Fig. 1. PAW results compared with FP-LAPW results. (a) Pressure of bcc vanadium as a function of volume. The black diamonds and crosses are the FP-LAPW results and the data from Young et al.,⁵³ respectively. (b) Relative deviation of the pressure R_i as a function of volume. The PAW results are represented by colored symbols and lines, with blue, dark cyan, and red lines with closed symbols indicating the results using PBE-V, PBE-V_pv, and PBE-V_sv, respectively. The black dashed line is zero, corresponding to the FP-LAPW results in (a). (c) PAW results (colored lines) compared with FP-LAPW results with (green open circles) and without (purple closed squares) 3s3p electrons treated as core electrons.

Fig. 2. Comparisons of the calculated energy bands and DOS between two PAW potentials V and V_sv at volumes (a) 9.84 ų and (b) 6.91 ų.

Fig. 3. Comparison of the potentials and forces obtained using the two PAW potentials V and V_sv.

Fig. 4. Charge density difference of the [110] planes in the bcc lattice described by the PAW potentials V and V_sv. The warmer (colder) the color, the higher (lower) is the electron density in that region. The gray circles indicate the positions of the atoms.

Fig. 5. (a)–(c) Comparisons of isochoric curves between the potentials V (black squares) and V_sv (red circles) at volumes (a) 12.84 ų, (b) 9.84 ų, and (c) 6.91 ų. The blue diamonds and green triangles indicate our coexistence results²⁴ and the Z-method results from Errandonea et al.,²⁵ respectively. (d) Pressure difference as a function of temperature at each volume. Symbold in different colors indicate systems in different volumes (the straight lines are to guide the eye).

Fig. 6. Comparison of VDOS obtained using the potentials V (dashed lines) and V_sv (solid lines) at volumes (a) 9.84 ų and (b) 6.91 ų.