Generalization of Dielectric-Dependent Hybrid Functionals to Finite Systems

The accurate prediction of electronic and optical properties of molecules and solids is a persistent challenge for methods based on density functional theory. We propose a generalization of dielectric-dependent hybrid functionals to finite systems where the definition of the mixing fraction of exact and semilocal exchange is physically motivated, nonempirical, and system dependent. The proposed functional yields ionization potentials, and fundamental and optical gaps of many, diverse molecular systems in excellent agreement with experiments, including organic and inorganic molecules and semiconducting nanocrystals. We further demonstrate that this hybrid functional gives the correct alignment between energy levels of the exemplary TTF-TCNQ donor-acceptor system.

Popular Summary

Physicists, chemists, and material scientists have used density-functional theory for decades to understand and predict many properties of molecules and solids. Despite the numerous successes of this theory, predicting the spectroscopic properties that arise from the interaction of matter with light is an ongoing challenge. Such an interaction may result in electronic excitation (e.g., absorption) or even in the ejection of charges (e.g., photoemission) and is exploited, for example, in solar-energy conversion and storage processes. Here, we present a method without any empirical parameters, based on density-functional theory. We use this method to predict the absorption and emission properties of molecules. Our method generalizes previous methods used to study solids and accordingly provides a unified framework to compute spectroscopic properties of molecules and condensed systems.

More than two decades ago, researchers introduced hybrid density functionals within density-functional theory. These functionals are not only based on the density but also on electronic wave functions, and numerous studies have focused on optimizing their specific functional form using, in some cases, adjusted empirical parameters. The work presented here proposes a nonempirical functional form by deriving an expression of the average screening of the electronic interactions in finite systems. We test our method, using organic and inorganic molecules, for both photoemission and absorption properties, as well as for energy-level alignment. We find that the computed ionization potentials of a variety of molecular compounds are in good agreement with experimental data. Our proposed method is more accurate and efficient than many popular functionals used in the literature; it yields accurate predictions of both the photoabsorption and photoemission properties of molecules.

We expect that our findings will substantially advance the field of computational spectroscopy of materials and molecules.

Figure 1

Vertical ionization potentials (VIP) of the $\mathrm{G}2/97$ subset consisting of 36 closed-shell molecules computed as the highest occupied molecular orbital energy using the SX hybrid functional (SX), ${\mathrm{G}}_0{\mathrm{W}}_0$ starting from PBE wave functions (${\mathrm{G}}_0{\mathrm{W}}_0@\mathrm{PBE}$; data from Ref. [56]) and SX wave functions (${\mathrm{G}}_0{\mathrm{W}}_0@\mathrm{SX}$), and total energy differences [$\mathrm{\Delta }\mathrm{SCF}(\mathrm{PBE})$; data from Ref. 62].

Figure 2

The fundamental gaps of several hydrogen passivated silicon nanostructures ${\mathrm{SiH}}_4$, ${\mathrm{Si}}_{35}{\mathrm{H}}_{36}$, ${\mathrm{Si}}_{66}{\mathrm{H}}_{64}$, and ${\mathrm{Si}}_{87}{\mathrm{H}}_{64}$ predicted using the SX hybrid functional (see text), ${\mathrm{G}}_0{\mathrm{W}}_0$ starting from PBE wave functions (${\mathrm{G}}_0{\mathrm{W}}_0@\mathrm{PBE}$), and SX wave functions (${\mathrm{G}}_0{\mathrm{W}}_0@\mathrm{SX}$). Fundamental gaps obtained from total energy differences [$\mathrm{\Delta }\mathrm{SCF}(\mathrm{PBE})$] are included for comparison.

Figure 3

The first lowest optical singlet excitations predicted by the TDSX compared to the revised best theoretical estimates (see text) of Thiel’s test set for 28 molecules. Values predicted for the same transitions by TDPBE0 (time-dependent density functional calculations with the PBE0 functional) and $\mathrm{BSE}@{\mathrm{G}}_0{\mathrm{W}}_0@\mathrm{PBE}0$ (results from the solution of the BSE, starting from single-particle energies computed at the ${\mathrm{G}}_0{\mathrm{W}}_0$ level of theory, with DFT results obtained with the PBE0 functional) are taken from Ref. [89].

Figure 4

MAE for (from left to right) the ionization potentials (photoemission) of Thiel’s test set (with the exception of propanamide because of the lack of experimental data) predicted by the highest occupied molecular orbital energy computed using PBE0, ${\mathrm{G}}_0{\mathrm{W}}_0@\mathrm{PBE}0$, and the screened exchange constant functional (SX); the lowest optical singlet transitions predicted by the SX functional [TDSX, i.e., time-dependent density functional calculations using the SX functional, Eq. (10)], TDPBE0 and PBE0 with many-body perturbation theory corrections ($\mathrm{BSE}@{\mathrm{G}}_0{\mathrm{W}}_0@\mathrm{PBE}0$) TDPBE0 and $\mathrm{BSE}@{\mathrm{G}}_0{\mathrm{W}}_0@\mathrm{PBE}0$ are taken from Ref. [89].