The energetics and atomic structure associated with the localized hole formed near an Al-atom dopant in α-quartz are calculated using a variational, self-consistent implementation of the Perdew–Zunger self-interaction correction with complex optimal orbitals. This system has become an important test problem for theoretical methodology since generalized gradient approximation energy functionals, as well as commonly used hybrid functionals, fail to produce a sufficiently localized hole due to the self-interaction error inherent in practical implementations of Kohn–Sham density functional theory. The self-interaction corrected calculations are found to give accurate results for the energy of the defect state with respect to both valence and conduction band edges as well as the experimentally determined atomic structure where only a single Al–O bond is lengthened by 11%. The HSE hybrid functional, as well as the PW91 generalized gradient approximation functional, however, gives too small an energy gap between the defect state and the valence band edge, overly delocalized spin density and lengthening of more than one Al–O bond.

Theoretical calculations of Rydberg excited states of molecular clusters consisting of N,N-dimethylisopropylamine molecules using a Perdew-Zunger self-interaction corrected energy functional are presented and compared with results of resonant multiphoton ionization measurements. The binding energy of the Rydberg electron in the monomer is calculated to be 2.79 eV and 2.27 eV in the 3s and 3p state, respectively, which compares well with measured values of 2.88 eV and 2.21 eV. Three different stable configurations of the dimer in the ground state were found using an energy functional that includes van der Waals interaction. The lowest ground state energy conformation has the two N-atoms widely separated, by 6.2 Å, while the Rydberg state energy is lowest for a configuration where the N-atoms of the two molecules come close together, separated by 3.7 Å. This conformational change is found to lower the Rydberg electron binding energy by 0.2 eV. The self-interaction corrected functional gives a highly localized hole on one of the two molecules, unlike results obtained using the PBE functional or the hybrid B3LYP functional which give a delocalized hole. For the trimer, the self-interaction corrected calculation gives a Rydberg electron binding energy lowered further by 0.13 eV as compared with the dimer. The calculated results compare well with trends observed in experimental measurements. The reduction of the Rydberg electron binding energy with cluster size can be ascribed to an effective delocalization of the positive charge of the hole by the induced and permanent dipole moments of the neighboring molecules. A further decrease observed to occur on a time scale of tens of ps can be ascribed to a structural rearrangement of the clusters in the Rydberg state where molecules rotate to orient their dipoles in response to the formation of the localized hole.

A method is presented for calculating the wave function and energy of Rydberg excited states of molecules. A good estimate of the Rydberg state orbital is obtained using ground state density functional theory including Perdew-Zunger self-interaction correction and an optimized effective potential. The total energy of the excited molecule is obtained using the Delta Self-Consistent Field method where an electron is removed from the highest occupied orbital and placed in the Rydberg orbital. Results are presented for the first few Rydberg states of NH3, H2O, H2CO, C2H4, and N(CH3)3. The mean absolute error in the energy of the 33 molecular Rydberg states presented here is 0.18 eV. The orbitals are represented on a real space grid, avoiding the dependence on diffuse atomic basis sets. As in standard density functional theory calculations, the computational effort scales as NM(2) where N is the number of orbitals and M is the number of grid points included in the calculation. Due to the slow scaling of the computational effort with system size and the high level of parallelism in the real space grid approach, the method presented here makes it possible to estimate Rydberg electron binding energy in large molecules.

An overview of a collaborative experimental and theoretical effort toward efficient hydrogen production via photoelectrochemical splitting of water into di-hydrogen and di-oxygen is presented here. We present state-of-the-art experimental studies using hematite and TiO(2) functionalized with gold nanoparticles as photoanode materials, and theoretical studies on electro and photo-catalysis of water on a range of metal oxide semiconductor materials, including recently developed implementation of self-interaction corrected energy functionals.