Unraveling the role of V-V dimer on the vibrational properties of VO$_2$ by first-principles simulations and Raman spectroscopic analysis

We investigate the vibrational properties of VO2, particularly the low temperature M1 phase by first-principles calculations using the density functional theory as well as Raman spectroscopy. We perform the structural optimization using SCAN meta-GGA functional and obtain the optimized crystal structures for metallic rutile and insulating M1 phases satisfying all expected features of the experimentally derived structures. Based on the harmonic approximation around the optimized structures at zero temperature, we calculate the phonon properties and compare our results with experiments. We show that our calculated phonon density of states is in excellent agreement with the previous neutron scattering experiment. Moreover, we reproduce the phonon softening in the rutile phase as well as the phonon stiffening in the M1 phase. By comparing with the Raman experiments, we find that the Raman-active vibration modes of the M1 phase is strongly correlated with the V-V dimer distance of the crystal structure. Our combined theoretical and experimental framework demonstrates that Raman spectroscopy could serve as a reliable way to detect the subtle change of V-V dimer in the strained VO$_2$.