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The crystal structure of perdeuterated pyrene II at 4.2 K
16 August 1996
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 258 (1996) 490-494
The crystal structure of perdeuterated pyrene II at 4.2 K Kevin S. Knight a,*, Kenneth Shankland a, William I.F. David a Norman Shankland b Steve W. Love b a ISIS Facility, RutherJbrd Appleton LaboraWry, Chilton, Didcot, Oxon OXI 10QX, UK b Department of Pharmaceutical Sciences, University ofStrathclyde, Strathelyde GI IXW, UK
Received 28 May 1996; in final form I l June 1996
Abstract The crystal structure of pyrene II, previously postulated from electron diffraction measurements and potential energy calculations, has been confirmed and refined from high-resolution neutron powder diffraction data collected from a fully deuterated sample at 4.2 K.
1. Introduction Crystals of pyrene I undergo a first-order phase transition to pyrene II when cooled below -~ 1 10 K, with firm evidence for the transition provided by fluorescence [1], Raman scattering [2] and transmission electron microscopy [3] experiments. Despite the "clear and pressing need for a structural determination of pyrene I I " [2], only the molecular structure of pyrene I is known from single-crystal diffraction [4,5]. Measurements on pyrene II single crystals are precluded by the extensive crystal cracking that accompanies the transition [2]. In cases such as this, high-resolution powder diffraction can be used to attempt an ab initio structure solution (see, for example, malonic acid [6]), or to refine a hypothetical
" Correspondingauthor.
model, such as one derived from electron diffraction data and potential energy calculations [7]. As a structure for pyrene II has already been postulated [8], we have tested, confirmed and refined this model against neutron powder diffraction data collected at 4.2 K, using the Rietveld method [9].
2. Experimental
2.1. D a t a c o l l e c t i o n
Approximately 3 g of perdeuterated pyrene (C16D l0, MSD Isotopes, 99.8 atom % D) were lightly packed in an 11 mm diameter, thin-walled, cylindrical vanadium sample can. Neutron diffraction data were collected at 4.2 K in time-of-flight using HRPD [ 10], the high-resolution neutron powder diffractometer at the ISIS spallation neutron source, Rutherford Appleton Laboratory. Details of the experimental
0009-2614/96/$12.00 Copyright © 1996 Elsevier Science B.V. All rights reserved PH S0009-2614(96)00670-7
491
K.S. Knight et a l . / Chemical Physics Letters 258 (1996) 490-494
Table 1 Data collection and ref'mement parameters for perdeuterated pyrene II
Table 2 Fractional coordinates and isotropic temperature factors for perdeuterated pyrene II at 4.2 K (esds in parentheses)
Instrumental diffractometer
Atom
x
y
x
B~so (,~2)
CI C2 C3 C4 C5 C6 C7 C8 C9 C10 Cll C12 C13 C14 C15 C16 D1 D2 D4 D5 D7 D8 D9 D11 DI2 D14
0.2736(3) 0.2723(4) 0.2091(3) 0.2113(4) 0.1465(3) 0.0769(3) 0.0104(3) - 0.0590(3) - 0.0627(3) 0.0049(3) -0.0016(3) 0.0635(3) 0.1371(4) 0.2045(3) 0.1398(3) 0.0721(3) 0.3238(4) 0.3275(4) 0.2623(3) 0.1464(3) 0.0123(3) - 0.1071(3) -0.1164(4) -0.0570(4) 0.0584(3) 0.2022(3)
-0.0108(4) 0.0509(3) 0.0047(4) 0.0662(4) 0.0169(4) - 0.0985(4) -0.1450(3) - 0.2523(4) - 0.3160(4) -0.2688(4) -0.3280(4) -0.2797(4) -0.1719(4) -0.1234(4) -0.1049(4) -0.1554(4) 0.0262(4) 0.1373(4) 0.1534(4) 0.0660(4) - 0.0995(4) - 0.2949(4) -0.4036(4) -0.4106(4) - 0.3270(4) -0.1698(4)
0.3866(5) 0.2365(5) 0.0957(5) - 0.0596(5) -0.1953(5) - 0.1856(5) -0.3210(5) - 0.3027(5) - 0.1556(5) -0.0128(5) 0.1457(5) 0.2799(5) 0.2672(5) 0.4023(5) 0.1133(5) -0.026605 0.4961(5) 0.2210(5) - 0.0652(5) -0.3150(6) - 0.4384(5) - 0.4109(5) -0.1437(5) 0.1585(5) 0.3969(5) 0.5187(5)
0.54(5) 0.55(3) 0.36(3) 0.41(3) 0.41(3) 0.36(3) 0.55(3) 0.54(5) 0.55(3) 0.36(3) 0.41(3) 0.41(3) 0.36(3) 0.55(3) 0.23(5) 0.23(5) 1.15(2) 1.15(2) 1.15(2) 1.15(2) 1.15(2) 1.15(2) 1.15(2) 1.15(2) 1.15(2) 1.15(2)
flight path temperature detector sample position data range
HRPD, neutron time-of-flight powder diffractometer 95.9647 m 4.2 K 6Li-doped ZnS scintillation counters, 168.239 ° 20 1m 30000-130000/~s time-of-flight
(0.6-2.6/~ d-spacing) time channel binning A t / t = 1 X 10 -4 experiment duration 12 h Sample compound formula mol. wt.
pyrene C x6Dl0 212.32
Refinement space group Z unit cell refinement
monoclinic, P2 ~ / a 4 whole pattern
unit cell (,~)
D x (g cm -3) observations refined parameters structural profile cell extinction constraints strict (equal ITF) a
a = 12.30267(1), b = 9.98788(1), c = 8.22064(1); /3 = 96.4046(1) ° 1.405 4582 84 20 4 1
C1 = C8, C2 = C7 = C9 = C14, C3 = C6 = CI0 = C13, C4 = C5 = C11 = C12, C15 = C16 D1 = D2 = D 4 = D 5 = D 7 = D8 = D9 = D l l = D12 = D14 thermal parameters all atoms isotropic agreement factors b: X 2 = 11.77, R,~p = 3.16%, Rp = 2.69%, R t = 7.10%, R E = 0.92%
a Isotropic temperature factor. t, defined in Ref. [12].
setup and data collection times are given in Table 1. The data set was focused to a Bragg angle of 168.329 °, normalised to the incident monitor spectrum and corrected for detector efficiency using a spline smoothed diffraction pattern collected from a vanadium rod. After reduction, data in the range
D4 D2
D5
~
D7
16__ Fig. 1. An ORTEP plot of the perdeuterateA pyrene molecule at 4.2 K, with isotropic thermal ellipsoids shown at 85% probability.
492
K.S. Knight et al. / Chemical Physics Letters 258 (1996) 490-494
31000-122500 /zs (0.64-2.54 ,~) were binned in time channels of At/t = 3 × 10 -4 for use in Rietveld refinement.
2.2. Structure refinement
identical. These constraints are summarised in Table 1, along with other relevant refinement parameters.
3. Results
Refinement of the proposed pyrene II structure [8] against the diffraction data was achieved by the Rietveld method [9], as implemented in the time-offlight least-squares program TF12LS [11]. The peak shape used in the refinement was a convolution of a Voigt function with a wavelength-dependent sum of two decaying exponential functions. Strict constraints, which reduce the number of independent variables in the least squares, were used to modify the refinement process by forcing the isotropic temperature factors of chemically equivalent atoms to be
The initial structural model converged rapidly, but assessment of the profile fit showed the presence of extinction due to the high crystalline quality of the sample. A refinable extinction parameter, based on the model of Sabine [13], was introduced for the final cycles of least squares, resulting in the agreement factors listed in Table 1. The refined fractional atomic coordinates and isotropic temperature factors are given in Table 2, and Fig. I shows an ORTEP [14] plot of the refined pyrene molecule. The final
Table 3 Covalent bond lengths (A) and angles (°) for perdeuterated pyrene at 4.2 K (esds in parentheses) C 1- C 2 C2- C3 C3-C4 C4-C5 C5-C6 C6-C7 C7-C8 C8-C9 C9-C 10 CIO-CI 1 C 1- C 2 - C 3 C2-C3-C4 C3- C4-C5 C4-C5-C6 C5-C6-C7 C6-C7-C8 C7-C8-C9 C8- C9-C 10 C9-C10-C11 C10-CI 1-C12 CI 1-CI 2-C13 C12-C13-C14 C13-C14-C1 C14-C1-C2
1.378(6) 1.399(6) 1.420(6) 1.387(6) 1.443(6) 1.386(6) 1.389(5) 1.372(6) 1.440(6) 1.441(6) 122.9(4) 122.5(4) 120.2(4) 122.0(4) 121.6(4) 119.1(4) 122.3(4) 119.6(4) 121.2(3) 119.7(4) 121.8(4) 122.2(4) 120.6(4) 119.1(4)
C 11- C 12 C 12-C 13 C 13-C 14 C 14-C 1 C3-C 15 C 13-C 15 C6-C 16 C 10-C 16 C 15-C 16
C 2 - C 3 - C 15 C14--C13-C15 C3-C 15 - C 13 C 4 - C 3 - C 15 C12-C13-C15 C3-C15-C16 C 13-C 15-C 16 C6-C 16-C 15 C10-CI6-C15 C5-C6-C16 C11-C10-C16 C7-C6-C16 C9-C10-C16 C6-C16-C10
1.376(6) 1.418(6) 1.397(6) 1.424(6) 1.405(6) 1.435(6) 1.433(6) 1.41 4(6) 1.434(6)
117.4(4) 118.0(4) 121.9(4) 120.2(4) 119.8(4) 119.8(4) 118.3(4) 120.8(3) 120.6(4) 116.9(4) 119.5(4) 121.3(3) 119.1(4) 118.4(4)
C1-DI C2-D2 C4-D4 C5-D5 C7-D7 C8-D8 C9-D9 C11-DI 1 C12-D12 C14-D14 C2-C1-D1 C1-C2-D2 C3-C2-D2 C3-C4-D4 C5-C4-D4 C4-C5-D5 C6-C5-D5 C6-C7-D7 C8-C7-D7 C7-C8-D8 C9-C8-D8 C8-C9-D9 C10-C9-D9 CI0-C1 l-D11 C12-C1 I-D11 CI 1-C12-D12 C13-C12-D12 C13-C14-D14 C1-C14--D14 CI4-CI-D1
1.097(6) 1.114(6) 1.077(6) 1.099(6) 1.069(6) 1.098(6) 1.107(6) 1.083(6) 1.080(6) 1.066(6)
122.2(4) 120.2(4) 116.8(4) 117.2(4) 122.5(4) 120.3(4) 117.7(4) 120.8(4) 120.1(4) 119.6(4) 117.8(4) 121.5(4) 118.9(4) 120.0(4) 120.4(4) 118.3(4) 119.9(4) 119.3(4) 120.0(4) 118.6(4)
K.S. Knight et al. / Chemical Physics Letters 258 (1996) 490-494
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Whilst powder diffraction experiments provide an alternative in structure determination/refinement when single crystals of a compound are not available, the information content of a one-dimensional powder diffraction pattern does not rival that of a three-dimensional single-crystal equivalent. Accordingly, the refinement of a crystal structure with a large number of independent parameters (such as pyrene) against a powder pattern requires high-quality data, both in terms of instrumental resolution and signal-to-noise ratio. The narrow intrinsic line width of the pyrene sample and the high resolution afforded by HRPD (Ad/d = 4 × 10 - 4 o v e r the whole data range) ensure that the first criterion is met, whilst perdeuteration of pyrene and the large sample volume fulfill the latter. The strict constraints applied to the isotropic temperature factors (ITFs) of chemically equivalent atoms improve the observation-toparameter ratio in the least-squares calculation still further. The ITFs refine to chemically sensible values, and show the increasing extent of atomic vibration moving out from the centre of the molecule towards the periphery.
7x10'
Fig. 2. The final observed (points) and calculated (line) profiles for perdeuterated pyrene II at 4.2 K. The difference [YobsYcate]/o'(Yobs) plot is also shown.
observed, calculated and difference [YobsO'(Yob~) profiles are shown in Fig. 2.
493
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4. Discussion
Fig. 2 shows the excellent fit of the refined pyrene II model to the data, with no evidence in the pattern of residual pyrene I. The fractional atomic coordinates obtained via Rietveld refinement are in good agreement with those tabulated [8], showing the proposed crystal structure of pyrene II to be essentially correct. The covalent bond lengths and angles for the refined structure (Table 3) are in generally good agreement with those obtained from the single-crystal neutron refinement of pyrene I [4] and, as expected, both the powder and single-crystal neutron diffraction studies yield more accurate values for the C - H (C-D) bond distances than the low-temperature X-ray study [5].
5. Conclusion
The structure of pyrene II, postulated by Jones et ai. [8], has been shown to be substantially correct. More importantly, the high quality of the refinement points to the possibility of obtaining accurate structural information as a function of temperature, up to and through the phase transition.
References [1] R.M. Hochstrasser and A. Malliaris, Mol. Cryst. Liq. Cryst. 11 (1970) 331. [2] R. Zallen, C.H. Griffiths, M.L. Slade, M. Hayek and O. Brafman, Chem. Phys. Lett. 39 (1976) 85. [3] W. Jones and M.D. Cohen, Mol. Cryst. Liq. Cryst. 41 (1978) 103. [4] A.C. Hazell, F.K. Larsen and M.S. Lehmann, Acta CrystalIogr. B 28 (1972) 2977. [5] Y. Kai, F. Hama, N. Yasuoka and N. Kasai, Acta Crystallogr. B 34 (1978) 1263. [6] R.G. Delaplane, W.I.F. David, R.M. Ibberson and C.C. Wilson, Chem. Phys. Lett. 201 (1993) 75.
494
K.S. Knight et a L / Chemical Physics Letters 258 (1996) 490-494
[7] S. Ramdas and J.M. Thomas, J. Chem. Soc. Faraday Trans. 2 72 (1976) 1251. [8] W. Jones, S. Ramdas and J.M. Thomas, Chem. Phys. Lett. 54 (1978) 490. [9] H.M. Rietveld, J. Appl. Crystallogr. 2 (1969) 65. [10] R.M. Ibberson, W.I.F. David and K.S. Knight, Rutherford Appleton Laboratory Report RAL-92-031 (1992).
[11] W.I.F. David, R.M. lbberson and J.C. Matthewman, Rutherford Appleton Laboratory Report RAL-92-032 (1992). [12] R.A. Young, in: The Rietveld method, ed. R.A. Young (Oxford University Press, Oxford, 1995) p. 1. [13] T.M. Sabine, Aust. J. Phys. 38 (1985) 507. [14] C.K. Johnson, Oak Ridge National Laboratory Report ORNL-3794 (1994).
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 258 (1996) 490-494
The crystal structure of perdeuterated pyrene II at 4.2 K Kevin S. Knight a,*, Kenneth Shankland a, William I.F. David a Norman Shankland b Steve W. Love b a ISIS Facility, RutherJbrd Appleton LaboraWry, Chilton, Didcot, Oxon OXI 10QX, UK b Department of Pharmaceutical Sciences, University ofStrathclyde, Strathelyde GI IXW, UK
Received 28 May 1996; in final form I l June 1996
Abstract The crystal structure of pyrene II, previously postulated from electron diffraction measurements and potential energy calculations, has been confirmed and refined from high-resolution neutron powder diffraction data collected from a fully deuterated sample at 4.2 K.
1. Introduction Crystals of pyrene I undergo a first-order phase transition to pyrene II when cooled below -~ 1 10 K, with firm evidence for the transition provided by fluorescence [1], Raman scattering [2] and transmission electron microscopy [3] experiments. Despite the "clear and pressing need for a structural determination of pyrene I I " [2], only the molecular structure of pyrene I is known from single-crystal diffraction [4,5]. Measurements on pyrene II single crystals are precluded by the extensive crystal cracking that accompanies the transition [2]. In cases such as this, high-resolution powder diffraction can be used to attempt an ab initio structure solution (see, for example, malonic acid [6]), or to refine a hypothetical
" Correspondingauthor.
model, such as one derived from electron diffraction data and potential energy calculations [7]. As a structure for pyrene II has already been postulated [8], we have tested, confirmed and refined this model against neutron powder diffraction data collected at 4.2 K, using the Rietveld method [9].
2. Experimental
2.1. D a t a c o l l e c t i o n
Approximately 3 g of perdeuterated pyrene (C16D l0, MSD Isotopes, 99.8 atom % D) were lightly packed in an 11 mm diameter, thin-walled, cylindrical vanadium sample can. Neutron diffraction data were collected at 4.2 K in time-of-flight using HRPD [ 10], the high-resolution neutron powder diffractometer at the ISIS spallation neutron source, Rutherford Appleton Laboratory. Details of the experimental
0009-2614/96/$12.00 Copyright © 1996 Elsevier Science B.V. All rights reserved PH S0009-2614(96)00670-7
491
K.S. Knight et a l . / Chemical Physics Letters 258 (1996) 490-494
Table 1 Data collection and ref'mement parameters for perdeuterated pyrene II
Table 2 Fractional coordinates and isotropic temperature factors for perdeuterated pyrene II at 4.2 K (esds in parentheses)
Instrumental diffractometer
Atom
x
y
x
B~so (,~2)
CI C2 C3 C4 C5 C6 C7 C8 C9 C10 Cll C12 C13 C14 C15 C16 D1 D2 D4 D5 D7 D8 D9 D11 DI2 D14
0.2736(3) 0.2723(4) 0.2091(3) 0.2113(4) 0.1465(3) 0.0769(3) 0.0104(3) - 0.0590(3) - 0.0627(3) 0.0049(3) -0.0016(3) 0.0635(3) 0.1371(4) 0.2045(3) 0.1398(3) 0.0721(3) 0.3238(4) 0.3275(4) 0.2623(3) 0.1464(3) 0.0123(3) - 0.1071(3) -0.1164(4) -0.0570(4) 0.0584(3) 0.2022(3)
-0.0108(4) 0.0509(3) 0.0047(4) 0.0662(4) 0.0169(4) - 0.0985(4) -0.1450(3) - 0.2523(4) - 0.3160(4) -0.2688(4) -0.3280(4) -0.2797(4) -0.1719(4) -0.1234(4) -0.1049(4) -0.1554(4) 0.0262(4) 0.1373(4) 0.1534(4) 0.0660(4) - 0.0995(4) - 0.2949(4) -0.4036(4) -0.4106(4) - 0.3270(4) -0.1698(4)
0.3866(5) 0.2365(5) 0.0957(5) - 0.0596(5) -0.1953(5) - 0.1856(5) -0.3210(5) - 0.3027(5) - 0.1556(5) -0.0128(5) 0.1457(5) 0.2799(5) 0.2672(5) 0.4023(5) 0.1133(5) -0.026605 0.4961(5) 0.2210(5) - 0.0652(5) -0.3150(6) - 0.4384(5) - 0.4109(5) -0.1437(5) 0.1585(5) 0.3969(5) 0.5187(5)
0.54(5) 0.55(3) 0.36(3) 0.41(3) 0.41(3) 0.36(3) 0.55(3) 0.54(5) 0.55(3) 0.36(3) 0.41(3) 0.41(3) 0.36(3) 0.55(3) 0.23(5) 0.23(5) 1.15(2) 1.15(2) 1.15(2) 1.15(2) 1.15(2) 1.15(2) 1.15(2) 1.15(2) 1.15(2) 1.15(2)
flight path temperature detector sample position data range
HRPD, neutron time-of-flight powder diffractometer 95.9647 m 4.2 K 6Li-doped ZnS scintillation counters, 168.239 ° 20 1m 30000-130000/~s time-of-flight
(0.6-2.6/~ d-spacing) time channel binning A t / t = 1 X 10 -4 experiment duration 12 h Sample compound formula mol. wt.
pyrene C x6Dl0 212.32
Refinement space group Z unit cell refinement
monoclinic, P2 ~ / a 4 whole pattern
unit cell (,~)
D x (g cm -3) observations refined parameters structural profile cell extinction constraints strict (equal ITF) a
a = 12.30267(1), b = 9.98788(1), c = 8.22064(1); /3 = 96.4046(1) ° 1.405 4582 84 20 4 1
C1 = C8, C2 = C7 = C9 = C14, C3 = C6 = CI0 = C13, C4 = C5 = C11 = C12, C15 = C16 D1 = D2 = D 4 = D 5 = D 7 = D8 = D9 = D l l = D12 = D14 thermal parameters all atoms isotropic agreement factors b: X 2 = 11.77, R,~p = 3.16%, Rp = 2.69%, R t = 7.10%, R E = 0.92%
a Isotropic temperature factor. t, defined in Ref. [12].
setup and data collection times are given in Table 1. The data set was focused to a Bragg angle of 168.329 °, normalised to the incident monitor spectrum and corrected for detector efficiency using a spline smoothed diffraction pattern collected from a vanadium rod. After reduction, data in the range
D4 D2
D5
~
D7
16__ Fig. 1. An ORTEP plot of the perdeuterateA pyrene molecule at 4.2 K, with isotropic thermal ellipsoids shown at 85% probability.
492
K.S. Knight et al. / Chemical Physics Letters 258 (1996) 490-494
31000-122500 /zs (0.64-2.54 ,~) were binned in time channels of At/t = 3 × 10 -4 for use in Rietveld refinement.
2.2. Structure refinement
identical. These constraints are summarised in Table 1, along with other relevant refinement parameters.
3. Results
Refinement of the proposed pyrene II structure [8] against the diffraction data was achieved by the Rietveld method [9], as implemented in the time-offlight least-squares program TF12LS [11]. The peak shape used in the refinement was a convolution of a Voigt function with a wavelength-dependent sum of two decaying exponential functions. Strict constraints, which reduce the number of independent variables in the least squares, were used to modify the refinement process by forcing the isotropic temperature factors of chemically equivalent atoms to be
The initial structural model converged rapidly, but assessment of the profile fit showed the presence of extinction due to the high crystalline quality of the sample. A refinable extinction parameter, based on the model of Sabine [13], was introduced for the final cycles of least squares, resulting in the agreement factors listed in Table 1. The refined fractional atomic coordinates and isotropic temperature factors are given in Table 2, and Fig. I shows an ORTEP [14] plot of the refined pyrene molecule. The final
Table 3 Covalent bond lengths (A) and angles (°) for perdeuterated pyrene at 4.2 K (esds in parentheses) C 1- C 2 C2- C3 C3-C4 C4-C5 C5-C6 C6-C7 C7-C8 C8-C9 C9-C 10 CIO-CI 1 C 1- C 2 - C 3 C2-C3-C4 C3- C4-C5 C4-C5-C6 C5-C6-C7 C6-C7-C8 C7-C8-C9 C8- C9-C 10 C9-C10-C11 C10-CI 1-C12 CI 1-CI 2-C13 C12-C13-C14 C13-C14-C1 C14-C1-C2
1.378(6) 1.399(6) 1.420(6) 1.387(6) 1.443(6) 1.386(6) 1.389(5) 1.372(6) 1.440(6) 1.441(6) 122.9(4) 122.5(4) 120.2(4) 122.0(4) 121.6(4) 119.1(4) 122.3(4) 119.6(4) 121.2(3) 119.7(4) 121.8(4) 122.2(4) 120.6(4) 119.1(4)
C 11- C 12 C 12-C 13 C 13-C 14 C 14-C 1 C3-C 15 C 13-C 15 C6-C 16 C 10-C 16 C 15-C 16
C 2 - C 3 - C 15 C14--C13-C15 C3-C 15 - C 13 C 4 - C 3 - C 15 C12-C13-C15 C3-C15-C16 C 13-C 15-C 16 C6-C 16-C 15 C10-CI6-C15 C5-C6-C16 C11-C10-C16 C7-C6-C16 C9-C10-C16 C6-C16-C10
1.376(6) 1.418(6) 1.397(6) 1.424(6) 1.405(6) 1.435(6) 1.433(6) 1.41 4(6) 1.434(6)
117.4(4) 118.0(4) 121.9(4) 120.2(4) 119.8(4) 119.8(4) 118.3(4) 120.8(3) 120.6(4) 116.9(4) 119.5(4) 121.3(3) 119.1(4) 118.4(4)
C1-DI C2-D2 C4-D4 C5-D5 C7-D7 C8-D8 C9-D9 C11-DI 1 C12-D12 C14-D14 C2-C1-D1 C1-C2-D2 C3-C2-D2 C3-C4-D4 C5-C4-D4 C4-C5-D5 C6-C5-D5 C6-C7-D7 C8-C7-D7 C7-C8-D8 C9-C8-D8 C8-C9-D9 C10-C9-D9 CI0-C1 l-D11 C12-C1 I-D11 CI 1-C12-D12 C13-C12-D12 C13-C14-D14 C1-C14--D14 CI4-CI-D1
1.097(6) 1.114(6) 1.077(6) 1.099(6) 1.069(6) 1.098(6) 1.107(6) 1.083(6) 1.080(6) 1.066(6)
122.2(4) 120.2(4) 116.8(4) 117.2(4) 122.5(4) 120.3(4) 117.7(4) 120.8(4) 120.1(4) 119.6(4) 117.8(4) 121.5(4) 118.9(4) 120.0(4) 120.4(4) 118.3(4) 119.9(4) 119.3(4) 120.0(4) 118.6(4)
K.S. Knight et al. / Chemical Physics Letters 258 (1996) 490-494
0
I
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4
i
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I
i
8x10
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I
*
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,
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Whilst powder diffraction experiments provide an alternative in structure determination/refinement when single crystals of a compound are not available, the information content of a one-dimensional powder diffraction pattern does not rival that of a three-dimensional single-crystal equivalent. Accordingly, the refinement of a crystal structure with a large number of independent parameters (such as pyrene) against a powder pattern requires high-quality data, both in terms of instrumental resolution and signal-to-noise ratio. The narrow intrinsic line width of the pyrene sample and the high resolution afforded by HRPD (Ad/d = 4 × 10 - 4 o v e r the whole data range) ensure that the first criterion is met, whilst perdeuteration of pyrene and the large sample volume fulfill the latter. The strict constraints applied to the isotropic temperature factors (ITFs) of chemically equivalent atoms improve the observation-toparameter ratio in the least-squares calculation still further. The ITFs refine to chemically sensible values, and show the increasing extent of atomic vibration moving out from the centre of the molecule towards the periphery.
7x10'
Fig. 2. The final observed (points) and calculated (line) profiles for perdeuterated pyrene II at 4.2 K. The difference [YobsYcate]/o'(Yobs) plot is also shown.
observed, calculated and difference [YobsO'(Yob~) profiles are shown in Fig. 2.
493
Ycalc]//
4. Discussion
Fig. 2 shows the excellent fit of the refined pyrene II model to the data, with no evidence in the pattern of residual pyrene I. The fractional atomic coordinates obtained via Rietveld refinement are in good agreement with those tabulated [8], showing the proposed crystal structure of pyrene II to be essentially correct. The covalent bond lengths and angles for the refined structure (Table 3) are in generally good agreement with those obtained from the single-crystal neutron refinement of pyrene I [4] and, as expected, both the powder and single-crystal neutron diffraction studies yield more accurate values for the C - H (C-D) bond distances than the low-temperature X-ray study [5].
5. Conclusion
The structure of pyrene II, postulated by Jones et ai. [8], has been shown to be substantially correct. More importantly, the high quality of the refinement points to the possibility of obtaining accurate structural information as a function of temperature, up to and through the phase transition.
References [1] R.M. Hochstrasser and A. Malliaris, Mol. Cryst. Liq. Cryst. 11 (1970) 331. [2] R. Zallen, C.H. Griffiths, M.L. Slade, M. Hayek and O. Brafman, Chem. Phys. Lett. 39 (1976) 85. [3] W. Jones and M.D. Cohen, Mol. Cryst. Liq. Cryst. 41 (1978) 103. [4] A.C. Hazell, F.K. Larsen and M.S. Lehmann, Acta CrystalIogr. B 28 (1972) 2977. [5] Y. Kai, F. Hama, N. Yasuoka and N. Kasai, Acta Crystallogr. B 34 (1978) 1263. [6] R.G. Delaplane, W.I.F. David, R.M. Ibberson and C.C. Wilson, Chem. Phys. Lett. 201 (1993) 75.
494
K.S. Knight et a L / Chemical Physics Letters 258 (1996) 490-494
[7] S. Ramdas and J.M. Thomas, J. Chem. Soc. Faraday Trans. 2 72 (1976) 1251. [8] W. Jones, S. Ramdas and J.M. Thomas, Chem. Phys. Lett. 54 (1978) 490. [9] H.M. Rietveld, J. Appl. Crystallogr. 2 (1969) 65. [10] R.M. Ibberson, W.I.F. David and K.S. Knight, Rutherford Appleton Laboratory Report RAL-92-031 (1992).
[11] W.I.F. David, R.M. lbberson and J.C. Matthewman, Rutherford Appleton Laboratory Report RAL-92-032 (1992). [12] R.A. Young, in: The Rietveld method, ed. R.A. Young (Oxford University Press, Oxford, 1995) p. 1. [13] T.M. Sabine, Aust. J. Phys. 38 (1985) 507. [14] C.K. Johnson, Oak Ridge National Laboratory Report ORNL-3794 (1994).