Modeling Excited States in TiO₂ Nanoparticles: On the Accuracy of a TD-DFT Based Description

Abstract

We have investigated the suitability of Time-Dependent Density Functional Theory (TD-DFT) to describe vertical low-energy excitations in naked and hydrated titanium dioxide nanoparticles. Specifically, we compared TD-DFT results obtained using different exchange-correlation (XC) potentials with those calculated using Equation-of-Motion Coupled Cluster (EOM-CC) quantum chemistry methods. We demonstrate that TD-DFT calculations with commonly used XC potentials (e.g., B3LYP) and EOM-CC methods give qualitatively similar results for most TiO2 nanoparticles investigated. More importantly, however, we also show that, for a significant subset of structures, TD-DFT gives qualitatively different results depending upon the XC potential used and that only TD-CAM-B3LYP and TD-BHLYP calculations yield results that are consistent with those obtained using EOM-CC theory. Moreover, we demonstrate that the discrepancies for such structures originate from a particular combination of defects that give rise to charge-transfer excitations, which are poorly described by XC potentials that do not contain sufficient Hartree–Fock like exchange. Finally, we consider that such defects are readily healed in the presence of ubiquitously present water and that, as a result, the description of vertical low-energy excitations for hydrated TiO2 nanoparticles is nonproblematic.

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

“…It is also interesting to note that the ranges of the half-reaction potentials in CPCM water model in the present study do well correspond to those of rutile nanocrystals immersed in explicit water environment with hydrated surfaces. 42 However, we also note that the results obtained by CPCM model artificially affect some properties such as localization of free electron/hole in the (unhydrated) structural defects such as under-coordinated titanium/oxygen as shown in…”

“…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.…”

“…correspond to results obtained with the CAM-B3LYP method since the B3LYP calculations exhibited a computational instability for geometry relaxation in excited state with charge transfer character. 42 …”

Design of Novel Visible Light Active Photocatalyst Materials: Surface Modified TiO2

“…Figure 7 shows the spin density from the relaxed triplet state for a selection of free and supported TiO2 nanoclusters; ref [81] shows a more extensive set of nanoclusters and see also ref [88] for high level DFT results on electron-hole localisation in TiO2 nanoclusters, showing consistency between the different DFT approaches and models. Reproduced from [81] , 2014, American Chemical Society…”

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.…”