text: The bulk electronic band structure of transition metal oxides consists of overlapping 2p orbitals from oxygen atoms, forming the lower energy, highly populated valence band, while the sparsely populated, higher energy conduction band consists of overlapping d orbitals of the transition metal cation. In contrast to metals, having a continuous band of electronic states, semiconductors have a band gap that prevents the recombination of electron/hole pairs that have been separated into the conduction band/ valence band. The nanosecond scale life times of these electron/hole separations allows for charge transfer to occur with an adsorbed species on the semiconductor surface. The Potential of an acceptor must be more positive than the conduction band potential of the semiconductor in order for reduction of the species to commence. Conversely, the potential of the donor species must be more negative than that of the valence band of the semiconductor for oxidation of the species to occur.
  Near the surface of a semi-conducting metal oxide the valence and conduction bands are of higher energy, causing the upward bending of the band energy as shown in the band energy diagram, such that promotion of an electron from the valence band to the conduction band by light of energy greater than the band gap results in migration of the electron towards the bulk of the solid or to a counter electrode, while the hole left in the valence band moves towards the surface. The increased concentration of holes near the surface facilitates electron transfer to the solid, such as the example shown in the figure of the oxidation of redox couple D-/D. In the absence of any mechanism to remove electrons from the bulk of the solid irradiation continues to excite electrons to the conduction band producing holes in the valence band. This leads to the reduction of the upward bending of the band energies near the surface, and the subsequent increase in excited electron availability for reduction reactions.
  The following equations are useful in describing the populations of valence and conduction bands in terms of holes and electrons for the bulk metal.  is the density of electrons in the bulk metal conduction band, and  is the density of holes in the bulk metal valence band. E is the lowest energy of the conduction band, E is the Fermi energy (electrochemical energy of the electrons), E is the highest energy of the valence band, N is the effective mass and mobility of an electron in the conduction band (constant), and N is the effective mass and mobility of a valence band hole (constant).
  where k is Boltzmanns constant and T is the absolute temperature in kelvins.
  The use of quantum mechanics perturbation theory can aid in calculating the probability of an electronic transition taking place. The probability is proportional to the square of the amplitude of the radiation field, E, and the square of the transition dipole moment |μ|.
  The quantum yield for an ideal system undergoing photocatalytic events is measured as the number of events occurring per photon absorbed. The typical assumption in determining the quantum yield is that all photons are absorbed on the semiconductor surface, and the quantum yield is referred to as the apparent quantum yield. This assumption is necessary due to the difficulty in measuring the actual photons absorbed by the solid surface. The relation between the quantum yield, the rate of charge transfer, k, and the electron/hole recombination rate, k, is given by the following equation.
  Photoinduced molecular transformations at transition metal oxide surfaces can be organized in two general classes. Photoexcitation of the adsorbate which then reacts with the catalyst substrate is classified as a catalyzed photoreaction. Photoexcitation of the catalyst followed by interaction of the catalyst with a ground state reactant is classified as a sensitized photoreaction.