Describing Excited State Relaxation and Localization in TiO₂ Nanoparticles Using TD-DFT

Abstract

We have investigated the description of excited state relaxation in naked and hydrated TiO2 nanoparticles using Time-Dependent Density Functional Theory (TD-DFT) with three common hybrid exchange-correlation (XC) potentials: B3LYP, CAM-B3LYP and BHLYP. Use of TD-CAM-B3LYP and TD-BHLYP yields qualitatively similar results for all structures, which are also consistent with predictions of coupled-cluster theory for small particles. TD-B3LYP, in contrast, is found to make rather different predictions; including apparent conical intersections for certain particles that are not observed with TD-CAM-B3LYP nor with TD-BHLYP. In line with our previous observations for vertical excitations, the issue with TD-B3LYP appears to be the inherent tendency of TD-B3LYP, and other XC potentials with no or a low percentage of Hartree-Fock like exchange, to spuriously stabilize the energy of charge-transfer (CT) states. Even in the case of hydrated particles, for which vertical excitations are generally well described with all XC potentials, the use of TD-B3LYP appears to result in CT problems during excited state relaxation for certain particles. We hypothesize that the spurious stabilization of CT states by TD-B3LYP even may drive the excited state optimizations to different excited state geometries from those obtained using TD-CAM-B3LYP or TD-BHLYP. Finally, focusing on the TD-CAM-B3LYP and TD-BHLYP results, excited state relaxation in small naked and hydrated TiO2 nanoparticles is predicted to be associated with a large Stokes' shift.

Effect of Size and Structure on the Ground-State and Excited-State Electronic Structure of TiO2 Nanoparticles

“…A set of (TiO 2 ) n nanoparticles with n = 4, 8, 16, 35 and 84 was selected encompassing systems containing up to 252 atoms (~ 3 nm in diameter). For the selection of the smaller particles we have been inspired in the recent works of Zwijnenburg and coworkers, 42,47,48 whereas for the larger TiO 2 nanoparticles we rely on the previous work of Barnard et al 34 Regarding the selection of the small nanoparticles, we know from previous work that excitation (or photoemission) energy of (TiO 2 ) n with n = 2, 8 were studied by many authors and it is known that, for these nanoparticles, DFT and TD-DFT approaches with hybrid functionals work well.…”

Chemical trends in the optical properties of rocksalt nanoparticles

“…Indeed, from our work on TiO 2 and MgO nanoparticles 8,20,21 we believe that this cut-off might be lower in the case of inorganic materials, because even local (i.e. A L value of 0 corresponds to no overlap and 1 to complete overlap between the orbitals involved.…”

“…A very clear illustration of the latter is the case of nanoparticles of magnesium oxide (MgO) studied experimentally by the group of Diwald, 6,7 and discussed from a theoretical perspective in our previous paper, 8 as well as in computational work of Shluger and co-workers. 18,19 The solution to this problem, in line with experience for inorganic 8,20,21 and organic 18,19,22 systems, was the use of XC-functionals with an increased percentage of HFLE (e.g. 14 Calculations using Time-Dependent Density Functional Theory (TD-DFT) reproduce this red-shift, both between MgO nanoparticles and the bulk and between MgO nanoparticles of different sizes, and show that these excitations involve a combination of 3-coordinated (3C) corner and 4-coordinated (4C) edge atoms.…”

Modelling materials for solar fuel synthesis by artificial photosynthesis; predicting the optical, electronic and redox properties of photocatalysts

“…TD-DFT, just like ground state DFT, requires the choice of a XC functional and there are plenty of cases where commonly used XC functionals fail dramatically. A good example of the latter is the description of charge-transfer (CT) states involving undercoordinated surface atoms on the surface of inorganic nanoparticles [66][67][68], which requires use of range-separated XC functionals (e.g. CAM-B3LYP [69]) for accurate predictions.…”