Resonance-stabilized partial proton transfer in hydrogen bonds of incommensurate phenazine–chloranilic acid

Correlated variations of chemical bonds demonstrate stabilization by the resonance of the chloranilic acid anion. Proton transfer in some of the intermolecular hydrogen bonds is responsible for the ferroelectic properties.


Introduction
Organic compounds are of interest as ferroelectric materials, because they have a low density and they are potentially cheap to produce (Horiuchi & Tokura, 2008). Furthermore, organic compounds offer more possibilities than inorganic compounds for designing properties. Organic materials based on hydrogen-bonded supramolecular chains with a polar space group form one class of ferroelectric materials. The co-crystal of phenazine (Phz) and 2,5-dichloro-3,6-dihydroxy-p-benzoquinone (chloranilic acid, H 2 ca) is one of several recently discovered hydrogen-bonded organic ferroelectrics (Horiuchi, Ishii et al., 2005;Horiuchi et al., 2009;Kumai et al., 2006Kumai et al., , 2012. Phz-H 2 ca contains chains of alternating Phz and H 2 ca molecules connected through O-HÁ Á ÁN intermolecular hydrogen bonds. At room temperature, all hydrogen bonds are equivalent by the symmetry of the centrosymmetric space group P2 1 =n (Z ¼ 2), and the crystal of Phz-H 2 ca is paraelectric (PE phase; Horiuchi, Ishii et al., 2005;Kumai et al., 2007). Below T I c = 253 K the symmetry is reduced to P2 1 (Z ¼ 2), allowing for two inequivalent hydrogen bonds. One of the two bonds exhibits partial proton transfer, which is responsible for the spontaneous polarization (FE-I phase; Horiuchi, Ishii et al., 2005;Kumai et al., 2007;Gotoh et al., 2007). Phz-H 2 ca has an incommensurately modulated structure between T IC c = 147 K and T II c = 137 K (FE-IC phase; Saito et al., 2006;Horiuchi et al., 2009). Below T II c another ferro-electric phase is stable that can be characterized as a twofold superstructure of the room-temperature structure (FE-II phase; Noohinejad et al., 2014).
Here we report the crystal structure of the incommensurate phase, employing the superspace formalism applied to singlecrystal X-ray diffraction data. The modulation is found to mainly affect the positions of the H atoms within the O-HÁ Á ÁN intermolecular hydrogen bonds. Evidence for proton transfer in part of these bonds is provided by the correlated variations of bond lengths reflecting resonance stabilization of the anion. A detailed comparison of the various phases reveals that the incommensurate phase has a crystal structure intermediate between the crystal structures of the FE-I and FE-II phases. A mechanism is proposed for the sequence of phase transitions.

X-ray diffraction
Single crystals of Phz-H 2 ca were obtained by cosublimation of phenazine and chloranilic acid (Horiuchi. Ishii et al., 2005;Noohinejad et al., 2014). A diffraction experiment at T = 139 K was performed on the same crystal as was employed in our previous study on the commensurate FE-II phase (Noohinejad et al., 2014). X-ray diffraction data have been measured at beamline F1 of Hasylab at DESY in Hamburg, Germany, employing a MAR165 CCD detector mounted on a kappa diffractometer. The temperature of the crystal was regulated by a nitrogen gas-flow cryostat. X-ray diffraction data were collected by ' scans and ! scans for various settings of the orientation of the crystal. To better evaluate strong and weak reflections, two measurements were performed with the same measurement strategies but with different exposure times of 20 and 160 s, respectively. Data processing of the measured images has been carried out with the software EVAL15 (Schreurs et al., 2010) to index and extract the integrated intensities of Bragg reflections, and with SADABS (Sheldrick, 2008) for absorption correction. The latter employed groups of equivalent reflections defined according to the point group 2=m, which appeared as the symmetry of the diffraction. Experimental details are given in Table 1.
Indexing of the diffraction images with EVAL15 resulted in an indexing with four integers on the basis of a monoclinic unit cell closely related to the unit cell of the FE-I phase at 160 K (Horiuchi, Ishii et al., 2005) together with the incommensurate modulation wavevector q 0 ¼ ð 1 2 ; 0 2 ; 1 2 Þ, where 0 2 = 0.4861. However, the integration routine of EVAL15 did not accept a modulation wavevector with rational components. Therefore, the integration has been performed within the supercentered setting with q 0 i = ð0; 0 2 ; 0Þ and centering translation ð 1 2 ; 0; 1 2 ; 1 2 Þ with respect to the transformed basic structure unit cell A = a À c, B = b, and C = a þ c (Stokes et al., 2011). The same setting has been employed in SADABS.

Choice of the superspace group
The low-temperature superstructure of the FE-II phase at 100 K has been described as a commensurately modulated structure with a basic structure similar to the structure at higher temperatures and the commensurate modulation wavevector q comm ¼ ð 1 2 ; 1 2 ; 1 2 Þ. The superspace group P2 1 ð 1 2 2 1 2 Þ0, with 2 ¼ 1 2 has been found to describe the symmetry of this phase (Noohinejad et al., 2014).
Presently, the indexing with modulation wavevector q 0 ¼ ð 1 2 ; 0 2 ; 1 2 Þ and 0 2 ¼ 0:4861 (see x2.1) leads to the superspace group P2 1 ð 1 2 0 2 1 2 Þs. The non-centrosymmetric superspace group is established by the lack of inversion symmetry of both the FE-I and FE-II phases (see x1) as well as by measurements of the electrical polarization, indicating a ferroelectric state below T I c (Horiuchi, Kumai & Tokura et al., 2005). The two superspace groups appear to be alternate settings of superspace group No. 4.1.6.3 with standard setting P2 1 ð 1 2 0 3 Þ0 (Stokes et al., 2011). The two settings can be transformed into each other by a shift of the origin. However, this would result in different coordinates of the atoms in the basic structures of the low-temperature and incommensurate phases, which is not desired. The setting with zero intrinsic translation along the fourth coordinate can also be obtained by the choice of a different modulation wavevector for the incommensurate modulation, according to Diffraction data were re-indexed according to this transformation [equations (1) and (2)], and the superspace group P2 1 ð 1 2 2 1 2 Þ0 with 2 = 0.5139 has been used for all refinements.

Structure refinements
Initial values for the parameters of the basic structure have been taken from the basic structure at 100 K (Noohinejad et al., 2014). Anisotropic atomic displacement parameters (ADPs) have been used for all non-H atoms. H atoms were placed at calculated positions with a bond length d(C-H) of 0.96 Å , and they were refined using a riding model with isotropic ADPs equal to 1.2 times the equivalent isotropic ADPs of the bonded C atoms. H atoms of the hydroxyl groups were located in the difference Fourier map. They were then shifted to positions fulfilling the restraints d(O-H) = 0.85 (2) Å and /(C-O-H) = 109.5 (2) (Mü ller et al., 2006;Engh & Huber, 1991), while their isotropic ADPs were restricted to 1.5 times the equivalent isotropic ADPs of the adjacent O atoms. Employing JANA2006 (Petricek et al., 2014), the positions of all atoms were refined with these restraints in effect. In the last step the restraints were released, resulting in a good fit to the main reflections with R obs = 0.0412.
Three approaches have been chosen for determination of the atomic modulation functions for the incommensurate phase. In one approach, the modulation functions of the model at 100 K (Noohinejad et al., 2014) were used as a starting model. The same superspace group was employed, but with 2 ¼ 0:5139 instead of the commensurate value of 0.5. The refinement converged smoothly to a good fit to the combined set of main and satellite reflections, resulting in model A (Table 1). Model A involves one harmonic wave for the displacive modulation of all atoms as well as one harmonic wave for the modulation of ADPs of all non-H atoms. The origin was fixed on the Cl2 atom. Inversion twins are expected to be present, because the IC phase has been reached by phase transitions, starting with the centrosymmetric PE phase at room temperature. Twinning did have a marginal effect on the refinement, while a significant deviation from equal volume fractions of the twin domains was not found. Therefore, equal volume fractions were employed for the final refinements. A model with the alternative symmetry P2 1 ð 1 2 2 1 2 Þs did not lead to a good fit to the data.
Starting with the same basic structure, model B was developed by assigning arbitrary but small values to the modulation parameters of the heaviest atom (chlorine). Refinements alternated with the subsequent introduction of modulation parameters for the O, N, C and H atoms, finally resulting in a fit to the diffraction data of equal quality as that of model A (Table 2).
In a completely different approach, charge flipping was applied for the direct solution of the incommensurately modulated structure in superspace (Palatinus & Chapuis, 2007;Palatinus, 2013). For the solution, the software SUPERFLIP suggested the centrosymmetric symmetry P2 1 =nð 1 2 2 1 2 Þ00. Since we knew that the modulation is noncentrosymmetric, we have chosen the superspace group

Figure 1
Phenazine C 12 H 8 N 2 and chloranilic acid C 6 Cl 2 H 2 O 4 with the atom labels as employed in the present work.
R main F ¼ 0:0420 and R sat F ¼ 0:5998. Small values were applied to the displacive modulation functions of the H atoms. Refinement of the modulated structure resulted in R F ¼ 0:0472, R main F ¼ 0:0412 and R sat F ¼ 0:1787. Finally, modulation parameters were introduced for the ADPs of the non-H atoms, resulting in the final fit of model C to the diffraction data as given in Table 2. 3. Discussion

The structure model
The final fit to the diffraction data is excellent for the main reflections ( Table 1). The rather high value of R obs F ðsatÞ ¼ 0:127 can be completely explained by the weakness of the satellite reflections and the resulting values for R ðsatÞ ¼ 0:151, representing the average standard uncertainty over intensity, and R int ðsatÞ ¼ 0:129 for averaging satellite reflections. Model A and model B give the same fit to the diffraction data (Table 2). Although modulation parameters are different, these two models are completely equivalent. They differ from each other by a phase shift (Fig. 2). Further support for model A comes from difference-Fourier maps obtained after refinements of model A and of a similar model without the acidic H atoms (see the supporting information). Model C has been obtained by solving the modulated structure by charge flipping in superspace. The modulation of model C is different from the modulations in models A and B, but R obs F ðsatÞ is clearly higher for model C than for the other two models (Table 2). Therefore, model C provides a less good description of the modulation than models A and B do. Difficulties in obtaining the correct structure model by charge flipping are probably related to the pseudo-symmetry of the structure, with deviations from inversion symmetry being mainly the result of rearrangements of H atoms.
These properties provide strong support that model A (as well as the equivalent model B) is the correct model for the modulated crystal structure of the incommensurate phase. In view of these results, we have restricted the analysis to model A.

Resonance-stabilized proton transfer
The modulated structure of the incommensurate phase of Phz-H 2 ca has been successfully determined at a temperature of 139 K. The magnitudes of the modulation amplitudes of the atoms reveal that the major effect of the modulation is a displacive modulation of the H atom of one of the two hydrogen bonds in which each molecule is involved in. This feature is in complete agreement with the crystal structures of the FE-I and FE-II phases, where also one half of the hydrogen bond is involved in the distortions of the structure.
More precisely, the crystal structure of the FE-I phase contains one crystallographically independent molecule H 2 ca with two independent O atoms involved in O-HÁ Á ÁN Interatomic distances (Å ) as a function of phase t of the modulation. The t plot for model B (in blue) is superimposed onto the t plot for model A (in black), after application of a phase shift of À0.5139 in t to model B. Table 3 Geometry of the intermolecular hydrogen bonds O1-H1o1Á Á ÁN1 and O2-H1o2Á Á ÁN2 at different temperatures corresponding to the FE-I, FE-IC and FE-II phases, respectively.
Interatomic distances are given in Å and bond angles in degrees. (Max-min) provides the difference between the maximum (max) and minimum (min) separation depending on the phase t of the modulation in the FE-IC phase. The mean gives the value averaged over t. Standard uncertainties are given in parentheses.  (15)  hydrogen bonds, denoted by O1 and O2 (Gotoh et al., 2007). The basic structure of the FE-IC phase is the same as the crystal structure of the FE-I phase, so that the FE-IC phase contains modulated atoms O1 and O2. Finally, the FE-II phase represents a twofold superstructure of the structure of the FE-I phase. Together with a reduction of the point symmetry to triclinic, this results in four crystallographically independent molecules H 2 ca with atoms O1A through to O1D derived from O1, and atoms O2A through to O2D derived from O2 (Noohinejad et al., 2014). In all three phases, the hydrogen bonds O2-H1o2Á Á ÁN2 are not involved in superstructure formation. For the FE-IC structure, Table 3 and Fig. 3(a) show that bond lengths involving the O2, H1o2 and N2 atoms exhibit only a weak dependence on phase t of the modulation. For the FE-I and FE-II structures this property has been previously determined by Gotoh et al. (2007) and Noohinejad et al. (2014), and it is summarized in Table 3. Therefore, the hydrogen bonds O2-H1o2Á Á ÁN2 do not play a direct role in the ferroelectricity of this compound. The largest variation in bond lengths within the FE-IC phase is found for the hydrogen bond O1-H1o1Á Á ÁN1, with a variation of Ád(O1-H1o1) = 0.25 Å and Ád(N1-H1o1) = 0.42 Å (Table 3). All other bonds are much less affected by the modulation, with a maximum variation of 0.06 Å for C3-O1 in H 2 ca and of 0.019 Å for C14-C15 in Phz (see the supporting information). The next largest variations of bond lengths are found for C3-C2, C1-C2 and C1-O4 (Table 4). These bonds are precisely those involved in resonance stabilization of the Hca À ion, as it is obtained after transfer of the proton within the O1-H1o1Á Á ÁN1 hydrogen bond. Further evidence for this interpretation comes from t-plots (Fig. 3), which show that an elongation of the O1-H1o1 bond (interpreted as proton transfer) correlates with an elongation of the C3-C2 and C1-O4 bonds, for which resonance represents the admixture of single-bond character into these formally double bonds (Fig. 4). Concomitantly, C1-C2 and C3-O1 have become shorter due to the admixture of doublebond character into formally single bonds. A similar variation of bond lengths is found in the crystal structure of the FE-II phase ( Table 4). The results support the model of partial proton transfer (see x3.3).

The ferroelectric phase transitions
Ferroelectricity in Phz-H 2 ca at low temperatures is the result of intermolecular proton transfer within the O1-H1o1Á Á ÁN1 hydrogen bonds (Horiuchi, Kumai & Tokura, 2005;Kumai et al., 2007Kumai et al., , 2012Gotoh et al., 2007;Noohinejad et al., 2014). Consideration of the positions of the H atoms within the O1-H1o1Á Á ÁN1 hydrogen bonds of the crystal structures of the three phases leads to the following model for the phase transitions.   At room temperature (PE phase) all hydrogen bonds are equivalent by symmetry of the centrosymmetric space group. Consequently, any dipole moment of the O1-H1o1Á Á ÁN1 hydrogen bond will be perfectly compensated by a dipole moment of the O2-H1o2Á Á ÁN2 hydrogen bond on the same molecule that points in the opposite direction, because O1 and O2 are related by the inversion center. The ferroelectric phase transition towards the FE-I phase is characterized by loss of inversion symmetry. The O2-H1o2 remains short and should be interpreted as a covalent O-H bond that acts as a hydrogen-bond donor towards N2 (Table 3). The O1-H1o1 bond is clearly elongated compared with a covalent bond, but it is not completely broken. The N1-H1o1 distance is clearly shorter than in the PE phase, but it is not yet the distance of $ 1.03 Å of a covalent N-H bond. Therefore, it can be concluded that this structure exhibits partial proton transfer within the O1-H1o1Á Á ÁN1 hydrogen bonds.
The low-temperature FE-II has four crystallographically independent O1-H1o1Á Á ÁN1 hydrogen bonds. The partial proton transfer of the FE-I phase is replaced in the FE-II phase by complete proton transfer in one half of these hydrogen bonds (B and D), and the absence of proton transfer in the other half (A and C) ( Table 3). The FE-I phase transfers into the FE-II phase via the intermediate FE-IC phase. Structurally, the FE-IC phase appears intermediate between the high-and low-temperature ferroelectric phases too. The incommensurate modulations represents a modulation of the O1-H1o1Á Á ÁN1 hydrogen bond between one with almost full proton transfer and one which can be characterized as almost no proton transfer (Table 3 and Fig. 3a). Despite an incommensurability of the FE-IC phase, it appears that -on average -one quarter of the hydrogen bonds has full proton transfer in both the FE-IC and FE-II phases, while half of the hydrogen bonds in the FE-I phase are affected by partial proton transfer. These similarities might explain the only marginal effects of the ferroelectric incommensurate and lock-in transitions on the macroscopic electric dipole moment (Horiuchi et al., 2009).

Conclusions
The incommensurately modulated structure of the ferroelectric incommensurate (FE-IC) phase of Phz-H 2 ca has been successfully determined. It is shown that this structure is intermediate between the ferroelectric FE-I and FE-II phases. Half of the intermolecular hydrogen bonds exhibit partial proton transfer within the FE-I phase. This becomes an incommensurate variation between strong and very weak proton transfer within the FE-IC phase, while in the FE-II phase the active half of the hydrogen bonds splits into a hydrogen bond with complete proton transfer and one without proton transfer. Strong support for proton transfer in part of the hydrogen bonds has been obtained through the variations of the lengths of precisely those bonds that are involved in resonance stabilization of the Hca À ion (x3.2). Proton transfer in only part of the hydrogen bonds has been explained as the result of Coulomb interactions between the resulting ionic species (Kumai et al., 2012). Proton transfer is in line with the acidities of the two molecules with pK a1 = 1.23 for the proton acceptor Phz, and pK a1 = 0.76 for the proton donor H 2 ca (Albert & Phillips, 1956;Molcanov & Prodic, 2010). One could thus suggest that the incommensurability will be the result of competition between the inclination towards proton transfer of single hydrogen bonds and avoiding unfavorable Coulomb repulsion within the crystalline lattice of molecules.