Solid-state optical absorption from optimally tuned time-dependent range-separated hybrid density functional theory

We present a framework for obtaining reliable solid-state charge and optical excitations and spectra from optimally tuned range-separated hybrid density functional theory. The approach, which is fully couched within the formal framework of generalized Kohn-Sham theory, allows for the accurate prediction of exciton binding energies. We demonstrate our approach through first principles calculations of one- and two-particle excitations in pentacene, a molecular semiconducting crystal, where our work is in excellent agreement with experiments and prior computations. We further show that with one adjustable parameter, set to produce the known band gap, this method accurately predicts band structures and optical spectra of silicon and lithium fluoride, prototypical covalent and ionic solids. Our findings indicate that for a broad range of extended bulk systems, this method may provide a computationally inexpensive alternative to many-body perturbation theory, opening the door to studies of materials of increasing size and complexity.

Figure 1

(a) Band structure (left) and density of states (right) of the pentacene solid, calculated using LDA (gray dashed lines), ${\mathrm{G}}_0{\mathrm{W}}_0$@LDA (red dashed lines), and OT-SRSH (black solid lines). For all methods, the middle of the band gap is shifted to zero. (b) The imaginary part of the dielectric function of the pantacene solid, with incident light polarization averaged over the $a,b$, and $c$ main unit-cell axes, calculated using TDLDA (gray dashed lines), ${\mathrm{G}}_0{\mathrm{W}}_0$/BSE (red dashed lines), and TD-OT-SRSH (black solid lines). For visualization purposes, the leading absorption feature (between 0.5 and 2.5 eV) was multiplied by a factor of 10 with all computational methods used. The OT-SRSH and TD-OT-SRSH results were obtained using the parameters $\gamma =0.16 {\mathrm{bohr}}^{-1},\alpha =0.2$, and $\varepsilon =3.6$. For computational details and convergence information, see the SM [51].

Figure 2

Top: The band structure of bulk (a) silicon and (b) LiF, calculated using LDA (gray dashed lines), SRSH (black solid lines), and ${\mathrm{G}}_0{\mathrm{W}}_0$@LDA (red dashed lines). The Si band structure is also compared to empirical pseudopotential values taken from Ref. [55] (blue dashed lines). For all methods, the middle of the band gap is shifted to zero. Bottom: The imaginary part of $\varepsilon$ for (a) silicon and (b) LiF, calculated using TDLDA (gray dashed line), TDSRSH (black solid line), and ${\mathrm{G}}_0{\mathrm{W}}_0$/BSE (red dashed line), and compared to experiment (blue dashed line, Ref. [56] for Si, and Ref. [57] for LiF). The optimized SRSH and TDSRSH parameters are $\gamma =0.11 {\mathrm{bohr}}^{-1},\alpha =0.2$, and $\varepsilon =12$ for silicon, and $\gamma =0.58 {\mathrm{bohr}}^{-1},\alpha =0.2$, and ${\varepsilon }_0=1.9$ for LiF. For computational details, see the SM [51].