Anharmonicity in the $\mathrm{V_2O_3}$ molecule and thermodynamic properties of $\mathrm{V_2O_3}$ in the gas phase

A quantum-mechanical calculation of the relative stability, structural parameters, and vibrational frequencies of $\mathrm{V_2O_3}$ molecule isomers for different spin states was carried out using the $\text{BPW91/6-311}+G(d, p)$ method. It was shown that the isomer with the $C_s$ structure (nonplanar VOVO rectangle with an O atom attached to it) in the $X^5A''$ electronic state possesses the maximum stability. The energy of the $C_{2v}$ symmetry structure was higher than the lowest energy by just $23 \text{ cm}^{-1}$. It definitely indicated the impossibility of usage of the harmonic model in order to calculate the thermodynamic functions of $\mathrm{V_2O_3}(g)$. A model is proposed based on which the energy levels and vibrational sums of states for this type of motion were calculated for the $C_s\to C_{2v}\to C_s$ transition coordinate. These data, as well as results obtained from quantum-mechanical calculations, were used to calculate the thermodynamic functions of $\mathrm{V_2O_3}(g)$ in the temperature range of $T=100$–$6000$ K. The calculations were performed with the five excited electronic states with energies from $1000$ to $9000\text{ cm}^{-1}$ taken into account. A comparison with the data calculated in the “rigid rotator-harmonic oscillator” approximation was performed.