Fundamental gaps of finite systems from the eigenvalues of a generalized Kohn-Sham method

Abstract

We present a broadly-applicable, physically-motivated first-principles approach to determining the fundamental gap of finite systems. The approach is based on using a range-separated hybrid functional within the generalized Kohn-Sham approach to density functional theory. Its key element is the choice of a range-separation parameter such that Koopmans' theorem for both the neutral and anionic is obeyed as closely as possible. We demonstrate the validity, accuracy, and advantages of this approach on first, second, and third row atoms, the oligoacene family of molecules, and a set of hydrogen-passivated silicon nanocrystals. This extends the quantitative usage of density functional theory to an area long believed to be outside its reach.

References in corpus (12)

• Localization and delocalization errors in density functional theory and implications for band-gap prediction
• Fractional charge perspective on the band-gap in density-functional theory
• A density functional theory with correct long-range asymptotic behavior
• Polaronic hole localization and multiple hole binding of acceptors in oxide wide-gap semiconductors
• A well-tempered density functional theory of electrons in molecules
• Combining GW calculations with exact-exchange density-functional theory: An analysis of valence-band photoemission for compound semiconductors
• Koopmans' condition for density-functional theory
• Optical excitations in organic molecules, clusters and defects studied by first-principles Green's function methods
• Optical spectra and exchange-correlation effects in molecular crystals
• Density-relaxation part of the self energy
• Hybrid density functional calculations of the band gap of Ga${}_x$In${}_{1-x}$N
• Efficient Total Energy Calculations from Self-Energy Models

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