There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The detection methods and generation mechanisms of the intrinsic reactive oxygen species (ROS), i.e., superoxide anion radical (•O2–), hydrogen peroxide (H2O2), singlet oxygen (1O2), and hydroxyl radical (•OH) in photocatalysis, were surveyed comprehensively. Consequently, the major photocatalyst used in heterogeneous photocatalytic systems was found to be TiO2. However, besides TiO2 some representative photocatalysts were also involved in the discussion. Among the various issues we focused on the detection methods and generation reactions of ROS in the aqueous suspensions of photocatalysts. On the careful account of the experimental results presented so far, we proposed the following apprehension: adsorbed •OH could be regarded as trapped holes, which are involved in a rapid adsorption–desorption equilibrium at the TiO2–solution interface. Because the equilibrium shifts to the adsorption side, trapped holes must be actually the dominant oxidation species whereas •OH in solution would exert the reactivity...

Generation and Detection of Reactive Oxygen Species in Photocatalysis

: The unpolarized absorption and circular dichroism spectra of the fundamental vibrational transitions of the chiral molecule, 4-methyl-2-oxetanone, are calculated ab initio. Harmonic force fields are obtained using Density Functional Theory (DFT), MP2, and SCF methodologies and a 5S4P2D/3S2P (TZ2P) basis set. DFT calculations use the Local Spin Density Approximation (LSDA), BLYP, and Becke3LYP (B3LYP) density functionals. Mid-IR spectra predicted using LSDA, BLYP, and B3LYP force fields are of significantly different quality, the B3LYP force field yielding spectra in clearly superior, and overall excellent, agreement with experiment. The MP2 force field yields spectra in slightly worse agreement with experiment than the B3LYP force field. The SCF force field yields spectra in poor agreement with experiment.The basis set dependence of B3LYP force fields is also explored: the 6-31G* and TZ2P basis sets give very similar results while the 3-21G basis set yields spectra in substantially worse agreements with experiment. jg

Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields

Quantum Mechanical Studies of Large Metal, Metal Oxide, and Metal Chalcogenide Nanoparticles and Clusters.

Review of two-dimensional materials for photocatalytic water splitting from a theoretical perspective

We performed an experimental and density functional theory (DFT) investigation of the reactions of H2O2 with ZrO2, TiO2, and Y2O3. In the experimental study we determined the reaction rate constants, the Arrhenius activation energies, and the activation enthalpies for the processes of adsorption and decomposition of H2O2 on the surfaces of nano- and micrometer-sized particles of the oxides. The experimentally obtained enthalpies of activation for the decomposition of H2O2 catalyzed by these materials are 30 ± 1 kJ·mol–1 for ZrO2, 34 ± 1 kJ·mol–1 for TiO2, and 44 ± 5 kJ·mol–1 for Y2O3. In the DFT study, cluster models of the metal oxides were used to investigate the mechanisms involved in the surface process governing the decomposition of H2O2. We compared the performance of the B3LYP and M06 functionals for describing the adsorption energies of H2O2 and HO• onto the oxide surfaces as well as the energy barriers for the decomposition of H2O2. The DFT models implemented can describe the experimental reactio...

Mechanism of H2O2 Decomposition on Transition Metal Oxide Surfaces

The kinetics, mechanism, and activation energy of H2O2 decomposition in ZrO2 particle suspensions were studied. The obtained first-order and second-order rate constants for the decomposition of H2O2 in the presence of ZrO2 at T = 298.15 K produced the values k1 = (6.15 ± 0.04) × 10−5 s−1 and k2 = (2.39 ± 0.09) × 10−10 m·s−1, respectively. The dependency of the reaction first-order rate constant with temperature was studied; consequently, the activation energy for the reaction was obtained in the temperature interval 294.15−353.15 K having yielded the value Ea = 33 ± 1.0 kJ·mol−1. The dependency of the zeroth-order reaction rate constant with pH was investigated and discussed. A mechanistic study encompassing the investigation of the dynamics of formation of hydroxyl radicals during the course of the reaction was performed. A version of the modified Hantzsch method was applied for this purpose, and it was verified that the dynamics of formation of hydroxyl radicals during the reaction are in good agreement...

Kinetics, Mechanism, and Activation Energy of H2O2 Decomposition on the Surface of ZrO2

We have investigated the reactions of H2O2 with Fe2O3, CuO, HfO2, CeO2 and Gd 2O3 in aqueous solution. The reactions rate constants at room temperature were determined. From the temperature depende ...

Catalytic decomposition of hydrogen peroxide on transition metal and lanthanide oxides

We have performed a density functional theory (DFT) investigation of the interactions of H2O2, H2O and HO radicals with clusters of ZrO2, TiO2 and Y2O3. Different modes of H2O adsorption onto the clusters were studied. In almost all the cases the dissociative adsorption is more exothermic than molecular adsorption. At the surfaces where H2O has undergone dissociative adsorption, the adsorption of H2O2 and the transition state for its decomposition are mediated by hydrogen bonding with the surface HO groups. Using the functionals B3LYP, B3LYP-D and M06 with clusters of 26 and 8 units of ZrO2, the M06 functional performed better than B3LYP in describing the reaction of decomposition of H2O2 and the adsorption of H2O. Additionally, we investigated clusters of the type (ZrO2)2, (TiO2)2 and (Y2O3) and the performance of the functionals B3LYP, B3LYP-D, B3LYP*, M06, M06-L, PBE0, PBE and PWPW91 in describing H2O2, H2O and HO˙ adsorption and the energy barrier for decomposition of H2O2. The trends obtained for HO˙ adsorption onto the clusters are discussed in terms of the ionization energy of the metal cation present in the oxide. In order to correctly account for the existence of an energy barrier for the decomposition of H2O2, the functional used must include Hartree–Fock exchange. Using minimal cluster models, the best performance in describing the energy barrier for H2O2 decomposition was obtained with the M06 and PBE0 functionals – the average absolute deviations from experiments are 6 kJ mol−1 and 5 kJ mol−1 respectively. With the M06 functional and a larger monoclinic (ZrO2)8 cluster model, the performance is in excellent agreement with experimental data. For the different oxides, PBE0 was found to be the most effective functional in terms of performance and computational time cost.

Reactivity of metal oxide clusters with hydrogen peroxide and water – a DFT study evaluating the performance of different exchange–correlation functionals

Cláudio M. Lousada

Papers

Mechanism of H2O2 Decomposition on Transition Metal Oxide Surfaces

Kinetics, Mechanism, and Activation Energy of H2O2 Decomposition on the Surface of ZrO2

Catalytic decomposition of hydrogen peroxide on transition metal and lanthanide oxides

Reactivity of metal oxide clusters with hydrogen peroxide and water – a DFT study evaluating the performance of different exchange–correlation functionals

Reactivity of H2O2 towards different UO2-based materials: The relative impact of radiolysis products revisited