Periodic ab initio calculations of the spontaneous polarisation in ferroelectric NaNO2

We present periodic ab initio calculations for ferroelectric NaNO2. The spontaneous polarisation (Ps) has been calculated with three different models based on: (i) point charges; (ii) a multipolar expansion of the charge distribution; and (iii) the Berry phase approach. Both the Hartree–Fock and LDA Hamiltonians were employed. Within the Hartree–Fock scheme, at the optimised geometry, we obtain Ps values of 20.3, 13.0 and 16.4 µC cm−2 with the three models, compared to the experimental value of ∼11.9 µCcm−2. The Berry-phase approach at the Hartree–Fock level gives a value very close to experiment (namely 12 µCcm−2) when the experimental structure is used. At the optimised LDA structure, the LDA Ps values are 16.8, 10.0 and 16.9 µC cm−2 with models (i)–(iii). The optimised lattice parameters at the Hartree–Fock level are slightly shorter (between 0 and 4%) than those determined experimentally from X-ray-diffraction, while the lattice parameters of the LDA-optimised structure are up to 10% smaller than the experiment. The calculated lattice energies are 679 and 964 kJ mol−1 at the HF and LDA levels, compared with 729 kJ mol−1 from the experiment. Charge densities, Mulliken charges and dipole moments are discussed. Finally, we have studied the mechanism for the phase transformation in-between the ferroelectric and paraelectric crystal structures; a rotation of the NO2 group around the c-axis gives the lowest energy barrier.