2P-123
An examination of exchange-correlation functionals in solid-state calculations(Fuel Cell Nanomaterials Center, University of Yamanashi) A. Chutia and T. Tsuneda[Introduction]
Density functional theory (DFT) raises the stakes in quantum chemistry in predicting anddesigning reactions and materials, because sophisticated exchange-correlation functionals havebeen developed for investigating large and complicated systems. However, conventional
functionals represented by PBE have still been used in many solid state calculations, because
these functionals tend to give even better band gaps for semi-conductors than those ofsophisticated functionals with much less computational time. Kresse et al. actually suggested thatLDA and GGA functionals slightly underestimate the band gaps of semi-conductors, while longrange corrected (LC) LDA functional significantly overestimate these band gaps.1 However, notethat LDA and GGA functionals always significantly underestimate the band gaps of insulatorsthat are accurately reproduced by LC functionals. This appears to indicate that LC functionals
lack something to give accurate band gap energies of semi-conductors and error cancellation
causes the better band gaps for LDA and GGA functionals. In this study, we investigate thebarrier gap energies of solids thoroughly by calculating them with various functionals, basis sets,
and calculation models to make clear the reason for the band gap behaviors.
[Computational details]
The Kohn-Sham calculations of solid state properties are performed using DMol3 and thedevelopment version of Gaussian09 (G09), and Vienna Ab-initio Simulation Package (VASP)
programs. DMol3 calculations are carried out using DNP (double numerical plus polarization)basis set with various types of functionals and 20×20×20 Monkhorst-Pack like k-point grids. To
further extend this work to study the LC functionals, we also perform preliminary calculations
using the development version of G09 program. Pure LDA and GGA calculations are performed
using SVWN and SPW LDA, BOP, BLYP, BP, BP(VWN), PBE and PW91 GGA and semiempirical HCTH exchange-correlation functionals. All the calculations on G09 program areperformed using 6-31G and SDDALL basis sets. We also examine band calculations with plane
wave basis set on the VASP program.

[Results and discussion]
Figure 1 displays the deviations of band gap energies calculated on DMol3 program from theexperimentally-predicted values. As previously suggested, the figure shows that LDA and GGA
functionals slightly underestimate band gap energies. However, we found that there areFig. 1. The deviation of the band gap energies of various crystals calculated on Dmol3 in eV.
systematic differences in the errors of the small band gaps for Ge and Sn crystals and Ga and In
alloys: Functionals using PW91, PBE, and LDA correlation functionals provide better band gaps
than others. The difference between them comes from exchange interactions, which are included
as “parallel-spin correlation” in these correlation functionals.2 That is, exchange interactions
significantly affect band gap energies for near-degenerate bands. We therefore suppose that thenear-degeneracy effects neglected in conventional functionals may be partly compensated byexchange interactions in LDA, PBE and PW91 correlation functionals, while these correlation
functionals are usually used in band calculations. This result suggests the significance of neardegeneracy effects in solid state bands. We will further discuss the characteristics of band gap
energies and other solid state properties in the presentation.
[References]
1. I. C. Gerber, J. G. Angyan, M. Marsman, and G. Kresse, J. Chem. Phys. 127, 054101, 2007.
2. 「密度汎関数法の基礎」常田貴夫著 (講談社) .