Calculation of level alignments at dye-semiconductor interfaces: the role of exact exchange in density functional theory

Abstract In this work, density functional theory is applied to several models as representative parts in dye-sensitized solar cells (DSSCs). The performance of flexible hybrid exchange-correlation functionals is evaluated for the calculation of ground- and excited-state properties pertaining to DSSC model systems. The electronic structure of isolated dyes, TiO $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> clusters, and dyes anchored on a sizeable (TiO $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> ) $$_{38}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>38</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> cluster are calculated with hybrid exchange-correlation functionals based on different mathematical forms to incorporate exact exchange. This enables the analysis of level alignments at the dye-TiO $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> interface within the TDDFT framework, with respect to the role of the exact exchange in various hybrid functionals. Particular emphasis is placed on the assessment of a recently introduced local hybrid functional with range separation which has been shown to improve energies for charge-transfer excitations. Our results indicate that the HOMO–LUMO gap of TiO $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> clusters that are frequently used to represent the surface of the nanoparticles is significantly larger than the experimental band gap of bulk anatase TiO $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> (3.2 eV). It is also demonstrated that exchange-correlation functionals with long-range exact exchange perform well for the simulation of UV–Vis spectra of excited organic donor-acceptor dyes and the calculation of band gaps of TiO $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> clusters, but yield unphysical level alignments at dye-semiconductor interfaces with TDDFT. We further highlight the importance to allow excitations from all occupied orbitals for the calculation of UV–Vis spectra with linear-response TDDFT of organic dyes adsorbed on TiO $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> clusters.