whereET is the total energy of the complex, Ebare is the total energy of the bare TiO2 surface, ENO is the energy of an isolated NO molecule in the gas phase and n is the number of NO molecules absorbed on the surface. To determine the most stable ground-state structure of the ligand-TiO2 complexes several molecular orientations and binding sites were considered.
According to our findings, NO adsorbs favorably on the perfect (110) surface in a tilted con-figuration with the N atom oriented towards the surface and bonded to the Ti5c atom. The distance from the N atom to the metal site is 2.56 ˚A. These results are in line with previous theoretical predictions [18, 21, 22] and our PBE results. For the adsorption through the oxygen atom the O-Ti5c distance (2.80 ˚A) also compares well to our PBE findings, which returned an optimized distance of 2.75 ˚A. For the oxygen-reduced surface the N-Ti5c and O-Ti5c distances are shortened to 1.95 and 1.83 ˚A, respectively. In the case of adsorption on the anatase (001) surface, ligand-substrate distances are also in agreement with PBE. In terms of adsorption en-ergies, the correspondence of DFTB with higher-level theory is also remarkable with absolute errors equal or smaller than 0.08 eV.
Configuration Property DFTB PBE
rutile (110)
on perfect surface via N-Ti5c N-Ti distance 2.56 2.55
Eads -0.25 -0.27
on perfect surface via O-Ti5c O-Ti distance 2.80 2.75
Eads -0.15 -0.14
on O2c-reduced surface via N-Ti5c N-Ti distance 1.95 1.87
Eads -0.89 -0.86
on O2c-reduced surface via O-Ti5c O-Ti distance 1.83 1.99
Eads -0.29 -0.34
anatase (001)
on perfect surface via N-Ti5c N-Ti distance 2.25 2.26
Eads -0.47 -0.35
on perfect surface via O-Ti5c Eads -0.11 -0.16
Table 5.2: Comparison between DFTB and PBE in terms of optimized structures and energetics of the NO adsorption on TiO2. Distances are given in ˚A and energies in eV.
until the interatomic forces were smaller than 2.5×10−2 eV/˚A. For the anatase cluster the peripheral oxygens were kept fixed during the geometry optimizations as the structure otherwise undergoes large deformations. For those systems involving NO, spin-unrestricted calculations were performed.
[110]
[001]
[110]
[001]
[110]
[001]
[100]
[010]
[010]
[100]
Ti5c
O2c
O3c
Ti5c
O3c
O2c
Figure 5.2: Side (left) and top (right) views of the optimized geometries of the rutile Ti21O68H52
(top) and anatase Ti19O57H38 (bottom) clusters.
To test the validity of the employed models, we first compare the DFTB structural and elec-tronic properties of the clusters with first-principle results. Surface Ti5c-O2cand Ti5c-O3cbond lengths are in correspondence with those found at the PBE level. The interatomic distance
between the central pentacoordinated Ti and the adjacent O3c atoms on the rutile cluster is 2.00 ˚A which agrees with the PBE value of 1.95 ˚A for the periodic system. In the anatase case, Ti5c-O2c and Ti5c-O3c interatomic distances are 1.89 and 1.96 ˚A, respectively, compared to the PBE values of 1.75 and 1.95 ˚A. Band gaps are also accurately described. DFTB yields a HOMO-LUMO gap of 2.98 eV for the rutile cluster and 3.05 eV for the anatase cluster. The UV-vis absorption spectra for both TiO2 clusters are shown in Fig. 5.3. These findings are in agreement with very recent room-temperature optical absorption measurements, reproducing the relative steepness degree of the absorbance curves for rutile and anatase at the vis-UV frontier [276].
0 10 20
2.5 3 3.5 4
energy (eV) Rutile Anatase
(103 M-1cm-1)ε
UV-A
Figure 5.3: Left panel: UV-vis absorption spectrum for rutile and anatase TiO2 clusters as obtained with TD-DFTB. See Fig. 4.2 for details on the calculation of ε. The Lorentzian FWHM was set to 0.1 eV. Right panel: experimental UV-vis absorption spectrum for rutile (1) and anatase (2) TiO2 nanocrystalline powders. Reprinted from [276]. Copyright 2014, with permission from Elsevier.
The most stable configuration of the NO adsorption on the rutile cluster is depicted in Fig. 5.4.
The pollutant binds to the Ti5c site in a tilted configuration via N with a N-Ti5c interatomic distance of 2.55 ˚A, in total agreement with the PBE findings reported above (see Table 5.2).
The adsorption configuration through the O atom also resembles that found at a higher level of theory with a O-Ti5c distance of 2.75 ˚A.
In order to assess the suitability of our cluster models in terms of electronic structure of the TiO2-NO compound system, we employed the range-separated hybrid scheme HSE as the ref-erence method. Periodic single-point calculations were performed using the PBE optimized geometry. The Brillouin zone was sampled with a (3×1×3) MP grid. The highest occupied molecular orbital (HOMO) of an isolated NO molecule is a degenerate antibonding π orbital (π∗) which is singly occupied in one spin component (say spin-up). The two degenerateπ∗ states with spin down are the lowest unoccupied molecular orbitals (LUMO). When the molecule ad-sorbs on the TiO2 surface, the system loses its symmetry and the orbital degeneracy is broken.
Thereby one of the former spin-up degenerate states turns into the LUMO. Our HSE results indicate that the HOMO lies in the band gap of rutile TiO2 at 0.8 eV above the valence band maximum (VBM) with marked localization on the molecule. The LUMO lies in the conduction band edge and is more delocalized. Besides, the two unoccupied π∗ orbitals of the spin-down
channel are also inserted close to the conduction band minimum (CBM) of the semiconductor (see Fig. 5.4 right). DFTB results agree about the insertion of the NO levels in the energy gap region, although their positions differ from the HSE findings. Within HSE the HOMO lies deeper in the band gap compared to DFTB results. Moreover, the HOMO-LUMO energy difference amounts to only 0.3 eV according to DFTB whereas HSE yields a value of approx-imately 2.6 eV. More importantly for the study of CT excitations is however the position of the HOMO with respect to the CBM. DFTB underestimate the HOMO-CBM energy difference by about 0.8 eV taking HSE results as reference. However, as mentioned above, hybrid DFT approaches generally overestimate the band gap of TiO2. In the present case HSE yields a, too large, value of approximately 3.4 eV. All this should be borne in mind for the subsequent analysis of the absorption spectra. The fact that NO also introduces unoccupied KS states in the band gap is indeed remarkable as this might enable a CT mechanism which is generally not regarded, that is, a metal-to-ligand charge transfer (MLCT) process.
0 5.0
DOS (arb. units.)
0 15.0
-1 0 1 2 3 4
energy (eV) spin up
spin up
spin down spin down HSE
DFTB
Figure 5.4: Optimized structure (left) and density of electron states (DOS) (right) of the NO adsorption on the neutral rutile cluster. Oxygen, titanium, nitrogen and hydrogen atoms are represented by red, dark gray, blue and white spheres, respectively. In the DOS plot the zero of energy is set to the valence band maximum and the dashed line indicates the Fermi level position.
To compute the absorption spectra in the region of interest (up to about 4 eV), the first 1200 excitation energies and oscillator strengths for the TiO2-NO complexes were obtained. We used expression II.83 in Ref. [216] to evaluate the expectation value of the square of the total spin operator, hS2i, of the excited states for the open-shell systems (those involving NO) (see section 4.3). For computing the absorption spectra we considered only those states with a hS2i contamination of less than 0.5. The set of KS transitions entering the calculations were truncated by a cutoff KS energy difference of roughly 30 eV. This constraint leads to similar results as for the TD-DFTB calculation without any restriction for the investigated systems whereas the computational time is reduced by a factor of up to 7.
The UV-vis absorption spectrum corresponding to the NO adsorption on rutile is shown in Fig. 5.5. We observe weak absorption bands in the visible region of the spectrum corresponding to CT from both the molecule to the surface and the surface to the molecule. Specifically, the electron is transferred from the singly occupiedπ∗ orbital of NO to 3dorbitals of the Ti atoms of the substrate for the LMCT mechanism. In the case of a MLCT process the electron is promoted from the O-2p states of TiO2 to a virtual π∗ molecular orbital. The most intense LMCT peak is assigned to a transition todstates of surface Ti5c and subsurface Ti6c atoms. It is important to stress that the CT peaks may be red-shifted with respect to the actual behavior as suggested by the HSE results. Additionally, CT excitation energies are commonly underestimated by TD-DFT calculations using conventional XC functionals [277, 278]. In particular, the MLCT component may be completely displaced to the UV-A region of the spectrum. In this region, a band-to-band excitation leading to the generation of an electron-hole pair is much more likely to occur as indicated in Fig. 5.5.
Absorption of visible radiation by the TiO2-NO complex may lead to formation of nitrosonium ions (NO+), which may in turn react with water to form nitrous acid,
NO++ H2O→HONO + H+, (5.2)
thus fulfilling the first step in the oxidation reaction of NO. As pointed out above, our results suggest that under illumination with UV light, NO is likely to oxidizevia reaction with oxidizing species formed from the interaction with the photoinduced electron or hole.
0 5 10
1 1.5 2 2.5 3 3.5 4
0 5
1 1 5 2 2 5 3 3 5 4
energy (eV)
Total LMCT
MLCT band-band
(103 M-1cm-1)ε
x10
x10
IR UV-A
Figure 5.5: Absorption spectrum for the TiO2(rutile)-NO complex depicted in Fig. 5.4. The spectrum has been projected onto three different components: the red dotted line denotes ligand-to-metal charge transfer excitations, the orange dotted line metal-to-ligand charge trans-fer excitations and the black dotted line band-to-band excitations.
Let us now investigate the photodegradation of NO on anatase TiO2. The most stable config-uration for the NO adsorption on the anatase cluster is shown in Fig. 5.6 (right). The binding on the Ti5c site weakens one of the adjacent O2c-Ti5c bonds, eventually leading to its division.
This results in the formation of reactive Ti4c and O1c surface sites. Within DFTB, this config-uration is circa 1 eV more stable than that depicted in Fig. 5.6 (left) where no bond breaking is observed. Let us denote the most stable adsorption mode configuration B and that featuring no bond breaking configuration A. For a 1 ML coverage of NO the surface Ti-O bond is not disturbed and NO attaches to the surface as in Fig. 5.6 (left). In both cases the distance from the molecular N atom to the metal site is 2.25 ˚A. The bond breaking at a low-coverage regime was confirmed by periodic PBE calculations where a tetragonal supercell with a (2×3) surface unit cell and a single NO molecule were considered. PBE yields a N-Ti4c distance of 2.24 ˚A and a N-O1c distance of 1.94 ˚A. The latter compares well to the value of 2.01 ˚A obtained with DFTB. The adsorption energy is -0.65 eV at the PBE level, whereas DFTB yields a value of -1.47 eV. The transition from configuration A to B occurs barrierless at low NO concentrations within both DFTB and PBE approaches.
2.01 2.25 2.25
Figure 5.6: Optimized geometries of the NO adsorption on the neutral anatase cluster. The color code is that employed in Fig. 5.4.
(103 M-1cm-1)ε
1 1.5 2 2.5 3 3.5 4
1 1 5 2 2 5 3 3 5 4
energy (eV) 0
2 4
1 1.5 2 2.5 3 3.5 4
0 2 4
1 1 5 2 2 5 3 3 5 4
energy (eV) Total
LMCT MLCT band-band
IR UV-A IR UV-A
Figure 5.7: Absorption spectra for the TiO2(anatase)-NO complexes depicted in Fig. 5.6. See Fig. 5.5 for information.
Fig. 5.7 shows the absorption spectra corresponding to both configurations. Both spectra indicate vis-light activation of the CT complexes. The CT excitation energies for the 1 ML-like configuration are in general blue-shifted with respect to those for the low-coverage adsorption.
The main distinctive feature among both spectra is however the enhanced LMCT absorbance for the low-coverage case. Also, the probability of occurrence of a MLCT process is diminished for configuration B whereas this type of transition has a higher relevance for configuration A.
The most dominant sp transitions of the CT excitations corresponding to the highest peaks of Fig. 5.7 are depicted in Fig. 5.8. The occupied and virtual KS orbitals are represented with blue and orange wireframes, respectively. For the structure A, the transition takes place mainly from threefold coordinated O-2p orbitals to the unoccupiedπ∗ state of NO. On the other hand, configuration B is the only adsorption mode with clear indication of a covalent bond between NO and the TiO2 surface with the HOMO having a strong component onto the N-Ti4cbonding orbital.
Figure 5.8: Charge density corresponding to the occupied (blue) and virtual (orange) Kohn-Sham states for the most dominant single-particle transition in the many-body wavefunction for the main CT peaks in the visible spectra of Fig. 5.7.
The adsorption mode for low NO concentrations suggests that the direct interaction of the pollutant with the surface could lead to formation of nitrite or nitrate species. The photoinduced transfer of the unpaired electron from NO to the substrate may provoke the weakening of the N-Ti5cbond as the corresponding molecular orbital shows a Ti-O bonding character. In addition, this orbital has a small component on the O1c-Ti5c bond and so a promotion of this state to the conduction band of the semiconductor may also weaken this bond, thus leading to the oxidation of the pollutant. In a DFT study, Minotet al. suggested that the formation of nitrite or nitrate would be possible if monocoordinated surface O atoms react with NO [279]. They proposed a model of the (001) facet with the presence of terminal O1c atoms. They observed an improved reactivity of the surface (the NO adsorption energy went from 0.4 eV for the regular (001) surface to 2.96 eV for the O-terminated one). According to our findings, the existence of this less stable surface termination would not be required as NO can itself evoke the formation of such reactive O1c atoms at the conventional surface.
We now turn to the adsorption of acetaldehyde on the surfaces of TiO2. The most stable binding configuration on the rutile and anatase clusters are depicted in Fig. 5.9. Acetaldehyde favorably attaches to the rutile surface through the carbonyl O atom at the Ti5c site with the H atom of the -CHO group oriented towards and adjacent bridging O2c atom. A dissociative adsorption where a proton is transferred from the ligand to the substrate was found to be unstable. The O-Ti5cinteratomic distance obtained within DFTB is 2.73, which is larger than the value (2.16 ˚A) reported in a recent GGA investigation [29]. In the anatase case, acetaldehyde binds through the carbonyl group onto the undercoordinated metal site whereas the H atom relaxes to a position between two neighboring O2c atoms. The O-Ti5c interatomic distance is identical as for the rutile case. Unlike NO, the adsorption of the volatile compound was not found to cause Ti-O bond breaking at the surface.
Figure 5.9: Optimized geometries of the adsorption of acetaldehyde on the rutile (left) and anatase (right) clusters. The color code is that employed in Fig. 5.4. Additionally, cyan spheres represent carbon atoms.
Unlike NO, the HOMO of acetaldehyde lies in the valence band of TiO2 and the LUMO is located in the conduction band. The electronic structure of TiO2 is hence not substantially modified upon adsorption of the pollutant organic compound. The absorption spectra of the complex is neither expected to change considerably from that of the bare surfaces of titania.
To plot the absorption spectra in the UV(A)-vis region, the computation of the first 415 S-S excitation energies and oscillator strengths of the modified TiO2 clusters was required. The same KS orbital constraint as for the NO based complexes was employed. The resulting spectra are given in Fig. 5.10. As expected from the electronic structure analysis, no vis-light activation is observed for the acetaldehyde case. Furthermore, the absorption profiles for rutile and anatase systems resemble those of the clean TiO2 surfaces (Fig. 5.3).
(103 M-1cm-1)ε
0 10 20
1 1.5 2 2.5 3 3.5 4
energy (eV) Rutile
Anatase
IR UV-A
Figure 5.10: Absorption spectrum for the TiO2-acetaldehyde complexes depicted in Fig. 5.9.