<p>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<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="214_2025_3240_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(_2\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> clusters, and dyes anchored on a sizeable (TiO<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="214_2025_3240_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(_2\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>)<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="214_2025_3240_Article_IEq3.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(_{38}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>38</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> 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<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="214_2025_3240_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(_2\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> 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<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="214_2025_3240_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(_2\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> clusters that are frequently used to represent the surface of the nanoparticles is significantly larger than the experimental band gap of bulk anatase TiO<InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="214_2025_3240_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(_2\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> (3.2&#xa0;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<InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="214_2025_3240_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(_2\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> 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<InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="214_2025_3240_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(_2\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> clusters.</p>

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

  • Natalia Belen,
  • Hilke Bahmann

摘要

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 \(_2\) 2 clusters, and dyes anchored on a sizeable (TiO \(_2\) 2 ) \(_{38}\) 38 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 \(_2\) 2 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 \(_2\) 2 clusters that are frequently used to represent the surface of the nanoparticles is significantly larger than the experimental band gap of bulk anatase TiO \(_2\) 2 (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 \(_2\) 2 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 \(_2\) 2 clusters.