CHAPTER 1
Part I
ELECTRON DIFFRACTION
Introduction to Part I : Electron Diffraction
BY L. E. SUTTON
This year, the section on electron diffraction is brief. Our intention and hope was that it should be much longer than it is; but the electron diffraction community is a relatively small one, its members are busy with all sorts of tasks and so, being somewhat exhausted, it was unable to repeat the effort made for Volume 1. We do, however, have a very useful chapter on Results, again contributed by Dr. Brian Beagley. Next year we hope to have a more normal-sized section.
The general remarks about conventions, especially the use of rg and the reporting of error, which were made in the Introduction to Volume 1, still apply.
Structures Determined by Gas-phase Electron Diffraction
BY B. BEAGLEY
1 Introduction
The previous volume (ref. 1, Chapters 2 and 3) reported structure determinations by electron diffraction mostly published before early 1972. The present chapter continues this work, covering the literature to mid-autumn 1973. More precisely, the coverage includes all relevant papers abstracted in Bulletin Signalétique up to and including the October 1973 edition, and all relevant papers found under the keywords ELECTRON DIFFRACTION or MOLECULAR STRUCTURE in Chemical Titles up to and including issue no. 19, 1973. As in ref. 1, parameters quoted are rg values, and error estimates are estimated standard deviations (unless otherwise stated); the Reporter has made subjective estimates where necessary.
The trend reported earlier (ref. 1, Chapter 4) of combining data from rotational spectroscopy with data from electron-diffraction studies, to give increased precision, continues to gain momentum, as many of the papers reported below will confirm. A discussion of the various kinds of structural parameters (rg, rα, rz, etc.) has been given in that chapter, and an extremely useful summary of the way in which they may be obtained and interconverted has been given in Chapter 12 of ref. 2. Other chapters of ref. 2 discuss various aspects of vibrational spectroscopy associated with the calculation of vibrational amplitudes, and review the literature of the subject, including coverage of numerical results. Other important work in this area includes new methods for the calculation of perpendicular amplitudes, which, as well as the better known parallel amplitudes, are required during the interconversions of the structural parameters mentioned above. Both types of amplitude are being used increasingly as fixed parameters in structure determinations, particularly where there are resolution problems. Ref. 2 also includes chapters on the interpretation and precision of gas-phase electron diffraction data, and some experimental results.
Conformational calculations are also being used increasingly in conjunction with electron-diffraction studies, primarily as corroboration of the results, but occasionally as constraints in the refinement (rather as rotational constants are often used). Considerable success in predicting molecular geometry by conformational calculations has been achieved (as comparison with the electron-diffraction results often shows); this is particularly so for molecules which are strained by steric factors or ring formation, i.e. where non-bonded interactions are important. However, conformational calculations are not entirely adequate in their present form, because exact forms of the necessary energy functions are not available.
The traditional wave-mechanically-based methods of rationalizing bond lengths in terms of changes in conjugation and hybridization (ref. 1, p. 64) are still proving of value. Of course, the various kinds of fuller wave-mechanical treatments continue to be applied to predict molecular geometry: e.g. the CNDO and CNDO/2 methods, and the ab initio method, although the latter requires a vast amount of computing time.
Where lone pairs of electrons are present the valence-shell electron-pair repulsion (VSEPR) theory is being increasingly cited to rationalize results. However, in cases where considerable electronegativity differences occur across bonds, there is a growing tendency to invoke electrostatic attraction as well as repulsion to explain their lengths (ref. 1, p. 95). The geometry of molecules having second-row atoms (especially Si, P, and S) adjacent to electron donors continues to be discussed in terms of π-bonding involving d-orbitals
2 Hydrocarbons
A new calculation of zero-point average parameters for ethane gives: for H3C-CH3, r0α = rZ = 1.5323 Å; for D3C-CD3, r0α = rZ = 1.5299 Å; for D3C-CH3, rz = 1.5310 Å. This work employs 'large amplitude theory' to deduce, using electron-diffraction and rotational spectroscopic data, whether D3CCH3 is geometrically distorted in the torsionally excited state; the conclusion is that the C-C bond is elongated by 0.0028 Å upon excitation, and [??] HCH decreases by 0.05°.
New work on propane and isobutane supersedes all earlier studies (ref. 1, p. 61). In propane, the C-C bond length is found to be rg = 1.532 [plus or minsu] 0.001 Å by electron diffraction alone; other parameters are C-H (mean) = 1.107 [+ or -] 0.002 Å, [??] LCCC = 112.4 [+ or -] 0.4°, and [??] HCH = 107 [+ or -] 3° in the methyl groups if the methylene [??]HCH angle is assumed to be 106.1°. Vibrational amplitudes were fixed at values calculated from spectroscopic data, and similarly calculated shrinkage corrections were applied. Rotational constants from microwave spectroscopy were used jointly with the electron diffraction data to give a zero-point average structure (rav, see ref. 1, pp. 61, [??] CCC = 112.0°, [??]HCH(CH3) = 107.9°, and [??]HCH(CH2) = 107.8°.
The new study of isobutane (1) also incorporated vibrational and rotational spectroscopic data, and gave rise to the rg and zero-point average structural parameters given in Table 1.
Comprehensive results for substituted ethylenes are now becoming available (Table 2; see also ref. 1, pp. 64 — 65). The authors of the most recent work draw attention to the possible trends in both C–C and C=C bond lengths which appear to increase as additional methyl groups are added, and they further note that the values of [??] C–C=C can be accounted for in terms of steric interaction between methyl groups. Distinguishing structurally between the geometric isomers (2a) and (2b) of 3-methylpent-2-ene has caused confusion in the past, and electron diffraction has now been used to assist the resolution of the prob1em. The isomer boiling at 70.4 °C has the so-called E-configuration (2a) and that boiling at 67.7 °C the Z-configuration (2b). The bond lengths and angles are largely in keeping with the trends discussed above. The authors discuss the possibility of non-planar arrangements around the double bond, but in both isomers the only carbon atom definitely out of the skeletal plane is C(5). Although lacking geometrical isomerism, related 2-methylbut-l-ene (2c) is a mixture of two conformers, one of which has C(4) in the skeletal plane (ref. 1, p. 66); in the pentene, extra steric factors presumably prevent the existence of a skeletally planar form.
Electron-diffraction studies show that cyclic molecules often have flexible rings, i.e. the rings possess at least one torsional degree of freedom. A theoretical analysis has been made of the geometric constraints in six- and eightmembered rings. It is shown that a six-membered ring with given bond distances and bond angles is rigid (no torsional degrees of freedom) unless it possesses a non-intersecting two-fold axis of symmetry, in which case it is flexible. (A non-intersecting axis is one which does not pass through any atoms or bonds.) Thus the chair form of cyclohexane is rigid with torsion angle τcccc related to bond angle θCCC by cos τ = -cos θ/(1 + cos θ), but the C2v boat form and the D2 twist form are members of a family of flexible forms which can be changed continuously into each other by changing the torsion angles. The eight-membered ring with fixed bond distances and bond angles, and with two torsion angles fixed at zero (e.g. cyclo-octa-1,5-diene) also exists in rigid or flexible forms, depending on the absence or presence of a non-intersecting two-fold axis. Molecules such as cyclo-octa-1,4-diene, for which such two-fold symmetry can only be approximately fulfilled, may also appear to be flexible.
The confusion reported in ref. 1 (p. 69) over the length of the C-C bond in cyclohexane has been resolved by the combined work of two groups; their averaged results are C-C = 1.53 [+ or -] 0.001 Å, C-H = 1.121 [+ or -] 0.002 Å and [??] CCC = 11 1.4 [+ or -] 0.1° (the larger value for C- C quoted earlier was in error). Other recent values for these parameters are: 1.530 [+ or -] 0.003, 1.123 [+ or -] 0.004 Å, and 11 1.1 [+ or -] 0.1°. The dihedral angles found by these two studies (according to the above constraint) are τcccc = 54.9 and 55.8°, respectively. In methylcyclohexane,16 the mean dihedral angle is 55.2 [+ or -] 0.9°, C- C (mean) = 1.529 [+ or -] 0.003 Å, [??] CCC(endocyc1ic) = 11 1.3 [+ or -] 0.3°, and [??] CCC(exocyc1ic) = 110.1 [+ or -] 1.0°. The methyl group occupies an equatorial position. The authors compare their concurrent studies of cyclohexane and methylcyclohexane, noting that conformational calculations predict a slight flattening of the ring in the methyl compound. Their results do not conclusively confirm this, but the dihedral angle observed in 1,l-dimethylcyclohexane [τ (mean) = 51.7 [+ or -] 1.0°] suggests a significant flattening when methyl groups occupy both equatorial and axial positions of a given carbon atom. 1,l-Dimethylcyclohexane has C–C (mean) = 1.535 [+ or -] 0.002 Å, and the [??] CCC lie in the range 106 — 115°, in agreement with conformational calculations. New work on cis-1,4-di-t-butylcyclohexane suggests that at 110 °C it exists as a mixture of approximately one-third chair and two-thirds non-chair forms, rather than in one flexible non-chair form (ref. 1, p. 69). The new work is noteworthy because of the manner in which conformational calculations of the Westheimer–Hendrickson type were used to provide geometrical and other constraints to facilitate the interpretation of the electron-diffraction data. The procedure employed published force fields in the calculation of minimum energy conformations and corresponding amplitudes of vibration. The results derived were used to calculate radial distribution curves for comparison with the experimental one. The best fit between calculated and observed curves corresponded to a mixture of all three minimum energy conformations, all of which have similar conformational energies. Although the composition of the mixture was somewhat sensitive to the force field used, considerable confidence in the qualitative results is possible because of the excellent agreement with the diffraction data. The mean C–C length (1.542 [+ or -] 0.003 Å) agrees with the result of the earlier study, suggesting longer bonds, on average, than in cyclohexane and n-paraffins.
A more precise determination of the structure of bicyclopropyl (ref. 1, p. 70) has been carried out, and the origins of the large torsional amplitudes of vibration about the central C–C bond have been more precisely defined. To do this, it was necessary to calculate vibrational amplitudes for the nonbonded distances as a function of the dihedral angle c about the central bond, from [empty set] = 0° (syn form) to [empty set] = 180° (anti form). In least-squares refinements of the structure, calculated intensities allowing for the torsional vibrations were derived by summing contributions from individual structures with different [empty set], using the calculated amplitudes appropriate to each [empty set] as fixed parameters. Individual structures were given weights according to the potentials assumed to govern the vibrations. Best agreement with experiment was achieved for a 1 : 1 mixture of anti and gauche ([empty set] = 49 [+ or -] 7°) forms, where the governing potentials are those of a square well and a Gaussian distribution, respectively. The square (flat-bottomed) well stretches for 100° on either side of the anti conformation, and the torsional amplitude about the gauche form is 15°. This conformational behaviour is well supported by the authors' own conformational calculations. The main geometrical parameters found for the molecule are C–H = 1.108 [+ or -] 0.006 Å, C–C(bridge) = 1.50 [+ or -] 0.03 Å, and C- C(rings) = 1.509 [+ or -] 0.006 Å.
Continued Russian work on cyclohexene (see ref. 1, p. 71) gives more precise values for the bond lengths: C(l)=C(2) = 1.341 [+ or -] 0.009 Å, C(2)–C(3) = 1.503 [+ or -] 0.009 Å and C(3)–C(4) = C(4)–C(5) = 1.535 [+ or -] 0.009 Å. On the basis of the analysis of ring constraints discussed above, trans-cyclo-octene, which has C2 symmetry, could assume either a rigid chair conformation (3a) or a rigid 'crossed' form (3b), because the two-fold axis passes through bonds in both cases. Only the chair form (3a) is observed, presumably because it has the lower energy. A least-squares refinement based on radial distribution curves gave the following bond distances : C–C(mean) = 1.538 [+ or -] 0.003 Å, C=C = 1.363 [+ or -] 0.008 Å, and C–H = 1.107 [+ or -] 0.002 Angstrom. A new study of cyclohepta-l,3-diene (4) confirms the C8 symmetry with all the ring atoms, but one, coplanar (see ref. 1, p. 73). The ring-puckering angle α is 64 [+ or -] 1° and the bond lengths are C=C = 1.348 [+ or -] 0.005 Å, =C–C= = 1.45 [+ or -] 0.01 Angstrom, =C–CH2 = 1.51 [+ or -] 0.02 Å, and CH2CH2 = 1.52 [+ or -] 0.02 Å. The ring lengths are not unlike those found in other cyclic 1,3-dienes and in related acylic molecules with butadiene-like conjugation.
In bicyclo[2,1,0]pentene (5), a close relative of unstable cyclobutadiene, the two planar rings are inclined at an angle of 114.5° compared with the 109.4° in bicyclo[2,1,0]pentane (6). In the pentene, C=C = 1.341 Å, =C–C = 1.511Å, CH–CH2 = 1.533 Å, and C–C(bridge) = 1.543 Å (all [+ or -] 0.004 Å); the latter is much longer than in the pentane. It was noted in ref. 1 (p. 76) that frequently a fused cyclopropane (cp) ring has the same conformation-determining effect as a double bond. For example : (a) bicyclo[2,1,0]pentane (6) and cyclobutene (7) both have planar four-membered rings; (b) the conformation of the six-membered ring of bicyclo[4,1,0]heptane (8) resembles that of cyclohexene (9). It is not surprising, therefore, that the conformation of bicyclo[4,1,0]hept-2-ene (10) resembles that of cyclohexa-1,3-diene (1 1). This bicycloheptene exists as a mixture of the forms (10a) and (10b) in the ratio 70% : 30 % ([+ or -] 5 — 10%) and has bond lengths comparable with those in related molecules: C=C = 1.345 [+ or -] 0.006 [Angstorm], =C–Ccp = 1.475 [+ or -] 0.015 Å, Ccp–Ccp (mean) = 1.508 [+ or -] 0.006 Angstrom, Ccp–CH2 = =C–CH2 = 1.55 [+ or -] 0.02 Å, and CH2–CH2 = 1.556 Å. The constrained planarity of the four-membered rings in cyclobutene (7) and bicyclo[2,1,0]pentane (6) relaxes in bicyclo[2,2,0]hexane (12) to a pucker of β = 12 [+ or -] 2° compared with the 35° unconstrained puckering in cyclobutane itself. Bicyclo[2,2,0]hexane has C2 symmetry, and a mean C–C bond length of 1.556 [+ or -] 0.002 Å; the values obtained for individual bonds are C–C (bridge) = 1.58 [+ or -] 0.02 Angstrom, CH-CH2 = 1.56 [+ or -] 0.01 Å, and CH2–CH2 = 1.54 [+ or -] 0.02 Å. The inter-ring [??] CCC at the bridgehead carbon atoms is θ = 113.5 [+ or -] 1.1°. There is evidence to suggest that despite the large uncertainties in the individual bond lengths, the bridge bond is the longest in the molecule; the authors support this assertion by reference to other molecules in which four-membered rings are fused together.
In bicyclo[n,1,1] systems, the cyclobutane (cb) puckering angle is constrained to be larger than the 35° of cyclobutane itself, when n is small. Thus in bicyclo[2,1,1]hex-2-ene (13) the puckering angle is 56.5 [+ or -] 1.3°, which may be slightly larger than the 45-55° observed in the corresponding bicyclohexane (ref. 1, p. 77). The hexene has C2v symmetry, with C=C = 1.334 [+ or -] 0.005 Å, = C–Ccb = 1.539 [+ or -] 0.0008 Å, and Ccb - Ccb = 1.551 [+ or -] 0.006 Å. Related tricyclo[3,3,0,02,6]oct-3-ene(14) has C =C = 1.35 [plus or minus] 0.01 Å, =C–Ccb = 1.50 [+ or -] 0.01 Å Ccb - Ccb = 1.58 [+ or -] 0.04 Å; the authors note that some of these values are quite different from those for corresponding bonds in tricycl0[3,3,0,02,6]octane (ref. 1, p. 78). The [3,1,1] system β-pinene appears to exist as a mixture of the forms (15a) and (15b), with form (15a) predominant (65% according to conformational calculations). However, the five atoms associated with the fourbond bridge are almost coplanar as in α-pinene (ref. 1, p. 78). The average C–C single bond length is 1.536 [+ or -] 0.008 Å.
