358 Robertsort artd White The Crystal Structure of Pyrene. 72. The Crystal Structure of Pyrene. A Quantitative X-Ray Investigation. By J. MONTEATH and J. G. WHITE. ROBERTSON The crystal and moleculaT structure of-pyrene has been determined by quantitative X-ray analysis. The molecular arrangement is more complicated than in anthracene or coronene because the unit cell contains four molecules and these do not coincide with any CrystaIlographic element of symmetry. Nevertheless the final results show that the molecule does contain an inherent centre of symmetry in conformity with the chemical evidence although this centre is not used in building the crystal structure. In the final analysis direct measurements of the positions of 9 out of the 16 carbon atoms can be made from the Fourier maps and the positions of the others can be estimated with a good deal of certainty.The bond-length measurements are not so accurate as in the coronene analysis owing to less favourable resolution and the possible errors may be as much as & 0.03 or 30.04 A. However the most probable atomic positions indicate bond-length variations in different parts of the molecule the distances varying from 1.39 to 1.45~. Details are given in Fig. 4. A rough qualitative explanation of these variations can be given in terms of the 6 stable valency bond structures applicable to pyrene and the usual Pauling-Brockway bond character-distance curve. WE recently made definite measurements of variable carbon-carbon bond lengths in the aromatic hydrocarbon coronene (J.1945 607) and these variations can be given at least a rough qualitative explanation in terms of the 20 non-excited valency bond structures applicable to coronene. A more rigorous treatment of the problem by the molecular orbital method has been attempted by Coulson (Nature 1944 154,797) and these results also receive some support from the X-ray measurements. The extension of such measurements to other condensed-ring aromatic hydrocarbons is obviously a matter of importance but the work is beset with considerable difficulties. The expected bond-length variations (0*01-0*05A.) are of just about the same order as the errors which frequently arise even in careful and reasonably quantitative X-ray work. Further the coronene crystal structure is of a type which yields a particularly clear two-dimensional resolution of all the atoms in the molecule by Fourier series methods and so it represents a specially favourable case for accurate bond-length determination.In the general case we must expect less sharply defined results unless full three-dimensional Fourier methods are employed. For complicated structures the use of such methods is a formidable task and in any case they must be preceded by some preliminary analysis carried out with as much accuracy as possible. In the present paper we describe such a preliminary analysis by two-dimensional Fourier series methods of the crystal structure of pyrene. The arrangement in the crystal is much more complicated than that of coronene because the unit cell contains four molecules and these do not contain any symmetry element.On general chemical grounds one expects the pyrene molecule to contain a centre of symmetry and this is very likely true ; but the molecular centre is found to occupy a general position which does not coincide with any of the crystallographic centres of symmetry. In other words it is not used in building the crystal structure. With regard to the orientation of the molecule in the crystal we find that the inclination of the molecular plane to the symmetry axis is not very different from what it is in coronene or in the phthalocyanines. Nevertheless in our principal Fourier projection (Fig. 2) only 9 out of the 16 carbon atoms are separately resolved owing to the overlapping effects of adjoining molecules.This greatly limits the amount of accurate information which can be derived in a direct manner from the present analysis but in spite of this some significant bond-length variations can be detected and a reasonable model for the whole molecule can be constructed. Description of the Structure.-Crystal data. Pyrene ClsHlo; M 202.2; m. p. 150"; d calc. 1.288 found (Dhar and Guha) 1.27; monoclinic prismatic a = 13.60 50.05 b = 9-24& 0.03 c = 8.37 -J= 0.10 A. p = 100.2" & 0.2". Absent spectra (h01)when h is odd; (OKO) when K is odd. Space-group C;(P2,/a). Four molecules per unit cell. No molecular symmetry. Volume of the unit cell 1035 A.~. Absorption coefficient for X-rays A = 1.54 c~.= 6.76 per cm.; A = 0.71 [-L = 0.86 per cm.Total number of electrons per unit cell = F(000) = 424. Further goniometric and optical crystal data are given by Groth (" Chemische Krystallographie " 1919 5 437) and the crystal structure has been investigated by Dhar and Guha (2.Krist. 1935 91 123). The lattice contents given by Dhar and Guha particularly a and p differ appreciably from ours. Their X-ray work was carried out by means of rotation and oscillation photographs and leads to a determination of the space-group. They suggest [To [19471 A Quantitative X-Ray Investigation. probable arrangements for the molecules in the crystal but the work does not lead to the determination of any atomic positions. Analysis of the structure. We may consider the asymmetric crystal unit to consist of one complete molecule and it is reasonable to assume as a first approximation a regular planar structure in conformity with the chemical evidence.Now the length of the b axis in pyrene is 9-24~.,which is very nearly twice that of coronene (Robertson and White Zoc. cit.) and of phthalocyanine (Robertson J. 1935 615). Both these structures belong to the same space-group but have only two molecules per unit cell. It therefore seemed a reasonable assumption that in pyrene the molecular planes might have a similar tilt to the b axis (about 45') but with two molecules instead of one accommodated in each b translation. These two molecules would be grouped about one crystallographic centre of symmetry. This enables one orientation angle to be estimated; but to specify completely the position of our molecular model in the crystal five degrees of freedom remain viz.two other orientation angles and the co-ordinates (xp,yp,zp) of its centre with respect to the crystallographic origin (centre of symmetry). Another clue to the molecular arrangement is provided by the characteristic appearance of the c axis rotation photograph (see Plate) and by comparison with naphthalene and anthracene FIG.1. 1hA. Periodicities in the anthracene naphthalene and pyrene structures. (Robertson Proc. Boy. SOG.,1933 A 140 79; 142 674). In pyrene there is a tendency for the third and the fourth layer line (I = 3 and I = 4) to be enhanced. The naphthalene photograph is similar while in anthracene the fourth and the fifth layer line (I = 4 and I = 5) are enhanced.The analysis may be carried further by a study of the general reflections from planes beyond the limits of these photographs when it is found that in pyrene and in naphthalene planes with I = 7 and in anthracene planes with I = 9 give enhanced reflections. These results are given more quantitatively in Fig. 1 where CF for a 1.22A:-,-, .fc -----selection of planes are plotted against ZIc for each crystal. There is /-::44 A. clearly an important periodicity at about 1.22 A. on this reciprocal scale \----(1.) in each crystal and a further periodicity at about 2.44 A. in naphthalene and anthracene but this latter periodicity is much less defined in pyrene. Now the width of a benzene ring of radius 1-41A. is 2-44A. and the half width is 1.22 A.It may therefore be inferred that the arrangement of the rings in these crystals is such that the above periodicities coincide at least approximately with the direction of the c axis in each case as indicated in (I). This correlation has been confirmed in the case of naphthalene and anthracene by detailed structure analysis (Robertson EOG. cit.). In pyrene we may expect a less exact alinement and the condensed four-membered ring system will further suppress the 2-44 A. periodicity. The remaining degrees of freedom can be determined with considerable precision from a survey of certain (h02)structure factors for small spacing planes. Absolute measurements show 360 Robertsofl artd White :The Crystal Structure of Pyrefie. Sccr /e 0 I 2 3 4 5A.I ,I,,, ,II,I,II,_-,,,,Ill FIG. 2b. I-Pr0jectio.n along the b axis on the (010)plane. The overla9ping molecules are inclined at about 40" to the projection plane the molecular direction S lying in the projection plane. Each contour line corresponds to one electron per A.=~the one-electron line being dotted. [19471 A Qualztitative X-Ray Imestigatio fi. FIG.3a. FIG.3b. Normal projectiort along the c axis shoevirag the relative positions of 10 molecules. Contour scale as in Fig. 1. that for the (007) (206) (403) (801) (l2,08) and (12,Ol) and (12,02) planes the contributions of many of the atoms must be in phase. A diagram similar to that given for coronene (Robertson and White Zoc. it. Fig. 1) can be constructed from which it is found that only one orientation of the proposed model will satisfy the conditions.Other outstanding features of the spectra are the almost complete quarterings of the (hOO) 362 Robertson and White The CrystaL Strwtwe of PyrePte. and (OKO) series of reflections. This serves to fix the molecular centres at approximately ab S' s (xp= 1.70 A. yp = 1-16A.) from the centre of symmetry. Further calculations show that a small translation along the c axis of about 0.5 A. (zp)is also necessary. Trial calculations based on the above considerations led to excellent agreements between the measured and the calculated values of the structure factor and it was possible to proceed immediately to further refinement of the atomic positions by Fourier series methods.For the principal projection along the b axis 50 terms were included representing separately measured values of the (h0Z)structure factors (Table IV). The results are given by the contour map of Fig. 2(a),from which it can be seen that 9 out of the 16 crystallographically independent atoms are separately resolved. The other atoms are obscured by the overlapping effects of the adjoining molecules as will be clear from Fig. 2(b). The y co-ordinates of all the atoms and the x and z co-ordinates of the 7 unresolved atoms cannot be obtained directly from Fig. 2 but may be calculated on the assumption that the molecule is planar that the L and M axes [Fig. 2(b)] are at right angles and that the molecule is symmetrical about these axes.These assumptions are in conformity with the chemical &evidence, but they receive direct and fairly detailed support from the agreements found between the measured and the calculated values of the structure factor (Table IV) and also from a second Fourier projection of the structure along the c axis which is shown in Fig. 3. For this projection the 36 measured values of the (hkO) structure factors were employed. While no individual atoms are resolved in this projection the separate molecules can be very clearly distinguished and the positions of their centres can be fixed with some accuracy. The general shape of the contours gives very strong support to the assumption that the molecule contains an inherent centre of symmetry even although such a centre is not utilised crystallographically.Orientation co-ordinates and dimensions. By assuming a planar centrosymmetrical model and averaging certain distances as described more fully in the Experimental section it is possible to calculate the orientation of the molecule precisely. The result are given in Table I where x $ and w are the angles which the molecular axes L and M [Fig. 2(b)]and their perpendicular N make with the a b and c' crystallographic axes (c' is the perpendicular to a and b). These results show that the inclination of the molecular plane to the (010)plane expressed by r,h~ is 40.2". This is rather less than the corresponding angle in coronene (43.7') or in the phthalocyanines (44.2'). The perpendicular distance between successive molecular planes is given by &b cos t,hN = 3.53 A.a value rather larger than the interplanar spacing in graphite (3'41 A*) coronene (3.40A.) or phthalocyanine (3.38 A.). TABLEI. Orientation of the molecule in the crystal. XA = 61.1' cos XL = 0.4834 xx = 52.2" cos XH = 0.6130 XN = 128.7" cos XN = -0.6248 = 77.7" COS+A = 0.2130 +M = 52.4" COS~ = 0.6101 #N = 40.2" COSZ)~= 0.7630 = = 31.9" COSOA = 0.8487 WH = 120.1" cos wu = -0.5017 OR = 80.5' COSW~~ 0,1648 The co-ordinates with respect to the crystal axes are collected in Table 11. The x and z co-ordinates of the nine resolved atoms can be measured directly from the projection in Fig. 2 and these values are given in bold type. The other crystal co-ordinates follow from the assumption of a planar molecule with symmetry about the L and M molecular axes.The figures in Table I1 give the co-ordinates of all the carbon atoms (A-P) in one pyrene molecule. The other three molecules in the unit cell can be derived from the one given by the usual symmetry operations and translations applicable to the space-group P21/a. The molecular dimensions and bond lengths may be calculated from these co-ordinates and the results are shown graphically in Fig. 4. The ringed atoms A B C E,F M N,0 P are separately resolved in Fig. 2 and the bond distances between these atoms may be obtained by direct measurements combined with the orientation angles of Table I. The other bond lengths can only be derived by assuming exact symmetry about the L and M axes. This symmetry may be confirmed by comparing the original direct bond-length measurements of symmetrically placed pairs of resolved atoms.The results are AN = 1.40 AB = 1.38 Assumed mean value 1.39 A. NM = 1.43 BG = 1.42 , , , 1-42A. 9, MO = 1.38 CO = 1.42 , , 1-39 A. 1, PF = 1.38 CO = 1.42 , , 1.39 A. The deviations from the mean values are nowhere greater than 0.03 A. and we do not feel that [19471 A Quadtative X-Ray IwestigatioN. TABLE11. Co-ordinates. Centre of symmetry as origin. x y,z are referred to the monoclinic crystal axes. x' y zJ,are rectangular co-ordinates referred to the a and b crystal axes and their perpendicular c'. x = x' -z' cot 8; z = z' cosec 8. Atoms (cf. Figs. 2 and 4). X A. y A. 2 A. X' A. Z' A. 27rxja. 27rylb. 27rzlc. A ............3.85 -0.41 3.51 3.229 3.463 101.9" -16.0" 151.0" B ............ 4.04 0.18 2-31-3.630 2.27 1 106.9 7-1 99.4 c ............ 3.14 -0.12 1.08 2.943 1.065 83-1 -4.6 46.5 D ............ 3.33 0.49 -0.18 3.364 -0.181 88.1 19.3 -7.9 E ............ 2-45 0.19 -1.38 2.692 -1.361 64.9 7.7 -59.4 F ............ 1.33 -0.73 -1.37 1.571 -1.345 35-2 -28.5 -59.0 G ............ 0.43 -1.03 -2.59 0,884 -2.551 11.4 -40.2 -111.4 H ............ -0.65 -1.91 -2.58 -0.189 -2.537 -17.2 -74.8 -111.0 I -0.83 -2.50 -1.37 -0.590 -1.345 -22.0 -97.8 -59.0 ............ ............ 0-07 -2.20 -0.14 0.097 -0.139 1.9 -86.0 -6-0 ............ -0.12 -2.81 1.12 -0.324 1.107 -3.2 -109.9 48.2 L ............ 0.76 -2-51 2.32 0.348 2-287 20.1 -98.3 99.8 M ............1.88 -1.59 2.31 1.469 2.271 49-8 -62.1 99.4 hT ............ 2-78 -1.29 3.53 2.156 3.477 73.6 -50.5 161.8 0 ............ 2-08 -1.01 1.09 1.870 1.078 54-5 -39.5 46.9 P ............ 1.14 -1.31 -0.15 1-170 -0.152 30.2 -51.2 -6.5 Centre of mol. ...... 1-604 -1,160 0-470 1.520 0.463 42.5 -45.3 19.9 any significance can be attached to these deviations. The mean values have therefore been used in Fig. 4. FIG.4. FIG.5. AL I I 1.39 1.45 1.39--Dimensions of the pyrene molecule. Normal projection of two parallel molecules. For the bond lengths OP and EF we obtain the value of 1.45 A. It is unfortunate that these unusually large values cannot be further confirmed by direct measurements on the bonds CD JK or LM. From the nature of the projection it is clear that the possible error in the bond lengths is fairly large and it may easily amount to & 0.03 A.However the balance of the evidence is fairly strong that the bonds OP and EF (directly measured) and probably CD,JK and LM as well are distinctly longer than any of the other bonds within the molecule. With regard to the hexagon angles there is no evidence that any of these differ appreciably from 120". It is convenient to summarise the molecular structure by giving the co-ordinates of the atoms 364 Robevtson ad White The CrystaL Strzicture of Pyrene. with reference to the molecular axes L,M and N. These are collected in Table 111. When these figures are combined with the crystal co-ordinates of the molecular centre (xP’,yp zp’) and the orientation angles according to the relations X‘ = L COS XL f M COS XM f N COS XN f Xp’ y = L cos #L + M cos 9hf + N cos *I? + yp Z’ = L cos wl; + M cos w~ + N COSWN + zP where xp’ = 1.520 yp = -1.160 4’ = 0.463 A.the crystal co-ordinates of Table I1 are reproduced. TABLE111. Co-ordinates with respect to molecular axes. Atoms. A H ............... B,G,I N ......... C,F J M ...... L,A. k3.535 f2-840 fl.420 M A. 0 &1.203 -+1*203 N,A. 0 0 0 Atoms. D,E,K,L ....... 0,P ............... L A. &Om695 f0-725 M A. k2.469 0 N,A. 0 0 InterunoZecular distances. The closest approach of adjacent pyrene molecules occurs along the b axis where the interplanar distance is 3-53A. Here the molecules are grouped in pairs about the symmetry centres and the normal projection of one of them in the plane of the other is shown in Fig.5. The hexagons are clearly arranged so as to avoid any direct overlap. Four pairs of atoms PP’ MG’ CI’ and KE’ are nearly over each other and for these the approach distance is 3-54A. The other pairs are in staggered positions at rather greater distances. From atom D on the standard molecule to atom 0’ (inverted) on the reflected molecule half a translation along the a axis the distance is 3.61 A. and from D to P’it is 3.64 A. From A on the standard molecule to N’(inverted) on the reflected molecule half a translation along a and one translation along c the distance is 3.96 A. All other intermolecular distances appear to be greater than 4 A. Discussion of Results.-The bond-length variations in the pyrene molecule as depicted in Fig.4 are even greater than those found for coronene. On the other hand we cannot expect as high an accuracy from the present analysis as from the coronene analysis for reasons which have been explained. The data given in Fig. 4 represent the most probable values for the bond lengths after averaging. But as the possible error in individual bond-length measurements may be as high as & 0.03 or &-0.04 A. the results must obviously be accepted with caution. It should however be emphasised that the bond-length variations shown in Fig. 4 for the resolved atoms (circled) are based entirely on X-ray measurements and are not in any way derived from chemical theory. The initial trial model which was set up in order to determine the phase constants consisted of perfectly regular planar hexagons of radius 1.39~.The final shifts from these initial positions are considerable and they arise from the measured values of the structure factors which were employed as coefficients in the Fourier series. In view of this the results receive a rather striking qualitative confirmation from a study of the simple valency bond structures which are applicable to pyrene. For a fixed position of the carbon atoms there are six different ways of drawing the bonds (11)-(VII) and these may perhaps be considered as the structures which make the most important contributions to the normal state of the molecule. A I II /\/\ II t II \/\/ I It \/ (111.) (VII.) Assuming in the first instance that these structures make equal contributions (this is unlikely to be true) ,it is easy to compute the average double-bond character for each link in the molecule.This is shown in (VIII) as percentage double-bond character and in (IX) these figures are translated into distances on the basis of Pauling and Brockway’s empirical curve relating double-band character and distance (J.Amer. Chem. SOG. 1937 59 1223). In (X)the measured values of Fig. 4 are repeated for convenient comparison. I]19471 A Quantitative X-Ray hvestigation. There is a distinct general resemblance between the measured values and those predicted on the basis mentioned above. The largest deviations occur in the central bonds where the 1.39/ \1-39 50 )*39 1.42 1.39( /\I7 1.46/\ /\1.46 1.46/\ /\l.45 (A)/33 \1.8 f 'I 1.39\/1*39 \ s3 33 Il-36 (1.39 1.42Y1*42 1.3( Il-46 11.42 601 \33 lo/ 1'35( 1*42/\1.42 ]r/ 146\f 1.39)\1.39 / ii:" 1*46\ 17\/ \/" 1.i 1*4a~ \/ \/ 1.39\/1*39 60\/60 1*39v1-39 Bond orders.Distances calculated. Distances found. (VIII.) (1x4 (X.1 measured values vary from 1.38 to 1-45 A, while the predicted values are constant at 1.42 A. In the upper and the lower ring the predicted values are again more constant than the measured values. The average bond length over the whole molecule is in excellent agreement the predicted value being 1.408 A. and the measured value 1.412 A. Chemical evidence appears to suggest that the structures (11)-(V) are those most consistent With the reactivity of pyrene (see for example Cook Ann.Reports 1942 39 163). If the contributions of these structures are increased relatively to the others the main effect on the above calculations is to increase the length of the central bond in agreement with the observations. More detailed discussion of the bond distances is probably not justified until more reliable measurements can be made or until other similar ring structures have been measured. EXPERIMENTAL. X-Ray Measurements.-Small tabular crystals displaying the (001) and (110) faces were employed. They were mounted for rotations about the a b and c crystallographic axes the weights of the principal specimens employed for intensity measurements being 0.077 0.048 and 0.147 mg. The dimensions of the specimens were such as to make relative absorption corrections for different reflections in the same zone unnecessary.Absorption corrections were applied however in calculating the scale of absolute values of F. All the X-ray work was carried out with copper-Ku radiation X = 1.54. Rotation oscillation and moving-film photographs were taken the latter mainly for intensity records. The observed halvings led to the space group P2Ja without ambiguity. The intensity measurements were carried out on a number of calibrated moving-film exposures by means of a photometer of the type described by Robinson (J.Sci. Instr. 1933 10 233) and the different sets were correlated through the common axial reflections. Very strong reflections were reduced by a factor of 12 by means of automatic shutters in order to give accurate comparisons with the weaker reflections.Absolute measurements were made by comparisons with standard crystals on the two-crystal moving-film spectrometer (Robertson Phil. Mug. 1934 18 729). In one experiment a small crystal of i-erythritol and in another experiment a small crystal of oxalic acid were used as standards. (Direct absolute measurements had previously been made on these standards with an ionisation spectrometer.) Good agreements were obtained in the two experiments. The absolute values of F were calculated by the usual formulae applicable to mosaic-type cjrstals and the results are collected in Table IV under " F meas.". Fourier A naZysis.-Using the phase constants determined from the trial structures and the measured values of F a double Fourier series was set up according to the usual formulae.For the projection along the b crystal axis on the (010) plane the electron density was computed at 450 points on the asymmetric unit the a axis being divided into 60 parts (intervals of 0.227 A.) and the c axis into 30 parts (intervals of 0.279 A.). The summations were carried out by means of 3-figure strips (Robertson Phil. Mag. 1936, 21 176). The positions of the contour lines were obtained by graphical interpolation from the summation totals by making sections of both the rows and the columns. The resulting contour map is shown in Fig. 2 three-quarters of the unit cell being included. The projection along the c axis (Fig 3) was computed in a similar manner.In this case each axis was divided into 60 parts the intervals being 0.154 A. along b and 0.223 A. along a sin 8. Orientation of the Molecule and Co-ordinates.-From a consideration of the observed lengths in projection of ON and parallel distances [Fig. 2(b)] which can be only slightly tilted it was found that the best average radius of the hexagon was 1.41 A. With this average value and the assumption that the molecule is flat and the axes L and M are at right angles it was possible to calculate the orientation of the molecule with regard to the crystallographic axes. 366 Robeytson and White The Crystal Strim%we of Pyrene. The distances NB MC and PE are 1.938 f0.030 A. in the projection hence JIM the angle which M makes with the b axis is 52.4".This method cannot be used to find the tilt of L as the line lies so nearly in the projection plane that a small discrepancy in the observed value would lead to a large difference in the angle calculated. The calculation can be made however from the observed angle between L and M in the projection. Let vL and T~ be the angles which L and M make with the a axis in projection. vL is taken as the mean of the angles which BCF AOP and KIM make with a which are 60-2" 60.0" and 61.3". The last is probably less reliable than the others as it is drawn through only two atoms and hence it was given only half the weight of the first two angles in deriving the mean value of 60-34". vH is the mean of the angles which NB MC and PE make with a and is observed as -39.3" & 0.4".From these observations the complete orientation of the molecule may then be derived by making use of the nine relations which were given in the coronene analysis (Robertson and White J. 1945 607 615). From the orientation of the molecule thus deduced it is possible to obtain the actual bond lengths connecting the best estimated centres of the various atoms by reducing each line for its calculated tilt. In this way the bond-length determinations already discussed were reakhed. The finally accepted centres for the resolved atoms are plotted on the contour map in Fig. 6. FIG.6. a. Co-ordinates assigned to the resolved atoms in the pyrene b axis projection. Table I1 gives the finally accepted co-ordinates for the atoms and includes the co-ordinates of the centre of the molecule (x- yp,zp).The latter position can be estimated with considerable accuracy from the b axis projection (Fig. 2) and with rather less certainty from the G axis projection (Fig. 3). Even on the assumption of a strictly planar molecule the b axis projection gives no information concerning the value of yp,as the molecules may be translated up or down the b axis. The best value of yp was therefore found by calculations of the (hK0) structure-factors and confirmed from the c axis projection (Fig. 3). On the basis of the @a1 co-ordinates the structure factors were re-calculated and the results are given in Table IV under F calc.". The scattering curve formerly given for hydrocarbons (Robertson Proc. Roy. Soc. 1935 A 150,110) was found rather unsuitable for pyrene and the fc values given below (max.fc = 100) were used instead.sin 8 (A = 1.54) ......... 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0-9 fc ........................... 70 56 43 30 19 12.5 8.5 5 3.5 [1947] A Qaantitative X-Ray Investigation 367' TABLEIV. Measured-and calculated values of the structure factor. sin 0 sin 0 hkl. (A = 1.54). F meas. F calc. hkZ. (A = 1.54). F meas. F calc. 200 0.115 7.5 3.7 20g 0.462 2-5 -12 400 0.230 47 + 46 204 0-370 19.5 ++ 21 16 600 0.345 (2 -4 203 0-285 15.5 800 0.460 3 -6 202 0.202 40-5 -35 10,oo 0.575 <3 -1 201 0.135 48 + 43 12,oo 0.690 <3 -1 201 0.160 6.5 14,OO 0.805 4.5 +2 202 0-235 18 _f 1; 020 0.167 < 1.5 +2 203 0.320 22 + 259 040 0.333 19 + 23 204 0.409 7 +l 060 0.500 (3 +1 205 0.500 10.5 -12 080 0.667 3.5 +5 206 0.591 21.5 + 24 0,10,0 0.833 (3 0 207 0.683 6.5 +6 001 0.094 65 + 66 20s 0.775 <3 +1 002 0.187 32.5 -31 209 0.868 <3 0.003 0-281 5 +6 408 0-743 (3 +3 004 0.374 (2 -2 407 0.657 (3 +s 005 0.468 < 2.5 -3 406 0.567 <3 +2 006 0-561 9.5 405 0.484 6.5 +4 ++ 33 14 007 0.654 33 403 0.403 <3 -2 008 0.748 4-5 +1 403 0.330 3 -7 009 0.841 4 -4 402 0.270 12.5 ++ 32 18 4oi 0.233 38 011 0.125 13 + 12 401 0.264 20.5 -16 012 0.205 (5 -4 402 0.320 27.5 013 0.293 9 403 0.393 40.5 ++ 29 40. 2 1: 014 0.383 10.5 404 0.472 <3 +1 015 0.475 <S 4 7 405 0.555 <3 0 016 0.567 <9 -9 406 0.641 <3 +3 017 0.660 11 -13 407 0.729 <3 +3 018 0.752 <10 +1 408 0.820 <3 -2 021 0.191 <5 -2 60s 0.767 <3 0.022 0.251 8.5 +7 607 0.685 <3 +2 023 0.326 26.5 -25 606 0.605 <3 +4 024 0.409 24 -14 606 0.531 17 -14 025 0.496 <8 +7 603 0.461 17 -14 026 0-585 <9 -3 603 0.405 <3 -1 027 0.675 <10 I 1 602 0.362 3.5 -5 031 0.267 (6 -1 6oi 0.342 9.5 -11 032 0.312 11.5 601 0.373 <2 -1 ++ 30 10 033 0.376 35 602 0.42 1 17.5 -13 034 0.450 12 -12 603 0.482 9 -9 035 0.530 <9 0 604 0.550 <3 +1 036 0.614 <10 44 605 0.625 <3 -3 037 0.701 <10 +2 606 0-707 <3 -3 041 0.346 9 + 14 607 0.790 <3 -1 042 0.382 13.5 -15 60s 0.875 <3 +1 043 0-436 6.5 -6 809 0.885 4 +4 044 0.501 <9 -3 80s 0.806 5 + 10-045 0.574 <9 +2 802 0.732 <3 3-1 046 0.652 <10 +2 805 0.660 <3 +3 047 0.734 <10 +4 805 0.595 <3 +6 051 0.427 10.5 -7 804 0.540 (3 +2 052 0,457 <8 -4 803 0.494 <3 +3 053 0.502 <9 +3 802 0.466 23.5 054 0.560 (9 -7 soi 0.455 35 ++ 20 31 055 0.626 <10 +3 801 0-486 <3 +4 056 0-698 <10 +3 802 0.528 9 + 12 -061 0.509 7.5 5 803 0.580 5.5 +6 062 0.534 (9 -3 804 0.641 <3 0 063 0.574 <9 -5 805 0-7 10 (3 -9 071 0.591 9 +9 806 0-785 (3 42 072 0-613 <10 + 2 10,oe 0.730 <3 -1 073 0.647 <10 +6 10,05 0.675 3 + 10 10,og 0.630 <3 -2 -209 0.830 <3 -2 10,03 0.593 <3 6 208 0.737 (3 -1 l0,OZ 0.574 22 + 17 20l 0.647 7 -7 io,oi 0.569 <3 -2 206 0.552 <3 +5 10,Ol 0-600 (3 0 i.368 Robertson and White The Crystal Strtm!ure of Pyrene.TABLE IV.-continued. Measured and calculated values of the structure factor. sin 8 sin e hkl. (A =1.54). F meas. F calc. hkl. (A =1.54). F meas. F calc. 10,02 0-637 (3 360 0.529 2.5 -4 10,03 0.683 <3 -+ X 370 0.608 (3 -3 10,04 0.738 <3 0 380 0.689 <3 0 10,05 0-802 5-5 2; 410 0.245 11 -10 10,06 0.870 <3 420 0.284 <3 +5 12,OT 0.865 <3 -3 430 0.340 20 12,06 0.809 14 440 0-405 30.5 ++14 13 ++20 30 12,OE 0-764 10-5 450 0.476 9 +7 l2,05 0.725 (3 -2 460 0.551 <3 -1 12,03 0.698 <3 0 470 0.627 <3 -2 12,oZ 0.682 (3 0 480 0-705 <3 12,oi 0.682 <3 -2 510 0.300 10 _f 1; 12,Ol 0.715 27 520 0.333 7.5 -6 ++28 16 12,02 0.749 18 530 0.381 <3 +1 12,03 0.792 (3 -4 540 0-440 10.5 +s 12,04 0-840 <3 0 550 0.506 <3 0 12,05 0.885 <2 0 560 0.577 3 -4 14,OT 0.944 <2 0 570 0.650 (3 +3 14,Og 0.897 4.5 -4 610 0.355 10 -11 14,Olj 0-856 4 -1 620 0.383 15 -14 14,OS 0.828 <3 -1 630 0.426 <3 -1-3 1 14,03 0.806 <3 -+ 640 0.480 <3 -1 14,02 0.795 <3 650 0-541 5 -5 i4,oi 0.798 <3 660 0-607 <3 +3 14,Ol 0.830 4 + 710 0.411 <3 +4 14,02 0.861 <3 720 0.436 (3 +4 14,03 0.898 < 2.5 0 730 0.474 <3 +4 14,04 0,943 <2 -1 740 0.523 <3 -1 750 0.580 <3 4 -+; 110 0.102 43 760 0.642 ++46 45 120 0.176 42 770 0.709 <3 -4 130 0.257 12.5 -21 780 0-778 t3 -2 140 0.338 14.5 -10 810 0-468 <3 -2 150 0.421 21.5 -22 820 0-490 <3 3-1 160 0.503 15 -14 170 0.586 6 + 830 0.524 <3 -+2 4 840 0.568 t3 180 0.669 <3 850 0.621 (3 210 0.142 42 +43 860 0.679 (3 -+; 220 0.203 83 -107 910 0.524 <3 -3 230 0.275 32.5 +33 920 0.544 <3 -1 240 0.353 2 -3 930 0.575 <3 -1 250 0-432 17 -18 940 0-616 <3 -4 260 0.513 17 -18 950 0.665 (3 0 270 0.594 3.5 -4 10,lO 0.581 <3 +I 280 0.677 (3 0 10,20 0.599 3 +6 310 0.192 26.5 -22 10,30 0-627 <3 -1 320 0-240 35.5 10,40 0.665 (3 -1 ++23 32 330 0-304 22 11,lO 0.638 (3 340 0.375 17.5 +1; 11,20 0.654 t3 +4 0 350 0.451 6-5 -11,30 0-680 <3 +3 These are generally smaller than the previous values.This may be due in part to errors in the absolute scale but in addition there is a definite tendency for pyrene reflections of high order to fall off in intensity more rapidly than in anthracene and other hydrocarbons. This points to a curious difference in temperature factor or possibly to some randomness in the structure but further measurements are required before definite conclusions can be drawn. The general agreements are very good the average discrepancies expressed as a sum of all the discrepancies divided by the sum of the measured F values being 14.3% for the (hOZ),12.9% for the {hkO),and 8.8% for the (OkZ)structure factors and 12.6% for all the structure factors together. THEUNIVERSITY, GLAsGOW. [Received,July lst 1946.1