Time-independent excited-state DFT
There has been considerable interest in applying Kohn-Sham density functional theory (KS-DFT) for dealing excited-states within time-independent framework. Only in the recent past, the theoretical framework for individual excited-state time-independent density functional theory (e-DFT) has put forward by Görling (ρ-stationary state theory), Levy and Nagy’s (bi-functional approach). The next key challenging problem in e-DFT is to develop a methodology for constructing the approximate energy functionals for excited-states. However, due to the lack of energy functionals for excited-states, ground-state functionals are used in practise to calculate the excited-state properties; thus leading to both qualitative incorrect as well as quantitatively inaccurate. In this project, I will present our method of constructing the energy functionals for excited-states with application to kinetic- and exchange parts.
(a) Our method of construction energy functionals and exchange-potential for excited-states
The excited-state energy density functional is constructed by splitting the k-space of homogeneous electron gas (HEG) in accordance to the orbital occupation of the real system to get an local density-approximated (LDA)-like functional. Thus the method takes care of state-dependence of the energy functional due to non-occupation of some orbitals.
(Figure)
The exchange energy functional developed on the basis of this method for excited-states leads to accurate transition energies. We have studied this method in connection with the kinetic energy density functional and exchange potential for excited-states. The key findings of my investigation are summarized below.
Generality of the split k-space approach through the construction of the kinetic energy density functional for excited-states
The local density-approximated (LDA) and gradient-energy approximtion (GEA) based kinetic energy density functional constructed by splitting k-space for excited- states is shown to give accurate kinetic energies. Further, the generality of the method is shown by studying another form of kinetic energy functional, the Gázquez and Robles functional. The interesting aspect of this study is that the kinetic energy density functionals for excited-states proposed have the same accuracy for the excited-states as the ground-state functional do for the ground-states. This indicates that the proposed kinetic energy functionals are appropripate functionals for the excited- states and points to the correctness of physics invoked to construct the functionals.
M. Hemanadhan and Manoj K. Harbola, J. Mol. Struct.: Theochem 943, 152-157 (2010).
Robustness of our method through the linear density response function study of the non-interacting kinetic energy density functional
We have shown through the response function study that it may not be easy to expand the kinetic energy functional for excited-states beyond the zeroth-order in terms of the total excited-state density. Thus although the excited-state energy is a bifunctional E[ρ,ρ0] of the corresponding excited (ρ) and ground-state (ρ0) densities, for systematic development of the energy functionals it is useful to work in terms of the densities ρ1, ρ2, ρ3, · · · .
M. Hemanadhan and Manoj K. Harbola, Eur. Phys. J. D 66, 57(1)-57(4) (2012).
Testing the energy functional and potential through ionization potential (IP) theorem
Ionization potential (IP) theorem serves as a severe test to the approximations used in constructing the exchange-correlation functional and the corresponding potential. The split k-space based exchange functional, the modified local spin density (MLSD) functional with self-interaction correction for the orbitals involved in the transition (MLSDSIC), and the corresponding asymptotic corrected exchange potential (MLB) using van Leeuwen and Baerends (LB) correction for excited states are examined through the IP theorem. The IP theorem for excited-states is satisfied more accurately with the MLB potential, whereas the ground-state LB potential with excited-state density does not lead to accurate satisfaction of the IP theorem.
M. Hemanadhan, Md. Shamim, and Manoj K. Harbola, J. Phys. B: At. Mol. Opt. Phys. 47, 115005 (10pp) (2014).
Behaviour of the excited-state potential
The MLB potential for an excited-state of Li (3s1 2S) matches with the exact exchange potential (KLI) better than the ground state LB potential in the outer region. However, in the intermediate region, the LB potential is not close to the KLI potential and has an unphysical negative spike at the minimum of radial density which is not present in our MLB potential. Thus it is clear that the exchange potentials obtained on the basis of split k-space give a much better description of an excited-state than the ground- state LB potential.
(b) Estimation of correlation energies of excited-states through a modelled Coulomb hole
The Coulomb hole is modelled in this work for estimating the correlation energies of various atoms in their ground- and excited-states. The parameter in the model is fixed by making the corresponding modelled Coulomb hole to satisfy the exact constraint of charge neutrality. The ground-state correlation energies so obtained are independent of Z. The excited-state correlation energies calculated, by extending the ground- state parameter to the excited-states, matches with the exact values for majority of cases, except for ions with high ionicity.
M. Hemanadhan and Manoj K. Harbola, arXiv:1409.5242v2 [physics.chem-ph] (2014).
M. Hemanadhan, Md. Shamim, and Manoj K. Harbola, J. Phys. B: At. Mol. Opt. Phys. 47, 115005 (10pp) (2014) [Link]
"Testing excited-state energy density functional and potential with the ionization potential theorem"
M. Hemanadhan and Manoj K. Harbola, AIP Conf. Proc. 1591, 1170 (2014) [Link]
"Excitation energies of molecules within time-independent density functional theory"
Manoj K. Harbola, M. Hemanadhan, Md. Shamim, P. Samal, J. Phys.: Conf. Ser. 388, 012011-626 (2012) [Link]
"Excited-state density functional theory"
M. Hemanadhan and Manoj K. Harbola, In Crystal Growth and Computational Materials Science, Eds. S. Jayakumar, P. Ravindran, R. Arun Kumar, C. Sudarshan, MacMillan Advanced Research Series, 2012 (ISBN: 9789350590485) [Link]
"Linear Response Function of Excited-homogeneous electron gas; Implications for the kinetic energy functional for excited-states"
M. Hemanadhan and Manoj K. Harbola, Eur. Phys. J. D 66, 57(1)-57(4) (2012) [Link]
"Response function analysis of excited-state kinetic energy functional constructed by splitting k-space"
M. Hemanadhan and Manoj K. Harbola, J. Mol. Struct.: Theochem 943, 152-157 (2010). (Special Issue : Conceptual Aspects of Electron Densities and Density Functionals) [Link]
"Is it possible to construct excited-state energy functionals by splitting k-space?"
Manoj K. Harbola, M. Hemanadhan, Md. Shamim and P. Samal, In Concepts and Methods in Modern Theoretical Chemistry, Vol. 1 : Electronic Structure and Reactivity, Eds. S. K. Ghosh and P. K. Chattaraj, CRC Press, 99-118 (2013) [Link]
"Energy functionals for excited states"
Hemanadhan Myneni, Department of Physics, Ph.D. Thesis, Indian Institute of Technology Kanpur, India (2014).
"Study of excited-state energy density functionals constructed by splitting k-space for homogeneous electron gas"
M. Hemanadhan and Manoj K. Harbola, arXiv:1409.5242v2 [physics.chem-ph] (2014) [Link]
"Estimation of correlation energy for excited-states of atoms"
M. Hemanadhan and Manoj K. Harbola, "Excitation energies of molecules within time-independent density functional theory", at 58th DAE-Solid State Physics Symposium 2013 (DAE-SSPS), Thapar University, Patiala, Punjab − India (17 Dec.–21 Dec. 2013) [Poster].
M. Hemanadhan and Manoj K. Harbola, "Testing excited-state energy density functional and potential with the ionization potential theorem", at DAE BRNS Symposium on Current Trends in Theoretical Chemistry (CTTC-2013), Bhabha Atomic Research Centre, Mumbai − India (26 Sep.–28 Sep. 2013) [Poster].
M. Hemanadhan and Manoj K. Harbola, "Response function analysis of excited-state kinetic energy functional", at The Symposium Challenges in Density Matrix and Density Functional Theory (DFTM2012), Ghent University, Ghent − Belgium (01 Apr.–06 Apr. 2012) [Poster].
M. Hemanadhan, "Linear response function of excited-homogeneous electron gas; Implications for the kinetic energy functional for excited-states", at International Conference on Advanced Materials (ICAM-2011), PSG College of Technology, Coimbatore, Tamil Nadu − India (12 Dec.–16 Dec. 2011) [Talk].
M. Hemanadhan and Manoj K. Harbola, "Excited-state kinetic energy functional", at Current Trends in Condensed Matter Physics 2010 (CTCMP 2010), NISER, IOP Campus, Bhubaneswar, Orissa − India (15 Dec.–19 Dec. 2010) [Poster].
# Last update: 21 August 2024