360
W. Piskorz and F. Zasada
limits the absorption of light by TiO 2 to the UV part of the spectrum dramatically
lowering its efficiency towards solar light. On the other hand, the semiconductors
with narrow bad gap are prone to the photocorrosion. The solution of this deadlock
is the sensitisation of the semiconductor by the agent able to absorb visible light and
inject carriers into the substrate.
Although there is wealth of experimental articles on TiO 2 , there is not many of
them on computational studies.
The number of various titania catalysts was studied by Anpo et al. [176] in the
form of: highly dispersed, powdered, and the monocrystal. They found the important
dependence of the kind of catalyst and the CO 2 /H 2 O ratio, and temperature on its
efficiency and selectivity. In the case of rutile monocrystal, the higher selectivity
towards methanol and methane was observed for (100) than for (110) facet. The
reactants and intermediates were studied by high-resolution electron energy loss
spectroscopy. The difference in activity between (100) and (110) is attributed to the
different Ti/O surface atomic ratio, and the more spacey (100) surface allows for the
contact with CO 2 and H 2 O molecules, and also have higher reductive potential in
the excited state, facilitating the reduction of CO 2 towards CH 4 . Besides, the TiO 2
polymorphs, rutile and anatase, belong to the most studied single crystal systems
[177].
The computational description of defected TiO 2 requires the usage of the hybrid
functionals or, when the computational cost thereof is prohibitively high, the DFT+U
functional.
Since the zero-dimensional (0-D) TiO 2 NPs are the most fundamental nanostructures of TiO 2 which can be utilised as starting points for more complex materials
with more specified and improved performance, they belong to the group of the
most investigated solid-state materials of the past 20 years. In these investigations,
the DFT (and more advanced QChM) cluster calculations are of indisputable importance. In this context, numerous experimental and theoretical studies investigated
isolated titanium oxide clusters to correlate their structures and properties with those
of the bulk phases [178–181]. In particular, the Ti n O 2n and Ti n O 2n+1 clusters were
found to be the most stable neutral ones, while Ti n O 2n−1 and Ti n O 2n−2 clusters were
formed by fragmentation [182]. Zhai et al. [183] have probed the electronic structure
and band gap evolution of titanium dioxide clusters, (TiO 2 ) n (n = 1, . . . , 10), using
photoelectron spectroscopy (PES) comparing the results with available theoretical
data [184] showing that they are valuable to verify future high-level theoretical calculations. The possibility of antiferromagnetic stabilisation in the titania clusters was
predicted (thanks to the evolutionary algorithm USPEX and DFT+U calculations)
within a high-symmetry geometric structure of the bare cube-shape Ti 8 O 12 cluster,
in excellent agreement with experimental results [185]. For such TiO 2 NP, unique
chemical bonding was described where electrons of Ti atoms interacting in antiferromagnetic fashion to lower the total energy of the system. Illas et al. investigated
the electronic band gap of (TiO 2 ) n nanoparticles (n = 1, . . . , 20) using a relativistic
all-electron description, within the G 0 W 0 method [186]. It was shown that high-level
G 0 W 0 approach may be successfully implemented to study the electronic band gap
of realistic size nanoparticles at an affordable computational cost giving results that
W. Piskorz and F. Zasada
limits the absorption of light by TiO 2 to the UV part of the spectrum dramatically
lowering its efficiency towards solar light. On the other hand, the semiconductors
with narrow bad gap are prone to the photocorrosion. The solution of this deadlock
is the sensitisation of the semiconductor by the agent able to absorb visible light and
inject carriers into the substrate.
Although there is wealth of experimental articles on TiO 2 , there is not many of
them on computational studies.
The number of various titania catalysts was studied by Anpo et al. [176] in the
form of: highly dispersed, powdered, and the monocrystal. They found the important
dependence of the kind of catalyst and the CO 2 /H 2 O ratio, and temperature on its
efficiency and selectivity. In the case of rutile monocrystal, the higher selectivity
towards methanol and methane was observed for (100) than for (110) facet. The
reactants and intermediates were studied by high-resolution electron energy loss
spectroscopy. The difference in activity between (100) and (110) is attributed to the
different Ti/O surface atomic ratio, and the more spacey (100) surface allows for the
contact with CO 2 and H 2 O molecules, and also have higher reductive potential in
the excited state, facilitating the reduction of CO 2 towards CH 4 . Besides, the TiO 2
polymorphs, rutile and anatase, belong to the most studied single crystal systems
[177].
The computational description of defected TiO 2 requires the usage of the hybrid
functionals or, when the computational cost thereof is prohibitively high, the DFT+U
functional.
Since the zero-dimensional (0-D) TiO 2 NPs are the most fundamental nanostructures of TiO 2 which can be utilised as starting points for more complex materials
with more specified and improved performance, they belong to the group of the
most investigated solid-state materials of the past 20 years. In these investigations,
the DFT (and more advanced QChM) cluster calculations are of indisputable importance. In this context, numerous experimental and theoretical studies investigated
isolated titanium oxide clusters to correlate their structures and properties with those
of the bulk phases [178–181]. In particular, the Ti n O 2n and Ti n O 2n+1 clusters were
found to be the most stable neutral ones, while Ti n O 2n−1 and Ti n O 2n−2 clusters were
formed by fragmentation [182]. Zhai et al. [183] have probed the electronic structure
and band gap evolution of titanium dioxide clusters, (TiO 2 ) n (n = 1, . . . , 10), using
photoelectron spectroscopy (PES) comparing the results with available theoretical
data [184] showing that they are valuable to verify future high-level theoretical calculations. The possibility of antiferromagnetic stabilisation in the titania clusters was
predicted (thanks to the evolutionary algorithm USPEX and DFT+U calculations)
within a high-symmetry geometric structure of the bare cube-shape Ti 8 O 12 cluster,
in excellent agreement with experimental results [185]. For such TiO 2 NP, unique
chemical bonding was described where electrons of Ti atoms interacting in antiferromagnetic fashion to lower the total energy of the system. Illas et al. investigated
the electronic band gap of (TiO 2 ) n nanoparticles (n = 1, . . . , 20) using a relativistic
all-electron description, within the G 0 W 0 method [186]. It was shown that high-level
G 0 W 0 approach may be successfully implemented to study the electronic band gap
of realistic size nanoparticles at an affordable computational cost giving results that