Computational investigation of thermodynamic properties of gas phase vanadium nitride using Python

Abstract

Abstract This study examines the thermodynamic characteristics of gas-phase diatomic vanadium nitride (VN(g)) utilizing the Kratzer potential model and Python as the computational tool. By solving the Schrödinger equation for the vibrational energy spectrum, we compute the vibrational partition function, which serves as the foundation for determining essential thermodynamic functions such as heat capacity ( $$C_p$$ ), entropy ( $$S^\circ$$ ), internal energy, and enthalpy. The calculated thermodynamic parameters are juxtaposed with experimental data from the NIST Chemistry WebBook to evaluate the precision of the Kratzer potential in simulating the thermal behavior of diatomic VN(g). Our results indicate that the Kratzer potential serves as a dependable approximation for the thermodynamic properties of molecular VN(g), especially in forecasting entropy and enthalpy over an extensive temperature range. The calculated heat capacity exhibits strong concordance with experimental data in the intermediate temperature range, though deviations appear at both low and high temperatures due to effects not captured by the model. Despite these limitations, the overall agreement validates the application of quantum molecular models, such as the Kratzer potential, in the thermodynamic analysis of transition-metal-containing diatomic molecules. This framework may be extended to similar gas-phase systems to support predictive modeling in molecular thermodynamics.