-dK
-dw,WoJ(J+l)-d,,K
(1)
In eqn. (I) IV, is the energy of the rigid rotor and a function of the rotational constants A, B and C only, and d,, CIIJK, dK, dw, and dWK are the centrifugal distortion constants. The fitting procedure was the method of least squares1 3. The results are given inTable 3 and the calculated frequency differences are listed inTables 1 and 2.
STRUCTURE
Since no isotopically substituted forms of ethoxy ethyne were assigned, an accurate calculation of its molecular structure is not possible. However, the molecular parameters of methoxy ethyne’ can be assumed with some confidence since the replacement of a methyl group with an ethyl group is not expected to affect the framework appreciably. In addition, the methyl group was considered to be tetrahedral with C-H distance 1.094 A and the O-C-C,,,,, angle was taken to be 111.0”. The experimental moments of inertia of the anti rotamer can be reproduced satisfactorily if the COC angle is decreased to 111.6” (from 113.3”) and the C-Cmclhyl
65 TABLE 2 OBSERVED
AND
THE
(in MHz)
FOR
THE
Transrtion
DIFFERENCE GAUCHE
BETWEEN FORM
OF
Obserl;eda
OBSERVED
ETHOXY
AND
CALCULATED
GROUND
E~HYNE
Obserwd
Centrifugal
-caIcrrlated
distortion correction
lo.1 -
20.2
12595.35
0.06
-
II.0 -+
2 1.L
13 154.85
0.05
-
2 I.2 -
3 1.3
18113.07
20.2
-+
3 0.3
18831.23
0.11
22.1
+
32.2
I
8 930.65
0.01
22.0 +
32.1
19029.23
0.14
2 1.1 +
3 1.2
19715.98
30.3 -
40.4
24994.87
31.2
-
41.3
3 2.2
+
42-3
-0.02
-0.05
O.lZ 0.10 0 02
-
0.37 0.36 0.29
-
0.46
0.01
-
0.80
26256.85
0.01
-
25221.16
0.00
1.17 0.07
31.3 -
4 1.4
24 123.23
-0.02
-
022
4 1.d *
515
30111.87
-0.02
-
0.65
40.4 -+
50.5
31068.71
42.3 -
52..+
3 1494.84
5 0.5 + 60.6 -
5 1.4 61.5
13318.52
0.01
-
1.51
15516.21
0.01
-
335
61.5 +
62.4
22201.54
0.04
7 1.6 +
72.6
I8 852.76
004
70.7 +
7 1.6
18254.76
0.03
71.6 +
72.5
21750.05
0.10
8 0-E +
81.7
21546.62
0.04
8 1.7 -
82.6
21637.45
0.00
2.66
8 1.7 + 90,s -
82,7 9 I.8
17004.62 25 364.94
0.00 0.04
11.72 - 18.27
9 I.8 9 I.0 +
9 2.7
21956.98
-0.03
0.72
92.8
15 043.70
-0.05
16 35
0 05 -0.01
-
141
-
055
2.32 7.76 -
6.53 2.98
-11.43
22785.13
-0.07
-
11 l.lO-fll2.9 12 1.113122.10
24 184.15 26201.64
-0.08 -0.14
-11.26 -23.14
142,1~-+143,1z 15 2.1~-fl53.13
26053.99 23 075.33
0.01 -0.04
162,143
20076.61
-0.04
101.9
-
102.a
163~4
17,.,,+17,.,,
17 136 05
0.00
18 z.,~+~%Is
14333.21
0.14
183.16+ 183.15
21773.71
0.06
m fO.10
MHz.
3.62
79.39 96.41 113.02 127.86
139.39 -209.03
STAllI
FREQUENCIES
66 TABLE
3
GROUND-STATE
ROTATIONAL
CONSTANTS
AND
CENTRIFUGAL
DISTORTION
CONSTANTS
OF
ETHOXY
ETHYNE=
A (MHz) B (MHz) C (MHz) :, &K 4c dw, &K
Anti
Gauche
29 500 &200 2502.178 &0.007 2380 034&0.008
I 1799.84&0.02 3422.405f0.007 2887.69 I =tO.O07
-0.990984
-0.880003 -29.3 f0.3
(kHz)
--473.8&g 6 -796.1 +23.9 10.58 kO.05
W-fz) H-W (x
IO61
110.7+3.1
(Xl@)
a Uncertainties
are standard
deviations.
is 1.527 A. No attempt was made to refine the A rotational constant further since the observed value is encumbered with rather large uncertainty. The same parameters were then transferred to the gauche structure, and the dihedral angle was varied to get the predicted and observed rotational constants in agreement. It was, however, found necessary to open both the COC and the OCC angle by l.O”, and to increase the 0-CcthY, bond length by 0.01 A to make the gauche structure agree better than 0.1 %. This observation fits with the slight structural differences between rotameric forms found in other molecules studied4m lo, i4. r5_ Due to steric repulsion, which may exist between the methyl group and the acetylenic group, it is reasonable to expect a slight change in the gauche structure. A torsional angle for the gauche form of 108 +3” (from the anti form) results from the fitting. In Table 4 plausible structural parameters are listed, as well as the predicted and observed moments of inertia.
DIPOLE
MOMENT
as a function of the applied electric The displacement of the Stark lobesi field was used to determine the dipole moment of both rotamers. A number of measurements was made on several Stark components from at least three different lines for each rotameric form, and the data were used in a least squares fitting of the dipole moment components. For the anti form the PC-component, perpendicular to the plane of symmetry, was assumed to be zero. The 1 + 2 transition of OCS was used to calibrate the electric field in the cell, using po, = 0.71521 D17. The observed and calculated values of AvIE’ as well as the dipole moment components of the two rotamers are given in Table 5. The total dipole moment for
67 TABLE
4
PLAUSIBLE
STRUmURAL
PARAMETERS
AND
CALCULATED
1.210 A 1.060 1.527 1.313 1.100 1.095 I.415 anti 1.425 gauche
CGC S-H c-c EC-0
C-H mclhyl C-Hmc,hr,e.e o-C,,w o-CclhyI
AND
111.6” 112.6” 111.0” I 12.0” 109.5” 109.5’
LCOC LCOC iocc LOCC LCCH LOCH
Dihedral angle: 0” anti; 108*3” of inerria (amrr A’):
Monwnrs
OBSERVED
MOMENTS
OF
INERTIA
ant1 gauche anti
gauche
gauche
Obserced
Calculated
17.1 202.036 212.405
16.857 202.029 212.412
42.842 147.712 175.064
42.836 147.889 174.606
Anti I, Ib 1, Gauche 1. Ib I.
TABLE STARK
5
EFFECi-
AND
DIPOLE
MOMENTS
OF
ANTI
An:i form Transition
2 11 +
312
4 13 *
M
0
414
2 0
La
2 0
1
1 2
Dipole =
ISOMERS
OF
ETHOXY
h/E2
(Hz
V-2
cm2)
Obseroed
Calculated
-0 969 -44.4 - 173.7
-44.2 -173.9
10.9 16.5 32.5 -0 489 -1.51 -4.48
-0.945
11.5 16.6 31.7 -0.442 -1.31 -4-07
Transition
101+
202
3 03 *
404
312 *
413
M
0 1 0 1 2 0 1
moments
D j‘b = D pc = 0.0 (assumed) ,+ = 1.91&:0.05 D
p.
GAUCHE
1.62f0.03 1.01&0.03
ETHYNE
Gauche form
1 3 13 +
AND
p. = pb = pc = pLT=
1.72f0.04 0.64f0.07 0.85&0.02 2.02fO.07
D D D D
h/E2
(Hz
V-2
cm’)
Obsemed
Calculated
-12.6 24.0 1.74 -0.60 2 76 4.30 2.91
- 12.4 24.3 - 1.60 -0.53 2 68 4.36 2.96
68 the anti form, I .91 f0.05 D, is not significantly different from that for the gauche form, 2.02 k 0.07 D. These dipole moments may be compared to the value 1.94 D found by dielectric-constant measurements made in benzene solution’s. For comparison, the dipole moment of methoxy ethyne’ is p, = 1.41 D, IQ, = 1.32 D and /I,,~, = 1.93 +0.02 D. Th e relatively large difference between the dipole moments of cthoxy ethyne and diethyl ether (1.25 D”) has been attributed to an appreciable contribution of the resonance structure C,H,-&C&H derived from dipole momentrs
VIBRATIONAL
and NMR
data”.
SATELLITE SPECTRA
Anri form During the assignment of the a-type transitions, three sets of weaker lines with similar Stark effect were observed. The lines appeared consistently on the high frequency side of the ground state line. Their decreasing intensity as they became farther displaced from the ground state line was taken as an indication that these transitions belong to successive excited states of the same vibration. The lines were all sharp and unsplit. These vibrational satellites were assrgned to the torsion about the 0-Gel,.,,,, bond. The measured frequencies were fitted to a rigid rotor energy expression. As for the ground state, the fit was satisfactory. The observed frequencies and the difference between observed and calculated frequencies are given in Table 6 and the rotational constants in Table 7.
Gauche form For the gauche form, two vrbrational satellites were assigned on the low frequency side of the ground state line. The presence of these lines was not so readily apparent as for the anti form due to the larger displacement of the vibrational satellites from the ground state line. The measured transitions were fitted to a rigid rotor energy expression_ As for the ground state, the deviation from rigid rotor was significant. The mean square deviations were 0.3 MHz and 0.4 MHz for the first and second torsional excited states, respectively. The measured frequencies and the difference between observed and calculated frequencies are reported in Table 6, the rotational constants in Table 7.
RELATIVE IN-IENSLTY MEASUftEhlENTS
The measured played on of several
relative intensities of the vibrational satellites described above were both at dry ice and room temperature and the transitions were drsthe oscilloscope or recorder. Measurements were performed at intervals days with different settings on the spectrometer. Despite somewhat low
69 TABLE
6
OBSERVED TIONAL
AND
EXCITED
THE DIFFERENCE STATES
BETWEEN
OF ETHOXY
OBSERVED
ETHYNt?
(in
Gauche form 101 -+ 202 I 10 3211 2 12+3,, 202 - 303 221 - 322 220 + 3,, 2 11 -+ 31, 3 13 -+ 4,5 303 -+ 40, 322 - 4~~ 3 12 +4,x 41* + 51, 4OJ + 505 4 23 + s2,
CALCULATED
TRANSITIONS
1- = 2
T=l
Transitions
AND
IN THE VIBRA-
MHZ)
7=3
Obserued
Obs. talc.
Observed
Obs.talc.
Obserced
14506.75 14 867.20 19341 87 19 822.55 24 176.47 24485.41 24777.41 29010.74 29732.10
0.08 -0.07 0.09 -0.03 -0.04 -0.04 -0.09 -0.04 0.15
14553.93 14914.02 19404.91 19 884.95 24255.3 I
-0.01 -a.05 0.10 -0.03 -0.01 -
14606.62 19475.05 19933.89 24343.16 -
0.01 -oo.05 -0.05 -
0.02 -o_os
24916.84 -
-
24 855.52 29 105.30 29825 62
0.05
12521 14 13063.00 18021 43 I 8 724.43 18816.68 18907 63 19581.59 14003.35 24861.00 25070.66 26079.89 29 965.89 30913.55 3 I 308.95
-005 0.06 -0.04 - 0.02 0.61 007 0.08 -0.46 0 05 0.45 -0.46 0.07 0.05 -0.11
0.07 -
29 899.36
0.01 0.03
M=l
T=2
T=l
Obs. talc.
12955.29
-0.89 0.60
17914.13
-
-
-
18 103.30 I8 822.93
0.10 0.05
19709.71
0.22
-
19421.97 23 862.07 24702.07 25095.43 25 869.36 29791.46 30729.27
0.92 0.33 0.16 -0.52 0.08 -0.36 -0 36
-
24983.83
-0.10
25455.30 26248.80
-0_09 -0.09
-
-
-
’ T means internal torsion and M means methyl torsion. TABLE
7
ROTATIONAL
Rorarner
CON5rAMS
(in MHz)
T=l
FOR
ETHOXY
ETHYNE
IN
T=2
Anti A B c
(31 OOOf300) 2507.968 f0.008 2387.767&0.008
(31 lOOf900) 25 15.728 f0.007 2395.685 +0.007
Gauche A B c
11958.3 h7.8 3396.06&0.05 2875.97+0&I
12255.9&16.0 3364.72&0.09 2862.03 LO.08
z T means Internal torsion and M means methyl torsion.
VIBRATIONAL
EXCITED
T=3
(33000~2000) 2520.503f0.012 2405.776+0.007 -
STATES=
M=l -
1 I 807.5 k4.8 3421.54&0.03 2885.80~0.04
70 intensity, the most consistent
set of data was obtained
at room temperature and
with recorder tracing. The results for the gauche isomer are less satisfactory than for the anti due to the larger displacement from the ground state line to the satellite lines. The results for both rotamers are given in Table 8. The enerw difference between the lowest states of the two rotamers was determined by measuring the relative intensity of adjacent lines. Four pairs of transitions were used and the measurements, presented in Table 9 yielded Einli =
AE = E;.ushc-
TABLE
INTENSLN
MEASUREMENTS
Rorurmv
G+T=I
Anti Gauche
loo&
(Cm-
(2)
‘)
G+M=l
T=I+T=2 7
-
103p10 105f20
78&15
a T means
ENERGY
cal mole-‘.
8
RELATIVE
TABLE
138+90
270f30
internaltorsion and M means methyl torsion.
9 DIFFERENCE
Tratzsirionr
BEI-WEEN
GAUCHE
ETHOXY
ETTHYNE
compared
Anri
Garrche
3 12 -413
211 *31r
Average AE”
=
POTENTIAL
ANTI AND
138k90
FUNCTION
160*50
cal mole-‘.
FOR INTERNAL
ROTATION
OF THE ErHYL
GROUP
The rotational isomers of ethoxy ethyne can be considered as the conformations of the molecule at the minima of the potential function for the internal rotation of the ethyl group about the O-Cclhy, bond. A general form for the potential function governing this rotation is given by V(0) = c $V”(l -cos ”
n0)
(3)
71 where 0 is the torsional angle, taken as 0” in the anti form. The evaluation of the coefficients V, that characterize the potential function is based on an idealized model necessary to simplify the problem. The molecule is regarded as consisting of two rigid parts (the ethyl and the ethynyl groups) and only the ethyl torsron is allowed. Hence, this treatment neglects the interactions of all the other vibrations with the internal rotation. Furthermore, since only a small number of Fourier coefficients can be determined, it is assumed that eqn. (3) converges rapidly, so that only a few terms are needed to characterize the potentral. The coefficients in eqn. (3) are determined by the procedure given by HiTotal by relating some of the experimental qualities reported in earlierparts of this paper to the potential function. By expanding the potential in a Taylor series at both minima, the torsional frequencies can be related to the curvature of the potential. Thus (a’ F/l&92)B,00 = C _1(1Z2Y”)= 47E2V2p,~i(Gr,l)anr,_ (a’ V/ad2)e=
l,,Bo 1
2 +(n2Vn)
”
(4)
cos (II - 108”) = ~~~~~~~~~~~~~~~~~~~~~ (5)
where G,’ represents the diagonal element of the ethyl torsron of the G- ’ matrix2’. Two more relationships can easily be derived by making use of the difference in energy between the ground states of the rotamers and the condition that the potential has a minimum at v = lOga, V(108”) (8 v/av),,
= c +V,[l -cos
@I - lOSo)] = (E”--~~v)B”uchc-(Eo-~h~),,li
,,,l=
c n V, sm (n - 108”) = 0 n
(6) (7)
The values of the (GLr) elements needed in eqns. (4) and (5) were calculated according to the method of Polo” and yielded (G,l),,u = 14.65 amuA2 radB2 and (GLr%auche = 13.70 amu A2 rad2. The equations to obtain four of the coefficients in the potential function expansion are: 1 $zv, c+V,(l c +z2v, c
sin [n(lO8&3”)] -cos
= 0
[n(lO8+3’)])
= 12.44f2.61
+I’ V, cos [N( 108 +3”)]
(8) = 0.170+_0.090
kcal mole-r
kcal mole-l = 7.08 + 1.93 kcal mole-’
(9) (IO) (11)
and the deduced values are: VI = -0.41+0.10
v, =
0.04~040
v, =
1.42f0.38
v4
0.77+0.30
=
kcal mole-’
(12)
72 The uncertainties given in eqns. (10) and (I 1) reflect an uncertainty in the vibrational frequencies of 10 cm-‘. It is seen from eqn. (12) that the most important term is V, _ The V4 term is of significant magnitude, however, indicating a slower convergence of the Fourier expansion than assumed, and this fact introduces addrtional uncertainty in the potential function. Figure 2 shows a plot of the four-term potential.
DISCUSSION
The four-term Fourier expansion of the potential function for the torsion gives a barrier height between the anti and gauche wells of 2.0f0.5 kcal mole-‘, while the syn barrier (0 = 180’) is l.Of 1.5 kcal mole-’ from the anti minimum energy. Tt is important at this point to note that only classical, and no quantum mechanical, quantities have been used to evaluate the potential function, and that the barrier heights are determined by extrapolating the potential function determined from data obtamed in the anti and gauche minima. The dotted curve in Frg. 2, calculated by taking the maximum contribution from the given uncertainties in the Fourier coefficients, illustrates the uncertainty in the potential function. WilsonZ3 has proposed that the V3 term in the potential is approximately transferable for molecules with rotation about the same bond. It is interesting to note
kcal
mole-’
t-t I I I I 2.0
-
\
’ 1
I
/
,t
I
1.0
Fig. 2. The derived potential function for rotation about the 0-Cclhyl bond. The observed torsional levels are indicated. The dotted curve is the uncertainty, see text.
73 that the I/, term determined for ethoxy ethyne (1.42kO.38 kcal mole-‘) is in good agreement with the V, term found in methoxy ethyne3 (1.440+_0.030 kcal mole-l). The dihedral angle of 108” and the apparent structural changes going from anti to gauche conformation indicate that steric repulsions exist in the gauche form. The distance between the methyl carbon and the nearest acetylene carbon is 2.96 A, considerably less than the sum of the van der Waals radii (3.4 A). Therefore, some other factor must account for the increased stabilrty of the gauche form over what might be expected on the basis of steric considerations alone. For n-propyl derivatrves, CH3CH,CH2X, it is well known that increased electronegativity of X (X = CH,, C=CH, C=N) gives an increased stability to the gauche rotamer’“~24~2s. It has been suggested that the greater stability of the gauche form of I-pentyne compared to butane may be due to attractive dipoIedipole interactions’ O. It is believed that this argument is also valid for ethoxy ethyne. For CH,CH20CHa the anti form is found to be 1.35 kcal mole-’ more stable than the gauche form5. For ethoxy ethyne, where the energy difference IS only on the order of 0.1 kcal mole- ‘, it appears to be an even higher stabilization of the gauche form. This may be reasonable since the bond moment of 0-CCH is larger than the bond moment of C-CCH. A qualitative calculation of the classical dipole-dipole interaction ener_gy of two dipoles ji, and 2, was performed using the expressionz6 E
3(&
. R)(k lR12
- RI I)
where I i?I is the distance between the two dipoles. Using /icHJ = 0.1 D and po_,-c, = 2.0 D the interaction energy is on the order of 200 cal mole-‘. This result indicates that drpole-dipole interactions are of significance for the energy difference between the anti and gauche form of ethoxy ethyne.
ACKNOWLEDGEMENTS
The author wishes to express his appreciation to Professor J. E. Boggs for his hospitality and for numerous helpful discussions. Dr. C. 0. Britt is thanked for several discussions of instrumental problems. Professor J. F. Arens is gratefully acknowledged for providing the sample of ethoxy ethyne. Fil. lit. Hasse Karlson and Professor Carl Lagerkrantz are thanked for making available the commercial spectrometer used in parts of this work. Finally, United States Educational Foundation in Norway is thanked for a Fullbright Travel Grant.
74 REFERENCES
1 0.
Bastiansen.
specriues
H. M. Seip and J. E. Boggs, in J. D. Dunitz and J. A. Ibers (editors), Vol. 4, Wiley, New York, 197 1_ Engelsen. H. A. Dijkerman and J. Kerssen, Rec. Trac. Chinr , 84 (1965) 1357.
Per-
in Strrrctrwal Chemistry,
2 D. Den 3 D. Den Engelsen, f. Mol. .Specrrosc., 30 (1969) 466. 4 J. M. Riveros and E. B. Wilson, Jr., J. CIlem. P&-s_, 46 (1967) 4605. 5 I. P. Perchard. Spectrochim. Acfu, 26A (1970) 707. 6 T. Kitagawa, K. Ohno, H. Sugeta and T. Miyazawa, Bull. Clrerrl. Sot Jap., 45 (1972) 969. 7 M. Hayashi. H. Imaishi. K. Ohno and H. Murata, Brtll. Chenr. Sue. Jup., 44 (1971) 299. 8 L. Brandsma, H. F. T. Bos and J. F. Arens, in H. G. Viehe (editor), Chet~li.s/f_v of Acefyfettes, Marcel Dekker, New York, 1969. 9 C. 0. Britt, Rec. Sci. Instrtrm., 38 (1967) 1496. 10 F. J. Wodarczyk and E. B. Wilson, J_ Chenr. Phys., 56 (1972) 166. 11 J. E. Wollrab, Rorarronal Specrra and Molecular S(rucfwe, Academic Press, New York, 1967. I2 J. K. G. Watson, 1. CXenr. P~Jx, 45 (1966) 1360. 13 K.-M. Marstokk and I-I. Mnllendal, 1. Mol. Structrrre, 5 (1970) 205. I4 E. Hirota, 1. Chem. PhJs., 37 (1962) 283. I5 E. Saegbarth and E. B. Wilson Jr., f_ C’heln. Phys_, 46 (1967) 3088. 16 S. Golden and E. B. Wilson Jr., J. C/rem. Plr.ys_, 16 (1948) 669. 17 J. S. Mucn ter, J. Cherlr. Phys., 48 (I 968) 4544. 18 W. Drenth, G. L. Hekkcrt and B. G. Zwanenburg, Rec. Trarr. Chirn., 79 (1960) 1056. 19 T. L Jacobs, J. D. Roberts and W. G. MacMillan, J_ Amer. C/lelll Sot, 66 (1944) 656. 20 D. Rosenberg and W. Drenth, Tetrahedron, 27 (1971) 3893. 21 E. B. Wilson Jr., J. C. Decius and P. C. Cross, Molecrrlar Vibrurions, McGraw-Hill, New York, 1955. 22 S. R. Polo, 1. Cflenl. Pf~js., 24 (1956) 1133. 23 E. B- Wilson Jr., Adcan. Chem_ Phys., 2 (1959) 367. 24 N. I_. Allinger, M. A Miller, F. A. Van Catledge and J. A. Hirch, J. Amer. Chew. Sot., 89 (1967) 4345. 25 E. Hirota. J. Chew. Phys., 37 (1962) 2918. 26 J. M. Lehn and G. Ourisson, Brrll. Sot. Chinr. Fr., (1964) I 113.