Strongly Bound Frenkel Excitons on TiO₂ Nanoparticles: An Evolutionary and DFT Approach

Table 3

Energetic parameters of NPs obtained at the PBE0/def2-TZVP level of theory. Energies in eV.

Cluster size ()	IP	EA
2	9.764	1.508	8.255	4.139	4.116
3	9.630	2.880	6.750	3.629	3.123
4	9.718	2.234	7.485	4.090	3.395
5	9.227	2.972	6.255	4.153	2.102
6	9.276	3.339	5.936	4.240	1.696
7	9.221	3.302	5.919	4.350	1.569
8	9.059	3.150	5.909	4.334	1.575
9	8.993	3.517	5.476	4.391	1.085
10	8.965	3.431; 3.6^b	5.533	4.398	1.135
11	8.889	3.399	5.490	4.329	1.164
12	8.957	3.508	5.450	4.516	0.934
13	8.843	3.345	5.497	4.220	1.278
14	8.703	3.345	5.358	4.161	1.197
15	8.717; 8.57^d	4.353	4.364	3.998	0.366
16	8.484	3.987	4.496	4.233	0.263
17	8.353	4.022	4.331	4.005	0.326
18	8.679	3.964	4.716	4.157	0.559
19	8.576	4.552	4.024	3.892	0.132
20	8.504	3.698	4.806	4.129	0.677
TiO2	^a; ^c	3.9^e
Rutile	7.83^g	4.9^f	3.0^i
Anatase	8.30^g; 7.25^h	5.1^f; ~4.1^h	3.2^i

^aExperimental IP obtained by electron impact threshold measurements from Ref. [91]. ^bExperimental adiabatic EA of the (TiO₂)₁₀ neutral system obtained by magnetic-bottle photoelectron spectroscopy (PES) apparatus equipped with a laser vaporization cluster source from Ref. [92]. ^cFirst IP of TiO₂ from ionization efficiency curves and appearance potentials by electron impact [93]. ^dTheoretical adiabatic IP was obtained for the (TiO₂)₁₅ system from Ref. [28]. ^eExperimental EA of 3.9 eV for the TiO₂ nanoporous films from Ref. [94]. ^fExperimental EA for bulk anatase and rutile by ultraviolet photoelectron spectroscopy (UPS) from Ref. [95]. ^gTheoretical IP using DFT and the screened nonlocal exchange-correlation density functional (HSE06) from Ref. [96]. ^hExperimental IP by photoelectron yield spectra of anatase TiO₂ and EA estimated through the conduction band edge from Ref. [97]. ⁱFrom Ref. [98].