Determining Hubbard U of VO₂ by the quasi-harmonic approximation

Abstract

Vanadium dioxide ($\rm VO_{2}$) is a strongly correlated material that undergoes a metal-to-insulator transition around 340 K. In order to describe the electron correlation effects in $\rm VO_{2}$, the DFT+$U$ method is commonly employed in calculations. However, the choice of the Hubbard $U$ parameter has been a subject of debate and its value has been reported over a wide range. In this paper, taking focus on the phase transition behavior of $\rm VO_{2}$, the Hubbard $U$ parameter for vanadium oxide is determined by using the quasi-harmonic approximation (QHA). First-principles calculations demonstrate that the phase transition temperature can be modulated by varying the $U$ values. The phase transition temperature can be well reproduced by the calculations using the Perdew-Burke-Ernzerhof (PBE) functional combined with the $U$ parameter of 1.5 eV. Additionally, the calculated band structure, insulating or metallic properties, and phonon dispersion with this $U$ value are in line with experimental observations. By employing the QHA to determine the Hubbard $U$ parameter, this study provides valuable insights into the phase transition behavior of $\rm VO_{2}$. The findings highlight the importance of electron correlation effects in accurately describing the properties of this material. The agreement between the calculated results and experimental observations further validates the chosen $U$ value and supports the use of the DFT+$U$ method in studying $\rm VO_{2}$.