoms

Using an accurate semi-analytic wavefunction for two electron atoms, we construct the external potential for varying strength of electron-electron (e-e) interaction. Using this potential we explicitly calculate the energy of their positive ion and show that the ionization-potential of these systems remains unchanged with respect to the strength parameter for e-e interaction. Furthermore, using total energies of these systems as a function of strength parameter, we provide a new perspective into a variety of hybrid functionals.Comment: 6 Pages, 4 Figures and 2 Table