CONTRIBUTED PAPERS DETERMINATION OF A DIFFICULT STRUCTURE: A CASE OF STRONG CORRELATIONS BETWEEN PARAMETERS R. KURODA

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1 The Rigaku Journal Vol. 6/ No. 2 / 1989 CONTRIBUTED PAPERS DETERMINATION OF A DIFFICULT STRUCTURE: A CASE OF STRONG CORRELATIONS BETWEEN PARAMETERS R. KURODA Department of Chemistry, College of Arts and Sciences, The University of Tokyo, Komaba, Meguro, Tokyo 153, Japan 1. Introduction Each year many crystal structures are solved and the details published in scientific journals. Such articles report the successful solution of a crystallographic problem but it is often unclear to the reader exactly what path the author took in solving the structure and what pitfalls were negotiated along the way. Only productive approaches are reported in journals with little or no mention of the time an effort spent following approaches that although seemingly reasonable did not yield a satisfactory structure. However, it can be illuminating and intellectually rewarding to examine in some detail the steps and thinking involved in arriving at a difficult structure. Analysis of this kind serves to distinguish those methods of attacking a particular problem that may prove successful from those that consume time and are unlikely to be productive. This article describes my experience in solving a difficult crystal structure that had several snags: optical lability of the compound made it difficult to grow large crystals suitable for X-ray diffraction work and special crystal packing in the unit cell hampered a straightforward least-squares refinement of the structure. 2. Problem Structure determination of optically active tris[(- ) cyclic-o,o'](r),2(r)dimethylethylenedithiophosphato]chromium(iii). {Cr[(-)bdtP] 3 } This coordination complex exhibits an interesting feature from the point of chiral discriminations/ recognitions and the mode of crystal packing. Trisbidentate chelate metal complexes with D 3 symmetry normally possess a propeller type structure and become optically active even though the ligands do not contain a chiral center. One such example is tris(ethylenediamine)cobalt(iii) ion, [Co(en) 3 ] 3+. It exists as a right-handed propeller form, -form, as well as its enantiomeric left-handed propeller form, Λ-form. When these molecules, either in an optically active or racemic form, are packed in a crystal lattice, the chirality of the molecules is recognized by interactions among the propeller blades, and quite often these crystals adopt a unique crystal packing mode [1]-[3]. The compound we are considering here contains four-membered chelate rings and another 5- membered ring is joined to each four-membered ring at the phosphorus atom (Fig. 1). The phosphorus atom adopts a tetrahedral geometry and hence the two rings are almost perpendicular to each other. The result is that when the three inner rings form a right-handed propeller, the outer rings necessarily form a lefthanded propeller. Therefore it is interesting to find out the crystal packing pattern in order to compare it with that of optically active D 3 compounds of simple propeller shape. 3. Crystallization It was extremely difficult to obtain crystals of reasonable size and quality. The compound is optically labile as observed in the circular dichroism spectra of a chloroform solution: the ε value at 665nm decreased over a 40 min time period from a positive to a negative peak until it reached a diastereomeric equilibrium [4]. A solution of the compound in acetonitrile was optically more stable, therefore crystals were grown from this solution. There. appeared to be two types of crystal of different morphology. One was a small, very thin oblong plate type and the other had a large tetragonal prismatic shape. The prismatic crystals were generally soft and of poor quality. The Weissenberg photographs of the prismatic crystals usually showed a diffuse pattern. The thin plate-like crystals were often too small for intensity data collection or even for X-ray photography. Consequently many attempts had to be made over several years to obtain good crystals. 22 The Rigaku Journal

2 Fig 1. ORTEP drawing [7] of the molecular structure of (+) 589 -{Cr[(-)bdtp] 3 }. 4. Data Collection and Structure Determination 4.1 Experiment 1 (Data 1) A prismatic crystal of reasonable quality was eventually obtained and diffraction data were collected using a four-circle diffractometer (Mo Kα source, Enraf-Nonius CAD4) at King's College London. Crystal data: monoclinic, a=8.624(8), b=16.85(l), c = 8.632(7) Å, β=94.8(1), V=1249Å 3. Z=2. The diffraction peaks were broad. As the compound is optically active, the only possible space group which satisfies the systematic absence was P2 1. From the Patterson synthesis, the Cr atom was placed at (~0, 0.0, ~0). Scale fractor refinement gave an R value of and the difference Fourier map showed six peaks octahedrally located around the Cr atom at a distance of ~2.3 Å from the metal. Including these peaks as sulphur atoms, a scale factor refinement was carried out, which gave an R value of Refinement of the atomic coordinates and isotropic temperature factors reduced the R factor to Three phos-phorus and three oxygen atoms were located eventually from difference Fourier maps. Including all these atoms and assuming an anisotropic temperature factor for the Cr atom only, least-squares refinements were carried out to give an R value of The difference Fourier map at this stage revealed one carbon atom. Leastsquares refinement including the atom gave an R value of for 1116 reflections observed. All the parameters were refined reasonably, however, no other molecular fragments were developed in the difference map. The structure determination was abandoned at this stage due to the poor quality of the intensity data. 4.2 Experiment 2 (Data 2) Another set of intensity data were collected this time using a thin plate-type crystal of a relatively large dimensions, 0.07 x 0.17 x 0.24mm. Unfortunately, only a Cu Kα source was available at that time on the Enraf-Nonius CAD4 at King's College London. Cell parameters obtained were: monoclinic, a = 8.655(1), b=16.830(5), c=8.656(1) Å, β=94.83(1), V= Å 3, which were much the same as those from Data 1. However, this time, the cell could be converted to an orthorhombic cell of C centering, which was: a = (1), b=12.749(1), c=16.814(2) Å, V= (8)Å 3, Z=4. Preliminary X-ray photography clearly indicated a primitive orthorhombic rather than a C-centered cell and this was further confirmed on the diffractometer. After checking the Lane symmetry, intensity data were collected as a primitive orthorhombic cell. Thus, two morphologically different crystals observed were in fact of the same crystal type. Of 1737 reflections, 986 had I> 1.5 σ(i). The space group was assigned to P from the systematic absences. The Patterson maps indicated a position either (-0.25, -0.0, -0.0) or (-0.25, -0.0, ) for the Cr atom. Only the latter position was promising. After successive least-squares refinement and Fourier synthesis, all the 28 non-hydrogen atoms of the molecule were located. The R factor was Changing the temperature factors from isotropic to anisotropic decreased the R value to However, nine carbon atoms had non-positive definite temp- Vol. 6 No

3 erature fractors. The minimum transmission factor was as low as 35.91% and the empirical absorption correction did not improve the situation at all. Clearly, the Cu source was not a good choice. The number of reflections with respect to the number of variables (235) was also insufficient. 4.3 Experiment 3 (Data 3) Data were collected using a Mo Kα source at Queen Mary College London (Enraf Nonius CAD4). The largest crystal I obtained (0.04 x 0.11 x 0.49mm) was employed. Intensity data were collected as a primitive orthorhombic system, although, as mention-ed before, a C-centered orthorhombic cell was indica-ted by the instrument. Out of 1803 reflections, only 1095 had I>1.5σ(I). An absorption correction was ap-plied, and the minimum transmission factor was 90.3%. Taking the atomic coordinates from Experiment 2, least-squares refinement was carried out. Assuming isotropic temperature factors, the R index was Least-squares refinement with anisotropic temperature factors again produced non-positive definite temperature factors for the lighter atoms. Hence only the Cr, S and P atoms were refined with anisotropic temperature factors. The R value was The general features of the molecular geometry and the crystal packing could be seen, however, the molecular geometry was unsatisfactory, e.g. some C- O and C-C distances are either too long or too short. Number of observation (1095 reflections) was small compared with the number of parameters (235-assuming anisotropic thermal factors for all the nonhydrogen atoms, or 164-assuming anisotropic thermal factors only for the heavier atoms). All the computations in Experiments 1-3 were carried out either on a PDP11 or a VAX750 using SDP system [5]. 4.4 Experiment 4 (Data 4) Finally, intensity data were collected on a Rigaku AFC5R using a rotating anode Mo Kα radiation (60 kv, 150 ma) at Rigaku in Tokyo. A crystal of dimensions 0.03 x 0.11 x 0.38 mm was employed. Cell parameters were determined using 25 relatively lower order reflections and again a C-centered orthorhombic system was indicated. This was altered to a primitive cell of the same size. Cell parameters were later refined employing 24 higher-angle reflections with 30 < 2θ < 40. Crystal Data-CrS 6 P 3 O 6 C 12 H 24, F.W , Crystal system: orthorhombic, a=11.699(l), b= (2), c=16.827(2)a, V=2507.6(6) Å 3, Space group P , Z=4, D calc =1.59gcm -3, F(000) = 1236, µ (MoKα)=11.69cm -1. Intensity data were collected using a 2θ - ω scan mode up to 2θ = 65.1 at room temperature (23 C). Out of 5085 independent reflections, only 1537 had I> 3µ(I), and on relaxing the condition to I> lµ(i), still only 2170 reflections satisfied the condition, although this was far better than the previous data sets. The structure determination was begun afresh rather than using the atomic coordinates obtained from the previous work. Computations were carried out on a microvax11 using Texan system [6]. The position of the Cr atom was located from the sharpened Patterson synthesis, at (-0.75, -0.0, ). Scale factor refinement including only the Cr atom produced an R factor of The R factor after the refinement of the coordinates went down to Difference Fourier synthesis based on the Cr phase (0.734, 0.012, 0.259) revealed six S atoms octahedrally coordinated to the central Cr atom as well as six peaks corresponding to P atoms, though three of which should be ghost peaks. After the refinement of positional and isotropic thermal parameters of one Cr, six S and a correct set of three P atoms, the R value decreased to A series of Fourier and differential Fourier syntheses gradually revealed all the nonhydrogen atoms. Isotropic refinement at this stage gave an R value of Anisotropic temperature factor refinement reduced the R factor to 0.112, however, six lighter atoms had non-positive definite temperature factors. Hence only ten heavier atoms were refined anisotropically. The R value was Neither empircal absorption corrections nor extinction corrections improved the situation. No outstandingly strong peaks corresponding to solvent molecules nor disordered atoms were seen in the difference Fourier maps. Relocation of several lighter atoms at the positions found in the differential Fourier maps which were calculated omitting the atom concerned was not successful. Changing of the space group from P to P22 1 2, P222, etc. was also unsuccessful. The general features of the crystal structure had become clear by this approach, but the molecular geometry was not satisfactory, e.g. giving C-C distances of 1.76 and 1.21 Å. In fact, the data set from Experiment 2 or 3 using either a Cu Kα or a Mo Kα source from a sealed tube had already revealed the crystal structure and encountered the same problem, i.e., the final R index was as high as or and nonpositive definite temperature factors were observed for several lighter atoms. 24 The Rigaku Journal

4 Each of the first three experiments had a drawback of a different type, which could be blamed for the difficulty in obtaining the crystal structure. The reflection data set from Experiment 4 on the other hand was free from these drawbacks and yet encountered the same difficulty. It seemed that this trouble did not arise from a) poor crystal quality as in Experiment 1, nor b) strong absorption effect as in Experiment 2, nor c) weak intensity data (not enough observed reflections with respect to the number of parameters) as in Experiments 1-3. I had to reanalyse the problem. 5. Analysis and Solution Four positions of the Cr atom in the unit cell are ( 0.75, -0.0, -0.25), (-0.75, -0.0, -0.75), (-0.25, -0.5, 0.75), and (-0.25, -0.5, -0.25), possessing similar values for the coordinates. Not only that, the Cr-S bonds of the four molecules in the unit cell are almost parallel to each other. Thus, strong correlations among the parameters could hamper the least-squares refinement of the structure as experienced in the case of Cr(acac) 3 [3]. In that circumstance, alteration of the starting coordinates of least-squares refinements is often a useful tactic, as the structure might have converged to a local rather than a global minimum. The analysis of R factors for even/odd combinations of Miller indices exhibited a striking feature, i.e. only the reflections of h+k= odd had a much higher R factor of 0.244, as compared with the total R value of (see Table 1). Reflections with h + k = odd are related to C centering. Many reflections which exhibited poor Fo - Fe agreement had Fo > Fc, which indicates that the structure obtained by the calculations is closer to a C-centered one than it really is. In this space group and structure, a C-centered-like struc-ture could be violated if the whole molecule is translated along the crystal a or c axis, or when the molecule is rotated about an axis parallel to the a or c axis. The R factor of suggested that the structure so far obtained was not far removed from the true one. Shifting of the whole molecule means translation of the chromium atom as well, thus the effect on the R factor could be quite large. On the other hand, rotation of the whole molecule about the chromium atom would not affect the position of the heavy-atom, hence this approach appeared more promising. The molecule was rotated about an axis which is parallel to the crystal c axis and through the Cr atom. After applying a 5 rotation to all the atoms, several cycles of least-squares refinements were carried out carefully observing the movement of the R indices Table 1 Analysis of R factors for even/odd combinations of Miller indices, when the structure was converge on R value of classified according to the even/odd combinations of Miller indices. First, the R factor went up to 0.234, however, after four more cycles of least-squares refinement, the total R index went down to 0.07 and the R index for the reflections with h+k=odd to Further three cycles reduced the R factor to The geometry of the structure, was greatly improved compared with that with R= Using anisotropic temperature factors for all the non hydrogen atoms, least-square refinements were carried out to give an R value of All the thermal factors were normal with no non-positive definite temperature factors for any atom. A difference Fourier map at this stage did not reveal hydrogen atoms, hence they were generated assuming an idealized geometry. These hydrogen atoms were included in the calculations but not refined. The final R factor was for the reflections with I> 3σ(I). Comparison of the final atomic coordinates with those of the false minimum (R=0.124) is given in Table 2 and Fig. 2. None of the y and the z coordinates were shifted. Only the x coordinates of five atoms had substantial shifts: the largest shifts are 1.05 and 0.78 A for C3 and O4 respectively, and the other three atoms were shifted by ca Å Six other atoms were shifted by ca. 0.2 Å along the a axis, but the rest hardly moved. These shifts could be best explained as a rotation about an axis parallel to the c axis and through the chromium atom, although the y coordinates are not much shifted (Fig. 2). R No. of reflections h even h odd k even k odd l even l odd h+k even h+k odd h+l even h+l odd k+l even k+l odd h+k+l even h+k+l odd Total Vol. 6 No

5 Table 2 Compairson of positional parameters when the structure was at a local minimum of R=0.124 and when the structure was refine to an R value of Differences given in Å. Atom x y z Cr S(1) S(2) S(3) S(4) S(5) S(6) P(1) P(2) P(3) O(1) O(2) O(3) O(4) O(5) O(6) C(1) C(2) C(3) C(4) C(5) C(6) C(11) C(21) C(31) C(41) C(51) C(61) Conclusion The crystal structure of {Cr[(-)bdtp] 3 } was solved in the end. The structural details and comparison of the crystal packing mode with that of other optically active D 3 metal complexes will be published elsewhere. I shall finish this article by making a few comments. The structure of the crystal turned out to be fairly close to a C-centered one, as seen in Fig. 3. Therefore it is not surprising that a C-centered cell was indicated on each data acquisition by the diffractometer software. This is a warning to the many users of diffractometers nowadays who blindly trust the output of their machine and start a data collection automatically without prior checking of the crystal by photography. Some crystal structures may converge with a relatively high R factor, even though all the nonhydrogen atoms have been located. There are several reasons for this. It may be due to a disorder or bad quality of intensity data arising from small crystal size, a non-single (split) crystal, a crystal decay or a strong absorption effect, etc. Even after correcting all the obvious sources, the R factor may be still higher. In that case, analyses of R factors are quite useful. Most computer programmes provide analyses according to sin θ and the magnitude of F's. In the present case, these did not help. Instead, an analysis of R factors according to even/odd combinations of Miller indices, supplied in Texsan programme, was very suggestive. Clearly, in some instances it is important to analyse these statistics carefully, in order to obtain the true structure. Fig. 2 Comparison of atomic coordinates when the structure is in the local minimum and when the structure is in the global minimum. The arrows indicate the sifts in the c axis projection. Hardly any shifts were observed in the c direction. 26 The Rigaku Journal

6 Fig. 3 Crystal packing of (+)589-{cr[(-)bdtp]3}. References [1] R. Kuroda, S. F. Mason, C. D. Roger and R. H. Seal, Mol. Phys., 42 (1981), 33. [2] R. Kuroda, in preparation. [3] R. Kuroda and S. F. Mason, J. Chem. Sec. Dalton, (1979), 273. [4] P. Biscarini and R. Kuroda, Inorg. Chim. Acta, 154 (1988), 209. [5] B. A. Frenz, Enraf-Nonius Structure Determination Package, (1980), Enraf-Nonius, Delft, Holland. [6] TEXSAN Structure Analysis, (1987), Molecular Structure Corporation, Texas, USA. [7] C. K. Johnson, ORTEPII, (1976), Report ORNL-5138, Oak Ridge National Laboratory, Tennessee, USA. (Received August, 1989) Vol. 6 No