Optical properties of anatase TiO2: synergy between transition metal doping and oxygen vacancies.

Charge carriers (electrons and holes) are generated on the TiO2 using UV radiation; this excitation energy can be reduced by modifying the material electronic structure, for example, by doping or creating oxygen vacancies. Here, the electronic structure of a transition metal-doped anatase, bulk and surface, and their interaction with oxygen vacancies are studied using density functional theory. The visible light response of metal-doped TiO2 (101) is also determined. Transition metals generate intra-band gap states, which reduce the excitation energy but may also act as charge recombination sites. Dopants Fe, Co, and Ni remarkably enhance the visible light response due to the states in the middle of the gap. However, Co and Ni create heavier charge carriers. Our results show that Pd and Pt-doped TiO2 generate states near the valence and conduction band with a "clean" band gap (without states in the middle of the gap). Moreover, Pt-doped TiO2 maintains the charge mobility because it presents a small charge carriers mass. Hence, Pt-doped TiO2 represents the best alternative to activate TiO2 under visible light. The optical response of transition metal-doped TiO2 follows the order 3d > 4d > 5d. The oxygen vacancies reduce the response of metal-doped TiO2 to visible light because the unpaired electrons generated occupy the empty states of metal-doping. Graphical Abstract Density of states of TiO2 (101) surface doped with transition metals and oxygen vacancies.

Robust and efficient density fitting.

In this paper we propose an iterative method for solving the inhomogeneous systems of linear equations associated with density fitting. The proposed method is based on a version of the conjugate gradient method that makes use of automatically built quasi-Newton preconditioners. The paper gives a detailed description of a parallel implementation of the new method. The computational performance of the new algorithms is analyzed by benchmark calculations on systems with up to about 35,000 auxiliary functions. Comparisons with the standard, direct approach show no significant differences in the computed solutions.