578
J. Phys. Chem. 1995, 99, 578-585
Enthalpy Difference between Conformers of n-Butane and the Potential Function Governing Conformational Interchange W. A. Herrebout and B. J. van der Veken Department of Chemistry, Universitair Centrum Antwerpen, 171 Groenenborgerlaan, Antwerpen 2020, Belgium
Aiying Wang and J. R. Durig* Department of Chemistry, University of Missouri-Kansas City, Kansas City, Missouri 64110-2499 Received: June 20, 1994; In Final Form: September 2, 1994@
The enthalpy difference between the more stable s-trans and high-energy gauche conformer of n-butane, C H ~ C H Z C H ~ Chas H ~ been , determined in the vapor state using variable-low-temperature infrared spectra of the gas to be 234 f 33 cm-’ (669 f 96 caymol). Additionally, the enthalpy difference has been obtained from n-butane dissolved in liquefied argon, krypton, and xenon from variable-temperature studies of the infrared spectrum and the determined values ranged from 243 f 8 cm-’ (693 f 19 caumol) to 218 f 8 cm-’ (621 f 19 caymol) in going from liquid argon to xenon, respectively. Utilizing the asymmetric torsional fundamentals of the s-trans and gauche conformers of 121.28 and 116.60 cm-’, four excited state transitions for the s-trans and two for the gauche conformers, and the new value for the enthalpy, as well as the dihedral angle of 62.8’ for the gauche conformer, the potential function governing conformational interchange has been determined. The resulting potential coefficients are VI = 242 f 7, VZ = 43 f 5, V3 = 1146 f 2, V4 = 40 f.2, VS = -6 f 2 and vf, = -36 f 1 cm-’. From this potential function the s-trans to gauche, gauche to gauche, and gauche to s-trans barriers are determined to be 1266 f 20 cm-’ (3.62 f 0.06 kcavmol), 1146 f 20 cm-’ (3.27 f 0.06 kcaymol), and 1032 f 10 cm-’ (2.95 f 0.03 kcaymol), respectively. Additionally, this potential has a “syn” barrier, which is the energy difference between the s-trans minimum and the gauche to gauche transition state of 1380 f 10 cm-I (3.95 f 0.03 kcavmol).
Introduction
the gas phase enthalpy difference between the conformers has not been well determined since the values obtained range from 4.4 to 2.8 kcdmol with various values of the experimental uncertainties. However, it is clear that a rather accurate value for the enthalpy difference in the gas phase has to be known in order to compare the gas phase result with the results obtained using liquefied noble gas solutions. Therefore, because of the doubts that have been raised with respect to the larger gas phase values,12 as well as the need for a value for comparison with the results from the liquefied noble gas solutions, we embarked upon a study to obtain a new, accurate value for the enthalpy difference in the gas phase using low-temperature gas phase infrared spectroscopy.
Since liquefied noble gases are the most inert solvents presently known for diluted solutions, only very small interactions are expected to occur between the solute molecules and the surrounding noble gas atoms. Therefore, the properties of compounds dissolved in such liquefied noble gases and those of the corresponding gas phase are expected to be quite comparable. In a first approximation, the liquefied noble gas solutions may therefore be described as a so-called “pseudo gas For some time, we have been using such liquefied noble gas solutions in order to obtain a better determination of the conformational behavior of the molecules in which we are interested? However, during this period, some doubts have been raised about the “pseudo gas phase” characteristics of the Experimental Section liquefied noble gases (argon, krypton, and xenon) used. Therefore, we have started a more detailed investigation on the The n-butane sample was purchased from Aldrich Chemical influence of the liquefied noble gas solutions upon the conforCo., Milwaukee, WI, with a stated purity of 98%. The sample mational equilibria of some simple molecules like n-butane, was dried over 4A molecular sieves and used without further 1,2-dichloroethane, etc., dissolved in them. In this study, we purification. are presenting the determination of the enthalpy change between All infrared spectra were recorded on a Bruker Model IFS the s-trans and gauche conformers for the n-butane molecule 113v Fourier transform spectrometer, equipped with a Globar dissolved in liquefied argon, krypton, and xenon compared to source, a G e m r beam splitter, and a broad-band MCT detector. that obtained for the gas. All spectra were recorded at 0.5 cm-’ resolution. For all cases Since n-butane, C H ~ C H ~ C H Z C H is ~the , simplest alkane 200 interferograms were co-added, Happ-Genzel apodized, and which may exist as a mixture of rotational conformers, the Fourier transformed with a zero filling factor of 4. conformational behavior of it has been of interest for many For the studies in liquefied noble gases, a specially designed years. For example, the s-trans to gauche enthalpy difference cryostat cell was used. It consists of a copper cell with 4 cm in both the liquid and vapor phase has been the subject of path length, equipped with wedged silicon windows sealed to numerous previous and theoretical s t u d i e ~ . ~ ~ - ~the~ cell with indium gaskets. It is cooled by controlled cold Although there have been a large number of studies reported, nitrogen bursts and can withstand an internal pressure of 15 bar down to 77 K without leaking. The temperature is controlled Abstract published in Advance ACS Absrracts, October 15, 1994. by two Pt 100 thermoresistors. The complete cell is connected ~
~~~~~
@
0022-3654/95/2099-0578$09.00/0 0 1995 American Chemical Society
Enthalpy Difference between Conformers of nButane
J. Phys. Chem., Vol. 99, No. 2, 1995 579
TABLE 1: Temperature and Intensity Ratios for the Conformational Study of Gaseous n-Butane TIK 297 273 263 253 243 233 223
291 K
1
1375
1325
223K
1275
'vlcml
Figure 1. Comparison of the experimental contours of the CH2 wagging conformer doublet in the gas phase spectra with the calculated contours and their resulting sum, for both the spectra recorded at 297 and 223 K.
to a pressure manifold, allowing the filling and evacuation of the cell. After the cell is cooled to the desired temperature, a small amount of the compound is condensed into the cell. Next, the pressure manifold and the cell are pressurized with the noble gas, which immediately starts condensing in the cell, allowing the deposited compound to dissolve. Due to the density changes in the solution with the temperature,38the frequencies of the band maxima are slightly shifted during the temperature studies. Therefore, all frequencies given in this study correspond to the spectra recorded at the lowest temperatures for each solvent, Le., 88 K for the argon, 120 K for the krypton, and 168 K for the xenon solutions. Using the same sample cell, the low-temperature spectrum of gaseous n-butane was recorded at several temperatures between 297 and 223 K. For the lower temperatures, the corresponding maximum vapor pressure was used. In order to obtain information on the solubility of n-butane in liquid argon, krypton, and xenon, the spectra of the liquefied noble gas solutions were compared to that obtained from a crystalline solid film. The films was obtained by condensing a small amount of the compound onto a boiling liquid nitrogen cooled CsI window, followed by annealing until no further changes were observed in the infrared spectrum, Conformational Analysis Gas Phase. Because of the rotational structure of the infrared absorption bands of the vapor, the use of infrared spectroscopy of the gas for the determination of an enthalpy difference between two or more conformers is rather limited to those cases where all the absorption bands needed for the temperature study are well separated. However, as will be described herein, in some cases a simple, accurate intensity determination as a function of temperature can be obtained by fitting the experimental contours using rigid harmonic asymmetric top contour ~imulation.~~ In order to obtain a reliable value for the enthalpy difference between the trans and gauche conformers of n-butane, the midinfrared spectrum of gaseous n-butane was recorded at seven different temperatures varying from 297 to 223 K. In Figure 1, a part of the mid-infrared spectrum recorded at 297 and 223
It
4
ln(Ig/It)
985 864 805 732 649 589 527
1714 1668 1574 1569 1372 1393 1351
-0.555 -0.658 -0.671 -0.774 -0.748 -0.861 -0.940
K is shown. The part shown is the only region of the midinfrared spectra where trans (1292 cm-') and gauche (1343 cm-') absorption bands appear well ~ e p a r a t e d . ~As ~J~ can be seen in Figure 1, the relative intensity of the 1343 cm-' absorption band due to the gauche conformer strongly decreases when the temperature of the gas is decreased, which is not surprising since the gauche conformer is known to be the less stable form. As can also be seen in Figure 1, next to the absorption bands at 1343 and 1292 cm-', which are assigned to the CH2 wagging fundamentals for the gauche and trans conformers, two other absorption bands can be observed in this region, a relatively weak one near 1263 cm-' and a rather intense one near 1383 cm-', which were assigned1'J3 to a CH2 twisting and a CH3 rocking fundamental in both conformers, respectively. However, as will be discussed later, those absorption bands do not hamper the determination of the integrated intensity of the 1292 and 1343 cm-' absorption bands. It is interesting to note that another well-separated absorption band belonging to the gauche conformer can be observed' ',13 at 1136 cm-', but because of the appearance of several excited states and because of the appearance of two other absorption bands near 1165 and 1080 cm-', an accurate determination of its integrated intensity is rather difficult. Therefore, only the CH:! wagging conformer doublet described above was used for the AH determination from the gas phase temperature study. Using the structural parameters obtained from the RHF/631G* a b initio calculations'' for both conformers, the pure A-, B-, and C-type transitions were calculated using the harmonic rigid rotor approximation,a slit width of 0.5 cm-', a 0.125 cm-' interval, and a limiting value of the rotational levels of J = 200. However, since the relative intensity of the respective P-, Q-, and R-branches strongly depend upon temperature, for all temperatures at which the gas phase was investigated, new pure transitions had to be calculated for both trans and gauche n-butane. Using these calculated pure types for each temperature, the experimental contours were simulated. Most parameters, such as the orientation of the dipole gradient vector (lip/ aQ)o, the intensity of the band maxima, etc., were adjusted manually until a good agreement between the experimental and the calculated contours was obtained. In Figure 1, the experimental spectra recorded at 297 and 223 K are compared with the simulated contours and their resulting sum. As can be seen, the calculated spectra agree very well with the experimental spectra. Therefore, the intensity of the 1343 and 1292 cm-' absorption bands can be determined accurately by integrating the simulated contours. In order to obtain an idea about the relative error upon the intensities obtained as described above, the room temperature spectrum was simulated several times, using slightly different parameters. From the resulting intensities, the relative error upon the intensities, obtained using rigid harmonic asymmetric top contour simulations, was estimated to be 3.5%. For all temperatures studied, the integrated intensities for both the 1292 and 1343 cm-l bands, obtained using the technique described above, are summarized in Table 1. Using these intensities a
Herrebout et al.
580 J. Phys. Chem., Vol. 99, No. 2, 1995
-0.6
-
-0.8-
-1
.o 3.5
4.5
4.0
TIK x
I@
Figure 2. A van? Hoff plot for gaseous n-butane using the intensities of the CH2 wagging conformer doublet.
----I
4000
3WO
2003
IS00
IWO
h n -I
Figure 3. Mid-infrared spectra of n-butane dissolved in liquefied (A) argon, (B) krypton, and (C) xenon respectively recorded at 88, 190, and 168 K.
van't Hoff plot was constructed which is shown in Figure 2. From this plot the enthalpy difference was calculated to be 234 f 33 cm-l. Liquefied Noble Gases. In addition to the conformational equilibrium studies of n-butane in the gas phase, information was obtained on the relative stability of n-butane dissolved in the liquefied noble gases (argon, krypton, and xenon). In Figure 3, the mid-infrared spectra of solutions of liquefied argon (88 K), krypton (120 K), and xenon (168 K) containing apM n-butane are shown. Because only proximately 2.5 x
small interactions are expected to occur between the dissolved molecules and the surrounding noble gas atoms, most absorption bands were expected to undergo only small frequency shifts when passing from the gas phase to the liquefied noble gas s o l ~ t i o n s ,which ~ is in good agreement with the observed experimental results. In order to determine the relative stability of trans and gauche n-butane, dissolved in liquefied argon, krypton, and xenon, variable-temperature studies were carried out. For all solutions several spectra were recorded at different temperatures, varying from 88 to 128 K for the argon, 120 to 165 K for the krypton, and 168 to 223 K for the xenon solutions. Even at the relatively low temperatures at which the solutions were investigated, no kinetic effects could be observed, so all solutions may be considered to be in thermodynamical equilibrium. Furthermore, no experimental evidence was found for the existence of solid particles in any of the spectra, i.e., all of the n-butane molecules can be considered to be dissolved in the liquefied noble gas solutions studied herein. The mid-infrared spectra of n-butane dissolved in liquefied noble gases show several conformational splittings that can be used for temperature studies. However, in order to obtain a reliable value of AH, one has to look for a well-separated conformational doublet, where both absorbtion bands are characterized by a good signal-to-noise ratio. As described above in the mid-infrared spectra of n-butane, two well-separated absorption bands were observed at 1343 and 1292 cm-', which were assigned to gauche and trans n-butane, respectively. In the corresponding spectrum of n-butane, dissolved in liquefied argon, two absorption bands are observed at exactly the same frequency. However, due to the very weak intensity of the 1343 cm-' absorption band, an accurate determination of its integrated intensity is not possible. Therefore, the 1343/1292 cm-l conformer doublet was not used for the temperature study. As described before, in the gas phase mid-infrared spectrum of n-butane, two rather overlapping transitions are observed near 733.6 and 747.5 cm-', which have been a s ~ i g n e d ~ ~toJ the ~%*~ CH2 rocking fundamental of the trans and gauche conformers, respectively. As shown in Figure 4in the mid-infrared spectrum of the liquid argon solution, two well-separated absorption bands appear at 733 and at 748 cm-', the latter of which strongly increases its relative intensity when the liquefied argon solution is cooled further. Another transition, belonging to the gauche conformer, is found near 790 cm-', but because of its very low signal-to-noise ratio, it was not used further in the temperature study described. In Figure 4 the CH2 rocking conformer doublet described above is shown at four different temperatures, varying between 88 and 128 K. In order to obtain reliable intensities for both absorption bands, all experimental spectra were least squares fitted using a set of two Gauss-Lorentz sum profiles. Using the resulting integrated intensities summarized in Table 2, a van't Hoff plot was constructed which is shown in Figure 5 . The corresponding value for AH was calculated to be 243 f 25 cm-' (695 f 71 caYmol). Next to the influence of the temperature upon the conformational equilibrium between trans and gauche n-butane when dissolved in liquefied argon, also experimental results were gathered on the influence of the changing liquid density upon the conformational equilibrium. Therefore, several spectra of n-butane dissolved in liquefied argon were recorded at the same temperature but at a difference gas pressure, varying from 2 to 12 bar. When comparing all spectra, no pressure effects upon the conformational equilibrium between trans and gauche n-butane could be observed, which is not surprising. The effect
Enthalpy Difference between Conformers of n-Butane
J. Phys. Chem., Vol. 99, No. 2, 1995 581
I
w
3
-
.2.5
-
v
-
-3.0
-3s
t 0.008
0.009
0.011
0.010
TIK
Figure 5. A van? Hoff plot for n-butane dissolved in liquefied argon.
n 750
730
Jlcm-1
Figure 4. Details of the mid-infrared spectra of a liquefied argon M n-butane: (A) 118 solution containing approximately 2.5 x K, (B) 108 K, (C) 98 K, (D) 88 K, and (E) simulated profdes for 88 K.
TABLE 2: Temperature and Intensity Ratios for the Conformational Study of n-Butane in the Liquid Argon, Liquid Krypton, and Liquid Xenon
88 98 108 118 krypton 118 128 138 148 158 168 xenon 168 173 183 193 203 213
argon
66.3 92.1 115.7 155.7 226.9 283.1 196 216 266 320 384 421
30.9 45.5 94.6 148.4 117.4 166.5 231.0 312.5 410.1 543.6 400 43 1 541 667 785 868
849 1012 1243 1496 1083 1247 1435 1646 1890 2099 1616 1680 1876 2092 2311 2532
-2.79 -2.61 -2.51 -2.36 -2.12 -2.00 -2.11 -2.04 - 1.95 -1.87 -1.80 -1.71
-3.31 -3.10 -2.58 -2.31 -2.22 -2.01 -1.82 -1.66 - 1.53 -1.35 -1.40 -1.36 -1.24 -1.14 -1.07
of pressure upon the conformational equilibria is rather small and is, therefore, only observed when using pressures up to 20 kbar.6,40 In the mid-infrared spectra of n-butane, dissolved in liquefied krypton, several conformational splittings can be observed that can be used for temperature studies. The first region contains both the CH2 wagging fundamentals which were also used in the gas phase temperature study. In the spectra taken from the liquefied krypton solutions, the absorption bands belonging to these fundamentals can be observed at 1292 and 1341 cm-', the frequencies of which agree reasonably well with the gas phase results described above (1292 and 1343 cm-'). However, next to these absorption bands, two other absorption bands are observed near 1273 and 1258 cm-', which have to be assigned to impurities in the krypton. Because of these impurity bands, a reliable integration of the 1292 cm-' absorption band belonging to the trans conformer of n-butane is rather difficult. Therefore, the wagging CH2 conformer doublet was not used
G 100
760
120
Ilctn-1
Figure 6. Details of the mid-infrared spectra of a liquefied krypton M n-butane: (A) 163 solution containing approximately 2.5 x K, (B) 158 K,(C) 148 K,(D)138 K, (E)128 K, (F) 193 K, and (G) simulated profiles for 123 K. for the temperature studies. However, as described before, in the region between 800 and 700 cm-', some other well separated bands belonging to gauche and trans n-butane can be observed. As can be seen in Figure 6, the absorption band at 789.5 cm-', assigned to the more stable trans conformer, and two rather weak absorption bands belonging to the gauche conformer are observed at 748 and 732 cm-'. The latter two bands strongly increase in relative intensity when the liquefied krypton solution is warmed. As for the liquefied argon solution, the corresponding integrated intensities of all three of the absorption bands observed in this region were obtained by fitting the experimental spectra using Gauss-Lorentz sum profiles. In Table 2, the
582 J. Phys. Chem., Vol. 99, No. 2, 1995
6
Herrebout et al.
8
I
TIK
9
x I@
Figure 7. The van't Hoff plots (solid squares conformer doublet 748/ 789.5) for n-butane dissolved in liquefied krypton. resulting intensities for the 732, 748, and 789 cm-' absorption bands are summarized. Using these intensities for both the 748/ 789.5 and 732/789.5 cm-' conformer doublet, a van't Hoff plot was made. Using these plots, both shown in Figure 7, the enthalpy difference between the conformers was calculated to be 234 f 9 cm-' (695 f 25 caymol) and 221 f 21 cm-' (632 f 60 cavmol), respectively. In order to obtain the relative stability of the conformers in the liquefied xenon, the mid-infrared spectrum of n-butane dissolved in the liquid was recorded at six different temperatures, varying from 168 to 213 K. As can be seen in Figure 8, comparable results to those for the other rare gas solutions were obtained. Using the same least-squares refinement procedure, the experimental spectra were fitted using three Gauss-Lorentz sum profiles situated at 790, 747, and 732 cm-'. Using the integrated intensities summarized in Table 2 for both the 790/ 732 and 790/747 cm-' conformational doublets, van't Hoff plots were constructed. From these plots, both shown in Figure 9, the value for the enthalpy difference AH was calculated to be 213 f 8 cm-' (609 f 23 caumol) and 226 f 9 cm-' (646 f 26 caymol), respectively. From the integrated intensities described above, the fitting procedure also gives additional information about the parameters (intensity and frequency of the band maximum, full width at one-half height, fwhh, and GaussLorentz fraction) of all absorption bands involved. As can be seen, each absorption band exhibits a specific, different broadening as a function of temperature. Thus, it is emphasized that because of this characteristic, an accurate value for the enthalpy difference cannot be obtained using the intensities of the respective band maxima but that integrated intensities must be used.
Discussion The value of 234 f 33 cm-' (669 f 94 cavmol) for the enthalpy difference between s-trans and gauche n-butane in the gas phase obtained herein is in good agreement with most of the other values previously described in the literature. For example, using high-resolution tunable diode laser absorption spectra, Gassler et al.*' found a value for the AH of 246 f 18 cm-', which is in good agreement with the other values of 263 f 86,255 f 50, and 240 f 33 cm-' obtained using supersonic jet electron diffraction,*Omatrix-trapping technique^,^^ and the calculated Raman scattering intensity parameter^,'^ respectively. Therefore, the doubt about the reliability of the higher values obtained using Raman gas phase temperature studies' '.14 is justified.
L
1EO
E20
140
vim-I
Figure 8. Details of the mid-infrared spectra of a liquefied xenon solution containing approximately 2.5 x M n-butane: (A) 213 K, (B) 203 K, (C) 193 K, (D) 183 K, (E) 178 K, (F) 173 K, and (G) simulated profiles for 173 K.
I 1
1
,
I
.
5.5
5.0
TIK x
6.0
I@
Figure 9. The van't Hoff plots (solid squares conformer doublets 747/ 790) for n-butane dissolved in liquefied xenon. In addition to the experimental techniques mentioned above, the energy difference between the conformers of n-butane has been the subject of several ab initio c a l c ~ l a t i o n s , ~varying ~-~~ from simple restricted Hartree-Fock calculations to more sophisticated techniques, giving several values for the AE or AH, varying from 216 to 382 cm-I (618 to 1092 cdmol). Recently, Wiberg and M ~ r c k calculated o~~ the enthalpy difference to be 0.86 kcdmol, which is higher than the experimental values presented here. However, as noted by Mack and Oberhammer,41 one has to take into account that ab initio
Enthalpy Difference between Conformers of n-Butane TABLE 3: Comparison of the fwhh of the Absorption Bands Studied Here as a Function of Temperature noble gas TK ~ 7 3 cm-I 2 e748 cm-' ~ 7 9 cm-' 0 argon 88 1.Ooo 1.Ooo 98 1.136 1.192 108 1.400 1.402 118 1.680 1.770 krypton 118 1.000 1.Ooo 1.Ooo 128 1.024 1.080 1.174 1.347 138 1.049 1.200 1.390 1.552 148 1.122 158 1.203 1.480 1.739 168 1.293 1.680 1.957 xenon 168 1.om 1.Ooo 1.000 173 1.052 1.028 1.095 183 1.151 1.075 1.242 193 1.191 1.168 1.326 203 1.191 1.168 1.326 213 1.283 1.402 1.632 calculations even at the higher levels are not reliable when calculating the energy difference between molecular conformers with values less than 1.0 kcdmol. Despite the wide range of experimental"J6-l8 and theoreti~al33935-3~ studies, the potential function goveming the conformational interchange in n-butane is not resolved completely, since a reliable potential funcion from the asymmetric torsional transitions can only be obtained when both the structural parameters and the relative stability of the existing conformers are known accurately. In order to obtain a more reliable torsional potential governing the translgauche interconversion in n-butane, the torsional potential was recalculated using new parameters and the enthalpy difference obtained in this study. From the electron diffraction studyzoof n-butane, the dihedral angle for the gauche conformer was determined to be 72.4 f 4.8'. However, because of the rather low frequency of the intemal torsional mode, one expects this angle to be too large compared to the actual angle. In a more recent microwave the authors utilized the structural parameters obtained from the electron diffraction study, except for the dihedral angle, and recalculated this angle from the microwave rotational constants. The CH bond distances obtained from the electron diffraction study are inordinately long, which results in a calculation of a large dihedral angle from the microwave data. Therefore, in order to obtain more realistic structural parameters for the gauche conformer of n-butane, we maintain the differ-
J. Phys. Chem., Vol. 99, No. 2, 1995 583 ence in the two CC bond distances calculated by ab initio calculations, Le., 0.004 A. Additionally, we took the CH distances obtained from the RHF/6-31G* calculations, added a correction of 0.008 A, and then fit the microwave rotational constants. These parameters resulted in a dihedral angle in the range 62-63' rather than one around 72'. Finally, it should be noted that Snyder et aLZ6utilized the isolated carbonhydrogen stretching frequency for the ds molecule and obtained CH distances of approximately 1.085 A. If one uses the shorter CH distances, the dihedral angle becomes even smaller. However, these latter carbon-hydrogen distances seem to be unusually short for a saturated hydrocarbon. The final determined structural Parameters are listed in Table 4, along with those previously reported from the electron diffraction study. The reported distances should be good to at least 0.005 8, and the angles within approximately 0.5". The elongation of the carbon-carbon bonds results in one of the rotational constants being poorly fit if one maintains the differential of o.oo4 A for the two different carbon-cabon distances. With these the series has again been calculated, and it can be seen in Table 5 that the value does not significantly differ from that previously reported. However, we used the new to recalculate the function the conformer interconversion for n-butane. From three relatively recent investigations of both the farinfrared16,18 and low-frequency Raman17 spectra, the assignments of the torsional transitions arising from the stable s-trans and high energy gauche conformationsare well Using the structural parameters described above and a value of 234 cm-l for the enthalpy difference between bo&, conformers, the spectral data were fit to the usual expression for the potential function in the dihedral angle 4
~ ( 4=) l / z z ~ i (-l cos i4) i
using coefficients 1' to 6'. As previously described, l1 the torsional angular dependence of the intemal rotation constant F(4) can be represented as a Fourier series 6
F(4) = Fo + C F , cos i$J i=l
TABLE 4: Comparison of Potential Coefficients and Barriers to Interconversion (cm-') of nlutane from Several Studies ref 11 parameter this study a b ref 16 ref 18 ref 17 Fo 1.623 1.625 1.629 1.598 FI -0.0774 -0.0824 -0.105 -0.101 Fz 0.0420 0.0431 0.0668 -0.066 F3 -0.00789 -0.00823 -0.0146 -0.0144 0.00213 0.0042 0.00421 F 4 0.00204 F5 -0.000469 -0.000495 -0.001 1 -0.001 11 F6 0.000113 0.000120 Vl 242 f 7 524 f 12 584 f 7 418 f 6 181 f 3 395 f 2 VZ 43 f 5 -22 f 13 -96 iz 7 148 f 3 v3 1148 f 3 1168 f 3 1165 f 3 639 f 67 1154 f 3 1166 f 5 v4 40 f 2 15 f 1 45 f 3 -3f2 v5 -6f2 v6 -36 f 2 -38 f 1 -40f 1 136 f 23 -33 f 1 -34 f 2 dihedral angle (deg) 62.8 63.0 65.4 62.0 69.0 1274 769 1315 1271 s-translgauche barrier 1266 1288 1370 746 1090 1271 1146 1325 gauchelgauche barrier 891 459 1070 960 1032 905 gauchels-trans barrier AH (cm-l) 234 f 33 383 f 28 383 f 17 311 f 73 245 f 9 311 f 10
Herrebout et al.
584 J. Phys. Chem., Vol. 99, No. 2, 1995
TABLE 5: Comparison of Structural Parametere for n-Butane As Obtained by ab Initio Calculations and ExDerimental Methods parameter
RHF/6-3 lG*h MP2/6-3 lG*C electron s-trans gauche s-trans gauche diffractiond microwave'
r(CI-C2) 1.528 r(C2-Cj) 1.530 r(C1-H)) 1.086 ~ ( C I - H ~ ) 1.086 r(Cl-H?) 1.086 ~(C2-h) 1.088 r(c2-H~) 1.088 LClC2C3 113.1 LHlCiC2 111.3 LH2ClC2 111.1 LH3ClC2 111.1 L H ~ C ~ C I 109.4 LHsCzCi 109.4 H I C I C ~ Cdih ~ . 180.0 H~CIC~H dihI , 120.0 H~CIC~H dihI , -120.0 H4C:C1H3, dih 122.0 H s C ~ C I Hdih ~ , -122.0 C I C ~ C ~dih C ~ 180.0 ,
1.529 1.533 1.086 1.085 1.087 1.088 1.087 114.4 110.8 111.9 111.0 109.4 108.8 176.2 119.9 -119.6 122.9 -121.5 65.4
1.524 1.525 1.094 1.094 1.094 1.097 1.097 112.9 111.5 110.9 110.9 109.6 109.6 180.0 120.2 -120.2 121.8 -121.8 180.0
1.526 1.528 1.094 1.093 1.095 1.097 1.096 113.8 111.0 111.8 110.7 109.5 109.0 176.1 120.0 -119.7 122.4 -121.7 63.8
1.531 1.531 1.119 1.119 1.119 1.119 1.119 113.3 110.7 110.7 110.7 110.7 110.7
62.8
1.530 1.534 1.094 1.093 1.095 1.096 1.095 114.3 110.8 111.9 110.0 109.4 108.8 176.2 119.9 - 119.9 122.9 -121.9 62.4
Bond lengths in angstroms, bond angles in degrees. From ref 11. From this study, the structural parameters of the C1C2CjC4 skeleton compares well with those described before (ref 36). Reference 21. e From this study, structural parameters for gauche n-butane obtained by fitting the rotational constants given in ref 26.
TABLE 6: Asymmetric Torsional Transitions (cm-l) of n-Butane ~
conformer
transition
s-trans
1-0 2-1 3-2 4-3 5-4 F1r 2
gauche
F3
--
50 k1 1 2
~
obsb
obs - calc
121.28 118.82 116.08 113.00 109.84 116.60 114.10 111.30
0.01 0.02 0.00 -0.08 0.06
AEs01=
-/mb E - 1
2
Therefore, assuming that they have a comparable size, the difference in solvation energy for two species in equilibrium (A = B) is given by
0.00 -0.01 0.01
Calculated using the potential coefficients given in Table 5 . From one of the assignments given in ref 18, which is consistent with the assignment for the torsional fundamentals from the low-frequency Raman study of ref 17 and the far-infrared spectrum of ref 18. (I
In order to incorporate the relaxation of the structural parameters B(q)) during the intemal rotation into the equation mentioned above, all structural parameters were assumed to be small periodic functions of the torsional angle of the type
B(4) = A
lower than the values of 1700 cm-I represented before." However, this discrepancy can easily be explained as the result of the higher value of AH used in the fit, since comparable results as those previously described" are obtained when a value of 330 cm-' is used in combination with the F numbers calculated here. Using ab initio calculations, both Raghava~ h a rand i ~ Wiberg ~ and M ~ r c k calculated o~~ the syn barrier in the range 2000-2200 cm-', which is much higher than the experimental value of 1380 cm-I obtained herein. However, it should be noted that, with a recent ab initio using various basis sets up to and including triple-zeta with two sets of polarization functions on carbon and with varying amounts of electron correlation up to and including the coupled cluster with single and double excitations (CCSD) level of theory, a relatively smaller value of 1836 cm-I was obtained for the syn rotational barrier which, after adding the corresponding zeropoint and thermal corrections, decreased to only 1710 cm-', a value which is more comparable with the experimental value (1380 cm-I) obtained in this study. As described by Abraham et al.,4z the influence of the surrounding medium on a conformational equilibrium can be treated rather well using the reaction field theory.43 In a first approximation, the stabilization AEsol of a solute molecule, having a dipole moment p and radius a, can be calculated assuming that the surrounding medium is a uniform dielectric, characterized by a dielectric constant, E :
+ B cos 4 + C sin 4
Using the structural parameters for both the s-trans and gauche conformers, the kinetic constants F, were calculated. As can be seen in Table 5, the values obtained for F, compare very well with the other values reported in the literature, which is not surprising since the structural information used herein shows only small differences with the structural information used in the earlier studies. Using the values for F, obtained above, the asymmetric torsional transitions summarized in Table 6 were fitted using a fixed dihedral angle of 62.8" for the gauche conformer and a value of 234 cm-' for the enthalpy difference between both conformers. The resulting parameters V, are summarized in Table 5. Using these parameters, the s-trans to gauche, gauche to gauche, and gauche to s-trans barriers were calculated to be 1266, 1146, and 1032 cm-', respectively. Additionally, the syn barrier, which is defined as the energy difference between the s-trans minimum and the gauche to gauche transition state, was calculated to be 1380 cm-' (3.95 kcaumol), which is somewhat
Because both conformers of n-butane have only very low dipole momentsz3 (zero for trans conformer) and because of the very low dielectric constants of the liquefied noble gas (varying from 1.51 for argon to 1.88 for xenon3), only very small solvent effects on the conformational equilibrium of n-butane dissolved in liquefied noble gas are expected. This prediction is in good agreement with the similarity of the enthalpy differences obtained for the gas phase and for the solutions in liquefied noble gases. Using the reaction field model, no solvent effects are calculated when comparing the gas phase of n-butane with the corresponding liquid phase. However, the enthalpy difference seems to decrease to about 200 cm-' when going from the gas phase (240 cm-I) to the liquid phase^.^^^^ As can be seen using high-pressure spectroscopy6 andor statistical mechanics calculations,Mstabilization of the gauche conformer can be described as a result of the short-range packing effects, due to the intermolecular interactions present in the liquid. As described by DeVaure and Lascombe,6 the stabilization of the gauche conformer, due to so-called packing effects in the liquid, can be written as
Using the values for the difference in molecular volume AVlig and the intemal pressure (Pi P), given by DeVaure and Lascombe,6 the stabilization of the gauche conformer in the liquid phase is calculated to be 19 i 6 cm-' (54 f 17 caU mol), which is in relatively good agreement with the experimental value obtained when subtracting the gas phase value
+
Enthalpy Difference between Conformers of n-Butane obtained here and the liquid phase value described before. Similar stabilization effects of the gauche conformer may also be expected in the liquefied noble gases studied here. Therefore, the small changes in AH when going from the liquefied argon solutions (AH= 243 cm-') to the krypton (AH = 234-221 cm-') and the xenon solutions (AH = 213-226 cm-l) may be interpreted as the result of similar packing effects present in the liquefied noble gas solutions studied here. Acknowledgment. The NFWO (Belgium) is thanked for financial support toward the spectroscopic equipment used in this study and for a grant toward W.A.H.
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