A theoretical treatment based on the equations of motion of an electronic reduced density matrix, and related computational modeling, is used to describe and calculate relaxation times for nanostructured TiO2(110) surfaces, here for Ag and Ag2 adsorbates. The theoretical treatment deals with the preparation of a photoexcited system under two different conditions, by steady light absorption with a cutoff and by a light pulse, and describes the following relaxation of electronic densities. On the computational modeling, results are presented for electronic density of states, light absorbance, and relaxation dynamics, comparing results for Ag and Ag2 adsorbates. The aim of this work is to provide insight on the dynamics and magnitude of relaxation rates for a surface with adsorbed open- and closed-shell Ag species to determine whether the advantages in using them to enhance light absorbance remain valid in the presence of charge density relaxation. Different behaviors can be expected depending on whether the adsorbate particles (Ag metal clusters in our present choice) have electronic open-shell or closed-shell structures. Calculated electron and hole lifetimes are given for pure TiO2(110), Ag/TiO2(110), and Ag2/TiO2(110). The present results, while limited to chosen structures and photon wavelengths, show that relaxation rates are noticeably different for electrons and holes, but comparable in magnitude for pure and adsorbate surfaces. Overall, the introduction of the adsorbates does not lead to rapid loss of charge carriers, while they give large increases in light absorption. This appears to be advantageous for applications to photocatalysis.
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