J . Phys. Chem. 1987, 91, 1770-1778
1770
Vibrational Spectrum, Normal Coordinate Analysls, ab Inltio Calculations, and Conformational Stability of Ethyl Isocyanate J. F. Sullivan,* D. T. Durig,+ J. R. Durig,* Department of Chemistry, Unioersity of South Carolina, Columbia, South Carolina 29208
and Stephen Cradock Department of Chemistry, University of Edinburgh, Edinburgh, Scotland EH9 3JJ, UK (Received: October 13, 1986)
The infrared (3500 to 40 cm-') and Raman (3500 to 20 cm-I) spectra of gaseous and solid ethyl isocyanate, CH3CH2NC0, have been recorded. The infrared spectrum of the sample isolated in a nitrogen matrix has also been recorded from 3500 to 200 cm-'. Additionally, the Raman spectrum of the liquid has been recorded and qualitative depolarization values have been obtained. An assignment of the fundamental vibrations based on the infrared band contours, depolarization values, and group frequencies is given and discussed. This assignment is supported by a normal coordinate analysis utilizing a modified valence force field to calculate the normal modes and the potential energy distribution. The methyl torsional mode was observed at 265 cm-' in the vapor state from which the threefold barrier to internal rotation is calculated to be 1414 cm-'(4.04 kcal/mol). A complete equilibrium geometry has been determined by an ab initio Hartree-Fock gradient calculation employing STO-3G, 3-21G, and 6-31G* basis sets. These parameters are compared to those obtained from an electron diffraction study as well as those suggested from the microwave investigation. The calculations give only one stable minimum which is the one with the methyl group trans to the NCO moiety which is inconsistent with both the rotational and electron diffraction data where the stable conformer is the one with the methyl group eclipsing the NCO moiety. These results are compared with the corresponding quantities for some similar molecules.
Experimental Section Introduction We have recently carried out a series of vibrational and, for The sample of ethyl isocyanate was obtained from Chemical some cases, microwave or electron diffraction studies of several Procurement Laboratories, Inc., and purified by low-temperature molecules of the group IVA (group 14)32elements with the isofractionation on a vacuum sublimation column. The infrared thiocyanate For the carbon compounds the C N C spectra of the samples isolated in either an Ar or N 2 matrix at angle has been found to be relatively large (145 f 5 ' ) whereas ratios varying from 400:l to 1OOO:l were recorded with a Perfor the silyl and germy1 derivatives this angle has been found to kin-Elmer Model 225 grating spectrophotometer between 3500 be essentially linear. In the earlier vibrational studies of ethyl and 200 cm-'. The matrix samples were prepared by the and isopropyl i s o t h i ~ c y a n a t ethe ~ doublets observed in the "pulsed-deposition" method on a CsI window held at 10 K by 2200-cm-' range were interpreted as arising from two conformers an Air Products Model CS-202 microrefrigerator. Samples were of these molecules, but recent ~ t u d i e shave ~ * ~ shown that these annealed to 30-35 K, but no significant changes in the spectra doublets are due to a Fermi interaction of the ovetone of the symmetric NCS stretch with the fundamental antisymmetric NCS stretch. In fact, rather surprisingly, it has not been possible to ( I ) Durig, J. R.; Li, Y. S.; Sullivan, J. F. J . Chem. Phys. 1979, 7 1 , 1041. identify a second conformer for either ethyl or isopropyl iso(2) Durig, J. R.; Kalasinsky, K. S.;Kalasinsky, V. F. J. Phys. Chem. 1978, thiocyanate from their rotational8Sl0or vibrational ~ p e c t r a For . ~ ~ ~ ~ ~82, 438. the corresponding isocyanate molecules, again the silicon analogues ( 3 ) Durig, J. R.; Sullivan, J. F.; Heusel, H. L.; Cradock, S. J. Mol. Siruci. 1983, 100, 241. appear to have essentially linear heavy atom skeleton^^^-'^ but the (4) Durig, J. R.; Heusel, H. L.; Sullivan, J. F.; Cradock, S. Specirochim. carbon and germanium compounds have XNC angles in the 140 Acta, Part A 1984, 40A, 739. f 10' range, Le. H3GeNC0,14-'6LGeNC = 144 f 4'; H3CN( 5 ) Durig, J . R.; Sullivan, J . F.; Durig, D. T.; Cradock, S. Can. J . Chem. C0,17318LCNC = 139.98'. We7 recently carried out an electron 1985, 63, 2000. (6) Cradock, S.J . Mol. Spectrosc. 1982, 92, 170. diffraction investigation of ethyl isocyanate and found that the (7) Cradock, S.; Durig, J. R.; Sullivan, J. F. J. Mol. Struct. 1985, 131, 121. data could be adequately interpreted on the basis of a single (8) Durig, J. R.; Sullivan, J. F.; Little, T. S.; Cradock, S. J . Mol. Struct. conformer with the N C O group eclipsing the methyl group which 1984, 118, 103. is consistent with the earlier interpretation of the microwave data.lg (9) Kniseley, R. N.; Hirschmann, R. P.; Fassel, V. A. Specrrochim. Acta, However, the electron diffraction data would not be sensitive to Pari A 1967, 23A, 109. (10) Sakaizumi, T.; Ohashi, 0.;Yamaguchi, 1. Bull. Chem. Sot. Jpn. a 5% or less presence of a second conformer at ambient tem1976, 49, 948. perature and there were a large number of additional microwave ( 1 1 ) Durig, J. R.; Kalasinsky, K. S.;Kalasinsky, V. F. J . Chem. Phys. lines which were not assigned. Therefore, the presence of a small 1978, 69, 918. amount of a second conformer could have easily escaped detection (12) Duckett, J. A.; Robiette, A. G.; Mills, I. M. J . Mol. Spectrosc. 1976, 62, 34. in these earlier studies and in order to further investigate the (13) Glidewell, C.; Robiette, A. G.; Sheldrick, G. M. Chem. Phys. Leii. possibility for the presence of a second conformer at ambient 1972, 16, 526. temperature we have recorded the infrared and/or Raman (14) Durig, J. R.; Sullivan, J. F.; Li, Y. S.;Mohamad, A. B. J. Mol. Siruci. spectrum of ethyl isocyanate in all three physical states as well 1982, 7 9 , 235. (15) Ramaprasad, K. R.; Varma, R.; Nelson, R. J . Am. Chem. Sot. 1969, as an infrared study of the matrix-isolated material. Additionally, 90, 6247. we have carried out a normal coordinate calculation utilizing a (16) Murdoch, J. D.; Rankin, D. W. H.; Beagley, B. J . Mol. Struct. 1976, modified valence force field and an ab initio Hartree-Fock gradient 31, 291. calculation employing STO-G, 3-21G, and 6-31G* basis sets. The (17) Lett, R. G.; Flygare, W. G. J. Chem. Phys. 1967, 47, 4730. results of these studies are reported herein. (18) Anderson, D. W. W.; Rankin, D. W. H.; Robertson, A. J . Mol.
-
'Taken in part from the thesis of D. T. Durig which will be submitted to the Department of Chemistry in partial fulfillment of the Ph.D. degree.
0022-3654/87/2091-1770$01.50/0
Struct. 1972, 14, 385. (19) Sakaizumi, T.;Yamada, 0.;Ushida, K.; Ohashi, 0.;Yamaguchi, I. Bull. Chem. Soc. Jpn. 1976, 49, 2908.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 7, 1987 1771
IR and Raman Spectra of C H 3 C H z N C 0
n II
,
3000
,
,
,
I
, ,
,
,
I
,
,
,
,
I
,
2000 WAVENUMBER Ccni’)
,
,
,
I
,
,
,
,
I
1000
Figure 1. Mid-infrared spectra of gaseous (upper trace) and annealed solid (lower trace) ethyl isocyanate.
1
I
I
050
I
I
250 150 WAVENUMBER
I
I
I
I
I
I
,
I
L
C
I
50
Figure 2. Far-infrared spectrum of gaseous ethyl isocyanate.
were noted except for the appearance of greater amounts of aggregated molecules. Mid-infrared spectra of the gas and solid (Figure 1) from 3500 to 400 cm-I were obtained with a Digilab Model FTS-14C Fourier transform interferometer equipped with a Ge/KBr beamsplitter and a TGS detector. Far-infrared spectra (450 to 80 cm-I) of the gas and solid were obtained with a Digilab Model FTS- 15B Fourier transform interferometer equipped with either a 6.25- or 12.5-pm beamsplitter and a T G S detector. For the gas phase, 1000 scans of the empty cell and sample were collected at an effective resolution of 0.5 cm-’ and subsequently the Fourier transformation of these interferograms was accomplished with the use of a boxcar truncation. For the solid phase, the sample was condensed onto a silicon or cesium iodide plate which was maintained under vacuum and cooled with liquid nitrogen. Similarly, 500 scans of both the empty cell and sample were collected at an effective resolution of 1 cm-’ and the data were handled as for the gas. The gaseous sample was contained in a 1-m cell fitted with polyethylene windows for the far-infrared studies and in a 10-cm cell equipped with CsI windows for the mid-infrared studies. The far-infrared spectra below 300 cm-’ (Figure 2) were also recorded on a Nicolet Model 8000 interferometer equipped with a vacuum bench and a liquid-heliumcooled G e bolometer containing a wedged sapphire filter and polyethylene windows. Spectra were recorded with the sample contained in both 1-m and 20-cm cells at its maximum vapor pressure at ambient temperature. The Raman spectra were recorded on a Cary Model 82 spectrophotometer equipped with a S ectra-Physics Model 171 argon ion laser operating on the 5145- line. The spectrum of the gas was recorded by using a standard Cary multipass accessory and the laser power at the sample was 1 W. Reported frequencies
1
3000
2000 WAVENUMBER
1000
1
0
km-9
Figure 3. Raman spectra of gaseous (A), liquid (B), and solid (C) ethyl isocyanate.
are expected to be accurate to at least f 2 cm-’. The spectrum of the liquid was recorded from the sample sealed in a glass capillary. The variable temperature study of the liquid was carried out with a Cryodyne Model 20/70 cryopump connected to a Lake Shore Cryogenics Inc., Model DTC-5OA temperature controller. The spectrum of the solid phase was obtained by depositing the sample onto a blackened brass plate cooled by liquid nitrogen and contained in a cell fitted with quartz windows. Representative Raman spectra are shown in Figure 3. Vibrational Assignment The initial vibrational assignmentz0for ethyl isocyanate was made by utilizing only infrared spectral data since the earlier Raman data2’ were very incomplete. Since the predominant conformer has a plane of symmetry the Raman depolarization data will be very useful for distinguishing the A” vibrations from the A’ modes. The 24 normal modes span the representation of 15 A’ and 9 A” with the A’ modes having A-, B-, or A/B-hybrid-type infrared band contours whereas the A” modes will have C-type infrared bands with P-R separations of 20 cm-I and a relatively strong Q branch. Since the earlier infrared gas-phase (20) Hirschmann, R. P.; Kniseley, R. N.; Fassel, V. A. Spectrochim. Acta 1965, 21, 2125. (21) Kopper, H.; Pongratz, A. Monatsh. Chem. 1933,62, 7 8 .
Sullivan et al.
1772 The Journal of Physical Chemistry, Vol. 91, No. 7, 1987
dataZowere not recorded at a sufficient resolution to obtain distinctive contours, this information was not available for use in making the earlier assignment. Therefore, by utilizing the Raman depolarization data along with the infrared band contours it is possible to make a more definitive vibrational assignment (Table I) for the normal modes of ethyl isocyanate. Carbon-Hydrogen Modes. Whereas in the earlier studyz0only three bands were observed in the carbon-hydrogen stretching region, we have observed all five of the fundamentals at 2987, 2973, 2958, 2946, and 2927 cm-’ with the CH2 modes being assigned to the 2958 (A”) and 2927 cm-’ (A’) bands. Similarly only one of the CH3 antisymmetric deformations was previously observedZobut both were observed in the Raman spectrum of the solid at 1463 (A’) and 1458 cm-’ (A”). The Raman data also require a reassignment of one of the CH3 rocking modes since the 988-cm-’ band is depolarized but was previously assigned to the C-C stretch whereas the 1092-cm-’ band which is polarized was assigned as the A” CH3 rock. Thus, it is necessary to reverse these assignments. Finally, in the earlier study the C-N stretch and the CH2 rock were assigned as being degenerate at 794 cm-’ but the infrared spectrum of the gas shows two bands at 807 and 788 cm-’. The higher frequency band has a Raman counterpart that is polarized and therefore it is assigned to the C-N stretch. The other carbon-hydrogen bending modes have been assigned the same frequencies as those given earlier except the CH, torsion was not previously observed. This mode is found at 265 cm-’ in the infrared spectrum of the gas. Skeletal Modes. The stretches and bends of the N C O moiety have been assigned the same frequencies as before except the A” N C O bend is assigned to the lower frequency band (592 cm-l) rather than at 607 cm-’ (A’) since the former band is depolarized in the Raman spectrum; the infrared band contours are also consistent with this reversal of these assignments. The earlier investigatorsZ0assigned both the CCN in-plane and out-of-plane modes near 400 cm-l but the out-of-plane mode is better described as a C-N torsion (asymmetric torsion) which should be at a relatively low frequency, Le., 100 cm-’ or below. Although the broad band observed in the Raman spectrum of the liquid in this region appears to have two components (414 and 403 cm-’), both are polarized and can therefore not be due to the C-N torsion. The second band may be due to the presence of a small amount of a second conformer (see below). Alternatively, doubling of the CCN bend has been observed in some of the corresponding isothiocyanate molecules apparently as a result of the quasilinear nature of the CNCX moiety. The C-N torsion in ethyl isocyanate is observed as a very broad nondescript band beginning around 50 cm-’ with a maximum near 68 cm-’. The contour is similar to that found for other asymmetric torsions of molecules containing the NCX moiety with a quasilinear skeleton. Also the CNC bend is observed as a very broad band centered at about 144 cm-’ in the infrared spectrum of the gas; the center of the corresponding Raman band appears to be at a lower frequency. Matrix Data. A thorough search of the infrared spectrum of the matrix-isolated material was made to try to determine if a small percentage of a second conformer is present at ambient temperature. The only apparent doublets were the 1388/1383and 630/613-cm-’ bands; the former one is associated with a carbon-hydrogen bending motion which should not be sensitive to conformational changes. The latter one is a skeletal bending mode which of course should be sensitive to conformational change but none of the other skeletal bending modes showed such doubling. Therefore, there is really no evidence for a second conformer from these data. Normal Coordinate Calculations In order to determine the degree of mixing and to obtain a more complete description of the molecular motions involved in the normal modes, a normal coordinate analysis was carried out. This analysis was performed utilizing the Wilson GF matrix method22 ~
(22) Wilson, E B , Decius, J C , Cross, P C Molecular Vibrations, McGraw Hill New York, 1955
Figure 4. Molecular diagram showing internal coordinates for ethyl isocyanate.
with the computer programs written by Scha~htschneider.~,The G matrix was calculated by using the structural parameters reported in the electron diffraction study.’ A modified valence force field was used and the initial force constants for the ethyl moiety were taken from the earlier calculations for ethyl is~thiocyanate~ and those for the N C O moiety from those obtained for GeH3NC0.24 The symmetry coordinates were constructed from 26 internal coordinates (Figure 4) and are similar to those previously reported.24325From the modified valence force field listed in Table 11, the observed frequencies were fit to 12.5 cm-’ (1.2%) and the calculated frequencies and normalized potential energy distribution among the symmetry coordinates are given in Table I. The normal vibrations for the A” symmetry block are all relatively “pure” with the exception of the CH, and CH2 rocks which show significant coupling. However, for the vibrations of the A’ symmetry block there is strong mixing of all of the carbon-hydrogen bending modes with the skeletal stretching modes. Both the C-C and C-N stretches are “spread” over a number of frequencies but the calculations do support the assignment of the C-C stretch to the band at 1090 cm-’. However, it is difficult to choose a single band as the C-N stretch although based on the assignment of this vibration in other organic isocyanates the frequency of 801 cm-’ must be considered as characteristic for this vibration. Also it should be noted that the in-plane NCO bend is a relatively pure mode but the CCN bending coordinate is contributing to several modes beginning as high as 1090 cm-]. The values for the force constants for the ethyl moiety are well within the limits set by Schachtschneider and Snyder26from their studies of hydrocarbons as well as those from the studies of CH3CH2CN,25CH,CH2GeH3,27and CH3CHzSnH328or those for the corresponding isothiocyanate m ~ l e c u l e . ~ Semiempirical and ab Initio Calculations
Initially CNDO and INDO calculations were performed utilizing bond angles and bond distances reported from the microwave inve~tigation.’~These calculations predict the cis conformer (methyl group eclipsing the NCO group) to be more stable than the trans (methyl group trans to the N C O group) by approximately 2000 cm-’ (1989 cm-’ INDO, 2952 cm-’ CNDO). However, only the dihedral angle involving the NCO group was changed to provide representations of the two different conformers, without any structural relaxation to accompany this change. At this point the LCAO-MO-SCF restricted Hartree-Fock calculations were performed with the program GAUSSIAN-80 using Gaussian-type basis functions. The energy minima with respect to nuclear coordinates were obtained by simultaneous relaxation of all geometric parameters using the gradient method of P ~ l a y . * ~ (23) Schachtschneider, J. H. “Vibrational Analysis of Polyatomic Molecules”, Parts V and VI, Technical Reports No. 231 and 57, Shell Development Company, Emeryville, CA, 1964 and 1965. (24) Durig, J. R.; Sullivan, J. F. J. Mol. Struet. 1979, 56, 41. (25) Wurrey, C. J.; Bucy, W. E.; Durig, J. R. J. Phys. Chem. 1976, 80, 1129.
(26) Schachtschneider, J. H.; Snyder, R. G. Spectrochim. Acta 1963,19, 117. (27) Durig, J. R.; Lopata, A. D.; Groner, P. J. Chem. Phys. 1977, 66, 1888. (28) Durig, J. R.; Li, Y . S.; Sullivan, J. F.; Church, J. S.; Bradley, C. B. J . Chem. Phys. 1983, 78, 1046.
IR and Raman Spectra of CH,CH2NC0 Initially the STO-3G minimal basis set was employed. At this level of calculation the angular parameters are expected to be determined at a reasonable degree of accuracy and the bond distances should be in error only by small systematic amounts. Also,the relative energy values for the various possible orientations of the N C O moiety are expected to be relatively precise. The structural parameters obtained at this level of calculation are given in Table 111 where they are compared to those obtained from a recent electron diffraction study7 as well as those assumed in the microwave investigation.” At the STO-3G level, general agreement was found between the a b initio predicted structural parameters and the electron diffraction results. Particularly, the C=O and N=C distances and the NCO angle show better agreement with this basis set than with others employed later. There were some bond distances which were not well fit, particularly the C-C and C-N bond distances which are quite long compared to the values obtained from the electron diffraction data. Even at this level the C N C angle was predicted reasonably well and the N C O angle was calculated to be bent with a value of 169.03O compared to the experimental value of 167.8 f 2.5’. The calculations were then repeated using the 3-21G and 63 lG* extended basis sets of the GAUSSIAN 82 program again with optimization of the geometric parameters. At the 6-31G* level it is expected that all of the single bond distances should be well predicted but the double bond parameters are expected to be short by at least 0.01 A. However, a high degree of accuracy is expected for the relative energy values for the various possible conformers. The structural parameters obtained from this calculation for the cis conformer are listed in the next to last column of Table 111 and there is remarkable consistency between these results and the parameters obtained from the electron diffraction investigation with the exception of the two values for the double bonds. The N = C bond shows the largest deviation of 0.035 A with the C = O being next with a difference of 0.016 A whereas all of the single bond distances are in excellent agreement with the experimental values. It should be noted that these calculations predict a bent N C O group with an angle of 172’ which is in reasonable agreement with the 167.8 f 2.5O value obtained from the electron diffraction data. Therefore the bent N C O group seems to be real rather than an artifact of the electron diffraction studies. These calculations show the trans conformer to be more stable, but by only 46 cm-’ when both structures were optimized. Also accompanying the change in dihedral angle were changes in the CCN and C N C angles (trans LCNC 141.98’ to cis 144.87’, trans LCCN 110.51’ to cis 113.18’), providing a structural relaxation along the heavy atom skeleton of the molecule. These changes in the C N C and CCN angles greatly lower the energy difference between the conformers. The CNDO and INDO calculations were then repeated with the ab initio predicted structures and again the trans conformer was predicted to be slightly more stable = 227 cm-’ for CNDO and 77 cm-’ for INDO). Thus, although ab initio calculations predict the trans conformer to be more stable than the cis, a very low energy difference is predicted between the two conformers. The optimized structural parameters from the 6-3 lG* basis set for the trans conformer are given in the rightmost column of Table 111. Upon optimizing the trans structure significant changes were found only in the C N C and CCN angles, both of which are larger in the cis conformer. When optimizations were performed with C-N twist angles between those for these two conformers, no local maxima or minima were found and the energy as the . function of the dihedral angle was nearly linear. Also listed in Table I11 are the ab initio calculated dipole moments along with those reported from the microwave investigation. Both the 6-31G* and 3-21G basis sets predict values much larger than those obtained from the microwave data. This is believed to result from inadequate handling of the electrons in the nitrogen lone pair and the nitrogen-carbon and carbon-oxygen double bonds. It is interesting to note that the values from the (29) Pulay, P. Mol. Phys. 1969, 17, 197.
The Journal of Physical Chemistry, Vol. 91, No. 7, 1987 1773 CNDO calculations are in much better agreement. The CNDO treatment gave values of (pal = 2.71 D and I&l = 0.08 D while the INDO program gave Ikal= 2.65 D and lpbl = 0.02 D, which are very close to the microwave values of IIL,I= 2.81 D and I&l = 0.03 D. The 3-21G basis set was used to obtain the ab initio force constants and frequencies rather than the 6-31G* basis set due to greatly increased costs and computer time necessary for the larger basis set. From previous studies, it has been found that there is very little difference in the values of the force constants and frequencies when the smaller basis set is used. The following procedure was used to transform ab initio results into the form required for our iterative normal coordinate programs. The Cartesian coordinates obtained for the optimized structure were input into the G-matrix program, together with the desired set of nonredundant internal coordinates. Complete sets of internal coordinates with redundancies produce singular matrices which cannot be handled by our computer programs. Two internal coordinates, the (Y which lies between the out-of-plane hydrogens in the methyl group and Z which represent the CCN angle, had to be removed, and changes made to the appropriate symmetry coordinates, to produce this nonredundant set. The output of this G-matrix program consists of the B matrix and the unsymmetrized G matrix. The B matrix was used to convert the ab initio force field in Cartesian coordinates to a force field in the desired internal coordinates. All diagonal elements of the obtained force field in internal coordinates were assigned scaling factors. This force field (Table IV) was then used as input, along with the unsymmetrized G matrix and scaling factors, in the perturbation program written by Scha~htschneider.~~ Initially, all scaling factors were kept fixed at a value of 1.00 to reproduce the pure ab initio calculated vibrational frequencies and to determine the corresponding potential energy distribution in symmetry coordinates which is given in Table V. Subsequently, fixed scaling factors of 0.90 for stretching coordinates, 0.80 for bending coordinates, and 1.OO for off-diagonal interactions were used to calculate results labeled “fixed scaled”, as suggested by Fogarasi and P ~ l a y . ~ ~ Finally, the scaling factors for all diagonal elements of the force field were adjusted by the perturbation program in order to provide the closest possible fit to the observed vibrational frequencies (shown in Table V in the column labeled SAI). The values for the scaling factors which best reproduce the observed frequencies are listed in Table VI with their uncertainties. Again the offdiagonal interaction constants were not adjusted. There are large variations in the scaling factors with several of those for the heavy atoms larger than 1.0. Additionally, the frequency fit of 1.7% is not as good as the fit with only the 26 valence force constants (17 diagonal and 9 interaction force constants). Therefore, it does not appear to be worth the time and effort to vary each ab initio force constant to obtain individual scaling factors. The constant scaling factors provide useful information for making vibrational assignments and should be sufficiently accurate to indicate gross misassignments but, in general, they cannot be used to make judgments between bands with relatively close frequencies. The vibrational frequencies calculated from the ab initio force constants are in reasonably good agreement with those observed experimentally. They are all predicted to be too high by 10 to 20% with the exception of the low-lying CNC bend. This is within the range generally expected for ab initio results. The ab initio potential energy distribution shown in Table V helps verify the correct order within the vibrational assignment and shows the large degree of mixing of internal coordinates in some normal modes. The various scaling schemes used show somewhat better agreement with experimental results, but this is achieved with even more mixing, particularly when the scaling factors were iterated. The ab initio predicted force field contains many large interaction constants, almost 70 with absolute values of at least 0.10 mdyn/A and more than 20 with absolute values of 0.70 mdyn/A. This large number of interactions makes it difficult tc compare (30) Fogarasi, G.; Pulay, P. Vibrational Spectra and Structure, Vol. 14, Durig, J. R., Ed.; Elsevier: Amsterdam, 1985.
1774 The Journal of Physical Chemistry, Vol. 91, No. 7, 1987
Sullivan et a].
TABLE I: Observed' Infrared and Raman Frwuencies (an-')and Vibrational Assignment for Ethyl Isocyanate infrared re1 int
gas 3273 3096 2994 2989 2982
max vw max w R Q vs
sol re1 int
Raman
N2 matr re1 int
ga,s re1 int
liq re1 int, Depol
solid re1 int
assignment and PED calcd
anDrox descrhtion
u.
1.
2987 vs
3000 w
2988 s
2987 s, p
2990 s
2994
CH, antisymmetric stretch (99%)
2973 s
3000 w
2972 vs
2968 vs, p
2974 vs
2994 u I
C H 3 antisymmetric stretch (98%)
2958 m
2959 w
2947 s
2942 s, p
2958 s
2965 YI;
CH, antisymmetric stretch (98%)
2946 m
2916 m
2931 s, p
2947 m
2943
~2
CH, symmetric stretch (99%)
2927 m
2904 m
2907 m, p
2921 m
2896
~3
C H 2 symmetric stretch (99%)
P
2956 R 2949 min 2944 P 2913 R 2906 Q 2900 P 2885 2429 2294 R 2285 Q 2281 P 2236 1480
m
m
2887 m
mw, sh 2895 mw 2883 mw m vvs
2290 vs
2279
mw m, sh
1477 m
2100 1471
1473 R 1465 min
m
1470 m
1458Q
m
1456 s
1444 R 1437Q 1432 P
m
1433 m
1407 R 1403 min 1393 R 1385 Q 1380 P 1359 R 1352Q 1346 P
2898 mw 2879 mw
2283 vw
1465 m
2273 w, p
2277 w
2282 u4
N C O antisymmetric stretch (97%)
1479 w, p
1477 m
1498 u5
C H I deformation (22%); N C O symmetric stretch (39%); C H 2 wag (20%); C-N stretch (8%)
1461 m, p
1463 m
1460
Y6
1458 m
1457
CH, antisymmetric deformation (86%); CH, rock (9%) CH, antisymmetric deformation (91%); CH, rock (8%)
1435 s, p
1433 s
1434
V,
CH, symmetric deformation (24%); CH, wag (42%); C-C stretch (13%); C-N stretch (8%)
1387 vw, p
1378 m
1407
US
C H 2 deformation (29%); CH, symmetric deformation (22%); N C O symmetric stretch (14%); C-C stretch (6%); C-N stretch (1 3%); C H 2 wag (7%)
1349 m, p
1343 m
1367
Pq
1287 w, dp
1288 m
1276
v1q
CH, symmetric deformation (47%); C H 2 wag (8%); CH, deformation (32%); N C O symmetric stretch (20%); C-C stretch (9%) CH, twist (94%)
1063
~ 1 0 CH,
1090 m
1047
VI,
988 W,dp
986 m
989
~ 2 0 CH,
794 m, p
792 m
776
~ 1 2 C-N
1451 1437 s
m m
s
1376 s 1368 w, sh
1388 1383
1349 s 1336 w, sh
1353
1258 max vw 1170 w,sh 1140Q m
1279 m, bd
1110 1098 R 1089 Q 1084 P 1002 R 991 Q 984 P 813 R 807 min 801 P
1104 w, bd m, bd
1136 s 1130 m, sh
1087 s
1351 m
1140
1100
-990 VW,bd
C-C stretch (27%); C H I wag (9%); CH, rock (46%); C C N bend (12%)
m, bd
984 s 970 w, sh
m
793 s
(804)
788
w, sh
800 m
802
809 w
655 R 640Q 622 P
m
609 s 606 s
630 613
624 w
662 u13 N=C=O bend (56%); C N C bend (15%); C-N stretch ( 5 % )
579 w 426 vw 285 vw
609 ~ 2 2 N=C=O bend (97%) 425 vI4 C C N bend (56%); C-N stretch (10%); C-C stretch (10%); N C O bend (9%) 264 ~ 2 3 CH, torsion (97%)
163 w,vbd
138 u l 5 C N C bend (85%); NCO bend (12%)
610 max m, bd 409 265 Q w 254 Q vw 144 max m, bd
577 s 573 s 425 w
980
1092 m, p
1090 m
rock (24%); C N stretch (10%); C H I wag (14%); C-C stretch (1 8%); N C O symmetric stretch (27%)
807 m
584 380
405 vw
-
,
128 vw, bd
592 w, dp 410 vw, bd, p
rock (73%); C H 2 rock (16%)
stretch (39%); C-C stretch (20%); CH3 rock (10%); N C O bend (10%); CH, wag (9%) 785 c21 C H 2 rock (70%);C H 3 rock ( 1 3%); C H 2 twist (13%)
The Journal of Physical Chemistry, Vol. 91, No. 7 , 1987
IR and Raman Spectra of C H 3 C H 2 N C 0
1775
TABLE I (Continued)
infrared gas
re1 int
-68
vw
sol
re1 int
N2 matr re1 int
gas re1 int
Raman liq re1 int, Depol
solid re1 int
calcd 67
assignment and PED approx description v24 C-N torsion (97%) VI
123 m 104 s 98 s 82 s 73 sh 62 m 54 s
lattice modes
"Abbreviations used: s, strong; m, medium; w, weak; v, very; sh, shoulder; p, polarized; dp, depolarized; max, maximum; min, minimum; bd, broad; P, Q,and R refer to vibrational-rotational branches. TABLE 11: Valence Force Constants for Ethyl Isocyanate force value: constant description mdyn/A
Kr Kd KQ KR KT Ku H+ H,, H, H,
Ha Ha H6
H-, H8
H,
C-(H,) stretch C-(H,) stretch C-C stretch C-N stretch N=C stretch C=O stretch N=C=O in-plane bend N=C=O out-of-plane bend C-C-N bend C-N-C bend H-C-H (-CH,) bend H-C-C (-CH,) bend H-C-H (-CH,-) bend H-C-C (-CH,-) bend H-C-N bend Me torsion Et torsion H-C-C (-CH,) bend/C-C stretch N=C stretch/C=O stretch C-C stretch/C-N stretch C-H stretch/C-H stretch H-C-C (-CH2-) bend/H-C-N bend H-C-N bend/C-N stretch H-C-H (-CH,) bend/C-C stretch H-C-H (-CH,-) bend/C-C stretch C-N-C bend/C-C-N bend
4.83 4.60 4.84 4.76 15.23 12.92 0.67 0.64 1.53 0.35 0.53 0.65 0.50 0.52 0.85 0.012 0.00099 0.65 1.41 -0.86 0.069 -0.016 0.68 0.21 -0.10 0.25
"The bending coordinates are weighted by 1 A. the force field with the modified valence force field calculations where the number of interactions is limited. The stretching force
constants are generally too large by approximately 20%. The predicted bending force constants are much too large, often by a factor of 3. The main exception is the C N C bending force constant with an ab initio predicted value of 0.301 and a typical literature value of approximately 0.20 (although our best fit value has grown to 0.35). It should be noted that the ab initio interaction between the C N C bend and the C-N stretch is 0.441, which is larger than the bending force constant itself. A more interesting outcome of calculating the ab initio force constants for ethyl isocyanate is the reversal in relative values between the C 4 and N=C stretching force constants. In previous studies of similar molecules such as CH3NCO1' the C=O stretching force constant has been given a larger value than the N 4 , which is qualitatively consistent with the N=C bond being longer than the C = O bond. However, in the present study, the N=C stretching force constant has been calculated to be larger than the C=O, although, in our initial valence force field, the frequencies were calculated equally as well with reversed values. Methyl Torsion and Barrier to Internal Rotation The far-infrared spectrum of gaseous ethyl isocyanate shows a band at approximately 265 cm-' which has been assigned to the 1 0 transition of the methyl torsion. A second band appearing 1 transition for at about 255 cm-l could be assigned as the 2 this vibration. In the nitrogen matrix the vibration was observed at 270 cm-I. These values are in very good agreement with those found for ethyl isothiocyanate, where the methyl torsion was observed at 270 cm-' in the solid and 265 cm-' in the gas. Utilizing a potential energy function for a threefold torsional oscillation (V6/2)(1 - cos 6 a ) and the as V ( a ) = (V3/2)(l - cos 3a) reduced moment of inertia constant, F = h2/8ir2Z,,where Z, is the
-
-
+
TABLE III: Structural Parameters for Eclipsed &-Ethyl Isocyanate
microwave" r(H8-Cl), A 4Ha-Cl)t A r(C-C), A rG--H), 8, r(C-N), A r(N=C), A r(C=O), A LNCO, deg LCNC, deg LCCN, deg LHC,C,, deg LHC,H, deg LH,C& deg LHaClC,, deg LH,C,H,, deg
(1.091) (1.091) (1.520) (1.091) 1.461 (1.207) (1.171) (180) 142.11 109.14 (109.6) (108.8) (1 12.0) (112.0) (109.3)
7(CH3), deg
(0)
A , MHz B , MHz
141 10.00 30 17.91 2605.01 2.81 f 0.02 0.03 0.00 2.81 f 0.02
C, MHz D
IPal, bbl. IPel9 IPtL
D D
electron diffraction (r*av)b 1.084 f 0.007 1.084 0.007 1.524 f 0.01 1 1.084 0.007 1.448 f 0.009 1.218 f 0.005 1.174 0.004 167.8 f 2.5 132.2 f 2.2 114.7 f 1.6 110.1 1.6 108.8 f 1.6 111.4 f 1.9 111.4 f 1.9 107.5 & 1.9 9 f 3 13776.45 31 12.41 2620.62
* *
*
STO-3G
3-21G
6-31G*
cis
cis
cis
trans
1.086 1.086 1.545 1.094 1.481 1.227 1.189 169.03 128.44 115.21 109.72 107.2 109.425 110.82 108.7 0 128 19.49 3151.92 2612.57 2.09 1.11
1.084 1.083 1.536 1.080 1.460 1.178 1.176 175.00 135.42 112.35 110.55 107.55 109.84 110.46 108.85 0 13501.97 3 185.08 2661.35 3.70 1 .oo 0.00 3.83
1.085 1.085 1.524 1.082 1.442 1.179 1.159 175.20 144.87 113.18 110.57 107.13 110.20 110.79 108.56 0 15412.90 2925.39 2535.37 3.37 0.84 0.00 3.48
1.085 1.084 1.520 1.084 1.446 1.182 1.157 174.95 141.98 110.51 110.28 107.42 110.05 110.63 108.72 0 35844.26 2277.68 2199.74 2.99 1.38 0.00 3.29
0.00
2.36
"Taken from ref 19 where the values in parentheses were assumed parameters. bTaken from ref 7.
6-31G*
Sullivan et al.
1776 The Journal of Physical Chemistry, Vol. 91, No. 7, 1987
reduced moment of inertia for the internal rotation and F has a value of 6.159 cm-', we calculated the threefold barrier. The potential constants determined were V3= 1546.2 f 14.2 cm-' and V, = -45.8 f 6.9 cm-I, which leads to a barrier of 4.42 kcal/mol 1 torsional transition. A if the 255 cm-' is assigned as the 2 V, value as large as -46 cm-' seems too large. It is possible the 255-cm-I Q branch is the torsional mode in the first excited state of the C N C bend. If only the 1 0 transition is fit using only a V, term, a lower barrier of 1414 cm-' (4.04 kcal/mol) is calculated. This value is in good agreement with the values found for ethyl chloride and ethyl bromide, where for both molecules a barrier of 3.72 kcal/mol has been determined.31 This value for ethyl isocyanate appears to be the largest one reported for the methyl barrier for a monosubstituted ethyl compound.
-
-
Discussion In the microwave studyI9 of ethyl isocyanate a number of far-infrared vibrational frequencies are listed, of which some are from the study by Hirschmann et al.*Oand some are inferred from similar values in ethyl isothiocyanate.I0 Our assignment differs slightly from these values. We assign the NCO in-plane bend at 640 vs. 608 cm-', the out-of-plane bend at 610 instead of 595 cm-I, and the CCN in-plane bending at 409 vs. 395 cm-I. The C N C bending frequency coincides with our value of 144 cm-I. In regard to the C-C torsion, our observed frequency of 265 cm-I is considerably higher than the 224-cm-I value previously reported.49 This earlier value was inferred from the value for ethyl isothiocyanate but data published later4 corrected this frequency to 265 cm-I. The other torsional frequency (about the C-N bond) is given as 100 cm-I and we find a very broad band centered at 68 cm-I. A large number of unassigned lines are also mentioned in the microwave study. The authors tried to determine if these lines could originate from one of the other possible conformers but, based on the expected structures and rotational constants none of these transitions could be assigned. The rotational constants, from our ab initio predicted structure, do not differ significantly from those in the microwave structure, but careful measurements of the microwave transitions might show that some of these lines originate from another conformer. Another possibility involves the pseudolinear NCO group. There is a very low barrier to free rotation of this group and some of the unassigned lines may represent transitions in an excited state of this rotation. Finally, it should be mentioned that the structures predicted from the STO-3G and 3-21G basis sets provide rotational constants that are in better agreement with those Calculated from the microwave data than does the structure from the 6-3 1G* basis set (see Table 111). Once again we feel that this arises from the inability of the 6-31G* basis set to properly handle the electrons in the nitrogen lone pair and the C=O and N=C double bonds. There are four strong well-defined lattice modes in the Raman spectrum of the solid (Figure 5 ) . In the Raman spectrum of the unannealed solid the two modes of lower frequency appear to be doublets and the two higher frequency modes are much broader than the corresponding lines from the annealed solid. Also it should be noted that there are at least two additional lattice modes so one can confidently conclude that there are at least two molecules per primitive cell. Evidence for the presence of a second conformer is found in the Raman spectrum of solid ethyl isocyanate. In the unannealed sample, the N=C=O in-plane and out-of-plane bends and the CCN bend appear as doublets (Figure 5 ) . In each case a small side band is located at the lower frequency side of each peak and these side bands are approximately 1/10 the size of the peak (31) Durig, J. R.; Bucy, W. E.; Carreira, L. A,; Wurrey, C. J. J . Chem. Phys. 1974, 60, 1754. (32) In this paper the periodic group notation (in parentheses) is in accord with recent actions by IUPAC and ACS nomenclature committees. A and B notation is eliminated because of wide confusion. Groups IA and IIA become groups 1 and 2. The d-transition elements comprise groups 3 through 12, and the p-block elements comprise groups 13 through 18. (Note that the former Roman number designation is preserved in the last digit of the new numbering: e.g., 111 3 and 13.)
-
IR and Raman Spectra of C H 3 C H 2 N C 0
The Journal of Physical Chemistry, Vol. 91, No. 7, 1987
1777
TABLE V Comparison of the Experimental Fundamental Frequencies (cm-’) and Frequencies Predicted from ab Initio Calculations for cis -Ethyl Isocyanate ab fixed fundamental initio scaled SA1 expt a b initio PED A‘
SI s 2
s3 s5 s4 s6
s15
s7 s8 s9
SI0
SI2 SI,
CH3 antisym str CHI sym str CH2 sym str NCO antisym str CH2 def CH3 antisym def CH, sym def NCO sym str CH2 wag CH, rock C-C str C-N str N=C=O bend CCN bend CNC bend
3274 3246 3207 2496 1680 1670 1576 1573 1497 1210 1012 825 692 441 115
3104 3080 3045 2352 1583 1482 1212 1146 1082 980 919 680 605 396 92
2989 2953 2916 2285 1612 1483 1450 1395 1268 1161 1057 819 638 434 140
2991 2942 2906 2285 1480 1473 1437 1393 1352 1140 1098 807 640 425 144
91% SI,9% S2 90% S,, 9% SI 100% 60% S14, 38% SI5 61% S,, 37% SI2 84% S4, 7% S , 63% s6, 32% s4 28% SI53 18% s6, 12% SI43 10% s7. 9% SI, 69% S7? 11% Slo, 5% SI5 68% S,, 9% S,, 8% Si,, 6% S , 75% s,, 12% SI,, 5%’S, 59% slo, 13% s14, 6% sg, 5% s9, 5% s13 75% SI,, 11% SI,, 5% SI2 55% s12, 14% Sg, 8% si,,6% slo, 5% s, 77% SI,, 11% SI,, 7% Sl0
CH, antisym str CH2 antisym str CH3 antisym def CHI twist CH3 rock CH2 rock N=C=O bend CH, torsion C-N torsion
3294 3265 1664 1444 1275 884 63 1 299 100
3122 3089 1292 1085 988 595 561 263 110
2985 2948 1456 1296 1133 77 1 610 264 68
2996 2956 1458 1258 98 1 788 610 265 68
69% S18, 31% SI9 68% Si,, 31% Si8 92% S20, 8% S23 89% S21, 9% S23 43% S22, 42% S23, 9% S21, 5% S20 50% S22, 38% S23, 10% S2l 96% S2, 95% s24 96% S25
s3
8% S4, 8% slo, 6% s5
A”
s18
s19 s20 s21
s23 s22
s26 s24
s 2 5
TABLE VI: Calculated Scaling Factors Used Force Constants in the ab Initio Force Field internal descriution coordinate‘ C-H, (CH,) stretch C-Ha (CH,) stretch C-H (CH,) stretch HCH (CH,) bend H,CC (CH,) bend H,CC (CH,) bend HCH (CH,) bend HCC (CH,) bend HCN bend C-C stretch C-N stretch CNC bend NCO out-of-plane bend methyl torsion NCO in-plane bend ethyl torsion N=C stretch C=O stretch
To Scale the Diagonal
scaling factor
uncertaintv*
0.840 0.819 0.825 0.885 1.011 0.847 0.907 0.973 0.8 18 1.215 1.066 1.418 0.324 0.816 0.783 0.960 0.949 0.647
0.019 0.013 0.013 0.0 17 0.052 0.053 0.021 0.028 0.019 0.091 0.083 0.363 0.229 0.157 0.084 0.086 0.036 0.049
A
1
C
I
j
l 500
l
l
l
l 300
l
l
l
l
l
l
100
“See Figure 4. bThe uncertainties are standard deviations in the scaling factors calculated by ascribing weights of 1/(v(i))II2 to the frequency differences.
Figure 5. Low-frequency Raman spectra of ethyl isocyanate: (A) liquid, (B) unannealed solid, and (C) annealed solid.
arising from the stable conformer. Upon annealing these bands disappear completely. These vibrations are the ones expected to show differences upon changing from the cis to trans conformer. No other vibrations seem to show this doublet nature in the unannealed solid, so these doublets do not seem to result from different sites in a crystal. It should be noted that to obtain the unannealed solid form it was necessary to condense the liquid onto a slightly cooled surface and then freeze it into a solid as opposed to going directly to the solid form at liquid nitrogen temperature as per the normal procedure. The corresponding bands in the Raman spectrum of the liquid are broad, and that at 410 cm-’ in particular (due to the CCN bend) covers a frequency range containing both the stronger and the weaker component seen for the unannealed solid. It is therefore reasonable to argue that the spectrum of the unannealed solid, in which the lines are much sharper than for the liquid, allows us to detect the presence of a second form that is also present in the liquid. Whether or not it is also present in the gas phase is
at present unknown; a future study of the microwave spectrum may allow a decision on this point. The nature of the second form is unknown. It is most likely to be another conformer, probably trans, but it is also possible that some other conformer is at a local minimum of the torsional potential. As we have shown, the ab initio calculations which we have performed are of little value in determining the torsional angle of a less stable form. Three vibrational frequencies, all lower than those we have assigned to the stable cis conformer, are also insufficient for the determination of the torsional angle, and there is no polarization information available for the solid sample. In conclusion, there is no doubt from the vibrational spectrum that ethyl isocyanate exists mainly as a single conformer with a plane of symmetry, probably cis, in the liquid phase, and entirely as a single conformer, probably cis, in the annealed solid (crystal). However, there appears to be a small proportion of a second conformer, possibly trans, in the unannealed solid as well as in the liquid. Ab initio calculations at STO-3G, 3-21G, and 6-31G*
Wavenumber (cm-1)
J . Phys. Chem. 1987, 91, 1778-1785
1778
levels are unable to reproduce the experimental findings, suggesting that the trans form is slightly more s\able. In the gas phase we find no evidence of the presence of a second conformer, and we know that the cis form is both present (from the microwave spectrum)19 and predominant (from the electron diffraction study),’ but we still cannot exclude the possibility that a small proportion of a second conformer is also present in the gas phase.
Acknowledgment. The authors gratefully acknowledge financial support of this research by the National Science Foundation by Grant CHE-83-11279 and the NATO Scientific Affairs Division through their collaborative research program under Grant No. 140/82. Registry No. CH,CH,NCO, 109-90-0.
Vibrational Relaxation Rates of CO,(OOl) with Various Collision Partners for T < 300 K S. H. Bauer,* J. F. Caballero, R. Curtis, and J. R. Wiesenfeld Department of Chemistry, Cornell University, Ithaca, New York 14853-1 301 (Received: July 8, 1986; In Final Form: October 29, 1986)
Population decay rates of C02(001) due to self-collisionsand to encounters with ten other species [(CH,),N, (CHJ20, H20, CS2,HC1, N20,OCS, NO, 02,and N2] were measured as a function of temperature by recording the decay in fluorescence of C 0 2 ((001) (000)). The (001) level was overpopulated by exposing mixtures of C 0 2 with various collision partners to narrow pulses of 9.4-pm radiation from a mechanically chopped C 0 2 CW laser which selectively pumped the thermal populations of C 0 2 {(loo) + (020)). The lowest attained temperatures ranged from 190 to 240 K and were limited mostly by the population of C 0 2 {(loo)+ (020)). While, in general, the log of the probability for collisional deactivation is linear when plotted against for T > 400 K, significant departures appear at lower temperatures. In a substantial fraction of cases, the probability rises with decreasing temperature after passing through a minimum. In general, the probability for collisional deactivation is higher for polyatomics compared to diatomcs and is lowest for those molecules which possess no dipole moment.
-
Introduction The relaxation of an assembly of molecules to thermal equilibrium after having been exposed to a perturbation which overpopulates a specific vibrational state clearly involves collisional redistribution of the excess vibrational energy to lower vibrational states, to rotation, and to translational motion shared by the collision partners. The molecular dynamics of such processes have been experimentally investigated for over half a century; the results have been extensively reviewed,l and numerous models have been proposed and analyzed.* The relaxation rates were found to be not only temperature dependent, but also highly sensitive to the structure of the collision partner. Indeed, there was hope that the experimentally determined probabilities for energy transfer, when resolved for state-to-state transitions, could provide insight into the interaction potentials of the molecular pairs. Regrettably, the basic description of the dynamics of such encounters, which are based on simple molecular models involving three or four atoms, apparently cannot be extended to larger molecules because of the complexity of the potential energy surfaces and the unavoidable averaging over collision parameters (impact parameters; angles of attack; phases of the relative rotations and vibrations, etc.). Nonetheless, the proposed models (which in time became (1) For recent reviews see: (a) Lambert, J. D. Vibrational and Rotational Relaxation in Gases; Clarendon Press: Oxford, 1977. (b) Bailey, R. T.; Cruickshank, F. R. Gas Kinetics and Energy Transfer, Vol. 3; The Chemical Society: London, 1978. (c) Buchwald, M.; Bauer, S . H. J. Phys. Chem. 1972, 76, 3108. (d) Walsh, P.; Bauer, S. H. J . Phys. Chem. 1973, 77, 1078. (e) Weitz, E.; Flynn, G. W. Annu. Rev. Phys. Chem. 1978, 25, 275. (f) Yardley, J. T. Introduction to Molecular Energy Transfer; Academic: New York, 1980. (2) (a) Landau, L.; Teller, E. Phys. Sowietunion 1936, 10, 34. (b) Schwartz, R. N.; Slawsky, 2.I.; Herzfeld, K. F. J . Chem. Phys. 1952, 20, 1591. (c) Sharma, R. D.; Bau, C. A. J. Chem. Phys. 1969.50.924. (d) Shin, H. D. J . Am. Chem. SOC.1968, 90, 3029. (e) Widom, B.; Bauer, S . H. J . Chem. Phys. 1953,21,1670. (f) Pack, R. T. J . Chem. Phys. 1980,72,6140. (g) Clary, D. C. J. Chem. Phys. 1981, 75, 209. (h) Price, R.J.; Clary, D. C.; Billing, G. D. Chem. Phys. Lett. 1983, 101, 269. (i) Clary, D. C. J. Chem. Phys. 1984,81,4466. (j)Maricq, M. M.; Gregory, E. A.; Simpson, C. J. S. M. Chem. Phys. 1985, 95, 43. (k) Bacic, Z.; Schinke, R.; Diercksen, G. H. F. J Chem. Phys. 1985,82, 336.
0022-3654/87/2091-1778$01.50/0
increasingly more involved) do indicate which molecular parameters play dominant roles and how each of these affects the dependence of relaxation rate upon temperature. The relative probabilities for energy transfer are state-specific, and the rate constants measured at the lowest temperatures best reflect the specific features of the interaction potentials. Interest in C 0 2 extends beyond its being a suitable test species; it is directly involved in the heat balance of the earth’s atmosphere and is a significant constituent of the atmospheres of the other planets. It is the active medium of the most efficient and widely used infrared laser (which is solely dependent on balancing rates of excitation and deexcitation of populations in selected vibrational states) and is the major product of combustion of hydrocarbon fuels. Measurements of vibrational relaxation rates of C 0 2 were among the first to be undertaken in the mid-l930s, with sound dispersion technique^.^ Later more extended data were obtained by recording density profiles past shock fronts in suitable mixtures.lc,d Since these techniques determine lags in the equilibration of heat capacity, the measured rates applied primarily to the populations of the lowest vibrational state (010). Time-resolved fluorescence measurements are now the standard method for determining collisional efficiencies for vibrational state deex~itations.~The availability of high-powered lasers provides new routes for creating vibrationally excited m o l e c ~ l e s . ~While laser optimization depends upon high-temperature energy-transfer data, almost no information was available regarding relaxation rates below 300 IC, until the mid- and l a t e - 1 9 7 0 ~ ~Previous experiments have already indicated that extrapolation of relaxation rates from high-temperature measurements to obtain estimates (3) Cotrell, T. L.; McCoubrey, J. C. Molecular Energy Transfer in Gases; Butterworths: London, 1961, and references therein. (4) Hocker, L. 0.; Kovacs, M. A,; Rhodes, C. K.; Flynn, G. W.; Javan, A. Phys. Rev. Lett. 1966, 17, 233. (5) Photodissociation and Photoionization, Vol. LX, Prigogine, I., Rice, S., Ed.; Wiley: New York, 1985; Adv. Chem. Phys. (6) (a) Inoue, G.; Tsuchiya, S.J . Phys. SOC.Jpn. 1975, 38, 870. (b) Geuguen, H. G.; Yzambart, F.; Chakroun, A,; Margottin-Maclou, M.; Doyennette, L.; Henry, L. Chem. Phys. Lett. 1975, 35, 198
0 1987 American Chemical Society
