Catalytic Properties of Selected Transition Metal Oxides—Computational Studies
363
change of the diffusion coefficient, namely from 2.28 · 10
−9 m
2 s
−1 in the internal of
the water layer to the value of 4.67 · 10
−11 m
2 s
−1 for rutile and 6.48 · 10
−11 m
2 s
−1
for anatase.
The issue of water adsorption and the question whether H 2 O adsorbs associatively
or dissociatively is a matter of long dispute. As early as in 1995, Goniakowski and
Gillian [191] showed computationally that both forms are energetically favourable.
On the other hand, the embedded cluster Hartree–Fock studies [192] showed preferential occurrence of associative mechanism and argue that the contribution of dissociated forms postulated by planewave DFT studies is due to the overestimation of
the hydrogen bonds in the dissociated forms by planewave DFT [193]. This is in line
with conclusions of the Car–Parrinello simulations of Langel et al. [194], who found
that spontaneous dissociation of water occurs on the O vacancy of (100) surface and
does not at the (110) surface.
The experimental results suggest, however, that water adsorbs mainly associatively and the dissociation occurs at low coverages, what can be associated with surface defects. This conclusion is in line with recent STM experiment, which present the
ability of O vacancies on anatase (101) surface to dissociate water yielding bridging
hydroxyls [195]. The dominant role of O b vacancies in rutile (110) was also supported by Pang et al. [196] The analogous conclusion on high stability of bridging
hydroxyls on the rutile (110) surface is expressed in the article of Wendt et al. [197],
who studied the rutile system both experimentally (STM) and computationally, and
in the article of Morgan et al. [198]
Morgan et al. [198] also reviewed the former attempts to describe computationally
the rutile (110) surface. They note that hybrid functionals improve the description
of the band structure (an hence the bad gap width) [199], comparing to pure DFT,
and they show that the hybrid B3LYP calculations localise defect states where two
electrons are observed on Ti
3+
6c and Ti
3+
5c . Other article, by Bredow and Pacchioni
[200], shows that for B3LYP in the cluster model of the reduced titania (110) surface
although the excess charge is localised on the Ti
3+
6c and Ti
3+
5c , but as many as four sites
are engaged, not just two. For HF-LYP functional, the spread of the excess charge
is qualitatively different, is localised on two Ti
3+
5c centres, adjacent to the defect.
The authors of [198], based on their own work, attribute the B3LYP behaviour
to the fact that the amount of the HF exchange component has been fitted to the
results of calculations for the first and second rows of elements and for heavier
elements changing of the HF part could lead to more accurate results. The usage of
GGA+U(U 4.20) can reproduce the charge localisation on two Ti
3+
5c centres (see
Fig. 5), and generally the experimental band state.
Oxygen Vacancy Formation
Morgan et al. also discussed also the vacancy formation energy obtained by themselves (E(O vac ) = 3.66 eV for GGA+U(4.20)) and by Wu et al. [201] and by
Rasmussen et al. [202] (3.52 and 3.03 eV for different supercells).
363
change of the diffusion coefficient, namely from 2.28 · 10
−9 m
2 s
−1 in the internal of
the water layer to the value of 4.67 · 10
−11 m
2 s
−1 for rutile and 6.48 · 10
−11 m
2 s
−1
for anatase.
The issue of water adsorption and the question whether H 2 O adsorbs associatively
or dissociatively is a matter of long dispute. As early as in 1995, Goniakowski and
Gillian [191] showed computationally that both forms are energetically favourable.
On the other hand, the embedded cluster Hartree–Fock studies [192] showed preferential occurrence of associative mechanism and argue that the contribution of dissociated forms postulated by planewave DFT studies is due to the overestimation of
the hydrogen bonds in the dissociated forms by planewave DFT [193]. This is in line
with conclusions of the Car–Parrinello simulations of Langel et al. [194], who found
that spontaneous dissociation of water occurs on the O vacancy of (100) surface and
does not at the (110) surface.
The experimental results suggest, however, that water adsorbs mainly associatively and the dissociation occurs at low coverages, what can be associated with surface defects. This conclusion is in line with recent STM experiment, which present the
ability of O vacancies on anatase (101) surface to dissociate water yielding bridging
hydroxyls [195]. The dominant role of O b vacancies in rutile (110) was also supported by Pang et al. [196] The analogous conclusion on high stability of bridging
hydroxyls on the rutile (110) surface is expressed in the article of Wendt et al. [197],
who studied the rutile system both experimentally (STM) and computationally, and
in the article of Morgan et al. [198]
Morgan et al. [198] also reviewed the former attempts to describe computationally
the rutile (110) surface. They note that hybrid functionals improve the description
of the band structure (an hence the bad gap width) [199], comparing to pure DFT,
and they show that the hybrid B3LYP calculations localise defect states where two
electrons are observed on Ti
3+
6c and Ti
3+
5c . Other article, by Bredow and Pacchioni
[200], shows that for B3LYP in the cluster model of the reduced titania (110) surface
although the excess charge is localised on the Ti
3+
6c and Ti
3+
5c , but as many as four sites
are engaged, not just two. For HF-LYP functional, the spread of the excess charge
is qualitatively different, is localised on two Ti
3+
5c centres, adjacent to the defect.
The authors of [198], based on their own work, attribute the B3LYP behaviour
to the fact that the amount of the HF exchange component has been fitted to the
results of calculations for the first and second rows of elements and for heavier
elements changing of the HF part could lead to more accurate results. The usage of
GGA+U(U 4.20) can reproduce the charge localisation on two Ti
3+
5c centres (see
Fig. 5), and generally the experimental band state.
Oxygen Vacancy Formation
Morgan et al. also discussed also the vacancy formation energy obtained by themselves (E(O vac ) = 3.66 eV for GGA+U(4.20)) and by Wu et al. [201] and by
Rasmussen et al. [202] (3.52 and 3.03 eV for different supercells).