High-Level ab Initio Predictions for the Ionization Energies, Bond Dissociation Energies, and Heats of Formation of Titanium Oxides and Their Cations (TiOn/TiOn+, n = 1 and 2).

Abstract

The ionization energies (IEs) of TiO and TiO2 and the 0 K bond dissociation energies (D0) and the heats of formation at 0 K (ΔH°f0) and 298 K (ΔH°f298) for TiO/TiO+ and TiO2/TiO2+ are predicted by the wave-function-based CCSDTQ/CBS approach. The CCSDTQ/CBS calculations involve the approximation to the complete basis set (CBS) limit at the coupled cluster level up to full quadruple excitations along with the zero-point vibrational energy (ZPVE), high-order correlation (HOC), core-valence (CV) electronic, spin-orbit (SO) coupling, and scalar relativistic (SR) effect corrections. The present calculations yield IE(TiO) = 6.815 eV and are in good agreement with the experimental IE value of 6.819 80 ± 0.000 10 eV determined in a two-color laser-pulsed field ionization-photoelectron (PFI-PE) study. The CCSDT and MRCI+Q methods give the best predictions to the harmonic frequencies: ωe (ωe+) = 1013 (1069) and 1027 (1059) cm-1 and the bond lengths re (re+) = 1.625 (1.587) and 1.621 (1.588) Å, for TiO (TiO+) compared with the experimental values. Two nearly degenerate, stable structures are found for TiO2 cation: TiO2+(C2v) structure has two equivalent TiO bonds, while the TiO2+(Cs) structure features a long and a short TiO bond. The IEs for the TiO2+(C2v)←TiO2 and TiO2+(Cs)←TiO2 ionization transitions are calculated to be 9.515 and 9.525 eV, respectively, giving the theoretical adiabatic IE value in good agreement with the experiment IE(TiO2) = 9.573 55 ± 0.000 15 eV obtained in the previous vacuum ultraviolet (VUV)-PFI-PE study of TiO2. The potential energy surface of TiO2+ along the normal vibrational coordinates of asymmetric stretching mode (ω3+) is nearly flat and exhibits a double-well potential with the well of TiO2+ (Cs) situated around the central well of TiO2+(C2v). This makes the theoretical calculation of ω3+ infeasible. For the symmetric stretching (ω1+), the current theoretical predictions overestimate the experimental value of 829.1 ± 2.0 cm-1 by more than 100 cm-1. This work together with the previous experimental and theoretical investigations supports the conclusion that the CCSDTQ/CBS approach is capable of providing reliable IE and D0 predictions for TiO/TiO+ and TiO2/TiO2+ with error limits less than or equal to 60 meV. The CCSDTQ/CBS calculations give the predictions of D0(Ti+-O) - D0(Ti-O) = 0.004 eV and D0(O-TiO) - D0(O-TiO+) = 2.699 eV, which are also consistent with the respective experimental determination of 0.008 32 ± 0.000 10 and 2.753 75 ± 0.000 18 eV.