Thermodynamic and Kinetic Aspects of the Reactions of Titanium(I) ion with the Sulfurtransfer Reagent SCO via the C22O Bond Activation Pathway

Abstract

Theoretical studies on the thermodynamic and kinetic aspects of the reactions of Ti⁺ ion with the sulfur-transfer reagent SCO via the C22O bond activation pathway have been carried out over the temperature range 200 — 1200K using the DFT=B3LYP method, general statistical thermodynamics and Eyring transition state theory with the Wigner correction. The relevant reactions comprise: reaction 1 $\begin{array}{l}{}^{2}T{i}^{+}+SCO{\to }^{2}I{M}_1{\to }^{2}T{S}_1{\to }^{2}I{M}_2\hspace{0.17em}\hspace{0.17em}\left(Step\hspace{0.17em}1\right)\\ \hspace{0.17em}{\to }^{2}T{S}_2{\to }^{2}I{M}_3{\to }^{2}Ti{O}^{+}{+}^{1}CS\hspace{0.17em}(Step\hspace{0.17em}2)\end{array}$ , and reaction 2 ${}^{4}T{i}^{+}+SCO{\to }^{4}I{M}_1+CP{\to }^{2}T{S}_2{\to }^{2}I{M}_3{\to }^{2}Ti{O}^{+}{+}^{1}CS$ in which the spin multiplicity changes from the quartet state to the doublet state in the crossing region. It is concluded that the order of the equilibrium constants (K) and the reaction rate constants (k) are consistent with that of their corresponding exoergic energies DE and reaction barriers, respectively, and their differences at low temperature are larger than those at high temperature. Step 2 of reaction 1 is both thermodynamically and kinetically favoured over the entire temperature range. Moreover, both reactions 1 and 2 are exothermic and proceed spontaneously in which their entropy increases, and the magnitudes of their thermodynamic constants all decrease with rising temperature. The calculated DH8, DG8, and DS8 values of the two reactions are relatively similar. However, because reactants 4Ti⁺ and SCO have a lower energy than that of reactants 2Ti⁺ and SCO, it is reaction 2, in which the quartet state is changed to the doublet state through intersystem crossing, which should be seen as dominant.