The reaction path is a key concept in the theoretical description of a chemical reaction. The intrinsic reaction coordinate is defined as the steepest descent path in mass-weighted Cartesian coordinates that connects the transition state to reactants and products on the potential energy surface. Recently, a new Hessian based predictor-corrector reaction path following algorithm was presented that is comparable to a fourth-order algorithm developed earlier. Although the method is very accurate, it is costly because second derivatives of the energy are required at each step. In this work, the efficiency of the method is greatly enhanced by employing Hessian updating. Three different updating schemes have been tested:  Murtagh and Sargent, Powell-symmetric Broyden, and Bofill. Bofill's update performs the best and yields excellent speed-up.

Central to the theoretical description of a chemical reaction is the reaction pathway. The intrinsic reaction coordinate is defined as the steepest descent path in mass weighted Cartesian coordinates that connects the transition state to reactants and products. In this work, a new integrator for the steepest descent pathway is presented. This method is a Hessian based predictor-corrector algorithm that affords pathways comparable to our previous fourth order method at the cost of a second order approach. The proposed integrator is tested on an analytic surface, four moderately sized chemical reactions, and one larger organometallic system.

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A theoretical investigation of eosin-Y (EY) loaded ZnO thin films, the basic components of a dye-sensitized solar cell (DSSC), is presented. The EY/ZnO wurtzite (10-10) system has been fully described within a periodic approach using density functional theory (DFT) and a hybrid exchange-correlation functional. Reduced systems were also analyzed to simulate an electron transfer from the dye to the substrate. Injection times from dye to the semiconductor were calculated using the Newns-Anderson approach. Finally, the UV-visible spectra of EY/ZnO films were simulated using a time-dependent DFT approach and compared to that of the EY molecule computed in solution. The results obtained highlight that EY strongly adsorbs on the ZnO substrate contributing significantly to the electronic structure of the adsorbed system. The UV-visible spectral signature of the isolated EY molecule is still found when adsorbed on ZnO but the analysis of Gamma-point crystalline orbitals reveals that a direct HOMO-->LUMO excitation cannot lead to a direct electron injection into the semiconductor, the first unoccupied orbital with contributions from the ZnO substrate being the LUMO + 1. As a consequence, a two photon injection mechanism is proposed explaining the low efficiency of the EY/ZnO solar cells. On this basis, possible strategies for enhancing the cell efficiency are presented and discussed.