2160
J. C. A. BOEYENS AND F. H. HERBSTEIN
Molecular Compounds and Complexes. 111. The Crystal Structures of the Equimolar *-Molecular Compounds of Anthracene and Perylene with Pyromellitic Dianhydridel
by J. C. A. Boeyens and F. H. Herbstein Chemical Physics Group of the National Physical and Chemical Research Laboratories, Council for ScientifLc and Industrial Research, Pretoria, South Africa (Received November 9, 1964)
A full three-dimensional X-ray diffraction analysis (by least squares, with anisotropic temperature factors) has been made of the perylene-pyromellitic dianhydride (PMDA) molecular compound. A limited two-dimensional analysis of the structure of anthracenePMDA is also reported. Both analyses were of the crystal structures a t 300°K. Accurate molecular dimensions were obtained in the first, but not in the second, of these analyses. The dimensions found for the perylene molecule agree well with those 111 perylene itself and in perylene-flwranil. The dimensions of the P,MDA molecule agree reasonably well with those of benzene and maleic anhydride. The molecular arrangements in both structures are of the mixed stack type familiar from earlier crystal structure analyses of other members of this group of molecular compounds. Within a particular stack the relative disposition of the two components resembles, in both structures, that of adjacent layers in graphite.
Theory2 predicts and experinien t3-10 confirms that the crystal structures of the n-molecular compounds formed between electron donors such as aromatic hydrocarbons and various electron acceptors have the common feature that the component molecules are arranged, plane to plane, in alternating array in mixed stacks. There is, as yet, no detailed theoretical guide to the relative arrangement of the component molecules within the stacks and the experimental results show a variety of mutual orientations. Thus the details of the arrangement within the stacks, which should be helpful in interpreting the interaction between the components, must be determined experimentally. We have therefore analyzed the crystal structures of the equimolar molecular compounds formed between pyromellitic dianhydride" (PMDA), a powerful electron acceptor, and the electron donors anthracene and perylene. The relatively high symmetry of the components and the absence of substituents should simplify the theoretical interpretation of the results. The analysis of the anthracene-PMDA molecular compound has The Journal of Physical Chemietry
only been taken far enough t,o establish the main features of the molecular arrangement, but the perylene(1) Part 11: J. C. A. Boeyens and F. H. Herbstein, J . Phys. Chem., 69, 2153 (1965).
(2) R. S. Mulliken, J . A m . Chem. SOC.,74, 811 (1952) (3) pIodoaniline-1,3,5-trinitrobenzene:H. 11.Powell, G. Huse, and P. W. Cook, J . Chem. Soc., 153 (1943). (4) Hexamethylbenzene-picryl chloride: H. LM.Powell and G. Huse, ibid., 435 (1943). (5) Hexamethylbenzene-chloranil: T. T. Harding and S. C. Wallwork, Acta Cryst., 8 , 787 (1955); N. D. Jones and R. E. Marsh, ibid., 14, 809 (1962); S.C. Wallwork and T. T. Harding, ibid., 15, 810 (1962). (6) Pyrene-1,3,7,9-tetramethyluric acid: P. De Santis, E. Giglio, A. M. Liquori, and A. Ripamonti, h'ature, 191,900 (1961); A. Damiani, P. De Santis, E. Giglio, A . M . Liquori, R. Puliti, and A. Ripamonti, Acta Cryst., 16, A57 (1963). (7) Perylene-fluoranil: A. W. Hanson, ibid., 16, 1147 (1963). (8) Anthracene-l,3,5trinitrobenzene: D. S. Brown, S. C. Wallwork, and A. Wilson, ibid., 17, 168 (1964). (9) Skatole and indole with 1,3.5-trinitrobenzene: A. W. Hanson, ibid., 17, 559 (1963). (10) S. C. Wallwork, J . Chem. Soc., 494 (1961). (11) L. L. Ferstandig, W. G. Toland, and C. D. Heaton, J . A m . Chem. 99c., 83, 1161 (1961).
CRYSTAL STRUCTURES OF EQUIMOLAR PMOLECULARCOMPOUNDS
PMDA molecular compound has been the subject of a full three-dimensional least-squares analysis with anisotropic temperature factors. These analyses are both of the room temperature structures of the molecular compounds.
The Crystal Structure of Anthracene-PMDA Experimental The equimolar molecular compound of anthracene and PMDA crystallizes as red triclinic needles from methyl ethyl ketone (previously dried with CaC12). Observation under the polarizing microscope shows these crystals to be twinned macroscopically but single crystals were easily obtained by splitting a twinned needle. Single crystals were elongated along [OOl ] and showed (loo), (OlO), and (210) faces. Standard X-ray diffraction techniques (oscillation, Weissenberg and precession photography with nickelfiltered Cu K a radiation) were used throughout this work. Cell Dimensions and Space Group. Following standard practice,12a primitive reduced cell was chosen with c < a < b and a , p, y > 90’. The value of [OOl], which lies along the needle axis, was determined directly from an oscillation photograph and a*, b*, and y* were determined from the corresponding zero-layer Weissenberg photograph. The angles a and 0 were determined by the method of level offsets,13using zero- and first-layer Weissenberg photographs. The remaining dimensions were calculated from standard formulas. The results were: a = 7.6 a* = 0.1556 k - l ; b = 10.0 8., b* = 0.1103 c = 7.3 A., C * = 0.1645 A,-’; a = 105”, a* = 67.5”; p = 115.5”,p* = 60”; y = 101”, y* = 70”. The measured density was 1.49 g. cm.+. With one molecule of each component per unit cell, the calculated density is 1.48 g. cm.-3, which is also the mean of the densities of the components in crystalline form. There are no systematic absences and the possible space groups are P1 and Pi. The latter was considered more probable because both components are centrosymmetric (see discussion of space group of naphthalene-PMDA in ref. 1) and this choice was vindicated by the success of the subsequent crystal structure analysis. On this basis the centers of both molecules must lie a t crystallographic centers of symmetry; consideration of cell dimensions and molecular shapes suggested that the anthracene molecules were centered a t (000) and related positions and the PMDA molecules a t (OOl/,) and related positions. Intensity Measurements. The intensities of 152 hkO reflections (38 with l o b a d = 0 ) and 184 hkl intensities (31 with l o h a d = 0) were measured visually from
s.,
2161
equi-inclination Weissenberg photographs taken with Cu K a radiation. The crystal used was approximately cylindrical in shape and was thin enough to warrant neglect of absorption corrections. Corrections for Lorentz, polarization, and spot-shape factors were applied using appropriate computer programs (the computer programs and other relevant information for both structure determinations are summarized below).
Determination and Refinement of Structure Comparison of the hexagonal distribution of near-in vector peaks in the hkO Patterson projection with the intramolecular vector patterns of the two molecules led to a trial structure which was substantiated using the Fourier transform m e t h ~ d . ’ ~ , ’The ~ molecular orientations were derived by comparison of the measured unitary structure factors for 51 low-index hkO reflections with values calculated from the transforms of the two molecules. Reasonable agreement for these reflections (R = 38%) supported the postulated structure. This structure was then refined by Fourier and difference syntheses until R(hk0) = 21%. The Fourier projection at this stage is shown in Figure 1. The positions of all atoms were further refined by least squares, using individual isotropic temperature factors, This reduced R(hlcO) to 15%. The z coordinates were calculated on the basis of standard molecular dimensions and refined by a trial and error procedure, R factors for hkl reflections being calculated for a series of tilts of the planar molecules to the (001) plane. The over-all R factor for the best coordinates was 18.5% (336 hkO hkl reflections, individual B factors), which was considered adequate to demonstrate that the phase problem had been correctly solved. The atomic coordinates are listed in Table I (see Figure 2) and observed and calculated structure factors are given in Table 11. Interatomic distances and angles are reasonable but are not accurate enough to warrant listing here.
+
Molecular Arrangement The molecular arrangements in projection down the three principal crystallographic axes are shown in Figure 3. The molecules are arranged in mixed stacks whose axes lie along [OOl]. These stacks are all (12) “International Tables for X-Ray Crystallography,” N. F. ,I4 Henry and K. Lonsdale, Ed., Vol. 11, Kynoch Press, Birmingham’ England, 1969,p. 106. (13) M. J. Buerger, “X-Ray Crystallography,” John Wiley and Sons, Inc., New York, N.Y.,1942,p. 375. (14) G.Knott, Proc. Phys. SOC. (London), 52, 229 (1940). (15) H.Lipson and C. A. Taylor, “Fourier Transforms and X-Ray Diffraction,” G. Bell and Sons, London, 1958.
Volume 69,.Vumber 7
J u l y 1966
2162
J. C . A. BOEYENS AND F. H. HERBSTEIX
\
Table I: Fractional Atomic Coordinatesa Atom
z
a,
-0.163 0.033 0.084 0.272 0,440 0.405 0.204 -0.174 0.022 0.189 0.104 0.365 0.005 0.305 0.545
2
0.055 0.146 0.301 0.382 0,327 0.185 0.094 0.049 0.143 0.093 0,299 0.216 0.381 0.335 0.226
-0.098 0.134 0.231 0.485 0.549 0.440 0.215 0.395 0.610 0.738 0.752 0.923 0.756 0.955 0.080
a Letter subscripts refer to the anthracene molecule and numeral subscripts refer to PMDA; the system used is shown in Figure 2.
metry. The plane of the anthracene molecule is given Figure 1 . Fourier projection down [OOl] showing overlapping PMDA and anthracene molecules.
+
0.6806~ 0.5506~- 0.4834~= 0 where u,v, w are orthogonal coordinates (in A.) related to the fractional coordinates x, y, z of the atoms in the triclinic axial system of the unit cell by the equations
u
= za
+ yb cos y + zc cos p
u = yb sin y - zc sin
w
= zc
sin B sin
p cos a* CY*
In the same set of orthogonal axes, the equation of the plane through t,he PMDA molecule is
+
0.6837~ 0.5483~- 0.4816~:= 3.234
Figure 2. Nonienclature of atoms and molecular axes of PMDA, anthracene, and perylene.
crystallograpliically identical, with any particular stack being siirrourided by six others in quasi-hexagonal array. The inclination of the molecular planes to the stack axes is such that some measure of interleaving occurs. The molecules were assumed to be planar and parallel, although this is not required by the crystal symThe Journal of Physical Chemistry
The small deviations from strict parallelism of the two molecules are due to approximations made in the derivation of the z coordinates of the atoms. The mean interplanar distance is 3.23 8., which is compared with other relevant values in Table XI. The molecular arrangement seen in projection onto the plane through the anthracene molecule is shown in Figure 4. No significance should be attached to the deviations from regularity that are evident in this figure; they result from the incompleteness of the refinement. The relative arrangement of carbon atoms of the two adjacent molecules is similar t o that in successive sheets of graphite.
CRYSTAL STRUCTURES OF EQUIMOLAR T-MOLECULAR COMPOUNDS
2163
~~
Table I1 : Observed and Calculated Structure Factors for Anthracene-PhIDA
2 -I2 0
3.6
3
4.5 6.0
-2.8 -3.0 -5.1
0 -11 0 I 2 3 4 5 6
4.4 2.1 2.2
-3.3 1.1. -1.7
2.2
-0.6
2.1 1.9 2.7
-1.4
0 -10 0 1
2.3 2.5 3.5 2.5 2.4 4.6 6.9 4.0
I .5 -1.5 -3.5 -2.5 2.2 -2.4 -4.6
16.1 7. I 4.5 6.7
-16.4 -5.2 -2.5 6.5 0.5 -1.1 -1.2
4
2 3 4 5 6 7
I -9 0 2 3 4 5 6 7 1
-8 0
3.6 3.3 1.9
6.8 9.3
2.2
-1.4
8
4.0
4.2
I
-7 0
2 3 4 5
6 7
8 I
4
0
10.7 2.2 18.2 9.7 2.6 11.1 5.2 1.8
9.4 -1.0 18.5 8.5 0.7 -ll,4 -4.0 2.2
-8.8
2
9.4 13.7
3
8.1
4 5 6 7 8
5.8 9.3
I 2 3 4 5 6 7 8
3.6 4,9 2.0 -5 0
33.9 11.9 10.0 4.6 2.3 2.6 5.7
2.1
-11.9 7.5 5.5 -9.7 -3.5 -2.2 1.9
-3.8 11.2 7.1 5.1 -1.9 3.3
16.7
2.2 10.5 2.6
6.6 -3 0
-17.2 3.9 -18.3 -14.5 -1 .o -13.1 -3.4 4. I
3 4 5 6 7 8
I -2 0 2 3 4 5 6 7 8
8.2 28.5 12.5 4.9 8.4 17.5 2.5 2.0
9.9 -25.5 -14.0 -4.0 8.3 21.9 2.0
I -I 0 2
55.0 12.7 13.1 12.0 16.2 13.3 3.5 I .8
2
20.7 13.1 2.5
10.0
n.0
12.0 -21.5 -16.1 -7.3 -0.9 1.4 8.3
-1.3
4 5 6 7
20.9 1.5
14.4 19.5 17.0 8.8 2.2 3.4 6.8 4.5
I
-4. I
-4 0
4 5 6 7 8
0.1
4.1 6.7 17.6 18.2 11.8 -0.9
2 3
I
2 3
3 4 5 6 7
8 1 0 0 2
3 4 5 6 7
8 0 I 2
1 0
27.8 13.1 9.0 2.5 2.2
5 6 7
3 4 5 6
25.5 32.5
l0,2
3 4
0 I 2
22.0 15.5 4.0 5.2 9.4 4.5 2.3 2.7
2 0
-3.2
-1.0 M.7
-11.1 12.9
10.5 16.3 12.0
-3.3 -1.8 24.7
12.3 3.1 6.0 9.8 6.0 3.1 -3.6 23.8 -34.7 -7.6 -18.0 -17.5
10.6 I .o -2.0
33.6 33.2 27.1 13.1 8.4 5. I
-35.7 33.2 -24.6 -12.4 8.5 5.5
5.1
4.3
2.0
-2.1
0 1
3 0
2 3 4 5
6
2.3 2.2
7
0 I 2
4 0
2
0 6 0 I 2 3 4 5 7 0
2 3 4
0 I
8 0
2
0
7.8
0.8
8.9
-4.1
3.8
3.6
6.7 11.0 1.6 4.6 2.3
8.0 11.6 1.3 -4.0
2.0 3.9 17.6 13.8 3.5 2.0
1.9 5.9 19.2 14.5 -3.1 -2.8
9.8 12.1 14.8 3.6 2.1
-10.1 13.1 15.3
4.5
-4.0
8.3
10.2 2.8
2.5 2.2
3 9 0
5.2
2.1
10.2
5 0
17.4 -9.3 5.2 2.5 -16.5 -1.8 -2.2 -22.9 -25.3 -a6 -9.6 -12.7 -9.1
1.9 9.2
3 4 5 6
0 1
27.1
21.0
3 4 5 6 0 I
19.7 7.0 9.5 6.3 2.3 14.7
3.0
1.7
-2.3 -3.5
-0.5
0.6
4.3 2.2
-1.9
2 4 -12 I
3.0
2.0
4 -11 1 5
I.o 4.0
0.2 -2.1
4 -10 I 5 6
6.2 1.1
4,9 -1.8 2.6
4 -9 I 5 6 7
4.7 3 7 1.1
1
3.6
0.8
0.3
-4.3
-3.3 0.2 0.9
4 -8 I 5 6 7
11.0
3 -7 1 4 5 6
7.7
-11.9 8.6
2.2 I.o
-0.8 -0.6
7.9 7.0 6.2 3.4 I.o
-7.7 7.2 4.6 4.6 0.3
3 -6 I 1 5 6 7
7.6 4. I 10.6 4.7 1.6
4.0
3 -5 I 4 5
0.9 2.9 4.7 8.1 2. I
1.7 5.7 10.3 -1.7
3.2
2.0
3.7 7.2 2.6 1.1
3.6 6.8 4.0 -1.6
7
6 7
3 - 4 1 4 5 6
7
3.4
-13.8 3.4 I .o
1.7
2 -3 I 3 4 5 6 7
20.9 13.3 10.9 3.1 1.6
1 .o
2 -2 I 3
17.7
21.3 .0.6
4 5 6 7
1.3 1,6
1
7 2 I
2 3 4 5
6 7
0.8 2.6 5.2
I -1 2 3 4 5 6
-3
3.2
2.6 6.8 1.8 I. 5
10.8
-14.5
4.1 17.4
6.0
11.1 9.7 1.8
1.0 0 1
-21.6 12.9 -13.8 -1.0 -3.9
1.8 3.6 3.8 4.3 5.6 4.4 5.5
1.2 1.3
-22.6 11.6 -11.0 -2.7 4.4
0.8 3.6 4.2 -6.1 6.0
4.3 -7.4 1.5 0.7
-4 3 2
19.0 8.7 5.4 8.5 10.7 4.1 3.2 9.0 11.0 5.6
I 1
I 0 I 2
3 4 5 6 7 -5
2
-4
3 2 I 0 I
2
3 4 5 6
3.6 2.2
21.7 -8.0 4.5 11.1 12.3 4. I -I .9 10.6 -10.9 5.9 0.8 2.0
5.7 15.2 13.1 13.9 8.4 24.8 5.0 3.8 6.3 I. 2 2.4 1.5
3.7 -15.9 -12.3 -12.3 6.2 -31.5 -1.1 -4.6 4.1 -1.6 0.5 4.4
4.2 8.4 6.7 19.0 9.0 2.5 13.9 13.7 4.5 3.7 5.2 3.0 2.8
4.7 6.4 -5.0 20.5 6.4
-7
6 1
4 5 4 3
2 I
0 1 2 3 4 -7
7 I
4 5 -4 3
2 I 0 1 2
7 1
3 4
4 3 1 5 -4 3 2 1 0 I
2 3 4 5 6
-7 5 r(
5 4
3 2 I 0 1 2
4.4 8.2 5.7 6.6 14.6 IO I 4. I 8.4 6,4
2.7 5.7 7.4 7.5
3
1.2
2 I 0 1 2 3
10.7 7.2 2.4 I .2 1.1 2.3
1 .o
-0.6
6.0
4.7
4
I.6
2.2
1.2
5
1 2
6.7 15.8 7.4 14.8 15.2 13.7 7.4
5.2 -11.7 4.8 -7.4 14.6 -14.6 5.5
-4
3.5 7.3 3.0 4.0 5.6 1.5 2.0
0.5 -1.0 I. 9 6.0 0.9 4.4 6.2 -1.0 -1.1
1.2 2.6 1.1
4 . 4 -1.7 -1.0
9 I
3
2 I
0 I
2 -7 I O 1
3 2
3.6
5 4
4 1 14.6 5.6
I
2.6 1.7 0.7
I .2
2.8 -2 2 -12.4 -5.3 7.9 -6.0 4.9 -3.0 1.7 -3.1 -0.7
0.9
I,3
4 5 4
8.3
I 0
6.7 7.0 2.2
-3.6 -0,3
1.0 -5.8 5.7 4.3 -1.9 10.4 .5,9 -1.2 0.3 1.9 -1.9
9.5 14.2 5.1 3.6 6.7 -1.2 2.7
-8.0
3 2
4.3 -5.7 -1.7
3.0
5 I
4.5 -9.7 -7.0 3.7
-0. I -1.9
8.9
-7
4.3 -8.7
-3.2
1.1 0.8
4
4 1
5.7 17.9 -5.4 7.9 .1.3 8.2 4 6 4.7 1.9
2.3
3.7 1.0 1.1 1.1 5.4
3 4 5
I.o 10.3 -10. I
3.3
-7
4 4 1
8 I
4
1.8 11.5 9.2 9.8 21.6 5. I 11.7 1.1 11.7 5.6 4.5 I O
6.2
4 2
0 I
d /I I
3.4
5
2.1
3 2
0.9 3.9 1.8 1.6
I
-3.8 1.1 0.4 2.3
-2.1 -3.3 2.9
-0.8 -2.3 4.0 2.1
-0.8 2.9 0.4 3.4
' ~
.
Crystal Structure of Perylene-PMDA Experimental The perylene-PMDA molecular compound crystallized from glacial acetic acid as long black needles (m.p. 287"), elongated along [OlO] and bounded by (loo), (201), and (001). The crystals shattered on cooling to 100'K. and thus, despite the large thermal vibration, the present analysis had perforce to be carried out at room temperature. Accurate cell diniensions were determined from backreflection Weissenberg photographs (a, c, p) and Mathieson-adaptor rotation photographs ( b ) using methods described previously. l6 The values and their estimated standard dzviations a t 20" were found to be (Cu K a , = 1.54!50 A.; CU Kan = 1.54436 A,): a = 14.613 f 0.003 A . , 6 = 7.16 f 0.01 c = 10.1309 * 0.0004 A,, and = 94.67 * 0.03". (The difference
s.,
in the accuracies of a and c is due to a lack of suitable reflections with large h.) Pmeasd
Pcalcd
(for 2
= =
1.50 g. CmP3 2)
=
1.504 g.
mi.-3
The space group was uniquely defined by the systematic absences as Czh6-P2Jn. The intensities of 1545 hkl refleelions (358 with lobad = 0) were measured visually, using equi-inchriation Weissenberg photographs taken with Cu K a (nickel filter). The crystal used was approximately cylindrical in shape and was thin enough t o warrant neglect of absorption corrections. Lorentz, polarization, and spot-shape corrections were applied using standard computer programs. (16) F. H. Herbstein, Acta C T y 8 t . , 16, 265 (1963).
Volume 69, Sumber 7
J u l y 1966
J. C. A. BOEYENS AND F. H. HERBSTEIN
2164
m
I1 I
thermal scattering on the second layer lines of [OlO] oscillation photographs suggested that the b axis is approximately normal to the molecular planes. The intramolecular vector pattern of perylene has a well-defined hexagonal arrangement of peaks (Figure 5a) whereas that of PMDA (not shown) is relatively featureless. The hexagonal peak pattern in the Patterson projection down [OlO] (Figure 5b) thus allowed the orientation of the perylene to be limited to three possibilities but gave no information about the PMDA. The Fourier transform^'^^'^ of both molecules were then calculated and unitary structure factor values derived for various molecular arrangements compared with measured values for 32 low-index h01 reflections. The strong reflection (303)provided crucial evidence for the orientation of the PMDA molecule, as it was clear from the transform that the perylene contribution to this reflection had to be small. The PMDA orientation was thus determined by the transform method to within a
C
0 oxygen o carton 0
suwrposed carbons
,JA,
Figure 3. The arrangement of PMDA and anthracene molecules in the unit cell as seen in projection down the three crystallographic axes. In (iii), greater clarity has been obtained by omission of molecules a t two of the cell corners. The centers of the molecules drawn with full circles are in the plane of the paper while those with open circles are one-half of the appropriate translation above (or below) the plane of the paper. This convention has also been used in other diagrams in this paper.
Q
W
w -
(b) t
C
Figure 4. The molecular arrangement in anthracene-PMDA seen in projection onto the plane of the anthracene molecule. The PMDA molecule is 3.23 A. above the anthracene molecule.
Determination of Trial Structure. The presumption that mixed stacks be formed and the mitations liimposed by the molecular shapes and sizes required that be centered at the the component posit'ions (000, '/2'/z1/2) and ('/201/2, 01/20) of the space group. The length of b and the presence of strong The Journal of PhysicaE C h m d r y
aFigure 5. (a) The arrangement of peaks and their relative weights in the int~amolecularvector Pattern of the (idealized) perylene molecule. (b) The Patterson projection down [OlO] for perylene-PMDA. Contours are a t equal but arbitrary intervals; the origin peak (center of the diagram) has been omitted.
CRYSTAL STRUCTURES OF EQUIMOLAR a-MOLECULAR COMPOUNDS
2165
few degrees but three possibilities remained for perylene. Calculation of intermolecular distances showed that only the molecular arrangement shown in Figure 6 (projection down [OlO]) was acceptable. The initial R factor for the h01 reflections was 30% and this was refined by Fourier and difference syntheses to 25%. The y coordinates of the atoms were calculated assuming standard dimensions for both molecules ; the angle between their (parallel) planes and (010) was calculated to be 18". At this stage structure factors were ea$lated for all 1545 hkZ reflections using ( B ) = 3.9 A.2, and R(hk1) = 35% was obtained.
Refinement of Atomic Parameters Further refinement was carried out by least squares, &,klw(F, - kF,12 being minimized. The weighing scheme originally suggested by Hughes" was used. At first, individual isotropic temperature factors were used for all atoms other than the hydrogens, which were omitted throughout. One cycle of refinement under these conditions reduced R(hkZ) to 27%. The diffuse scattering on the photographs suggested that the structure was subject to much thermal vibration and individual anisotropic temperature factors were therefore introduced a t this stage. This meant that there were 167 paramerers to be adjusted, whereas the capacity of the 8K IBM 704 at our disposal was only 120 parameters. Accordingly, the refinement was carried out pieceurise, three groups of six atoms being chosen at random for each cycle. For each group, the 54 positional and temperature paramerers were refined together with five scale factors. The mean values of the refined scale factors and the new atomic parameters were then used as input data for the next cycle. The values of R(hkl) and Rl(hkZ) obtained for a series of cycles are given in Table 111. After R(hkE) had fallen to 17.6% all structure factors were printed out and some human errors in the preparation of the input data were
Table 111: Variation of R(hkl) = ( Z A F / Z F , ) and = . \ / ~ w ( A F ) ~ / ~ w F , , for Z ) a Series of Least-Squares Refinement Cycles with Anisotropic Temperature Factore Cycle
R(hk0, %
Rl(hk0, %
Start
26.6 21.5 19.0 17.6
33.0 25.7 22.2 20.1
1
2 3
Refinement interrupted (see text) Start 15.1 19.2 1 14.5 18.6 2 14.4 18.1
Figure 6. Arrangement of PMDA and perylene molecules in the unit cell as seen in projection down the three crystallographic axes.
corrected. Thirteen reflections suffering from extinction were given zero weight a t this stage. An error in the most probable values assigned to the intensities of the 358 reflections with Iobsd = 0 was also corrected. Use of '/$min instead of l / 2 I m i n led to an appreciable improvement in the agreement between /Fobsd/ and IFcalodl for these reflections. This change is in satisfying accord with theory.I8 A three-dimensional difference synthesis was also calculated a t this stage. There were no significant features as the excursions of the difference electron density did not exceed 0.3 electron A.-3. Failure to detect the hydrogen atoms can probably be ascribed to the relatively large thermal vibrations. A new series of refinements was then carried out on the corrected data (lower part of Table 111). The final atomic parameters and their standard deviations are given in Table V and observed and calculated structure factors (on an absolute scale) are listed in Table IV. When refinement was stopped, the shifts in atomic parameters were less than one-tenth of their standard deviations. It is noteworthy that the positional parameters changed very little during the refinement, the differences between a set of early coordinates and the final coordinates being summarized in Table VI. Thus the structure was essentially correct a t R 30y0 and the subsequent refinement to R 14% consisted primarily in taking the thermal motion into account.
- -
(17) E. W. Hughes, J . A m . Chem. ~ o c . 63, , 1737 (1941). (18) w. c. Hamilton, Acta C ~ y s t . ,8 , 185 (1956).
Volume 69,Number 7 July 1966
2166
Analysis of Thermal Motion. The thermal motion in the crystal was analyzed by the methods described by C r u i c k ~ h a n k ,assuming ~ ~ ~ ~ ~ that the molecules vibrated as rigid bodies and that intramolecular vibrations could be neglected. The translational tensor components Ti, and the librational tensor components wi, derived from the b,, thermal-vibration parameters are given in Table VII. The standard deviations of these components were obtained by comparing observed and calculated values of U,, (Table VIII) and are also given in Table VII. Separate sets of tensor components are given for each molecule and refer, of course, to the two different sets of molecular axes. For both molecules the off -diagonal terms are not significant and therefore the principal axes of the thermal motion coincide with the molecular axes within experimental error. The translational and librational amplitudes of vibration of the two molecules are summarized in Table IX. The in-plane translations are rather larger than those perpendicular to the molecular planes, but the translational anisotropy is not large. Large errors are attached to the librational amplitudes about X and Y axes and their significance is in doubt. The librations in the molecular plane (i.e., about the 2 axis) are well established. As one might expect, the smaller PMDA molecule librates more than perylene. There may well be some interaction between the layer-line scale factors and the temperature factors concerned with vibration in the [OlO]direction because adjustment of intensities on different layers to an absolute scale was not done experimentally. However, interpretation of the thermal vibrations in terms of rigid-body molecular motions does lead to reasonable physical results. The main importance of this for the present paper is to sllow correction of measured bond lengths for thermal libration effects. Correction of Bond Lengths for Thermal Vibrations. The atomic coordinates of Table V must be corrected for apparent inward displacements due to thermal librations.21Jz These corrections have been made by Cruickshank’s revised method,z3using a value of q2 = 0.1 A. to denote the breadth of the (assumed Gaussian) peaks. This value was taken from Cruickshank’s results for anthracene,z1as appropriate electron-density maps were not calculated during the course of the present structure determination. Uncorrected and corrected bond lengths are given in Table X; the changes are small and of the same size as the estimated standard deviations of the bond lengths. Revised values have not been calculated for the bond angles as ahWanCe for thermal librations does not give improved values.24 S7“arY (7.f Computing Procedures Used. These are The Journal of Physical Chemistry
J. C. A. BOEYENS AND F. H. HERBSTEIN
listed in ref. 25, to which reference should be made for details. The accession numbers in the “World List” are given in parentheses to facilitate tracing the entries: correction of intensities, Stantec Zebra program by Smits and Boonstra (3017) ; Fourier-type calculations, IBM 704 program MIFR 1 by Shoemaker and Sly (118) ; Fourier transform, unpublished IBM 704 program by R. A. Clews; least-squares refinements, IBM 704 program ORXLS by Busing and Levy (12) ; processing of results, IBM 704 program ORXFE by Busing and Levy (13); best plane, Stantec Zebra program QCDS 10 by Morgan (not listed); atomic scattering factors, the values given by Berghuis, et aZ.,z6for carbon and oxygen were used.
Results and Discussion Molecular Dimensions of Perylene. These have been determined recently for perylene itselfz7and for perylene in the perylene-fluoranil molecular compound’ so that adequate material for comparison with the present results is available. The perylene molecule is necessarily centrosymmetric in both molecular compounds but not in the polymorph28of perylene studied by Camerman and Trotter. However, in the latter case the deviations from centrosymmetry are not significant (except perhaps for bonds I H (1.428 0.006 A,) and I”’ (1.406 0.006 A.)) and the dimensions have been averaged for convenience. The three sets of molecular dimensions are shown in Figure 7. The differences among the three sets of results are small, except for bonds CD and D E of the present structure. We have no explanation for this except that it may be due to systematic errors. The measured bond lengths in perylene have been compared2’ with various theoretical estimates. The perylene molecule in perylene-PMDA is planar
*
*
D. W. J. Cruickshank, Acta Cryst., 9,747 (1956). D. W. J. Cruickshank, ibid., 9, 754 (1956). D. W. J. Cruickshank, ibid., 9,915 (1956). E. G. Cox, D. W. J. Cruickshank, and J. A. Smith, Proc. Roy. 9oc. (London), A247, 1 (1958). (23) D. W. J. Cruickshank, Acta Cryst., 14, 896 (1961). (24) W. R. Busing and H. A. Levy, ibid., 17, 142 (1964). (25) “International Union of Crystallography World List of Crystallographic Computer Programs,” 1st Ed., D. P. Shoemaker, Ed., (19) (20) (21) (22)
1962. (26) J. Berghuis, IJ. M. Haanappel, M. Potters, B . 0. Loopstra C. H. MacGillavry, and A. L. Veenendaal, Acta Cryat., 8 , 4 7 8 (1955): (27) A. Camerman and J. Trotter, Proc. Roy. SOC.(London), A279, 129 (1964). (28) J . Tanaka, Bull. Chem. SOC.Japan, 36, 1237 (1963). has reported the crystal structure of another polymorph of perylene in which the molecular symmetry is C , . However, the molecular dimensions were not determined with sufficient accuracy to warrant comparison with the other available results.
CRYSTAL STRUCTURES OF EQUIMOLAR 7-MOLECULAR COMPOUNDS
2167
Table IV : Observed and Calculated Structure Factors for Perylene-PMDA
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