Linearity condition for orbital energies in density functional theory: Construction of orbital-specific hybrid functional

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  • Yutaka Imamura
    Waseda University 1 Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, , 3–4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
  • Rie Kobayashi
    Waseda University 1 Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, , 3–4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
  • Hiromi Nakai
    Waseda University 1 Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, , 3–4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan

Abstract

<jats:p>This study proposes a novel approach to construct the orbital-specific (OS) hybrid exchange-correlation functional by imposing the linearity condition: ${{{\partial ^2 E}/{\partial f_i^2 }}} |_{0 \le f_i \le 1} = {{{\partial \varepsilon _i }/{\partial f_i }}} |_{0 \le f_i \le 1} = 0$∂2E/∂fi2|0≤fi≤1=∂ɛi/∂fi|0≤fi≤1=0, where E, εi, and fi represent the total energy, orbital energy, and occupation number of the ith orbital. The OS hybrid exchange-correlation functional, of which the OS Hartree–Fock exchange (HFx) portion is determined by the linearity condition, reasonably reproduces the ionization potentials not only from valence orbitals but also from core ones in a sense of Koopmans’ theorem. The obtained short-range HFx portions are consistent with the parameters empirically determined in core–valence–Rydberg–Becke-3–parameter–Lee–Yang–Parr hybrid functional [Nakata et al., J. Chem. Phys., 124, 094105 (2006); ibid, 125, 064109 (2006)10.1063/1.2227379].</jats:p>

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