Centrosymmetric or Noncentrosymmetric?* BY RICHARD E. MARSH

In cases where diffraction data do not provide a clear choice between a centrosymmetric and a noncentrosymmetric space group, it is better to opt for the centrosymmetric description even though disorder may result. The disorder model implies that the crystal is a composite of two or more molecular structures that cannot be distinguished from one another. On the other hand, attempts to refine a single, ordered model in the noncentrosymmetric space group (which *Contribution No. 7215 from the Arthur Amos Noyes Laboratory of Chemical Physics. should lead to poor convergence because of near singularities) may lead to the erroneous conclusion that a unique structure has been found. Three examples of this latter situation are given. One of the most troublesome problems in crystalstructure analysis is resolving the ambiguity between a centrosymmetric and a noncentrosymmetric space group when systematic absences are of no help. This ambiguity exists within many pairs of commonly occurring space groups, such as P1-P1, P21-P21/m, Cc-C2/c , Pna21-Pnam, and many others. If the 0108-7681/86/020193-06501.50 © 1986 International Union of Crystallography 194 CENTROSYMMETRIC OR NONCENTROSYMMETRIC? structure is very nearly centrosymmetric, the diffraction data are insensitive to the ambiguity: for a particular structure factor Fhk I the contribution due to the antisymmetric distortion is small (since the distortion from centrosymmetry is small) and imaginary at fight angles to the real contribution due to the centrosymmetric component; hence it has little effect on the magnitude of F unless F is very small (in which case the reflection is ignored in most laboratories). A particularly bothersome situation arises when the choice is between a disordered structure in the centrosymmetric space group and an ordered (or a more ordered) structure in the noncentrosymmetric space group. Here, the real component of F provides information concerning the average centrosymmetric structure while all the information concerning the ordering of the structure into two unrelated moieties (if such ordering indeed occurs) is contained in the small, imaginary component. It may well be impossible to recover these details from the diffraction data alone. In such cases, it seems preferable to resort to the disordered, centrosymmetric description, thus admitting that only the average structure is being determined. I describe here three examples of this situation. In all three the original authors chose to describe closely centrosymmetric structures in noncentrosymmetric space groups. The resulting deformations from centrosymmetry are somewhat unusual and suspect, and it seems preferable to describe all three structures as disordered in the corresponding centrosymmetric space groups. (I) Dichloro [ 1,2-ethanedione bis ( dimethylhydrazone ) ] ( r I-ethylene )platinum ( I I ) The structure of this compound, PtCI2(C2H4)(C6HI4N4), was described in space group P21 [monoclinic; a = 8.998 (3), b = 8.133 (4), c =9.872 (2) /~, /3 = 106.72 (3) °, Z = 2] and refined to an R of 0.050 for 1404 reflections (Bavoso, Funicello, Morelli & Pavone, 1984; BFMP). Surprising features of the structure included asymmetry in the bonding about Pt and in the hydrazone ligand, with one dimethylated N atom planar and the other pyramidal; the four N-CH3 distances ranged from 1.39 (3) to 1.53 (3) A. It seems preferable to describe the structure in space group P21/m. The P2~/m description can be derived from the coordinates in Table 1 of BFMP by placing the Pt, C, and N atoms on the mirror plane at y = 0.25 and the two C1 atoms in equivalent positions above and below this plane. Full-matrix leastsquares refinement quickly converged at R = 0.0505 for the 1388 reflections coded as 'observed' in Supplementary Publication No. SUP 39649. In this refinement, the Pt, C1, C, and N atoms were given anisotropic Uu's and the H atoms were ignored, as in BFMP. (Subsequent difference maps clearly showed the four H atoms of the coordinated ethylene group, lying on opposite sides of the molecular mirror plane, but the remaining H atoms were unclear.) These P2~/m coordinates are given in Table 1. The bond lengths (Fig. 1) obtained from this P2~/m refinement seem more satisfying than those from the P2~ refinement of BFMP in that the pairs of Pt-C1, Pt-N and Pt-C distances are statistically equal and the two halves of the hydrazone ligand appear identical. However, the differences among the terminal N-C distances are unrealistic: there is no reason to expect that the endo (relative to Pt) distances would be so much shorter than the exo distances. Another disturbing feature of the P2~/m model is the large U22 terms (Table 1), particularly for N(2) and N(4). These terms, which represent out-of-plane displacements with r.m.s, values up to 0-4-0-5 A, suggest that alternative models in P2~/m can be developed in which some of the atoms are disordered between pairs of sites on opposite sides of the plane. I investigated three such models, with four, six, and all ten hydrazone C and N atoms disordered in this way (and assigned isotropic B's). All three converged to essentially equal R's of about 0.051the same as reached for the ordered, anisotropic model of Table 1. Each of these models can lead to a variety of bond lengths and angles, depending upon the way in which the disordered atoms are presumed to be connected to one another; essentially any reasonable preconception of the structure can be satisfied. For all such models, however, the out-of-plane coordinate (y) of each atom couples strongly with the U22 component of B for that atom, and neither value can be determined with confidence (hence the necessity for assuming an isotropic B). All that can be said, then, is that the P21/m model of Table I probably describes an average of a number of structures in which the hydrazone atoms are displaced from the mirror plane in various ways we cannot determine. Hence, we cannot know with confidence the bond lengths and angles in an individual molecule, or whether the external N atoms N(2) and N(4) are planar or pyramidal. [The interior distances involving C(5) and C(6) should be fairly reliable, because the U22 terms of N(1), C(5), C(6) and N(3) are moderate; distances and angles involving N(2) and N(4) are especially conjectural.] The four N-CH 3 bond lengths could well be equal; if so, the minimum length would be about 1.45 A, for models in which the exo atoms C(4) and C(7) have nearly the same y values as their neighboring N atoms. Refinement in P2~, such as carried out by BFMP, must be based on a presumed starting model which is non-planar, since the planar model of Table I would lead to singularities (Ermer & Dunitz, 1970) if refinement in P2~ were attempted. (Thef t component of anomalous scattering by Pt would in principle break this singularity, but the effect is too small to RICHARD E. MARSH 195 Table 1. PtC12(C2H4)(C6H14N4): coordinates (x 104) and Uu's (X103); space group P21/m The Uq's are of the form: -2~2(Ullh2a*2+ . . . +2U23klb*c*). x y z U11 Uz2 U33 U~z Ul3 Uz3 Pt 7580.5 (8) 250