Hole Localization in Molecular Crystals from Hybrid Density Functional Theory

Abstract

We use first-principles computational methods to examine hole trapping in organic molecular crystals. We present a computational scheme based on the tuning of the fraction of exact exchange in hybrid density functional theory to eliminate the many-electron self-interaction error. With small organic molecules, we show that this scheme gives accurate descriptions of ionization and dimer dissociation. We demonstrate that the excess hole in perfect molecular crystals form self-trapped molecular polarons. The predicted absolute ionization potentials of both localized and delocalized holes are consistent with experimental values.Charge localization in organic solids and interfaces has important implications for the functioning of organic devices [1, 2]. It has been long suggested that charge carriers in organic molecular crystals may self-trap to form localized small polarons [1][2][3][4] through interaction with the surrounding electron and lattice. Models based on the concept of polaron have led to theoretical understanding of charge transport of these materials (see e.g. [1,5]). On the other hand, direct evidence and atomic scale probe of localized charge states in organic crystals remain lacking. Ab initio computations have recently been summoned to provide accurate quantitative description of polaron state in covalent solids [6,7]. In this work, we apply hybrid density functional theory (DFT) with carefully calibrated admixtures of exact exchange to molecular crystals and conclusively demonstrate from first principles the existence of self-trapped hole polaron in defect-free molecular crystals. Our choice to work with small organic molecules permits systematic analysis of DFT exchange correlation (xc) functionals in both gas and solid phases. It also allows predictions of the absolute ionization potentials (IP) of both polaronic localized and free delocalized hole state in solids, revealing large errors in semilocal (sl) DFT functionals that to our knowledge have never been discussed in the literature. This successfully treatment of hole localization and delocalization properties will aid the understanding of charge trapping [8,9] and carrier mobility [10] that are important for organic electronics.A key prerequisite to such studies is the correct choice of DFT functionals. Previous theoretical studies reveal an extreme sensitivity of charge localization to theoretical approximations [6,7,[11][12][13][14]. Standard semilocal functionals for the xc energy, such as the local density approximation (LDA) and generalized gradient approximation (GGA), have been successful in predicting atomic structures and electronic properties of many molecular complexes and solid state materials. But they tend to fail in systems involving fractional charges, e.g. they dissociate molecular ion H + 2 into 2 H 0.5+ rather than into H + and H. The problem stems from self-interaction error (SIE) in the standard density functionals [15]. For a one electron system SIE is conveniently described as the incomplete cancellation of spurious sel...

The Influence of One-Electron Self-Interaction on d-Electrons

“…Instead, one expects that SI is only effectively counteracted for large values of a (i.e., for large amounts of EXX included). This assumption is systematically confirmed by the results of Reference [63,67,[115][116][117].…”

Enforcing the linear behavior of the total energy with hybrid functionals: Implications for charge transfer, interaction energies, and the random-phase approximation

“…The basic idea is to parametrize the exact-exchange energy such that the linearity condition is restored [19][20][21][22][23]. This route has been predominantly followed with the long-range separated BaerNeuhauser-Livshiz (BNL) hybrid functional [24,25].…”

Generalization of Dielectric-Dependent Hybrid Functionals to Finite Systems

“…In Ref. [79], a mixing fraction of ¼ 0.70 for benzene was found to minimize the many-electron self-interaction error. Using Eq.…”