Structures of organic semiconductor molecules analyzed in this paper: 3,4,9,10-perylene tetracarboxylic dianhydride (PTCDA), 1,4,5,8-naphthalene tetracarboxylic dianhydride (NTCDA), Pentacene, Pyrene, Hexabenzocoronene (HBC), and Triphenylene (TPL).
Experimental photoelectron spectrum of PTCDA from Ref. 15 compared to the KS eigenvalue spectra obtained from the semilocal functionals LDA and PBE. KS eigenvalues are superimposed with Gaussians of width 0.08 eV and the HOMO-peaks are set to zero to make visual comparison easier. The shaded area marks the gap in the experimental spectrum that is absent in the KS spectra.
Simple model for understanding the relationship of one-electron self-interaction and localization: Hartree energy E H[n G], LDA energy , and sum of both for a Gaussian density distribution are plotted as a function of the Gaussian standard deviation σ. The total self-interaction energy is plotted again on a magnified energy scale in the upper part of the figure. It is positive for strongly localized densities and negative for delocalized ones. Note that in region 2 the self-interaction energy is negative, i.e., the LDA self-interaction is larger than the Hartree self-interaction, yet the system can still gain energy by delocalizing the one-electron density.
Self-interaction error and orbital localization in PTCDA: (a) Self-interaction energy according to Eq. (1); (b) Foster–Boys orbital localization according to Eq. (19); (c) OSIE , self-consistent eigenvalue shift , and one-shot eigenvalue shift for the KS-KLI approach according to Eqs. (15), (16), and (20), respectively; (d) OSIE , self-consistent eigenvalue shift , and one-shot eigenvalue shift for the LOC-KLI approach according to Eqs. (17), (18), and (21), respectively. The HOMO is orbital number 70. Dashed lines are just a guide to the eye. For comparison with the corresponding orbital structures, see Fig. 5.
Highest occupied orbitals of PTCDA as obtained from LDA calculation in PARSEC. Red Boxes mark the orbitals for which the corresponding eigenvalues lie inside the HOMO/HOMO-1 gap of the experimental spectrum.
KS eigenvalue spectra for PTCDA obtained from LDA, KS-KLI, and LOC-KLI compared to the experimental photoelectron spectrum. The arrows denote the shifts of the LDA eigenvalues corresponding to the HOMO-1 to HOMO-4 in KS-KLI and LOC-KLI, respectively. KS eigenvalues are superimposed with Gaussians of width 0.08 eV and all HOMO-peaks are set to zero.
Partial correlation function κ of the self-consistent eigenvalue shifts of KS-KLI and LOC-KLI as compared to LDA following Eq. (23) for a set of organic molecular semiconductors.
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