O $1s$ core-level shifts at the anatase TiO${}_2$(101)/N3 photovoltaic interface: Signature of H-bonded supramolecular assembly

We here report an atomic-scale first-principles investigation of the O $1s$ core-level shifts at the interface between TiO${}_2$ and the dye N3 found in dye-sensitized solar cells. We first perform extensive validation of our computational setup in the case of small molecules containing carboxylic acid groups in the gas phase. Then we calculate the O $1s$ core-level shifts for a variety of atomistic models of the TiO${}_2/$N3 interface. We investigate in detail the effects of water contamination, dye packing density, exchange and correlation functionals, and hydrogen-bonding interactions on the calculated core-level spectra. The quantitative comparison between our calculated core-level shifts and measured photoemission spectra [Johansson et al., J. Phys. Chem. B 109, 22256 (2005)] leads us to propose a new atomic-scale model of the TiO${}_2/$N3 interface, where the dyes are arranged in supramolecular H-bonded assemblies. Our interface models describe dry TiO${}_2/$N3 films as in [Johansson et al., J. Phys. Chem. B 109, 22256 (2005)], and are of direct relevance to solid-state dye-sensitized solar cells. Our present work suggests that the adsorption energetics is not a reliable indicator of the quality of an interface model, and highlights the importance of combining experimental and computational spectroscopy for determining the atomic-scale structure of nanostructured solar cell interfaces.

Figure 1

The N3 dye molecule. A central Ru atom is sixfold coordinated to the N atoms of two bipyridines and two thiocyanate ligands, with each bipyridine carrying two carboxylic acid groups (highlighted). The carboxylic acid groups anchor the molecule to the substrate via Ti–O bonds. Color code is as follows: Ru (green), S (yellow), N (blue), C (cyan), O (red), H (white).

Figure 2

Comparison of calculated O $1s$ core-level shifts of test molecules (cf. Table ) with the XPS data of Refs. 24 and 25. The shifts are referenced to the H${}_2$O molecule, the binding energy increases toward negative energies. Blue circles and red crosses indicate the shifts of molecules containing carboxylic acid groups. The ball-and-stick representation of acetic acid shows the carbonyl and the hydroxyl O atoms and the associated shifts (red crosses and blue circles, respectively). (Inset) Calculated splitting between the shifts of hydroxyl and the carbonyl O atoms vs experimental splitting. The rms deviation in the hydroxyl/carbonyl splitting is 0.17 eV (note the change of scale).

Figure 3

(a) Ball-and-stick representation and calculated O $1s$ core-level spectra of the six interface models based on isolated dye molecules considered in this work. The atomic color code is as in Fig. 1. The solid black lines are calculated spectra, and the red dashed lines the experimental spectrum from Ref. 8. Since core-level shifts calculated using the method of Refs. 13 and 14 carry an unknown constant, all the spectra have been aligned to the leftmost experimental peak for clarity. The relevant quantity is the splitting between the peaks. (b) Calculated adsorption energies for each interface model.

Figure 4

(a) Ball-and-stick representation of the interface model I2c with additional water molecules forming H-bonds with each carboxylic acid group in the dye. The bond lengths of the H-bonds formed with the hydroxyl group and with the carbonyl group are 1.80 Å and 2.05 Å respectively. (b) Calculated O $1s$ core-level spectrum of this interface model (black solid line), compared to experiment[8] (red dashed line).

Figure 5

(a) Ball-and-stick representation of interface model I2c with two dyes per simulation cell. The shortest distance between carboxylic groups of neighboring dyes is 4.4 Å. (b) Calculated O $1s$ core-level spectrum for the two different areal dye densities. The spectrum at the increased dye coverage of 0.5 nm${}^{-2}$ (blue dotted line) is indistinguishable from the one with a density of 0.25 nm${}^{-2}$ (black line).

Figure 6

(a) Ball-and-stick representations of the interface models H2a and H2b. (b) Calculated O $1s$ core-level spectra for the models H2a and H2b (black solid lines) and experimental spectra from Ref. 8 (red dashed lines). (c) Calculated O $1s$ core-level spectrum for the interface model H2a (black line) including finite escape depth effects, compared to the experimental spectrum (red dashed line) and to the isolated dye model I2a (blue dot-dash line).

Figure 7

Ball-and-stick representations and O $1s$ core-level spectra calculated within LDA (blue dot-dash lines) and PBE (black solid lines) for interface models (a) I2a optimized within LDA, (b) H2a optimized within LDA, and (c) H2a optimized within PBE. (d) The core-level shifts calculated within LDA and PBE for each oxygen atom in models with identical structures. (e) Calculations on test molecules (cf. Fig. 2 in the main text) using LDA shifts and geometries (filled symbols) and PBE shifts and geometries (unfilled symbols).