Orbital occupation

1. Response Function Analysis of Excited-state Kinetic Energy Functional M. Hemanadhan and Manoj K. Harbola Department of Physics, Indian Institute ofTechnology Kanpur, India hemanadh @ iitk.ac.in, mkh @ iitk.ac.in 2012 Introduction: Q. Can time-independent excited-state DFT be realized ? A. Construction of excited-state kinetic energy functionals for excited-states 2. Kinetic energy functional from Split k-space 1. Extension of ground-state functionals for excited-states • Within LDA, the energy functionals are constructed by splitting the • k-space according to the occupation of orbitals. • From the idea of ground-state DFT, energy is a functional of the • density • Within LDA, the kinetic energy functional f or excited-states then becomes ??? Current Work !!! k3 k2 • Now, the challenge is to develop a systematic method for constructing the kinetic, exchange and correlation energy functionals. • We now present a methodolgy for constructing excited-state energy functionalsby splitting k-space • The impressive results for kinetic and exchange energy functionals • Through response function, we show our method is a proper way for constructing excited-state energy functionals kF k1 k-space Orbital occupation k-space Orbital occupation • Results presented in Table shows that the idea works pretty good. • Similarly, exchange energy functional was constructed. • The approximations leads to large errors due to omissions of gaps • in k-space 1 2 3 Results : Exited State Kinetic Energies For Atoms Results : Exited State Kinetic Energies For 3D Oscillator potential Question ? • Since the occupation is different for different states, the kinetic energy is state-dependent. We present kinetic energies for different class of excited-states, pure-shell, core-shell (Figure)and shell - core- shell – core • The exact kinetic energies are obtained by solving the Kohn-Sham equations with Gunnarsson-Lundquist parameterization. Can we construct the energy functionals in terms of the excited-state density and alone ? • To answer this, we done response-function analysis for excited-state homogeneous electron gas (HEG) Response-function analysis • For the excited-states as shown in Fig., the response function is given by • Conclusions • The ground-state functional under-estimates the exact kinetic energy by very large amount. • The split k-space based functional brings the error down significantly. • The accuracy obtained by split k-space functional for excited-states is similar to accuracy obtained for ground-state functionals for the ground-state energies Where is the response function for the ground state with Fermi wave vector k What we have achieved Accurate excited-state energy functionals were constructed by writing in terms of and Comparision of excited-state kinetic energies obtained from the ground-state functional and from the split k-space based functional 6 4 5 • Conclusions: • Our analysis shows that this is a good idea to split • k-space for constructing excited state kinetic energy • functional for excited-states beyond the zeroth-order in • terms of the total excited-state density. • Although the excited-state energy is a bi-functional • for systematic development of the energy functionals it is • useful to work in terms of the densities and Term corresponding to gradient Cross Check for ground-states, and In asymptotic limit Gradient term Other studies with the idea of split k-space For excited-states, , the term corresponding to gradient expansion is approximated as • This idea has been successfully used by our group to calculate • exchange energy for atoms and • Band gaps of wide variety of semiconductors References [1] M. Hemanadhan and M. K. Harbola, Eur. Phys. J. D 66, 57 (2012). [2] M. Hemanadhan and M. K. Harbola, J. Mol. Struct.(Theochem) 943, 152 (2010). [3] Md. Shamim and M. K. Harbola , J. Phys. B 43 , 215002 (2010). [4] P. Samal and M. K. Harbola, J. Phys. B 38, 3765 (2005). [5] M. Rahaman, S Ganguly, P. Samal, M. K. Harbola, T. S. Dasgupta, A. Mookerjee, Physica B 404, 1137 (2009) For excited-states, as shown in Figure Diverges for Cannot be written in terms of • In the asymptotic limit, the gradient term for exited kinetic energy blows up if we insist on expanding it interms of density 7 8 9 We thank for the financial support from CSIR-UGC, Govt. of India and IIT Kanpur.