First principles calculations are done for a √ 2 × 4 × 2 √ 2 P nma structure, which has been recently discussed in several attempts to describe experiments in complex magnetoelectric perovskites and which experimentally was shown to compete with several ferroelectric phases. This makes these materials extremely attracting as switchers, starters, field-stimulated capacitors, high-voltage converters, transmitters, etc. The relative energies of the √ 2 × 4 × 2 √ 2 P nma structure have been calculated from first principles and analyzed as a function of pressure in BiFeO 3 . The stability of two polymorphs of the √ 2 × 4 × 2 √ 2 P nma structure has been studied for solid solution BiFe 1/2 Sc 1/2 O 3 . The main distortions and relative energies of these two polymorphs in BiFe 1/2 Sc 1/2 O 3 , in terms of P m3m parent symmetry, have been calculated from first principles as well.