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

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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: ω_e (ω_e+) = 1013 (1069) and 1027 (1059) cm-1 and the bond lengths r_e (r_e+) = 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+(C_2v) structure has two equivalent TiO bonds, while the TiO₂+(C_s) structure features a long and a short TiO bond. The IEs for the TiO₂+(C_2v)←TiO₂ and TiO₂+(C_s)←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+ (C_s) situated around the central well of TiO₂+(C_2v). 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 D(Ti+-O) - D(Ti-O) = 0.004 eV and D(O-TiO) - D(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.

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