I N T E R N A L R O T A T I O N AND R O T A T I O N A L I S O M E R I S M IN T H E

MOLECULE

OF N O R M A L

A. A. A b d u r a k h m a n o v , a n d L. M. I m a n o v

BUTYL

ALCOHOL

~. I. V e l i y u l i n ,

UDC

535.34-14

A computational analysis of internal rotation about the C - C and C - O single bonds in the CHsCHzCHzCHzOH molecule made it possible to assess the stability of the probable isomeric forms and the heights of the potential barriers. It was shown that the gauche positions of the OH and CH2OH groups are displaced from the ideal staggered configurations. Discussion of the rotation of the methyl group led to the conclusion that the distant C - H bonds have an effect on the magnitude of the methyl barrier. The relationship between the stability of the isomeric forms and the deformation of the structure is examined.

The high resolving power and great accuracy of frequency measurements in modern gas radiospectrometers make it possible to investigate the rotational isomerism of molecules with several degrees of freedom in their internal motion. The problem of identifying the spectra of such molecules is considerably facilitated by theoretical evaluation of the internal rotation potentials. In the present work for the purpose of investigating the stable isomeric forms and determining the heights of the potential barriers the internal rotation in the normal butyl alcohol molecule has been examined on the basis of the semiempirieal calculations in [1-4]. Analysis of the internal rotation in this molecule is also of definite independent interest for the discussion of certain experimental results on related molecules. The potential employed is the sum of the energies of the exchange interactions for the electron clouds of the bond adjoining the bonds about which internal rotation is being investigated (adjacent bonds) and the steric interactions of the valently nonbonded atoms:

h=t

r 'j"

The angle of internal rotation is measured from the cis position of the rotating group. The parameters of the free interactions ak, bk, c k and dk are semiempirical constants of the type employed in [2-4]. For normal butyl alcohol, which we are investigating by microwave gas spectroscopy, it is possible to indicate four bonds about which internal retarded rotation is possible, and rotation of the OH, CH2OH, and CH2CHa groups respectively about the C4-O, Cs-C4, and C2-Cs bonds can give a large number of isomeric forms (Fig. 1). The possible realization of one or the other conformation at a fixed temperature is conditioned by the depth of its energy minimum. The interaction potentials were calculated for each of the four degrees of freedom for internal rotation in the n-butanol molecule. During analysis of the rotation of the OH group about the C4-O bond the U0 value was taken as equal to 1 kcal/mole (from the data for methyl alcohol). The potential curve (Fig. 2a) plotted from the calculated interaction energies shows that the conformations 1, 2, and 3 (Fig. 1) are stable during rotation of the OH group. The position of the gauche minimum is somewhat displaced from the ideal staggered configuration and lies at ~0 ~ 66 ~ Institute of Physics, Academy of Sciences of the A zerbaidzhan SSR. Translated from Zhumal S~uktumoi Khimii, Vol. 13, No. 2, pp. 251-288, March-April, 1972. Original article submitted March 9, 1970. 9 Consultants Bureau, a division of Plenum P u b l i s h i n g Corporation, 227 West 17th Street, New York, N, Y. 10011. All rights reserved. This article cannot be reproduced for any purpose w h a t s o e v e r without permission of the publisher. A copy of this article is available from the publisher for $15.00.

231

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t ~I

LCI

;IN tH

/

,,I/H, I

II

/

z

-~

I I /

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2 H

3

HI"" H ~ HTC3H7

HqrCa~G~H "H ~

6ilo

h C~.HslID , 60H CH~OH@ 9

C~Hsl~

H

.

6H CH~OHoI/7

6~'H3 '~,,oH

6H~0

BzHsI

H

7

@d

OH BH~OHoII

CHzOHo12

c He

6H 6H C~.HslI~H C~.Hslk l~.,mH G

H~r

"~H

HCsH71~" ~ " ~ HHm

Htr

H

"oH

H

C~ slK.

H1r

/8 H ~H

Fig. 1. Molecule of normal butyl alcohol and its conformations. (Fig, 2b). With the height obtained for the cis barrier (about 2 k c a l / m o l e ) the spectral lines of the gauche form can be split or broadened even in the vibrational ground state. The results from analysis of the rotation of the CHsOH group about the C 3 - C 4 bond are of special interest. This arises from the fact that internal rotation of such type is an experimentally established fact. In file calculations U0 was taken as equal to 3.11 kcal/mole (from data for ethane-like molecules). On file U(~0) curve (Fig. 2c) there are three minima corresponding to conformations 5, 6, and 7 (Fig. 1). The energy minimum of the gauche isomer corresponds to a ~o angle of approximately 64~ (Fig. 2d). This result agrees well with file experimental v a l ues for the respective angle obtained in the similar folded configurations of the propyl fluoride (63~ [5], propyl chloride (V0~ [6], and propyl alcohol molecules (63.7 ~ [7]. The gauche-gauche "tunnelling" through the cis barrier (about 5 kcal/mole) evidently will not cause any appreciable splitting of the spectral lines for the gauche form in the ground state. The displacement of the gauche positions for the OH and CH2OH groups from the strictly staggered arrangement of the bonds clearly results from lack of symmetry in the potential field, due mainly to the predominant influence of the C3 and C2 carbon atoms respectively (Fig. 1). The potential curve for rotation of the CH2CHs group about the C2-C s bond (Fig. 2e) indicates the possible existence of conformations 9, 10, and 11 (Fig. 1), but the large difference in energies between the gauche and trans forms leads to small likelihood of conformations 10 and 11 at-50~ (the average temperature of the absorbing cell). 232

U, k c a l / m o l e

U,, k c a l / m o l e a

f 1,0

b/

250'

trans tP" g /

g

4S

Z30

{gj ~min ~

Z20

8o /go 18o U, k c a l / m o l e

so~ ~~

0

.... ~mi#88

80

75

~o

U, kcal] mole C

5,0~

/+g/

3,o 4o

O

Z30

ZgO

kill bd 80

ZSO

i

z~8 do

120 180

aE=g,Z~5 mole

2~5

I 83

~~

88 --

o

b k c a l / m o l e~rnin-#4 ?:r176

f

4o

40

/\/

- g ,x trans~ +g

s,O

///

9g

trans

g

1,5 80 120 180 @ 0 dO0 0 ~

0

180 2~0 800 too

AE=~s Fig. 2. Potential curves for rotation of groups: a, b) OH; c, d) CHzOH; e) CH2CH3; f) OH (at gauche-CH20) about C4-O, C 3 - C 4, C2-C~, and C 4 - O bonds, respectively, g: Gauche. The combined conformations 13, 14, 15, and 16 (Fig. 1) are obtained if the OH group is rotated about the C 4 - O bond, when the CH20 group is in the gauche position 6. CalcuIation showed that in this case the gauche conformations 14 and 15 differ greatly in energy; what is more, it was found that no energy minimum is observed in position I5 (Fig. 2f) and, consequently, the isomers 13 and 14 can be realized from the above-mentioned combined conform ations. The "relative stabilities" of the molecules of the two isomeric forms, obtained from the Boltzmann distribution with allowance for the statistical weights of the states, are presented in Table 1. Thus, the results of the calculation show that Iines due m the trans-trans-trans (1), gauche-trans-trans (2, 3), trans-gauche-trans (6, 7), and gauche-gauche-trans (14) isomers should be expected in the spectrum of the normal butyl alcohol molecule (Fig. 1). As far as rotation of the methyl group about the C1-C2 bond is concerned, the three staggered conformations are identical, and the main interest therefore lies in the determination of the magnitude of the retarding potential.

233

TABLE 1. Relative Number of Molecules, ~ Isomeric forms

Rotating groups OH

}

l

CI~0H CH2CH,~

OH

(CH:0-

gau che ) trans gauche

45 55

The calculated methyl barriers in substituted ethanes (U = 3.436 keel/mole for CHaCH2CN and 3.384 kcal/mole for CHaCH2OH) agree well with the corresponding experimental vanes of 3.280 =t 0.230 [8] and 3.413 keel/mole [9].

46 199,7 I 72 54 0,328

Microwave investigations of the propyl fluoride CHaCHzCHeF [6] and normal propyl alcohol CHaCH2CHaOH[10] molecules have shown that in these molecules the methyl retardation potential is approximately 0.5 kcal/mole lower than in the substituted ethanes.

Within the scope of the adopted model of interactions the orienting effect of the C - H bonds of the distant methylene group, which was not provided for in the potential calculations, does lead to such a decrease in the methyl barrier in the substituted propanes (compared with the ethanes); the steric influence of the hydrogen atoms of the distant methylene groups is negligibly small. On the basis of the foregoing it can be supposed that the value expected for the methyl barrier in the n-butanol molecule should also be approximately 0.5 kcal/mole lower than the calculated value, i.e., in the order of 2.9 kcal/mole. The retarded methyl rotation can lead to splitting of spectral lines. Calculation of the splittings by the Herschbach method [11] showed that, for the expected barrier height, splittings can only be detected in the spectra of the excited states of the rotation of the methyl group. We made similar calculations for the 3-fluoropropene and n-propanol molecules, for which there are reliable experimental data on the structure and stability of the isomeric forms [12, 7]. Microwave investigations showed that in these molecules the transition from one isomeric form to the other is accompanied by a change in their s=uctural parameters. Agreement between the calculated data on the stability of the isomers and the experimental data is only obtained when account is taken of s=ucmral deformation. Since the conditions for rotation of the CH2OH group in n-butanol and n-propanol are identical, it should be expected that, as observed in n-propanol [7], the gauche form (where the C2CaC4, CaC40, and CaC2H4, s angles should be rather greater than in the transform) (Fig. 1) would be more stable in the n-butanol molecule during rotation of the CH2OH group. LITERATURE CITED 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

234

M.V. Vol'kenshtein, Configurational Statistics of Polymeric Chains [in Russian], Izd. Akad. N auk SSSR, Moscow (1959). R.A. Scott and H k. Scheraga, I. Chem. Phys., 42, 2209 (1965). N.P. Borisova and M. V. Vol'kenshtein, Zh. Strukt. Khim., 2_, 346 (1961); 2_, 469 (1961). V.G. Dashevskii and A. I. Kitaigorodskii, Teor. i ~ksperim. Khim., 3, 43 (1967). E. Hirota, l. Chem. Phys., 37, 283 (t962). T . N . Sarachman, L Chem. Phys., 3__99,469 (1963). R.A. Ragimova, Candidate's Thesis [in Russian], IF kkad. Nauk kzerb. SSR, Baku (1967). R.G. Lemer and B. P. Dailey, L Chem. Phys., 2.66, 679 (1957). L.M. Imanov and Ch. O. Kadzhar, Izv. Akad. Nauk Azerb. SSR, Set. FTlvIN, 3-4, 33 (1967). A . k . Abdurakhmanov, R. k. Ragimova, and L. M. Imanov, Optika i Spektr., 2_~6,135 (1969). D.R. Herschbach, I. Chem. Phys., 31_, 91 (1959). E. Hirota, J. Chem. Phys., 4_22,2071 (1965).