J . Phys. Chem. 1991, 95, 1597-1600
1597
Molecular Structure and Conformation of Gaseous 3-Azetidinol As Determined by Electron Diffraction and ab Initio Calculations Kolbjarn Hagen,*,+Hans Vidar Volden,t Uffe Anthoni,s Carsten Christophersen,( Michael Gajhede,l and Per Halfdan Nielsenl Department of Chemistry, University of Trondheim, N - 7055 Trondheim, Norway, Department of Chemistry, University of Oslo, P.O. BOX 1033, Blindern, N-0315 Oslo 3, Norway, and The Chemical Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark (Received: February 27, 1990; In Final Form: September I I , 1990)
Gaseous 3-azetidinol has been investigated by electron diffraction (ED) and ab initio calculations. The molecules exist as a mixture of two conformers with the OH group either pseudoequatorial or pseudoaxial to the four-membered ring. At 100 'C the ED experiment gave a mole fraction for the equatorial form of 0.77 (8). The values obtained from ED, with estimated 2a uncertainties, of the principal distances (r,) and an les (La) are as follows: r(O-H) = 0.971 (26) A, r(N-H) = 1.033 (70) A, r(C-H) = 1.112 (19) A, r(C-0) = 1.406 (4) r(C-N) = 1.486 (2) A, r(C-C) = 1.562 (7) A, LC-C-C = 84.9 (9)', LC-C-0, = 117.2 (S)', LC-N-C = 90.7 (7)', LC-C-N = 89.0 (8)', and LO (the angle between the C-C-C and the C-N-C planes) = 153.2 (23)'.
fi,
full geometry optimization on isolated 3-azetidinol in the 'A' state (point group C,) using a 6-31G** basis set. The hydroxyl group The structure and conformation of 3-azetidinol has recently been studied by X-ray diffraction' and vibrational ~pectroscopy.~-~ was placed in the equatorial position. The minimum-energy conformation was determined at the Hartree-Fock (HF) level by Several conformers are possible with the OH group pseudoaxial analytical gradient proced~res.'~Harmonic vibration frequencies or pseudoequatorial to the four-membered ring (Figure 1). In were determined by using analytical second derivatives in order each of these two forms, the OH group may occupy different to characterize the stationary points found as minima or as saddle positions relative to the ring. Intramolecular hydrogen bonding points. A similar calculation was performed on 3-azetidinol with between OH and N may occur in the axial conformer while the hydroxyl group in the axial position. This conformer was intermolecular hydrogen bonding is possible in the condensed assumed to have C, symmetry because of the possible intramophases. The conformation and hydrogen-bonding properties are lecular hydrogen bond in this form. The results are summarized of interest because of the pharmacological activities of 3-azetidinol in Table 111. and N-substituted 3-azetidinols. This electron diffraction study To investigate the validity of the applied C, symmetry in the was initiated to provide structural data for 3-azetidinol in the gas equatorial conformation, the H-0-C-H torsional angle energy phase. surface was calculated with the smaller 6-31 1G basis set. Full geometry optimization was made for every 10'. The results are Experimental and Data Reduction Section shown in Figure 4. Since the lowest energy minimum was not found for = 0 or 180', these calculations did not confirm the 3-Azetidinol was prepared as described earlier.' Electron assumptions about C, symmetry. diffraction photographs were recorded at about 100 'C with a Balzers E1digraph4sson Kodak electron image plates. The electron Structural Analysis by ED wavelength was calibrated against benzene: and optical densities were measured with a Joyce Loebl microdensitometer. Five plates Except for the hydrogen atom of the OH group, 3-azetidinol from the long (498.94 mm) and four from the short (248.93 mm) was assumed to have C, symmetry. With some assumptions (see nozzle-to-plate distance experiments were selected for analysis. The data were reduced in the usual and a calculated ( I ) Gajhede, M.; Anthoni, U.; Christophersen, C.; Nielsen, P. H. Acto backgroundIOwas subtracted from the data for each plate to yield Crystallogr. 1989, 845, 562. experimental molecular intensity curves in the form SI&). The (2) Anthoni, U.; Hojgaard Christensen, D.; Christophersen, C.; Gajhede, M.; Henriksen, L.; Faurskov Nielsen, 0.;Nielsen, P. H. J . Mol. Struct. 1990, average experimental intensity curves are shown in Figure 2. The 220, 43. ranges of intensity data were 2.00 Is/A-' I14.75 and 4.00 I (3) Anthoni, U.; Christophersen, C.; Nielsen, P. H.; Hojgaard, D.; Faurs1A-I I29.50, and the data interval was As = 0.25 A-l. The skov Nielsen, 0.;Gajhede, M. Spectrochim. Acta 1989, 45A, 1157. intensity and background data are available as supplementary (4) Zeil, W.; Haase, J.; Wegmann, L. Z . Instrumentenkd. 1966, 74, 84. (5) Bastiansen, 0.; Graber, R.; Wegmann, L. Balzers High Vac. Rep. material (see paragraph at end of text). Radial distribution (RD) 1969, 25, I . curves (Figure 3) were calculated by Fourier-transforming the (6) Tamagawa, K.; Iijima, T.; Kimura, M. J . Mol. Struct. 1976,30, 243. function sf'(s) = SI&) ZCZNAc-IAN-Iexp(-B$), with B = 0.0020 (7) Hagen, K.; Hedberg, K. J . Am. Chem. SOC.1973, 95, 1003. A*. Electron scattering amplitudes (f=A/s2) and phases (q) for (8) Gundersen, G.; Hedberg, K. J . Chem. Phys. 1969,51, 2500. (9) Andersen, B.;Seip, H. M.; Strand, T.; Sterlevik, R. Acta Chem. S c a d . all calculations were taken from tables." Introduction
Ab Initio Calculations
Ab initio calculations on 3-azetidinol were performed by using the GAUSSIAN 86 (1984) program.'* The first calculation was a 'University of Trondheim. *University of Oslo. 5 University of Copenhagen.
0022-3654/91/2095-1597$02.50/0
1969, 23, 3224. (10) Hedberg, L. Abstracts of Papers, Fifth Austin Symposium on Gas Phase Molecular Structure, Austin, TX, March 1974; p 37. (11) Schafer, L.; Yates, A. C.; Bonham, R. A. J . Chem. Phys. 1971.56, 3056. (12) Frisch, M. J.; Binkley, J. S.; Schlegel, K. B.; Raghavachari, K.; Melius, C. F.; Martin, R. L.; Stewart, J. J. P.; Bobrowicz, F. W.; Rohlfing, C. M.; Kahn, L. R.; Defrees, D. J.; Seeger, R.; Whiteside, R. A.; Fox, D. J.; Fleuder, E. M.; Pople, J. A. GAUSSIAN 86; Carnegie-Mellon Quantum Chemistry Publishing Unit: Pittsburgh, PA, 1984. (13) Pulay, P. Mol. Phys. 1969, 17, 197.
0 1991 American Chemical Society
1598 The Journal of Physical Chemistry, Vol. 95, No. 4, I991
Hagen et ai.
I
\
\*
i
't'i
Figure 1. Diagram of the equatorial conformer of 3-azetidinol with atom numbering.
I
I
180
160
1LO
120
100
80
60
40
0
20
+,/deg
Figure 4. Calculated energy as a function of H 4 - C - H torsion angle *I.
TABLE I: Structure Results for 3-Azetidinol' param
Diff
-
-
Figure 2. Intensity curves, SI&), for 3-azetidinol. Experimental curves are averages of all plates for the two camera distances. The theoretical curve was calculated from structural parameters in Table I. Difference curves are experimental minus theoretical.
rBor La 0.971 (26) 1.033 (7oj 1.112 (19) 1.406 (4) 1.486 (2) 1.562 (7) 84.9 (9) [ 108.81 [110.0] [111.5] [116.6] 117.2 (5) 153.2 (23) [ 180.0] [ 180.01 77 (8)
ra
0.936 1.01 I 1.091 1.401 1.479 1.559
Dependent Parameters 90.7 (7) 89.0 (8) [ 114.01 [115.3] [ 110.61 [ 1 18.21 2.133 (16) 2.106 (14) 2.532 (6) 2.207 (1 2) 2.182 (15) 2.212 (12) 2.1 52 (55) 2.671 (29) 3.050 (22) 1.951 (18) 3.339 ( I I ) 2.665 (12) 3.416 (17) 2.665 (30) 4.049 (66) 2.926 (31) 2.665 (1 2) 2.852 (45) 2.980 (1 7) 4.016 (60) 0
I
2
3
r/A
4
Ib 0.066 0.070 0.075 0.037 0.042 0.042
1
0.066 0.063 (5) 0.078 0.115 0.1 13 0.1 IO 0.108 0.143 0.106 0.113 0.079 (13) 0.166 0.167 0.138 0.154
0.117 0.220 0.206 0.099 0.124
curves are calculated for 100%axial conformer (A), for 100% equatorial conformer (B), and for a mixture of 77% equatorial and 23% axial conformers (C). The vertical lines indicate the important interatomic distances; their lengths are proportional to the weights of the distances. Difference curves are experimental minus theoretical.
"Distances ( r ) and amplitudes (I) in angstroms; angles (f) in degrees. Uncertainties in parentheses are estimated 2u. Quantities in square brackets were kept constant in the final least-squares refinement. bQuantities in braces were refined as a group. 'Angle between the C-C-C and C-N-C planes. dH-O-C-H torsion angle in the equatorial conformer. H-0-C-H torsion angle in the axial conformer.
below), the geometry of 3-azetidinol can be defined by 15 parameters: 6 bond distances (r(O-H),r(N-H), r(C-H), r(C-C),
r(C-O), and r(C-N)), 6 valence angles (LC-C-C, LO-C-C, LH6-C-C, LH9-N-C, LH-C-H, LC-O-H), 2 torsion angles (@,
Figure 3. Radial distribution curves for 3-azetidinol. The theoretical
The Journal of Physical Chemistry, Vol. 95, No. 4, 1991 1599
Structure and Conformation of Gaseous 3-Azetidinol TABLE 11: Correlation Matrix (X100) for Parameters of 3-Azetidinol'
param
(rub 0.0092 0.0068 0.0248 0.0023 0.0014 0.0007 0.83 0.31 0.36 0.0062 0.0035 0.0013 0.0046 0.027
r(0-H) r(C-H) r(N-H) r(C-C) r(C-0) r(C-N) Le
LC-C-C LO-C-C
I(0-H) I(C-0) I(C2C4) I(N.0)
90eq
r,
r2
r3
r4
rs
r,
~7
La
~9
110
111
112
113
100
-17 100
10 -96 100
50 -57 52 100
-37 -6 9 -38 100
-40 37 -34 -65 45 100
-10 50 -53 -52 0 11 100
-32 43 -38 -60 17 39 34 100
-27 52 -45 -60 -14 31 42 71 100
40 -89 87 70 -8 -46 -53 -49 -52 100
-52 48 -42 -91 55 72 34 55 46 -60 100
-10 -10 12 -8 25 13 -24 35 10 10 25 100
0 28 -30 -19 -1 13 19 8 -3 -26 16 3 100
% eq 4 25 -29 -19 -5 9 31 -3 -21 -25
IO -10 46 100
'Distances ( r ) and amplitudes ( I ) in angstroms; angles ( L ) in degrees. bStandard deviation from least-squares refinement. TABLE III: Geometrical Structure of Azetidine and 3-Azetidinol'
3-azetidinol ED
param r(C-N) r(C-C) r(C-0) r(C2-H) r(C2-H) 4Ci-H) r(N-H) r(0-H) LC-N-C LC-c-c LN-C-C LC-c-0 LOP
LC-0-H LH-C-H LN-C-H, LN-C-H, LC-C-H, LC-C-H, LC-C-H (0)
6-31G**
azetidine X-ray
6-31G**
gas
ax
eq
solid
1.486 (2) 1.562 (7) 1.406 (4) 1.112 (19)
1.468 1.540 1.392 1.085 1.089 1.080 0.999 0.945 90.8 85.5 88.3 114.7 151.7 109.1 109.1 114.2 11 5.2 112.2 116.6 117.3
1.465 1.538 1.386 1.084 1.092 1.08 1 0.999 0.943 91.2 85.8 87.9 120.1 151.1 110.0 108.8 114.1 1 15.4 111.0 118.6 111.5
1.497 (3) 1.539 (3) 1.404 (3) 0.98 (3) 1.00 (3) 1.02 (3) 0.94 (3) 0.83 (6) 90.0 (2) 86.9 (2) 88.8 (2) 119.3 (2) 154.7 (3) 107.5 ( I ) 109.0 (9) 114.6 (6) 115.4 (6) 109.8 (6) 118.3 (5) 111.2 (5)
1.112 (19) 1.033 (70) 0.971 (26) 90.7 (7) 84.9 (9) 89.0 (8) 117.2 (5)b 153.2 (23) 1 10.0 108.8 114.0 115.3 1 10.6 118.2 111.5
'Distances ( r ) in angstroms; angles (puckering angle).
(L)
ED/MW gas 1.473 (3) 1.563 (3)
6-31G** 1.467 1.540
1.096 (4)
1.09
1.014 (3)
0.999
91.2 (4) 84.6 (4) 88.2 (4)
91.1 85.7 88.7
150.3 (1 4)
154.4
108.8 (8) 114.7 (6)
109.4 114.0 114.7 1 12.0 1 17.9
in degrees. bValue in equatorial conformer; see text. cAngle between C-C-C and C-N-C planes
and CP2, the H12-O-C-H6 torsion angles in the two conformers), and the puckering angle 8 between the planes C-C-C and CN-C. In early refinements, it was assumed that the C-C-H and N-C-H angles all had the same value; later this constraint was released and the differences between LC,-C2-H, and LCI-CZ-HB and between LN-C,-H, and LN-C,-H, were kept constant at the a b initio values obtained for the equatorial conformer. The puckering angle, 0, was assumed to have the same value for both the equatorial and the axial conformers. This is in agreement with the theoretical calculations, where a difference of only 0.6O was obtained for Ae. The calculated differences in the bond distances between the two conformers were also so small that these distances were assumed to have the same lengths in the two forms. The theoretical calculations did, however, indicate that one of the important valence angles, lC-C-0, was quite different in the two conformers, and the calculated difference (ALC-C-O = 5 . 4 O ) was included as a constraint in the ED model. The amino hydrogen was assumed to be in an equatorial position. When this assumption was tested, we did, as expected, find that ED could not distinguish between equatorial and axial positions for this hydrogen atom. R factors and fits between RD curves were very nearly the same for both possibilities. The vibrational properties were specified by 37 amplitude parameters, corresponding to the different interatomic distances. The structure was defined in terms of the geometrically consistent ra type distances. These were converted to the r, type required by the scattered intensity formula by use of values for centrifugal distortion ( b r ) , perpendicular amplitude corrections ( K ) , and
root-mean-square amplitudes of vibration ( I ) calculated from a harmonic vibrational force field (r, = ra - 12/r + K + 6r = rg l*/r). The force constants from related m o l e c ~ l e swere ' ~ used. Least-squares refinementsi5were carried out by fitting a theoretical intensity curve to the two averaged experimental intensity curves. Some of the valence angles involving hydrogen atoms could not be determined very well, and they were kept constant at the values obtained in the ab initio calculations. Comparison with theoretical R D curves clearly showed that the majority of the molecules had the OH group equatorial to the ring. In Figure 3, theoretical R D curves for models with 100% axial OH, 100% equatorial OH, and a mixture of 77% equatorial and 23% axial OH are shown, together with the experimental curve and difference curves. The R factors for the three models are 0.199, 0.069, and 0.055, respectively. We also tested the effect of changing the HI2-O-C-H6 torsion angle a,, and we did least-squares refinements for models with anti (9, = 180°), gauche (al = 60°), and syn (GI = Oo) H-C-0-H torsion angles. We also did a calculation for = 35O, where the ab initio calculations showed the lowest energy minimum. Values for the agreement factor R were 0.055, 0.057, 0.060, and 0.062 for 9,= 180, 60, 35, and Oo, respectively. The best fit between experimental and theoretical RD curves also was obtained for the anti conformation, but the differences in fit between the four models were small. (14) Giinter, H.; Schrem, G.; Oberhammer, H. J . Mol. Spectrosc. 1984.
104, 152.
(IS) Hedberg, K.; Iwasaki, M. Acta Crystallogr. 1964, 17, 529.
1600 The Journal of Physical Chemistry, Vol. 95, No. 4, 1991
Assuming both conformers have the same entropy, a mixture of 77 (8)% equatorial and 23 (8)% axial corresponds to an enthalpy difference of AHo = 3.7 (217 = 1.6) kJ/mol. Table 1 summarizes the final results from the refinements of the ED data. Nine geometrical parameters, four amplitude parameters, and the conformational mixture were refined simultaneously. The correlation matrix for the final model appears in Table 11.
Discussion In Table 111 the parameters for gaseous 3-azetidinol are compared with those determined in the solid phase and with the parameter values for azetidine obtained by a combined ED/MW (microwave) in~estigation.'~ Except for distances to hydrogen, which are expected to be determined differently from X-ray diffraction and ED, parameters for 3-azetidinol are very similar in the two phases. The crystal structure shows that both the O H and the N H groups of 3-azetidinol are part of infinite hydrogen-bonded chains; i.e., they participate in both active (e.g. N-H-) and passive (e.g. H-N-) hydrogen bonding. Ab initio studies of the water dimer close to the Hartree-Fock have revealed that both types of hydrogen bonding result in enhancement of the negative charge of the oxygen atoms at the expense of the electron density of the contiguous bonds; i.e., dimerization of water results in increased 0-H bond lengths. For hydrogen-bonded 0-H chains, cooperative effects have been demonstrated,'* which means that the electronic effects will be mutually strengthened by formation of additional hydrogen bonds. Provided these conclusions apply to hydrogen bonding of the type encountered here (0-H-N-H-), the observed increase in C-N bond length on crystal formation may reflect the hydrogen bonding introduced in the crystalline phase. On crystal formation, 3-acetidinol is trapped in a conformation determined by the hydrogen-bonded cage in which the 0-H group is situated in anti position to the C-H bond of the CHOH group. This leads to an increased repulsion between the hydroxyl group and the CH2 hydrogen atoms situated on the same side of the four-membered ring, predicting an opening of the CCO angles. However, 3-azetidinol is a molecule featuring several degrees of freedom, including inversion at nitrogen, four-membered ring puckering with folding of the ring across the CHI carbon atoms, and internal rotation of the OH group. These features have been thoroughly studied for the structurally related cyclob~tanol,'~-~~ (16) Reed, A. E.; Weinhold, F. J . Chem. Phys. 1983, 78, 4066. (17) Zilles, B. A.; Person, W. B. J . Chem. Phys. 1983, 79, 65. (18) Kleeberg, H.; Klein, D.; Luck, W. A. P. J . Phys. Chem. 1987, 91, 3200.
Hagen et al. where OH torsion is followed by concerted variation of other structural parameters, in particular the puckering mode and the rocking-type coordinate of the neighboring CH2 groups. The results from the gas-phase studies of azetidine and 3azetidinol reveal that substitution of a hydrogen atom by an O H group exerts only a marginal effect on the geometry of the remaining structures, since almost all comparable parameters are within error limits. The largest difference is found in the puckering angle (e),with 3-azetidinol being slightly less puckered. The ab initio calculations do predict a smaller degree of puckering for azetidine and a larger one for 3-azetidinol. However, all results are within the standard deviations of the experimental gas-phase results. The energy surface for the H 4 - C - H torsional angle is plotted in Figure 4. This shows that at the energy minimum 3-azetidinol has a torsion angle close to a gauche atomic arrangement. The surface can in broad terms be described as having two minima, one gauche/syn and one anti. The ED experiment indicated that the anti conformation gave the best agreement between experimental and theoretical data, but the differences between the models tested were too small to make it possible to determine the H-C-0-H torsion angle with certainty. The results from the ab initio calculations are in general agreement with the experimental results for the rest of the parameters. The value obtained for the difference in enthalpy between the conformers with the O H group in the pseudoequatorial and pseudoaxial positions, AIP = 3.7 (1.6) kJ/mol, is close to the value obtained in CCI4 solution from spectroscopy2(AIP = 4.2 kJ/mol) and to the value predicted from ab initio calculations2 in the 6-31G** approximation (AH' = 2.9 kJ/mol). The assumption that UTo = 0 is in agreement with the ab initio calculation, which gave AS" = 0.15 J/(mol.K). Acknowledgment. We are grateful to S. Gundersen for technical assistance. Financial support from the Norwegian Research Council for Science and the Humanities is acknowledged. Supplementary Material Available: Tables listing total intensities, final backgrounds, and average molecular intensities ( 5 pages). Ordering information is given on any current masthead page. (19) Durig, J. R.; Guirgis, G.A.; Bucy, W. E.; Compton, D. A. C.; Kalasinsky, V. F. J. Mol. Srruct. 1978, 49, 323. (20) Gunde, R.; Ha, T.-K.;Glinthard, H. H. Specrrochim. Acta 1986,42A, 259. (21) Gunde, R.; Gunthard, H. H. Spectrochim. Acta 1983, 39A, 315.
