Structure and energetics of a ferroelectric organic crystal of phenazine and chloranilic acid

We report first-principles calculations for a ferroelectric organic crystal of phenazine and chloranilic acid molecules. Weak intermolecular interactions are properly treated by using a second version of the van der Waals density functional known as vdW-DF2 [K. Lee et al., Phys. Rev. B 82, 081101 (2010)]. Lattice constants, total energies, spontaneous electric polarizations, phonon modes and frequencies, and the energy barrier of proton transfer are calculated and compared with PBE and experiments whenever possible. We show that the donation of one proton from a chloranilic acid molecule to a neighboring phenazine molecule is energetically favorable. This proton transfer is the key structural change that breaks the centrosymmetry and leads to the ferroelectric structure. However, there is no unstable phonon associated with the proton transfer, and an energy barrier of 8 meV is found between the paraelectric and ferroelectric states.

Figure 1

(a) Monoclinic unit cell of the paraelectric structure containing two H${}_2$ca molecules (at body-center and corner sites) and two Phz molecules (at $ab$-face-center and $c$-axis edge-center sites). (b) H-bonded chain of molecules running along [110]. (c) An $ab$ plane filled by H-bonded chains running along [110]. (d) Next higher (or lower) $ab$ plane filled by H-bonded chains running along $\left[1\overline{1}0\right]$. In panels (b)–(d), all Cl atoms, H atoms bonded to oxygens, and O atoms double-bonded to carbons have been omitted for clarity.

Figure 2

Possible proton transfer (PT) processes in the unit cell, as indicated by large unfilled arrows. (a) Structure FE1, in which a H${}_2$ca donates a proton to a nitrogen in a neighboring Phz, leaving behind an oxygen lone pair on the H${}_2$ca and creating an electric dipole along the PT direction. The direction of polarization $P$ is shown at the bottom left-hand corner as a thin arrow labeled as $P$; here the PT occurs along [$\overline{1}\overline{1}$0] so that $P$ has both $a$ and $b$ components. (b) Structure FE2b, in which another PT occurs along [1$\overline{1}$0] in the other H-bonded chain; $P$ points along $b$ by symmetry. (c) Structure FE2a, in which the second PT occurs along [$\overline{1}$10] instead; $P$ points along $a$ by symmetry. (d) Structure PE2, a doubly protonated paraelectric structure. (e)–(g) Enlarged view of the PT process.

Figure 3

Energies of competitive proton-transferred structures presented relative to the FE2b ground-state energy, which is taken as zero.

Figure 4

Energies relative to PE0 (left), as calculated with PBE and vdW-DF2, for the transition-state structure leading from PE0 to FE1 (middle) and for FE1 (right). The lattice constants are fixed to experimental values for this comparison, and zero-point energies are included at the harmonic level.