^{1,a)}, Ilaria Ciofini

^{1}and Carlo Adamo

^{1}

### Abstract

A comprehensive investigation of one of the basic components of ZnO-based dye-sensitized solar cells(DSSC) is presented, carried out using hybrid density functionals combined to a periodic formalism. Both semiconductor bulk and surfaces are discussed thoroughly, with a particular attention to structural and electronic aspects. Next, three possible adsorption modes of formic acid are compared and discussed at the same level of theory. The results confirm that formic acid appears as a suitable choice for an efficient anchoring of large organic molecules, such as the dyes commonly used for DSSC, to semiconductor surfaces since it allows both a stable adsorption and few but significant contributions to the density of states for all adsorption modes considered. More in general, our results suggest that hybrid functionals and, in particular the parameter free PBE0 (PBE denotes Perdew–Burke–Ernzerhof), can be considered as a reliable tool for modeling complex molecule-semiconductors interfaces such as the one of interest in DSSC, thus providing a powerful computational protocol for the *in silico* design of new systems for photovoltaic applications.

The “Centre Informatique National de l’Enseignement Supérieur” (CINES, Montpellier) is acknowledged for generous allocation of computer resources (Project No. 6064).

I. INTRODUCTION

II. COMPUTATIONAL DETAILS

III. RESULTS AND DISCUSSION

A. ZnO wurtzite bulk

1. Geometric investigation

2. Electronic investigation: Densities of states

B. ZnO nonpolar surface

1. Geometric properties

2. Electronic properties

C. Adsorption of formic acid on ZnO

1. Geometric investigation

2. Energetic investigation

3. Electronic properties

IV. CONCLUSION

## Figures

Bottom graph: total and (filled curve) contributions. Top graph: and (filled curve) contributions to the density of states of bulk ZnO wurtzite, computed at the PBE0 level with the basis set. Fermi level (as dotted lines) set at 0 eV. The red dashed lines outline the and band separation. Contributions originating from the states at lower energies are omitted.

Bottom graph: total and (filled curve) contributions. Top graph: and (filled curve) contributions to the density of states of bulk ZnO wurtzite, computed at the PBE0 level with the basis set. Fermi level (as dotted lines) set at 0 eV. The red dashed lines outline the and band separation. Contributions originating from the states at lower energies are omitted.

Relaxed structure of the ZnO wurtzite surface with used notations. Light blue and red circles represent Zn and O atoms, respectively.

Relaxed structure of the ZnO wurtzite surface with used notations. Light blue and red circles represent Zn and O atoms, respectively.

(a) Band structures of ZnO wurtzite , both considering unrelaxed (left) and fully relaxed (right) eight atomic plane slabs, obtained at the PBE0 level. Fermi level (black dashed line) of the relaxed structure set at 0 eV. Computed direct band gap at in red. (b) Corresponding Brillouin zone with point labeling.

(a) Band structures of ZnO wurtzite , both considering unrelaxed (left) and fully relaxed (right) eight atomic plane slabs, obtained at the PBE0 level. Fermi level (black dashed line) of the relaxed structure set at 0 eV. Computed direct band gap at in red. (b) Corresponding Brillouin zone with point labeling.

Side views of the (a) bridging , (b) unidentate type , and (c) unidentate type adsorption modes of formic acid on ZnO wurtzite . Zn, O, C, and H atoms as light blue, red, black, and white circles, respectively. Hydrogen bond as dashed line.

Side views of the (a) bridging , (b) unidentate type , and (c) unidentate type adsorption modes of formic acid on ZnO wurtzite . Zn, O, C, and H atoms as light blue, red, black, and white circles, respectively. Hydrogen bond as dashed line.

Calculated density of states of formic acid on ZnO for all investigated adsorption models displaying the band gap region. Fermi level set at 0 eV in all cases. Total density of states as solid black line. Formic acid-projected contribution as filled red line.

Calculated density of states of formic acid on ZnO for all investigated adsorption models displaying the band gap region. Fermi level set at 0 eV in all cases. Total density of states as solid black line. Formic acid-projected contribution as filled red line.

## Tables

Equilibrium geometry of ZnO wurtzite calculated with different Hamiltonians and basis sets. Lattice parameters ( and ) in angstrom; internal parameter , corresponding to the fractional coordinate of the oxygen atoms along the axis, in fractional units. In parentheses, computed error (in percent), with respect to the all-electron data, obtained when using large core pseudopotentials at the PBE0 level (see Sec. II).

Equilibrium geometry of ZnO wurtzite calculated with different Hamiltonians and basis sets. Lattice parameters ( and ) in angstrom; internal parameter , corresponding to the fractional coordinate of the oxygen atoms along the axis, in fractional units. In parentheses, computed error (in percent), with respect to the all-electron data, obtained when using large core pseudopotentials at the PBE0 level (see Sec. II).

Main properties of the density of states of ZnO wurtzite bulk structure obtained with different Hamiltonians and the basis sets. refers to the width of a band, is the separation between the and bands, and refers to a direct gap. All data are in eV.

Main properties of the density of states of ZnO wurtzite bulk structure obtained with different Hamiltonians and the basis sets. refers to the width of a band, is the separation between the and bands, and refers to a direct gap. All data are in eV.

Structural parameters of the ZnO surface upon relaxation obtained with the all-electron basis set at the PBE0 level for different numbers of Zn–O dimer planes of the slab. Distances ( and ) in angstrom; angles (from to ) in degrees. Labeling corresponds to that in Fig. 2. denotes the bond contraction (in percent) of the outermost Zn–O dimer when compared to the bulk value, while is that of the bond between the outermost Zn [O] surface atom and the O [Zn] atom is the second plane.

Structural parameters of the ZnO surface upon relaxation obtained with the all-electron basis set at the PBE0 level for different numbers of Zn–O dimer planes of the slab. Distances ( and ) in angstrom; angles (from to ) in degrees. Labeling corresponds to that in Fig. 2. denotes the bond contraction (in percent) of the outermost Zn–O dimer when compared to the bulk value, while is that of the bond between the outermost Zn [O] surface atom and the O [Zn] atom is the second plane.

Computed PBE0 atomic displacements (in angstrom) of the ZnO surface upon relaxation with both all-electron and large core pseudopotentials basis sets. refers to the number of atomic planes in the slab. and denote displacements along and , respectively.

Computed PBE0 atomic displacements (in angstrom) of the ZnO surface upon relaxation with both all-electron and large core pseudopotentials basis sets. refers to the number of atomic planes in the slab. and denote displacements along and , respectively.

Mulliken atomic charges and bond overlap populations of the ZnO wurtzite surface, obtained for eight atomic planes. All data are computed at the PBE0 level with the basis set. refers to the atomic plane number, considering the outermost plane as the first one.

Mulliken atomic charges and bond overlap populations of the ZnO wurtzite surface, obtained for eight atomic planes. All data are computed at the PBE0 level with the basis set. refers to the atomic plane number, considering the outermost plane as the first one.

Selected structural parameters of formic acid both adsorbed on a ZnO wurtzite supercell and isolated. The adsorbate labeling corresponds to that in Fig. 4. and are threefold coordinated substrate Zn and O atoms involved in the adsorbate/substrate bonding. Distances in angstrom and angles in degrees.

Selected structural parameters of formic acid both adsorbed on a ZnO wurtzite supercell and isolated. The adsorbate labeling corresponds to that in Fig. 4. and are threefold coordinated substrate Zn and O atoms involved in the adsorbate/substrate bonding. Distances in angstrom and angles in degrees.

Additional displacements (in angstrom) of selected outermost substrate atoms upon adsorption of formic acid on ZnO wurtzite when compared to atomic positions of a fully relaxed *clean* slab. Labeling corresponds to that in Fig. 4. For instance, is the substrate Zn atom bond to the adsorbate atom.

Additional displacements (in angstrom) of selected outermost substrate atoms upon adsorption of formic acid on ZnO wurtzite when compared to atomic positions of a fully relaxed *clean* slab. Labeling corresponds to that in Fig. 4. For instance, is the substrate Zn atom bond to the adsorbate atom.

Computed interaction energies of the formic acid molecule with a ZnO supercell in different adsorption modes. For definitions of , , and , see Sec. II. All data are in kJ/mol. refers to the surface coverage.

Computed interaction energies of the formic acid molecule with a ZnO supercell in different adsorption modes. For definitions of , , and , see Sec. II. All data are in kJ/mol. refers to the surface coverage.

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