The structure and pseudorotation of cyanocyclopentane as determined by gas phase electron diffraction

Journal of Molecular Structure, 116 (1984) 29-37 Elsevier Science Publishers B-V., Amsterdam -Printed

THE STRUCTURE AND PSEUDOROTATION CYANOCYCLOPENTANE AS DETERMINED ELECTRON DIFFRACTION

RICHARD

in The Netherlands

OF BY GAS PHASE

L. HILDERBRANDT*

Department of Chemistry, North Dakota State University, Fargo, ND 58105 HILARE

LEAVITT

Department

and QUANG

of Chemistry,

(U.S.A.)

SHEN

Colgate University, Hamilton, NY 13346

(U.S.A.)

(Received 18 July 1983)

ABSTRACT The structure of cyanocyclopentane has been determined by gas phase electron diffraction. The molecule w.as found to have a low barrier to pseudorotation with two minima corresponding to Cs envelope conformations with the -C=N in the quatorial and axial positions. The best least squares value obtained for the barrier to pseudorotation was 240(330) cal mol-‘, and the energy difference between the equatorial and axial conformers was found to be lBO(330) cal mol-’ with the equatorial form being preferred. The puckering amplitude for the five-membered ring was found to be O-426(28) X, and an average C-C(ring) distance of 1.544(l) A was obtained. Other parameters obtained from least squares analysis of the experimental data include: rs(CXN) = l.rL’iT(‘i) X, rdC=N) = 1.160(2) A, rx(C-H) = l-102(6) A, LC-C-CN = 112.1(1.3)“, and LHCH, = 107.2(3.2)“. The results obtained are in excellent agreement with related cyclopentyl compounds, and with the microwave spectroscopic results obtained for cyanocyclopentane. INTRODUCTION

In a recent publication [l] we reported on an electron diffraction study of the structure and pseudorotational motion of chlorocyclopentane. The molecule was found to have a pseudorotational potential function with two minima corresponding to an envelope, C,, conformation with the substituent in the axial and equatorial positions. The axial form was found to be preferred over the equatorial form by O-45(15) kcal mol-’ at 295 K, and the barrier to pseudorotation was found to be approximately 2.0(1.5) kcal mol-‘. The thermal average puckering amplitude for the five-membered ring was found to be O-394(35) 8, at 295 K, and O-429(30) A at 387 K. The results obtained from this study agree very well with the spectroscopic studies of Durig and coworkers [Z, 31. They investigated the temperature dependence of the infrared and Raman spectra of the ring puckering and *Author to whom correspondence should be addressed_ 0022-2860/84/803.00

0 1984 Elsevier Science Publishers B.V.

30

C-Cl stretching modes of cyclopentyl chloride. They interpreted their results in terms of a mixture of axial and equatorial conformers with a relatively low pseudorotational barrier, and an energy difference between the axial and equatorial conformations of 0.344(23) kcal mol-‘. These results are also consistent with the results of molecular mechanics calculations [l, 41 which indicate an axial/equatorial energy difference of 0.35 kcal mol-‘, and a barrier to pseudorotation for the twist conformation of 1.17 kcal mol-‘. Harmony and co-workers [ 51 have also reported on the microwave spectrum of chlorocyclopentane. They confirmed that the axial form was the most stable conformer; however, they were unable to observe any contribution from the equatorial conformation in the microwave spectrum of this molecule. Based on estimates of the dipole moments for the two conformers, they estimated that the equatorial form would have been observed if the energy difference between the conformers was less than 0.8 kcal mol-‘. It is difficult to rationalize the disagreement between these experimental observations. A possible explanation is that the pseudorotational potential function is rather flat in the region of the equatorial conformer, and therefore contains no bound vibrational states. If this were the case, and if the relative energy of the equatorial form were still relatively low, then it would explain why the equatorial form is observed in the diffraction experiment but not in the microwave spectroscopic experiment. More recently, Choe and Harmony [6] reported a microwave spectroscopic investigation of cyanocyclopentane. For this molecule both the axial and equatorial forms were observed, and the energy difference between the two forms was found to be 0.0(0.2) kcal mol. Several vibrational satellites were also assigned for the equatorial form of the molecule, but no vibrational satellites were observed for the axial form. Harmony concluded, on the basis of this observation, that while the two forms are approximately equal in energy, the minimum in the pseudorotational potential function is much deeper for the equatorial form than for the axial form. In light of the apparent disagreement between the experimental results obtained for chlorocyclopentane, we felt that a follow-up electron diffraction study of cyanocyclopentane would be important to help clarify the source of the difference in interpretation for these two different experimental techniques. We also feel that the factors influencing conformational preference in mono-substituted cyclopentanes are not well understood at present, and that more experimental data is needed. Our experience with chlorocyclopentane leads us to believe that electron diffraction is a very suitable experimental method for conformational analysis of these systems since there are separately identifiable features in the radial distribution curve which arise from the axial and equator&l forms. Furthermore, it appears to be possible to interpret the experimental data in terms of a dynamically pseudorotating model and thus obtain pseudorotational potential function parameters.

31 EXPERIMENTAL

A sample of cyanocyclopentane was obtained from Pfalz and Bauer. The sample purity (99%) was verified by gas chromatography, and the sample was used without further purification. Electron diffraction data were collected on Kodak 4 X 5 in. Electrc>n Image photographic plates using the NDSU gas phase electron diffraction instrument which is equipped with an r3 sector. An accelerating voltage of 40 kev was used with nozzle to plate distances of 248.71 mm and 95.85 mm as measured by a precision cathetometer. The nozzle tip temperature, as measured on an Omega digital thermocouple monitor, was maintained at 370 K during the exposures. The accelerating potential was measured with 5 digit precision on a DATEL digital voltmeter. The voltage was reproduced and stabilized to within 0.005% during exposures. Exposure times for the 0.5 pa beam current were 45-00 s for the long camera distance, and 100-120 s for the short camera distance. Residual gas pressure was maintained below 1 X 10e5 torr during exposure with the aid of a liquid nitrogen cooled surface situated opposite t.he inlet system. Precise voltage/distance calibrations were obtained by using benzene calibration A [7]), which were obtained under identical experiplates (r, = l-397(4) mental conditions as those used for the experiment. Three photographic plates from each camera distance were traced on the NDSU computer-controlled microdensitometer with data being collected at intervals of 0.150 mm. The data were corrected in the usual manner for plate flatness, emulsion saturation, and sector imperfections, and then interpolated at integral values of 9 [(40/X ) sin (6 /2)] for analysis_ The computer-controlled densitometer is capable of carrying out all of these operations including the analysis of the benzene calibration plates. Least squares analysis of the interpolated data was carried out on the NDSU IBM 370-158 computer using a least squares procedure similar to the one developed by Gundersen and Hedberg [8] and the elastic scattering factors and phase shifts calculated by Schafer et al. [9]. Anharmonicity corrections were made on the basis of the following assumed Morse parameters: a(C-H) = 2.5 A-‘, and a(C-C) = a(C=N) = 2.0 a-‘. DATA

ANALYSIS

Since no vibrational analysis has been reported for cyanocyclopentane, it was necessary to use an approximate force field in the calculation of the vibrational amplitudes. A simplified Urey-Bradley Force Field was constructed by supplementing the force field obtained for chlorocyclopentane Cl] with additional force constants characteristic of the cyanide moiety [lo]. The UBFF used in the calculations, and the vibrational amplitude parameters obtained from it are shown in Table 1. It is important to note that a few of the amplitude parameters (e..g. Cq-C6 and N-Cd) depend strongly on the pseudorotational phase angle. In order to take this dependence into

32 TABLE

1

UBFF force field for cyanocyclopentanea 2.320 mdyn A-’ 3.200 18.150 4.100

Kcc (rhz)

~GS-CB

G=N KC-H Hccc &ca

0.554 mdyn 0.317 0.513

HHCH

Fc.c Fc-+I Fc--N

0.260 mdyn .4-r 0.566 0.046 0.500

Tcccc ycx=N

0.101 mdyn 0.166

FH--H

Principal vibrational amplitude parameters at 370 Kb Distance

lij x 104

Kii x lo4

C-C (ring) G--c, C-C (gem) c, “C, C=N C;.N C, *.N C, ..N C-H C--H, N--H, H--H,

526 497 695 762(997)= 342 519 1161 869(920)c 791 1050 1220 1295

50 49 31 24 206 67 29 15 182 129 82 225

=UBFF taken from ref. 1 and supplemented with force constants from ref. 10. bOnly vibrational amplitudes and perpendicular amplitudes for principal distances are given in the table. ‘Numbers in parentheses are for the axial conformer when they are different from the equatorial conformer_

ticco-unt both of these vibrational amplitudes were included in the analysis as functions of the pseudorotational phase angle, 9, as follows Z(C4C6) Z(NC4)

= Z”(C4--C6) = P(NC4)

-!- O-0235(1

+ 0.0051(1-

-cos

@)/2

cos 4)/Z

(1) (2)

Another important factor which had to be taken into account in the calculation of the amphtude parameters was the separation of the framework and large amplitude motions. The amplitudes shown in Table 1 have been calculated with the pseudorotational motion frozen. This was done by simply not including the lowest vibrational frequency (the pseudorotation) in the

amplitude calculations. This is especially important in the present analysis since this vibrational degree of freedom is being averaged over separately. The structural model used for cyanocyclopentane is similar to the one defined for chlorocyclopentane. The numbering of the atoms used in defining

33

the structural parameters for the molecule is illustrated in Fig. 1. The ring geometry is completely defined in terms of a single average C--C bond length, a ring puckering amplitude, Q, and a pseudorotational phase angle parameter, 9. The Cartesian coordinates of the ring atoms are given by the approximate expressions =Sj= Yj

rj

sin [2nG -

1)/5]

(3)

[2flG -

1)/5]

(4)

= rj COS

zi = (z/5)“*

Q cos [4??G -

1)/5

+ @]

(5)

The z coordinates as a function of q and Q are those given in the work by Cremer and Pople [ll]. The it and y coordinates are obtained by assuming that the ring atoms undergo curvilinear motion in 5 fixed vertical planes with inter-plane angles of 27~/5. The distances of the ring atoms, rj, from the origin of coordinates are adjusted so as to maintain constant distances between neighboring atoms while the molecule pseudorotates. To a first approximation the rj distances are given by j+4 rj

=

r.

(

1 + 8/5[q

sin (2n/5)/rcc]*

C

(-l)‘-’

sin* [2iT(i -

1)/5

+ QJ I

(6)

i=j

where ro = rcc/{2[1

-

cos (2n/5)]}“’

(7)

Equations (3-5) completely specify the geometry of the five-membered ring as a function of rcc, q, and 9. For the values of q typically encountered

nN C6

Fig.

1. Atomic

numbering

used

in defining

structural

parameters

for cyanocyclopentane.

34

(0.3 A < Q < 0.5 A), this approximation constrains the C-C distances to be identical within about 0.005 A. The only additional parameters which are needed to define the geometry of the molecule are the LHCH angles for the methylene groups, the Cl-C6 bond length, the EN bond length, the average C-H bond length, and the LC&C6 = LCZC1C6angles. In addition 5 amplitude parameters were included in the analysis. They are: Z(C-C), Z(CCgem), Z(C=N), Z”(NC4), and I” (C4C6). The complete set of independent parameters used in the analysis is show:1 in Table 2 along with the results obtained from the least squares analys;S. A toi;al of seven pseudoconformers were included in the anaiysis of the dynamic model for cyanocyclopentane with values of Q ranging from 0 to 180”. The two Fourier components of the pseudorotational potential function VI and Vz were also varied where V(O) = V,(l

-

cos 9)/2 + Vz(l - cos 2@)/2

(8)

The weight assigned to each pseudoconformer was taken as

2 exp

P(O) = exp (-Vt@i)/RT)

(9)

(-vt4i)lRT)

Ii

The r’ormulation of the Jacobian elements of the molecular intensity curve with respect to the potential function parameters has been described elsewhere [ 121. There is one feature of the present analysis which is somewhat different from the analysis for chlorocyclopentane. In chlorocyclopentane, the degree of puckering was found to be different for the axial and equatorial conformers. TABLE 2 Results obtained from leas’; squares analysis of experimental data for cyanocyclopentanea Parameter

Value

Cb+ (ring)

1.544(l) O-426(28) 1.477(7) 1.160(2) l-102(6) 112.1(1.3)” 107.2(3.2)

LN C=N C-H LC-C-CN LIICH,

A A Is, 9, A

Parameter

Value

I(C-C) Z(C-Cgem) I(C=N) P (N*C4)C P (C4-C6)= V* V,

0.056(Z) 0.071(S) 0.034(3) 0.107(66) 0.080(43) O-18(33) 0.13(33)

A d A A A kcal mol-* kca! mol-’

“Distance parameters are reported as rz values whereas angles are reported as rcrparameters corrected for shrinkage effects. The quoted errors are three standard deviations obtained from the least squares analysis plus an estimate of the systematic error. bq is the puckering amplitude for the ring. ‘Yhe amplitudes corresponding to the C4--N and C!4-*C6 distances are functions of the pseudorotational phase angle as explained in eqns. (1) and (2) of the text.

35

As a result of this difference it was necessary to introduce an ellipticity parameter which made 4 a function of the pseudorotational phase angle 9. A similar parameter was investigated for cyanocyclopentane, but it was found to be unnecessary. Final results obtained from the least squares analysis of the data are shown in Table 2 while Figs. 2 and 3 illustrate the levelled intensity curves and radial distribution curves obtained from the final least squares model. DISCUSSION

The structural parameters obtained from the least squares analysis of the cyanocyclopentane data are in good agreement with corresponding parameters in related molecules. The average C-C distance (rg = 1.545(l) Ai) is in excellent agreement with the value obtained for chlorocyclopentane at 387 K (rg = 1.543(l) a) [l J, It is ako in escellent agreement with the room temperature average C-C distance obtained for cyclopentane (rs = 1.546(l) A) [ 131. The average C-H bond length obtained for cyanocyclopentane (rg = 1.102(6) A) is slightly longer than that obtained for chlorocyclopentane a) but agrees well with the value obtained for cyclopentane (Tg = 1.090(4) .&) is in good agree(rg = 1.113(l) A). The CEN bond length (rg = 1.160(2) ment with the corresponding distance in cyanomethane (rg = 1.159(2) a) [14], but is somewhat shorter than the corresponding distance obtained for distance (rg = 1.477(7) A) dicyanomethane (rO = 1.167 a) [15]. The Cl-C6 is quite a bit longer than the corresponding distance in cyanomethane (rg = 1.468(Z) A) or dicyanomethane (rO = 1.468 Ai)_ The’uncerttnties in the potential function parameters are large; however, the values obtained for VI and V, are in excellent agreement with the observations Choe and Harmony [6] _ The parameter V, determines the relative

10

20

30

40

50

60

70

a&’

1

Fig. 2. Levelled experimental Ordinate units are arbitrary.

80

90

and

100

110

120

theoretical

intensity

curves

for

cyanocyclopentane.

36

, 1.0

I

I

,

2.0

3.0

.

1

4.0

!

S.0

0

6.0

R(ii)

Fig. 3. Experimental and theoretical radial distribution curves for cyanocyclopentane. Only the principal peaks not affected by the pseudorotational motion are labelled. Ordinate units are arbitrary.

energy difference between the two conformers. Since cp= 0” corresponds to the equatorial conformer and Q = 180” corresponds to the axial conformer, a positive value for VI indicates that the equatorial conformer is more stable than the axial conformer by approximately 180 cal mol-‘. This energy difference is small, and is in fact smaller than the estimated standard deviation of 330 cal mol-‘. This result is consistent with the observation of Choe and Harmony who obtained an energy difference of 0 t 200 cal mol-‘. The value of V2 determines the height of the barrier to pseudorotation. For the potential function given in eqn. (S), the location of the barrier to pseudorotation is given by %naX=

Arcos

(-v1/4vz)

(10)

For the values of V, obtained from the least squares analysis (130(330) cal mol-*) one obtains a value for @mm of 110°, and a barrier height of 240 cal mol-I. Thus the barrier to pseudorotation is approximately 240 cal mol-’ relative to the equatorial conformer, and only 60 cal mol-’ relative to the less stable axial conformer. This is remarkably consistent with the observations of Choe and Harmony who observed two vibrational satellites for the equatorial conformer with energy spacings relative to the ground state of 140 and 80 cal mol-’ respective!y. Interestingly enough, the sum of these two energ spacings is essentially identical to the approximate barrier height obtained from our analysis. Furthermore, Choe and Harmony observed no vibrational sattelites for the axial conformer, and this is also consistent with the present observation that the barrier to pseudorotation from the axial conformer is only about 60 cal mol- I_ Thus, while, the uncertainties in the VI &rd VZ parameters are large, there is a remarkable (perhaps fortuitous)

37

agreement between the electron diffraction and microwave experiments on the qualitative features of the pseudorotational potential function. It seems reasonable to conclude from the present experiment that it is indeed possible to obtain consistent interpretations of pseudorotational potential functions from diffraction and microwave spectroscopic techniques, at least in certain circumstances. This still does not explain the disagreement in the experimental conclusions for chlorocyclopentane, however. It will be interesting to see whether other molecules such as fluorocyclopentane or bromocyclopentane lead to agreement or disagreement when subjected to the same scrutiny. ACKNOWLEDGEMENTS

The authors gratefully acknowledge the financial assistance of The National Science Foundation Grant No. CHE-8111739. We are also grateful to the computer center of The North Dakota State University for providing computer time for the calculations involved in the data analysis. SUPPLEMENTARY

MATERI_4L

AVAILABLE

Tables of experimental intensity data, and correlation and error matrices are available as Supplementary Publication Ilumber SUP 26250 (6 pages) from the British Library Lending Division (BLLD), Boston Spa, Wetherby, Yorks LS23 7BQ, Great Britain. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

R. L. Hilderbrandt and Q. Shen, 3. Chem. Phys., 86 (1982) 587. J. R. Durig, J. M. Kaniker and D. W. Wertz, J. Mol. Spectrosc., 31 (1969) 237. W. C. Harris, J. M. Kanikerand J. R. Durig, J. Mol. Struct., 9 (1971) 139. C. Altona, H. R. Buys and E. Havinga, Rec. Trav. Chim. Pays-Bas, 85 (1966) 973. R. Loyd, S. N. Mathur and M. D. Harmony, J. Mol. Spectrosc., 72 (1978) 359. J. Choe and M. D. Harmony, J. Mol. Spectrosc., 81 (1980) 480. K. Tamagawa, T. Iijima and M. Kimma, J. Moi. Struct., 30 (1976) 243. G. Gundersen and K. Hedberg, J. Chem. Phys., 51 (1969) 2500. L. SchZfer, A. C. Yates and R. A. Bonham, J. Chem. Phys., 55 (19il) 3055. I. Nakagawa and T. Shimanouchi, Spectrochim. Acta, 18 (1962) 513. D. Cremer and J. A. Pople, J. Am. Chem. Sot., 97 (1978) 1358. H. Schei, Q. Shen, R. F. Cunico and R. L. Hilderbrandt, J. Mol. Struct., 63 (1980) W. J. Adams, H. J. Geise and L. S. Bartell, J. Am. Chem. Sot., 92 (1970) 5013. K. Karakida, T. Fukayama and K. Kuchitsu, Bull. Chem. Sot. Jpn., 47 (1974) 299. E. Hirota and Y. Morino, Bull. Chem. Sot. Jpn.,‘33 (1960) 705.

59.