J. Phys. Chem. 1987,91, 3231-3244
used,39due to the relatively weak benzeneargon binding compared to benzene-benzene binding. Such species are therefore not expected to be important under the conditions chosen by Nishiyama and Hanazaki. Even more convincing, however, is that (39) Stephenson, T. A.; Rice, s.A. J . Chem. P h p . 1984,81, 1083-1101. (40) Johnson, R. D.; Burdenski, S.;Hoffbauer, M. A.; Giese, C. F.; Gentry, W. R. J. Chem. Phys. 1986, 84, 2624-2629.
3237
careful work has revealed that C6H6' produced by dissociative ionization cannot be detected by very good limits*' in nozzle beams formed under conditions very similar to those used by Nishiyama and Hanazaki. The experiment of ref 21 is expected to be very sensitive to the SpeCieS C,H6.Ar, (C&,)zAr, and C&Arz if they are present, in analogy with our past experience with many different heterodimers and mixed c.usters.25 Registry
NO. (C6H6)2,6842-25-7; (C6H6)2+, 34514-15-3.
Exploration of Structure, Electron Density Distribution, and Bonding in Coesite with Fourier and Pseudoatom Refinement Methods Using Single-Crystal X-ray Diffraction
K. L. Geisinger,? Department of Geological Sciences, Virginia Tech, Blacksburg, Virginia 24061
M. A. Spackman, Department of Chemistry, The University of New England, Armidale, N.S.W., 2351 Australia
and G. V. Gibbs* Department of Geological Sciences, Virginia Tech, Blacksburg, Virginia 24061 (Received: January 9, 1987)
The structure, the electron density distribution, and the bonding in coesite, a high-pressure polymorph of SiOz, is explored with Fourier summation and pseudoatom refinement of single-crystal X-ray diffraction data. Use of a small crystal (volume 0.29 X mm3) minimized the effects of extinction on the low-angle data but at the expense of reduced reflectivity at high angles. Results obtained are restricted by the resolution ((sin @/A),,, = 0.91 A-') of the data collected. Mean thermal and static deformation electron densities are reported and compared with ab initio SCF-MO results for model silicate molecular systems. The Si0 bond lengths in coesite, compiled from studies completed at a variety of temperatures and pressures, correlate with the angles within and between the silicate tetrahedra, the pressure at which the diffraction data were collected, and the root mean square displacement of the bridging oxygen. The electron density distribution as well as the bond length and angle variations in coesite are quite similar to those calculated for model silicate molecules.
Introduction Silicates are one of the most abundant and widespread mineral groups on earth, comprising more than 95% by weight of the earth's crust and mantle. In addition to being widely used as building materials, they have found widespread use in the manufacture of glasses, ceramics, sieves, selective sorbents, adsorbents, catalysts, silicone products, and electronic devices. If we are to improve our understanding of the properties of these materials, it is imperative that we have a good understanding of the properties of the S i 0 bond. Recent near-Hartree-Fock SCF-MO calculations completed on a variety of silicate molecules have generated S i 0 bond lengths and SiOSi and OSiO angles that duplicate those in chemically related silicate minerals. The close similarity of the S i 0 bond lengths and angles in both of these systems suggests that the forces that bind the atoms of a silicate molecule together are not unlike those in a chemically related silicate crystal. In this study, we report a study of the structure and the electron density distribution in the high-pressure silica polymorph coesite, using Fourier mapping and pseudoatom refinement of X-ray diffraction data in a continuing effort to improve our understanding of bonding in silicates.' The charge density difference maps provided by these data will be compared with theoretical difference maps calculated from SCF-MO results for silicate molecules. The fact that the theoretical maps reproduce many of the features observed in the experimental maps will be taken as evidence that molecular orbital results for selected molecules mimic rather well 'Current address: H P ME 03 070, Corning Glass Works, Corning, NY 14831.
0022-365418712091-3237$01.50/0
the charge density distributions in chemically similar crystals. Coesite is an ideal material for studying the properties of the Si0 bond for several reasons. First, its crystal structure is well-defined, having been solved by Zoltai and Buerger2 (1959) and refined several times for various purposes and under a variety of Second, it is centrosymmetric. Thus, there is little ambiguity in the assignment of structure factor phases in the refinement process. Finally, its fundamental domain contains eight nonequivalent S i 0 bonds involved in five nonequivalent disiloxy (SiOSi) groups, providing several observations that can be compared self-consistently. Coesite is a framework silicate in which each silicon atom is bonded to four oxygen atoms forming a silicate tetrahedron, and each oxygen atom is bonded to two silicon atoms forming a SiOSi disiloxy group. A drawing of the contents of the unit cell (Figure 1) shows some of the gross features of the framework and emphasizes the layerlike nature of the structure parallel to (010). As Zoltai and Buerger2 pointed out in their original structure determination, the silicate tetrahedra in the cell form two kinds of 4-membered rings. One contains two of each of the 0 3 and (1) Gibbs, G. V. Am. Mineral. 1982, 67, 421. (2) Zoltai, T.; Buerger, M. J. 2.Kristallogr. 1959, 1 1 1 , 129. (3) Araki, T.; Zoltai, T. Z . Krisfnllogr. 1969, 129, 318.
(4) Gibbs, G. V.; Prewitt, C. T.; Baldwin, K. J. 2. Kristallogr. 1977, 145, 108. ( 5 ) Gibbs, G. V.; Hill, R. J.; Ross, F. K.; Coppens, P. GACIMAC Abstracts with Programs 1978, 3, 407. (6) Levien, L.; Prewitt, C. T. A m . Mineral. 1981, 66, 324. (7) Smyth, J. R.; Smith, J. V.; Artioli, G.; Kvick, A. J . Phys. Chem. 1987, 91. 988.
0 1987 American Chemical Society
3238 The Journal of Physical Chemistry, Vol. 91, No. 12, 1987
Geisinger et al.
TABLE I: %A
Crystal Data
space group radiation cell dimensions
density (calcd), g/cm'
c2/c Zr-filtered Mo K a (A = 0.7107 A) a = 7.1367 (4)" b = 12.3695 (7) c = 7.1742 ( 5 ) fi = 120.337 (3) 2.921
Z
16
linear absorpn coeff b, cm-' 10.704 transmission factor range 0.859-0.948 "Esd's in parentheses refer to last decimal place. The electron distribution in coesite is examined with limited Fourier and direct space mappings of the mean thermal and static deformation density. Features in these maps are compared among the nonequivalent disiloxy groups. Deformation features in coesite are also compared with theoretical deformation densities in disiloxy-containing molecules as well as the deformation density in stishovite determined in a recent analysis of merged powdersingle-crystal X-ray data.l I Figure 1. An ORTEP drawing of the coesite structure viewed down [OOl]. Si and 0 atoms are represented by 50% probability thermal ellipsoids from the IAM + refinement.
Figure 2. An ORTEP drawing of the "double crankshaft" chain running parallel to [loll. The Si and 0 atoms are represented by 90% probability thermal ellipsoids from the IAM + refinement.
0 4 oxygens and lies approximately parallel to (101). The second contains two of each of the 0 3 and 05 oxygens and is approximately parallel to ( 1 10). These rings are linked together to form a "double crankshaft" chain similar to that observed in the feldspars and shown in Figure 2 . These chains run parallel to [loll and are cross-linked to each other by 01 and 0 2 to form a framework. The framework differs from that of feldspar in that the chains in m i t e are related by glide planes (space group 12/a in the feldspar setting with cell dimensions (A) a = 7.1 19, b = 12.370, c = 7.174; /3 = 120.09') whereas those in feldspar are related by mirror planes.*s9 Although single-crystal X-ray data have been collected and published for coesite several times, none of these data sets has the accuracy required for a multipole analysis of the electron density distribution. Therefore, we attempted to collect a more accurate X-ray data set using a small crystal to help reduce the severe extinction encountered in previous refinement^.^^'^ The analysis of the new data employs a pseudoatom expansion model that allows for aspherical deformations of electron density and is thus a more appropriate model for bonded atoms than a simple spherical scattering model. For comparison, refinement results using a spherical scattering model are provided. (8) Megaw, H. D.A d a Crystallogr. B 1970, 26, 261. (9) Boisen, Jr. M. B.; Gibbs, G.V. Mathematical Crystallography. Reviews in Mineralogy; Mineralogical Society of America; Washington, DC, 1985; Vol. 1 5 , p 246. (10) Ross, F. K. Trans. A m . Crystallogr. Assoc. 1980, 26, 79.
Experimental Procedures Crystal Sample. Crystals of coesite synthesized at 45 kbar and 650 'C were generously provided by Dr. C. T. Prewitt of the Carnegie Institute at Washington, D.C. The crystal selected for study was a transparent plate bounded by six plane faces; two of these had indices (010)while the remaining four were not indexed. The average dimensions of the crystal were measured to be 0.048 X 0.070 X 0.086 mm by using an image-splitting eyepiece on a polarizing microscope fitted with a spindle stage. The crystal was deliberately chosen to be small in an effort to minimize extinction effects. Optical examination as well as 100-h-exposure precession photographs indicated that the crystal was not twinned. The precession photographs indicated the crystal symmetry to be consistent with equivalent space group types B2/b, C2/c and 12/a determined in earlier s t u d i e ~ . ~ . ~ . ~ The crystal was mounted in an arbitrary orientation on a Picker four-circle diffractometer automated with the Kreisel Control X-ray diffractometer control system. The unit cell dimensions (Table I) and the orientation matrix were obtained in a leastsquares refinement using the setting angles for the Mo Ka,peaks of 20 automatically centered reflections in the range 28 = 52-62O. The cell dimensions are in good agreement with those determined for coesite by previous worker^.^^^^^ Data Collection and Reduction. Diffraction intensities were measured with Zr-filtered Mo K a radiation using the 8-28 step scan method with 0.04' 28/step and counting times of 10 s/step in the 0-40' 20 range and 20 s/step for 28 > 40'. Step scanning was employed because of the improved error estimates provided by the method relative to continuous scanning techniques and the advantage of being able to examine the individual diffraction profiles.I2 A dispersion-modified scan range (A8 = 2.0 0.7 tan 8) was employed to ensure that at least one-sixth of the total scan on both sides of the Mo K a peak was background. Due to the large amount of time involved with step-scan techniques only those diffraction data with h k = 2n consistent with a C-centered lattice type were collected. However, all h01 data were collected as a further check on the presence of a c-glide. With these s mmetry constraints, all diffraction data up to sin 8 / A = 0.91 1-l(2fImax= 80') were sampled for a total of 7255 data. Efforts to extend data collection beyond 28 = 80° proved unsuccessful due to the extreme weakness of these diffraction data. During data collection, three standard diffraction intensities sampled were checked at least every 6 h. Later analysis indicated two of these standards to be affected by the P-filter cutoff (discussed below), but the third was unaffected and showed a 0.8% agreement factor.
+
+
(1 I ) Spackman, M. A.; Hill, R . J.; Gibbs, G . V. Phys. Chem. Minerak,
in
press.
(12) Blessing, R. H.; Coppens, P.; Becker, P. J . Appl. Crystallogr. 1974,
7. 488.
The Journal of Physical Chemistry, Vol. 91, No. 12, I987 3239
Structure and Bonding in Coesite
TABLE 11: Scale and Extinction Parameters and Agreement Factors for Coesite Refinements‘ refinement scale k isotropic extinction 104a no nv €
IAM IAM+
1.019 ( l ) b 1.011 ( 1 ) C
0.20(1) 0.26( 1)
1716 1716
58 21 1
28233 2565
%R(F2)
%Rw(F2)
aof
2.70 1.09
3.87 1.17
4.12 1.31
‘no = number of observations. nv = number of variables. gof = goodness of fit = [ r / ( n o - n ~ ) ] l / ~ .bEsd’sin parentheses refer to last decimal place. ‘Scale estimated by (E monopole populations)/Fm. TABLE 111: Positional and Thermal Parameters from IAM Refinement parameter Si1 Si2 01 X 0.14030 (5)’ 0.50672 (5) 0 Y 0.10831 (3) 0.15806 (3) 0 z 0.07227 (5) 0.54066 (5) 0 UII, A2 0.0055 (1) 0.0058 (1) 0.0089 (5) U2,, A2 0.0046 (1) 0.0052 (1) 0.0060 (4) 0.0044 (1) U33,A2 0.0051 (1) 0.0095 (5) u12, A2 -0.0010 (1) -0.0004 (1) -0.0030 (4) U13, A2 0.0027 (1) 0.0028 (1) 0.0036 (4) u23,
B,,b
A2 A2
-0.0006 (1) 0.40 (1)
-0.0004 (1) 0.40 (1)
-0.0011 (4) 0.64 (2)
02
03
04
05
112 0.11631 (10) 314 0.0109 (5) 0.0084 (5) 0.0059 (4) 0 0.0057 (4) 0 0.66 (2)
0.26655 (13) 0.12315 (7) 0.94057 (13) 0.0086 (3) 0.0125 (4) 0.0097 (3) -0.0025 (3) 0.0065 (3) -0.0010 (3) 0.81 (2)
0.31104 (13) 0.10375 (8) 0.32787 (13) 0.0104 (3) 0.0112 (4) 0.0053 (3) -0.0027 (3) 0.0013 (3) -0.0016 (3) 0.71 (2)
0.01753 (14) 0.21195 (7) 0.47835 (15) 0.0099 (4) 0.0052 (3) 0.0128 (4) -0.0006 (3) 0.0062 ( 3 ) 0.0005 (3) 0.73 (2)
“Esd’s in parentheses refer to last decimal place. * B , = ( 8 r 2 / 3 ) ( U I + , U2, + ~ 7 ~ ~ ) . With the completion of data collection, the step-scan data were reduced to integrated intensities by using a profile analysis technique’* which incorporates an algorthimI3 for determining peak boundaries. Each of the profiles for which I 1 2 4 0 (a from counting statistics) was plotted and examined by hand to ensure that there were no profile analysis errors such as contamination by multiple diffraction maxima or exclusion of the a2 peak from the calculated peak region. Only the 5,0, 6 showed strong evidence of multiple diffraction. This peak showed large residuals in subsequent refinements and was downweighted by a factor of 10. Close examination of the profiles for the strong low-angle data (
