Abstract The relative stability Δ E of the cubic Pm 3 ¯ m (C), of the two tetragonal P 4 m bm (T1) and I 4 m cm (T2), and of the orthorhombic Pbnm (O) phases of KVF 3 has been computed both for the ferromagnetic (FM) and antiferromagnetic (AFM) solutions, by using the B3LYP full range hybrid functional and the Hartree–Fock (HF) Hamiltonian, an all-electron Gaussian type basis set and the CRYSTAL code. The stabilization of the T2 phase with respect to the C one (152 μ Ha for B3LYP, 180 μ Ha for HF, per 2 formula units) is due to the rotation of the VF 6 octahedra with respect to the c axis, by 4.1–4.6 degrees. The O phase is slightly less stable than the T2 phase (by 6 and 20 μ Ha for B3LYP and HF); it is, however, a stable structure as the dynamical analysis confirms. The mechanism of the stabilization of the AFM solution with respect to the FM one is discussed through the spin density maps, and is related to the key role of the exact exchange term (20% in B3LYP, 100% in HF). The G-AFM phase (the first six neighbors of the reference V ion with spin reversed) is more stable than the FM one by about 500 (HF) and 1800 (B3LYP) μ Ha per two formula units. A volume reduction is observed in the C to T passage, and in the FM to AFM one, both being of the order of 0.3–0.5 A ˚ 3 at the B3LYP level. Atomic charges, magnetic moments and bond populations, evaluated according to a Mulliken partition of the charge a spin density functions, complete the analysis. The IR and Raman spectra of the FM and AFM C, T2 and O cells are discussed; the only noticeable difference between the various space groups appears in the modes with wavenumbers lower than 100 cm −1 .