Fig. 4: Minimum-energy transition trajectory between the rutile and monoclinic phases of VO₂.

a Energy barriers for the transition paths between rutile and monoclinic VO₂ obtained from climbing image nudged elastic band with R-PBE. The relaxed (by R-PBE) rutile structure in the M-like unit cell and the monoclinic structure are used as the endpoints for the nudged elastic band calculations. The nonmagnetic configuration and the three magnetic configurations with zero global moment in the monoclinic-like unit cell (see Insets) are considered. b Average magnetic moment magnitudes over the V⁴⁺ ions in VO₂ that are equivalent for the nonmagnetic configuration but can separate into non-equivalent groups for magnetic configurations along the phase transition paths for the three magnetic configurations shown in a. c Band gaps of VO₂ along the phase transition paths for the three magnetic and nonmagnetic configurations.