J. Phys. Chem. 1980, 84, 1771-1782
quirements to reproduce B are very similar. Finally, in the light of our present deductions, it is interesting to reconsider furan-2-carbonitrile, for which a bend of some 13' in the C-CEN angle was deemed to be rea~onab1e.l~ Table IV contains the rotational constants of this molecule, exactly paralleling models a-d of Table 111. Much the same trends are found for the furan derivative as for the pyrrole derivative. Again model d reproduces the experimental rotational constants better than model c, and in fact, better than model d in the pyrrole derivative. Clearly similar conclusions can be reached for furan-2-carbonitrile as for pyrrole-2-carbonitrile, and extreme structural changes such as the 13' bend in the CC=N chain are not required.
Acknowledgment. We thank Dr. H. J. Anderson for the sample of pyrrole-2-carbonitrile. This work was supported by the Natural Sciences and Engineering Research Council of Canada.
References and Notes (1) H. J. Anderson, Can. J . Chem., 37, 2053 (1959). (2) C. E. Loader and H J. Anderson, Can. J . Chem., 49, 45 (1971). (3) H. J. Anderson, C. R. Riche, T. G. Costeilo, C. E. Loader, and G. H.
Barnett, Can. J . Chem., 58. 654 (1978). (4) H. Shigematsu, R. Ono, Y. Yamashita, and Y. Kaberaki, Agr. Biol. Chem., 35, 1751 (1971). (5) L. H. Deady, R. A. Shanks, and R. D. Topsom, Tetrahedron Left., 1881 (1973). (6) L. F. Elsom'and R. A. Jones, J . Chem. SOC.6 , 79 (1970). (7) T. Marey and J. Arriau, C . R . Acad. Sci. Paris, Ser. C , 272, 850 (1971). (8) D. M. Bertin, M. Farrier, and C. LiBgeois, Bull. SOC.Chim. Fr., part 1, 2677 (1974). (9) L. Nygaard, J. T. Nlelsen, J. Kirchheiner,G. Maltesen, J. RastrupAndersen, and G. 0. Sbensen, J . Mol. Strucf., 3, 491 (1969). (10) See, for example, C. R. Noiier, "Chemistry of Organic Compounds", 2nd ed., Saunders, Philadelphia, 1957. (11) J. Casado, L. Nygaard, and G. 0. Sbensen, J . Mol. Sfruct., 8 , 21 1 (1971). (12) L. Nygaard, I. Bojesen, T. Pedersen, and J. Rastrup-Andersen, J. Mol. Sfruct., 2, 209 (1968). (13) 0.Stiefvater, Z . Naturforsch. A , 30, 1765 (1975). (14) L. Engelbrechtand D. H. Sutter, Z . Naturforsch. A , 31, 670 (1976). (15) J. Wiese, L. Engeibrecht, and H. Dreizler, 2. Naturforsch. A , 32, 152 (1977). (16)T. K. Avirah, T. B. Malloy, and R. L. Cook, J . Mol. Struct., 29, 47 (1975). (17)J. Wiese and D. H. Sutter, Z . Naturforsch. A , 32, 890 (1977). (18) J. K. G.Watson in "Vibrational Spectra and Structure", J. R. Durig, Ed., Elsevier, Amsterdam, 1977,p 1. (19)C. C. Costain and B. P. Stoicheff, J. Chem. Phys., 30, 777 (1959). (20) B. Bak, D. Christensen, W. B. Dixon, L. Hansen-Nygaard,J. Rastrup-Andersen, and M. Schofflander, J. Mol. Spectrosc.,9, 124 (1962).
Vibrational Spectrum, Force Field, and Torsional Potential Function of Monothioformic Acid in the Gas Phases B. P. Winnewlsser" Physikallsch-ChemischesInstitut, Justus-Liebig-Universitat Giessen, 0-6300Giessen, West Germany
and W. H. Hocklngt Max Planck Institute fur Radioastronomie, 0-5300Bonn, West Germany, and Physikallsch-Chemisches Institut, Justus-Liebig-Universltat Giessun, 0-6300Giessen, West Germany (Received July 31, 1979)
The infrared absorption spectra of five isotopic species of monothioformic acid (thiolformic acid), HCOSH, HWOSH, HCl*OSH, DCOSH, and HCOSD, have been measured in the gas phase. As far as possible, the fundamental vibrations of both the cis and trans rotamers have been identified. These data were combined with centrifugal distortion constants from the rotational spectra for the above isotopic species and the 34Ssubstituted species to determine the force field for each rotamer. Some significant effects of isomerization on the spectra and force field were determined, and the barrier to internal rotation about the CS bond was determined. The coefficients of the cosine expansion of the torsional potential are Vl = 239 cm-l= 2.86 kJ/mol and V 2 = 3408 cm-l = 40.77 kJ/mol.
I. Introduction The rotational isomerism of monothioformic acid in the gas phase was established in the study of the microwave and millimeter wave spectrum by Hocking and Winnewi~ser.'-~The barrier to internal rotation in solution has been determined by dynamic NMR measurements, using CD2Clzand CClZFzas solvents.6 Because the two planar rotamers, cis-HCOSM and trans-HCOSH (in which the *Presented in part at the Thirtyfourth Symposium on Molecular Spectroscopy, The Ohio State University, Columbus, Ohio, June 11-15, 1979, as paper TC'4. 'Anatek Electronics Ltd., Hybrid Facility, 1332 Main St, North Vancouver, VIJ-LC3, Canada. *Address correspondence to this author at the PhysikalischChemisches Institut, Juslus-Liebig-Universitat Giessen, Heinrich Buff-Ring 58, D-6300 Giessen, West Germany. 0022-3654/80/2084-177 lS0l .OO/O
two hydrogens are cis or trans to each other), have a relative abundance of roughly 1:3 in the gas phase a t room temperature, this molecule is well suited for the study of rotameric effects. The pure rotational spectrum yielded the slightly different substitution structures of the two rotamers? a large difference in the dipole moment^,^ and precise relative intensity measurements at room temperature, from which the energy difference, AE,, between the ground states of the two rotamers was determinede3 In addition the quartic centrifugal distortion constants, which depend on the harmonic force field, were obtained for the parent species and each of the five singly substituted isotopic ~ p e c i e s . ~ ~ ~ ~ ~ We decided that the vibrational spectrum of monothioformic acid would allow the study of isomerism because of the small number of fundamental vibrations: seven a', 0 1980 American Chemical Society
Winnewisser and Hocking
The Journal of Physical Chemistry, Vol. 84, No. 14, 1980
TABLE I: Fundamental Vibrations (in em-') Observed for Monothioformic Acid HCOSH
2844.1d 2590.0 1722.0 1340.2 931.6 675.6 431.0
2835.8 2590.0b 1683.8 1335.7 922.7 663.8 427.5
2841.6d 2590.0b 1722.0' 1350.3 949.2 718.0 431.0e 924.2' 384.4
HC"0SH Trans 28 3 9. 6d 2590.0b 1683.5 1336.2 929.8 674.1 426.0
2590.0 2142.0d 1698.0 1027.0 921.8 641.0 427.0
2845.1d 1890.0b 1722.2 1341.7 800.9 621.7 393.0
2833.3 2590.0b 1683.8' 1347.8 944.0 704.4 427.5e
Cis 2837.1d 2590.0b 1683.5' 1346.3d 947.0d 715.7 426.0e
2590.0b 2139.5d 1698.0' 1027.0' 936.4 685.0 427.0e
2842.6d 1890.0b 1719.4 1351.2 819.5 621.7' 393.0'
Estimated uncertainty, the inverse square of which determined the weightin factor in force field fitting. Unobserved; assumed value, given zero weight. ' Cis and trans bands assumed coincident. CgCis-trans difference assumed the same as in parent or H''C0SH species. e Cis and trans bands listed as coincident, but probably not (see text).
in-plane, and two a", out-of-plane. Observable shifts between the fundamental vibrations of the two isomers do indeed occur. In the present work we have measured the gas-phase infrared absorption spectrum at medium resolution of the isotopic species HCOSH, H13COSH, HCI'OSH, DCOSH, and HCOSD. The assignment of the observed absorptions is discussed in section 111. In section IV, the force field calculations are discussed. These are based not only on the band centers of the fundamental vibrations, but also on the centrifugal distortion constants of the above five isotopic species and of HC034SH,the microwave spectrum of which was measured in natural abundance.2 From the torsional fundamental of the two isomers of the parent species and the energy separation, ABgs,between the two corresponding ground states, the one-dimensional torsional potential function could be determined, as discussed in section V. The effects of rotational isomerism on the vibrational spectrum and on the harmonic force field of HCOSH are considered in section VI in relation to the structure and in relation to other, related molecules.
11. Experimental Procedures Absorption spectra in the region 4000-350 cm-', and survey spectra to 200 cm-l, were obtained by using a Perkin-Elmer 225 spectrophotometer. The resolution at which the fundamental bands above 600 cm-I were measured varied between 0.27 and 0.40 cm-l. The samples were contained in a 13-cm Pyrex cell with KBr or CsI windows at pressures between 2 and 20 torr at ambient temperature. The far-infrared spectra of the parent species and the two singly deuterated species were recorded by using an RIIC Model FS-520 interferometer at a resolution of 0.86 cm-l. The absorption cell of this instrument was a 4.6-m brass tube (optical length ca. 5.75 m) cooled to 12 "C in order to reduce decomposition in the The v 1 band of H13COSH was recorded additionally with the Polytec MIR 160 interferometer with a resolution of 0.08 cm-I and the v6 band of the same species was recorded with a Bruker Physik IFS 113c at a resolution of 0.09 cm-l. Calibration was made by using selected atmospheric absorptions in the P E 225, and by using internal water lines in the interferometer.
The preparation of monothioformic acid followed the procedure of Engler and Gattow' as modified by Hocking and Winnewisser.l The isotopically substituted species were prepared for the work reported in ref 2 and 4 and were redistilled for the present investigation. Spectra of the deuterated species were obtained from samples from two different preparations. The enrichment of the 13C species was 9070, and that of the I'O species was 35%. Formic acid occurred as an impurity if traces of water were present. Several samples contained unidentified impurities which could not be completely eliminated despite repeated vacuum trap-to-trap distillations. However, the absorptions due to these impurities could be identified as such by their intensity variations relative to the monothioformic acid absorptions. Decomposition was negligible in the Pyrex cell, but both decomposition and H-D exchange were considerable in the brass pipe, even when cooled, until it had been conditioned with the appropriate sample. 111. Spectra and Assignment Survey spectra of four of the isotopic species studied are shown in Figures 1 and 2. The spectrum of the 13C-substituted species is qualitatively the same as that of the parent species. Bands showing obvious structure attributable to the less abundant rotamer are the band a t 750-600 cm-I and the torsional mode, with Q branches at 400 and 384 cm-l for the parent species. At higher resolution, some but not all of the other bands are also seen to show such structure. The assignment of the absorptions observed for all of the isotopic species studied is summarized in Table I, giving the fundamentals, and Table 11, giving other absorptions. The assignment was made initially in analogy with formic acidE10 and was supported at various stages by force constant calculations, as will be discussed below, and by comparison with the reported spectra for CH3SH,11CH3COSH,12r13 HCOSCH3,14and HCOC1.15 ul. The CH stretching mode is well isolated, except in DCOSH, and has a predominantly b-type band structure whose Q branches could be resolved. In Figure 3 it can be seen that each Q branch is accompanied by a satellite which is too strong to be a "hot" band, and too consistent from one Q branch to another to be due to P or R branch structure. Higher resolution scans of this band in the
The Journal of Physical Chemistry, Vol. 84, No. 14, 1980 1773
Vibrational Spectrum of iHCOSH
TABLE 11: Overtone and Combination Bands Observed and Most Probable Assignmentsa
Superscripts specify cis or trans rotamer, and lack of superscript indicates both rotamers.
c m e o o
Figure 1. Survey spectruiri of four isotopic species of monothioformic acid. Dotted lines indicate regions obscured by weak impurity absorptions but containing no strong absorptions of the sample. P indicates absorption due to the parent species, HCOSH, and F indicates normal or substituted formic acid absorptions.
H13COSH spectrum, which looks identical with that for HCOSH, were recorded with a Polytec MIR 160 interferometer and showed that each satellite is a distinct Q branch, as shown in the insets in Figure 3. We have assigned these satelites to cis-HCOSH and the main series to trans-HCOSH. There is some uncertainty in assigning the rotational quantum number ha for the weaker series and thus in locating the band center for the cis rotamer. However, by considering the reduction in intensity and
sharpness of the Q branches as they approach the band center a choice could be made, resulting in the assignment given in Table I. The direction of the small difference of the two band centers is consistent with calculations using the same CH stretching force constant for both rotamers. The cis-trans difference for this band was then assumed for the other isotopic species, for which the higher resolution spectra were not available, but for which an analogous satellite structure was observed. In DCOSH, another absorption is coincident with the band center, so that the structure is obscured and the accuracy with which the band centers could be determined is reduced. v2. The intensity of the SH stretching mode is too low to permit its identification for more than two of the isotopic species studied. For all species except HCOSD there are several combination bands falling in the region where this band is expected and the weak, complex absorption observed cannot be securely assigned. For HCOSD no absorption in the appropriate region was observed. Since the isomerization may influence this band, it was disappointing that it could not be observed more distinctly. The low intensity, however, is consistent with spectra obtained for, other molecules.16 vQ. The very strong absorption near 1700 cm-l is the GO stretching mode. It shows a poorly defined Q branch on either side of a central minimum, indicating a predominantly b-type band, but no extended Q-branch structure correspondingto that of v1 was resolved. A distinguishable absorption that could be attributed to the cis rotamer could only be observed for the deuterated species, as shown in Figure 4. Since the undeuterated species all show no such structure, it is probable that a Fermi resonance shifting one (or both) of the bands causes the splitting between the v3 of the cis and trans isomers of DCOSH in particular. A reasonable fit to the product rule and a consistent force field require that both the cis and trans band centers for v3 of DCOSH be taken as 1696 crn-l, the center of the strongest band. The presence of a resonance is further supported by the 2v3 band, which is split into two bands with an interval nearly identical with the interval between the bands at 1696 and 1713 cm-l, rather than twice that interval. The possibility of observing a band ca. 1:3 intensity next to the main band is illustrated by the spectrum of HClsOSH in Figure 4,since the l80 substitution was about 35%.
The Journal of Physical Chemistry, Vol. 84, No. 14, 1980
Winnewisser and Hocking
-s 100o W 0
z < c i-
2 100 k-
0 L50 400 350 300 crn-1 250 Figure 2. The region of the v7 and vg absorption bands of the main species and the two singly deuteratedspecies of monothioformic acid, recorded with an RIIC interferometer at 0.88-cm-‘ resolution. c and t indicate the cis and trans Q branches of vg, o indicates residual water in the cell, and H indicates residual HCOSH absorptions.
2800 cm-l I
Figure 3. The C-H stretching band, v,, of Hi3C0SH. The lower resolutlon scan was made wtth 0,3&cm-’ resolution on the Pekin-Elmer 225, and the insets were made at 0.08-cm-’ resolution with a Poiytec MIR Fourier transform interferometer.
v4 The assignment of the v4 absorption was not difficult for the four species with an HCO group, since this corresponds to the HCO in-plane deformation, and is consistent with the spectra of other molecules. In the case of DCOSH, however, v4 moves into a frequency region where the mixing of valence coordinates is strong, the frequency is not distinctive, and the band form is apparently considerably different. This band is shown in Figure 5 for HCOSH and DCOSH only, since the band form for the other three species is nearly identical with that of HCOSH. In the spectrum of the nondeuterated species we assigned each of the two strongest peaks to an a-type Q branch for one of the two rotamers. The structure of the band is not clearcut, and in addition to the hybrid band structure there is probably absorption due to combination and overtone bands, particularly 2v6 for all isotopic species except the deuterated species. Conceivably the second sharp peak might be due to one of these nearly coincident bands, but as it occurs for all four species with the HCO group, we feel justified with the present assignment. The bands in DCOSH at 1071 and 1027 cm-l were originally assigned to the cis and trans rotamers, respectively, but that as-
HC 0 S D
The Journal of Physical Chemistry, Vol. 84, No. 14, 1980
Vibrational Spectrum of HCOSH
I n z
l t ( r
DCOSH I 1100
Flgure 5. The region of the v, absorption band of HCOSH and DCOSH.
LJJ 1 20 T O R R
12 TORR 101
Figure 7. The region of the species studied.
Flgure 6. The region of the v5 and u8 absorption bands of the five isotopic species studied.
Q branches at 1029.9 and 1024.7 cm-l are due to the more abundant trans rotmer. It may be that the v4 absorption for cis-DCOSH is responsible for the two weak peaks at 1026.7 and 1021.3 crn--l,or that it is coincident with the trans band at this resolution. This latter possibility was the assignment adopted finally with a large uncertainty. up The three lowest in-plane modes are quite strongly mixed in terms of valence coordinates. v5 may best be described as the HSC deformation, however, and it is more sensitive to H,D substitution on the sulfur than v g or v7. Since for each isotopic species a single band was observed in the corresponding region, it was not until force field calculations could be made with the full set of isotopic
vg absorption band of the five isotopic
species that the cis and trans absorptions could be distinguished. The form and intensity of this band apparently differ strongly for the two rotamers, so that v5 of the cis form is observed merely as a Q branch peak on the high-frequency side of the strong trans band. This is illustrated for each of the isotopic species in Figure 6. For the 'Sg species, the cis Q-branch peak is not clear enough for identification. If the parent species and the S-deuterated species are used in the force field calculation, then the predictions for this band agree well with the present assignment for the I3C species and the other deuterated species. Vg. The predominantly CS stretching mode shows the largest difference between cis and trans absorption frequencies for all species except HCOSD, for which only one band center could be found. In this case the cis absorption must be either coincident with the trans absorption or considerably weaker than in the other ,isotopic species. (The trans absorption is itself considerably weaker than in the other isotopic species.) The former assumption was adopted and is reasonably consistent with the product rule, although a value to higher frequency would seem better. The difference in band form for the two rotamers can be seen for the other species in the differing degradation of the central Q branches for the two isomers in Figure 7. As in the case of v3, we have the example of the l*O-substituted species to indicate the detectability of a band of 113 intensity close to the main band. v7. The lowest in-plane mode is approximately the OCS deformation and falls just above the torsional mode, vg. The distorted band shape, shown in Figure 2, indicates a strong Coriolis interaction analogous to that observed for the same two modes in HCOOH.7p9 Only one minimum
The Journal of Physical Chemistry, Vol. 84, No. 14, 7980
Winnewisser and Hocklng
TABLE 111: Structure of the Two Rotamers of Monothioformic Acid and the Appropriate Symmetry Coordinates _
substitution structure from ref 4 rCH/a rSH/a
rcolA rcslA a = LHSC, deg p = LOCS, deg y 1 = L H C O , deg ~y~= LHCS, deg
1.104 1.354 1.205 1.768 92.5 125.9 123.1 111.0
1.104 1,335 1.203 1.771 94.9 122.5 123.2 114.4
symmetry coordinate a' '
S, = 6rCH s, = 6rSH s, = 6rc0 S,=Sr
= 'TH-COS 8, = ' / z ( A 7 0 C S H
S6 = Sa
and are shown in Figure 2. Their assignment was confirmed by force field calculations and by calculations describing the torsional motion alone, as discussed in section V. Absorptions which were not assigned as fundamental vibrations are listed in Table 11. The strongest overtone is that of v3. Since a cis-trans difference between the fundamentals should be twice as large in the overtone, we recorded the band at 3423 cm-l for HCOSH at 0.3-cm-l resolution but could detect no useful stiucture, and only one minimum. For the l80 species, the bands for the two isotopic species were well separated, and served as the basis for checking the isotopic enrichment. For DCOSH, as mentioned above, the 2u3 band confirmed the suspicion of a resonance displacing the cis v3 band. Another strong overtone seems to be 2v4. Together with v3 + v5 and v3 v8 in HCOSH, this band obscures the v2 region. In DCOSH, the overtone of the v4 band at 1027 cm-l can be seen just below the v 2 (CD stretching) band, and the overtone of the 1071-cm-l band falls right in the middle of that band. Of the remaining absorptions listed in Table 11,only the bands at 1533 and 1071 cm-l in DCOSH are unexplained, in the sense of being too strong for whatever combination bands might lie there.
S,=(1/61/2)(2Sp-Sr,- S r I )
can be distinguished, which we have assigned to the trans absorption in each case. In HCOSD the v7 and vg absorptions are far enough apart so that there is little distortion, but again only one minimum could be observed. A low resolution scan with less residual HCOSH than in Figure 2 shows this minimum more clearly. Force field calculations showed that the cis and trans bands might be coincident for HCOSD but not for the other species, or vice versa, but they cannot be coincident for all five species. Since the minimum observed for HCOSD was particularly clear, and no other nearby absorption could be seen between 600 and 393 cm-l, we believe that the band for the two rotamers must coincide for HCOSD. We are thus forced to list v7 as unobserved for the remaining four isotopic species of the cis form. vg. The out-of-plane deformation of the formyl hydrogen is weak and could only be assigned with the help of the product rule and the force field calculations. In each of the nondeuterated species it is observable as a Q branch on the low-frequency side of the v5 band, as may be seen in Figure 6. In the deuterated species it moves free of this band and can be seen as a sharp, C-type Q branch. No cis-trans difference was observed for any of the isotopic species, and the band center was taken to be the same for both rotamers. up The torsional mode is a C-type band for which the trans and cis absorptions could be clearly distinguished,
IV. Force Field Calculations The evaluation of the data presented in section I11 was carried out by using computer programs originating in Chemical Laboratory V, University of Copenhagen. The force field fitting program uses a general valence force field and a damped least-squares procedure.17J8 The structures used for the two r o w e r s of HCOSH are the substitution structures reported in ref 4 and are reproduced in Table I11 together with the symmetry coordinates defined for the molecule. As a measure of the effects of geometry on the spectrum, for a given force field, Table 1V shows the difference between the spectra predicted for (1) the same (trans) structural parameters, but cis and trans conformations, and (2) the same (cis) conformation, but cis and trans structural parameters. The force field used was that given in Table VI as the final trans force field, but omitting the HSC interaction force constants. Omitting one or the other of the off-diagonal force constants leads to changes of up to f 3 0 cm-' in v5, vg, and v7, and the differences listed in column 1 are not a good representation of the observed spectrum. Rather, they indicate the necessity of fitting the two isomers separately. The figures in column 2, on the other hand, are less dependent on the force field, and
TABLE IV: Effect of Geometry on the Fundamental Vibrations of Monothioformic Acid for a Given Force Fielda Au/cm" obsd, trans-cis Av/cm" calcd for cis Av/cm-' calcd for trans structure, trans-cis conformationb conformation, trans-cis structureC conformation
Vl V l
HCOSH -0.1 -0.1 -0.3 0.4 -18.4 31.0 -13.3 -3.2 10.4
DCOSH 0.0 -0.4 0.0 2.7 -14.2 23.5 -12.0 -2.7 8.2
HCOSD -0.1 -0.1 -0.3 0.4 -33.3 66.5
-34.6 -3.0 12.5
HCOSH -1.1 -0.0 -3.1 -2.9 -8.6 -6.9 8.2 9.3 0.1
DCOSH -0.1 -2.8 -2.0 -4.3 -9.8 -3.9 7.4 13.2 -1.9
HCOSD -1.1 0.0 -3.1 -3.0 -2.2 -10.2 8.3 9.8 2.4
HCOSH 2.5 (0.0)
0.0 -10.0 -17.6 -42.4
2.8 -9.5 -18.6
(0.0) (0.0) (0.0)
20.4 All structural a Force field used was similar t o that given in Table VI, but LHSC interaction constants were omitted. All structural parameters except the parameters as in Table I1 for trans isomer; only the torsional angle was changed by rr. torsional angle were changed from trans to cis isomer values as in Table 111; torsional angle was held at n , giving cis conformation. Parentheses indicate assumed difference, where only one band was observed or because of Fermi resonance. v9
The Journal of Physical Chemistry, Vol. 84, No. 14, 1980 1777
Vibrational Spectrum of HCOSH
TABLE V: Centrifugal Distortion Constants (in kHz) of the Two Rotamers of Monothioformic Acida
3.42871(27) -43.1667( 51) 125 0.74( 1 5) 0 . 43 4 7 3 0 ( 3 2) 16.5158(84)
3.38315(76) -41.664( 1 3 ) 1232.70( 35) 0.437076( 72) 16.374(25)
Trans 3.06850(60) -42.807(12) 1240.91( 56) 0.378236(68) 14.827(20) Cis 3.29749(66) -47.478(13) 1296.41(48) 0.403526( 75) 15.864(25)
3.2769( 70) -41.66(20) 1245.1(23) 0.40447( 28) 15.823(28)
3.20376(55) -22.9348(95) 609.78(11) 0.489187(62) 15.0373(88)
3.42625(90) -22.105(18) 582.53(13) 0.486644(83) 16.642(10)
3.1865(10) 3.42549(68) 3.534(13) 3.62686(81) 3.67858( 36) -25.735( 1 1 ) -23.553(22) -46.95(36) -46.448( 1 4 ) -47.9619(65) 746.23(20) 1297.3(43) 627.28(11) 1281.86(38) 1305.68(18) 0.411391(96) 0.523121(76) 0.43568(58) 0.466269(75) 0.4631 22(37) 15.473(21) 16.072(11) 16.917(51) 17.485(28) 1 7.653;( 12) a The numbers in parentheses are standard errors in units of the last significant figure. The weights were determined not Reference 1. Reference 4. Reference by these errors, but b y the inverse square of 2% of the value of each constant. 2. TABLE VI: Final Force Field Obtained for Monothioformic Acida trans
F 5,5 / (mclgn A /rad ) F,,/(mclyn F,,,/(mdyn F,,/(mdw F,,,/(mclyn F,,,/(mdyn
A/radz) A /rad2) A/rad2) A /rad2) .&/rad2)
4.756(14)* 0.531(80) -0.40(17) 4.175(23) 13.35(1 6 ) 1.87(23) 0.468(67) 0.03(17) 3.22(1 2 ) 0.152( 53) 0.142(19) 0.224(46) 0.6049(49) -0.019( 1 2 ) 0.250(51) 0.7638(36) -0.2366( 72) 1.004(48)
4.727(23)c 0.600(129) -0.63( 2 4 ) 4.1 75 2d 13.350d 1.81(27) 0.467gd 0.08(15) 3.16(15) --0.002(123) 0.185(21) 0.038(56) 0.6256(68) -0.027(14) 0.213(105) 0.8371(41) 0.241(15) 0.935(67)
0.029(27) -0.069(152) 0.23( 29)
0.06(39) -0.05(23) 0.06(19) 0.154(134) -0.043( 28) 0.186( 72) -0.0207(84) 0.008(18) 0.037(117) -0.0733(54) -0.478(17) 0.069(82)
F & J (mclyn A /radz) F,,,/(mcl?jn A/radz)
0.0069(1 3 ) 0.00292( 57)
a Adjusted to vibrational fundamentals and centrifugal distortion constants. Anharmonic correction applied as described in text to data in Table I. Weighting based on uncertainties in Table I, and for the centrifugal distortion constants, on 2% of the value of each constant, Several isotopic shifts, with uncertainty 1.0 cm-’ for each measurement, were given uncertainty 0 . 5 cm-’. Force constants omitted were constrained t o zero. Units are defined by mdyn A = aJ, A = lo-’’ m. Standard error plus change in constants when fit with F,,or F , ,varied by plus or minus the standard Standard error, Fixed a t value found for trans rotamer. error from the trans fit.
show the contribution of the structural differences between the two isomers to the spectrum. The data set on which the force field was refined included, for each rotamer, the vibrational wavenumbers in Table I and the quartic distortion constants reproduced in Table V. The weighting factors were determined by the inverse square of the uncertainties, which were taken as the estimated errors of the vibrational frequencies, and as 2% of the value of each distortion constant, although the standard errors are all considerably smaller. The conversion from the distortion constants of the reduced Hamiltonian to the r constants for input to the program was made following Yamada and Winnewisser.lg As a comparison of the force fields calculated for HCOOH in the last few years indicates,s*20p21 the values of the force constants obtained depehd strongly on which off-diagonal force constants are included in the fit. This, again, depends on the completeness of the data available. The relative weighting of the centrifugal distortion constants and the vibrational frequencies is also critical. In
order that these two.groups of data be fit with one force field, it was necessary to “harmonize” the vibrational frequencies. This was done according to Dennison’s rule v? = vi(l Xi), as applied by Redingtons to the HCOOH data; X = 0.04 for the CH and SH stretch and the torsion, 0.02 for the other fundamentals of the undeuterated species, and XD = (vD/vH)XHfor the deuterated species. Because the data set for the trans rotamer is more complete, the force field was first refined for this rotamer. Starting from a force field analogous to that of Susi and Scherer for HCOOH,’O and adding off-diagonal force constants as the data would allow, we arrived finally at the force field listed in Table VI and the observed - calculated values for the trans data listed in Table VII. The off-diagonal element in the a’! force field was found to be undetermined and was subsequently omitted. Various weights of the centrifugal distortion data and the v7 band centers were used, and the results shown are considered optimum. The trans and cis data were also fit to one force field,
The Journal of Physical Chemistry, Vol. 84, No. 14, 1980
Winnewlsser and Hocking
TABLE VII: Deviations (Obsd - Calcd) for the Force Fields Given in Table VI HCOSH Vl V2
0.9 0.0 -0.8 -1.5 1.0 1.4 4.2
2.8 0 *O' -0.9 -2.9 0.3 1.8 3.0
1.14 -0.28 1.18 0.86 1.84
1.18 0.11 1.21 0.80 2.14
0.4 0.0' 0.0 -0.1 0.3 1.2 25.3b
2.7 0.0' -0.6 0.5 0.0 3.3 23.gb
HC"0SH Trans (in cm-l) -3.8 -0.0' -0.6 -0.1 2.1 0.9 10.Bb 0.6' 0.2
0.0 1.1 1.0 1.6 2.0 2.4 4.9
2.0 9.5' 0.9 0.4 2.0 2.6 2.1
Trans (in Units of 2%c) 1.17 -0.56 1.27 0.86 1.55
-0.47 4.62 -1.26 -0.93 1.60
0.77 -4.94 1.45 0.86 -0.60
Cis (in cm-') -4.3 0.0' 1.4 -0.7 1.7 0.1 31.3b
0.0 -2.3' -3.3 6.4 0.4 1.8 24.5b
1.6 9.7' 0.0 1.4 0.4 0.2 -2.3
1.14 0.41 0.98 0.80 1.86
Trans (in Units of 2%c) -0.27 -0.25 -0.14 -1.55 -0.16 -0.30 1.21 1.72 0.89 5.00 -4.85 1.38 0.85 0.81 0.94 -1.49 2.37 1.01 -0.03 -0.15 0.08 -1.26 0.33 -0.11 2.43 2.58 2.28 2.97 -0.84 2.21 a Given zero weight in fit. Given low weight in fit; see Table I. Deviations in kHz divided by 2% of value of each constant; see Table V. AJ AJK AK 65 6K
allowing certain force constants to differ. These results were not satisfactory, but were one attempt to deal with the incompleteness of the cis data. Fitting the cis data alone in the same manner as the trans data led to a diverging force field, in particular of the CO stretch and C0,CS interaction force constants. The method finally adopted allowed the convergence of the calculation, while restricting the cis force field as little as possible. We constrained the CO stretch and the CO, LHCO interaction constants to the values obtained for the trans species. These are relatively well determined in the trans data, and, especially since no significant cis-trans difference was observed for vg, it seems a reasonable assumption that these two force constants cannot differ significantly in the two rotamers. The resulting values of the force constants for the cis rotamer are given in Table VI and the observed - calculated values for the data are given in Table VII. The errors listed in Table VI for the cis force field were determined by combining the standard deviation resulting from the least-squares procedure with the variation occurring upon fixing the constrained force constants over the range of plus and minus their standard error from the trans force field fit. Considering the assumptions made in the assignments and in the corrections for anharmonicity, the overall fit is satisfactory. The centrifugal distortion constants D K and DJK are most strongly correlated with the lowest inplane modes, especially the OCS bend. Since just this mode is not well determined in the data and the spectrum of the important l80substituted species did not allow a determination of v7, the centrifugal distortion data are important in determining the corresponding part of the force field.
TABLE VIII: Product Rule for Monothioformic Acid niwi'lwi
HI3COSH HC"0SH DCOSH
Trans a' species obsda calcdb obsd - calcd
0.9379 0.9410 -0.003
0.9579 0.9430 0.015
0.5293 0.5167 0.013
0.5272 0.5150 0.012
a" species obsd calcd obsd - calcd
0.9814 0.9830 -0.002
0.9942 0.9949 -0,001
0.8180 0.8137 0.004
0.7919 0.7905 0.001
0.4972 0.5186 -0.021
Cis a' species obsd calcd obsd - calcd
0.9418 0.9411 0.001
a' species 0.9938 0.8199 obsd 0.9810 0.7720 0.9948 0.8159 calcd 0.9837 0.7738 -0.001 0.004 -0.002 obsd - calcd -0.003 a Vibrational frequencies w i of the parent species and w i ' of the substituted species are taken from Table I. Calculated quotients were obtained by using rotational constants in ref 1, 2, and 4.
The product rule, as calculated from the assignment in Table I, is shown in Table VIII. Since assumed values were used consistently for v2, and for vl of the cis rotamer, the agreement shown has limited usefulness. However, false assignments for u3 and u4 of DCOSH showed clear discrepancies, as did the initial assignment of ug of cisHCOSD to the Q branch at 310 cm-l. The low value for
Vibrational Spectrum of HCOSH
The Journal of Physical Chemistry, Vol. 84, No. 14, 1980 1779
cis-HCOSD may be partly accounted for by the difference in cis and trans v7 for the two species HCOSH and HCO-
SD. The most obvious differences in the force constants for the two rotamers are in the interaction constants, in particular the LOCS, LHSC interaction constant. Table VI summarizes the differences and the estimated significance of the differences. The L matrices for the parent species and the two deuterated species are shown for both rotamers in Table IX.
V. Torsional Potential The abundance of data concerning the torsional mode and the two rotamers of HCOSH allows a reliable evaluation of the potential function and barrier to internal rotation, and some quantitative indications of the validity of the approximations used. In determining the torsional potential function, we assume complete decoupling of the torsional mode from the other nuclear motions. In the harmonic approximation, the validity of thia assumption is shown by small contribution of S8to Q9(see Table IX). The structural differences found for the two isomers, on the other hand, indicate structural relaxation accompanying the torsional motion, and thus a finite coupling of the other nuclear motions with the torsion. We have tried to consider the effect of this coupling on the potential function by using both the cis and trans substitution structures in the calculations. However, structural relaxation at the top of the potential barrier, where it can be expected to be most important, was not considered. The second approximation is that of expanding the one-dimensional torsional potential function as a cosine series and truncating the series with two or three terms. The truncation is usually determined by the amount of data available, and the data imply in this case that, although three terms can be defined, two may be adequate, as will be seen below. The third approximation is in truncation of the polynomial expansion of the cosine functions, which is the high barrier approximation. This was checked by comparing some of the results obtained with perturbation theory, using the first andl second terms in the cosine expansion, with results obtained using the full matrix diagonalization of the torsional Hamiltonian with the same potential function. The data used for determining the potential function are the torsional fundamental, vg, for each rotamer of the parent species, HCOSH, and the difference between the ground-state energy levels of these two rotamers, AE,, = 231.3(6) cm-l, determined from the rotational s p e ~ t r u m . ~ Since we have three data, we can theoretically determine three coefficients in the expansion of the potential function V(0) = y2Cvn(l- cos ne) (1) n
First-order perturbation theory, using the first term in the cosine expansion, (ne)2,gives the equations determining these coefficients as1OsZ2
V1 i- V3 = AE,,
+ 7 2 ( V t - v,)
+ 4Vz + 9V3 = Vt2(Gtt-’)t/C -Vi + 4v2 - 9V3 = V,2(Gt<1),/C Vi
(4) ut and v, are the trans and cis torsional frequencies and (Gtt-l) is the inverse G-matrix element in yA2 for the torsional mode, determined from the trans and cis structures following The constant is given by C = hcN,/87r2 = 16.858 cm-I phi2. Use of the next term,
in the cosine expansion, as described by Miyazawa and Pitzer,loamounts to adding an anharmonic correction to the torsional frequency, so that in eq 2-4 we use for each frequency v = ~ ( 1 ~ 0C/(Gt<’) ) (5)
This correction is of the order of 13 cm-l for both species. The resulting potential coefficients are given in column I of Table X. Note that the estimated error, propagated from the estimated experimental errors, is large for V3. Calculations made by diagonalizing the torsional Hamiltonian matrix and by using just one geometry at a timez4 showed that our three data could be fit within experimental error with just two potential terms; however, the V2 term was different for the two geometries. The two values of Vz were averaged, and the coefficients obtained are given in column I11 of Table X. It can be seen from Table IV that a large part of the cis-trans difference in the torsional fundamental is due to the conformational difference in geometry. The remaining difference, apparently, can be accounted for with just two terms in the potential. If we eliminate V3 from eq 2-4, we obtain two values of V,. These values, and the average of the two, are given in column I1 of Table X. This average is seen to be nearly the same as the value found in column I. The potential maximum and the angle at which it occurs are included in Table X, and show close agreement for columns 1-111. In view of the model errors discussed at the beginning of this section, the uncertainty of V, is too large for the value determined to be significant. The values shown in column I1 are considered to be most reasonable, and are used in the potential function as shown in Figure 8. The torsional bands of HCOSD, and the “hot” bands of this mode for the various species, were not used directly in the determination of the potential function. The “hot” bands assigned are included in Table 11, and agree within 1.5 cm-I with predictions made by using the method of column I11 in Table X. However, a simultaneous fit of all this data, in view of model errors of the one-dimensional model such as structural relaxation, would not bring a physcially significant improvement in the potential function.
VI. Discussion The torsional potential function determined for HCOSH is consistent with that of formic acid, for which the coefficients V I = 1409 cm-l and V, = 4093 cm-l were determined by the same method.25 The height of the barrier indicates primarily the role of conjugation in the C-S bond toward stabilizing the two planar conformations. The corresponding barrier in HCOOH is higher, as may be expected, since the C-0 bond should have more double bond character than the C-S bond. The coefficient V1 reflects the separation of the ground states of the two isomers, which may be interpreted as a combination of dipole-dipole repulsion of the nearly parallel XH bonds in the cis rotamer and the stabilizing interaction between the C=O and S-H (0-H) bonds in the trans rotamer. Both of these effects will be smaller in HCOSH due to the length of the C-S bond. This interpretation of the differences between the potential functions for torsion in HCOOH and HCOSH corresponds qualitatively to the analysis of semiempirical calculations reported by Leibovici26for HCOOH. The difference between the individual and average values of Vz in column I1 of Table X indicates the error introduced when only two data are available, as in the case of HCOOH.25 For HCOOH, the difference UgS is much
The Journal of Physical Chemistry, Vol. 84, No. 14, 1980
Winnewisser and Hocking
TABLE IX: L Matrices Determined by the Force Fields in Table VI, in pi/' for Bond Stretching and p-'/' A-1 for Angle Bending Coordinates trans-HCOSH
s* s, 84 s, s, ' 6
1.036 0.006 -0.042 -0.043 -0.029 -0.051 0.137
Q8 S8 s 9
0.001 0.001 -0.020 0.021 -0.023
Q3 0.000 -0.004 -0.375
0.110 0.388 -0.149 0.158
0.015 -0.005 0.024 0.085 1.311 -0.026 -0.063
0.030 0.005 -0.043 0.108 0.100 0.663 -0.262
0.036 0.000 -0.026 0.277 -0.055 -0.325 -0.248
0.003 -0.001 0.007 0.071 -0.163 0.158 0.310
Q9 -0.106 1.159
sz 8 3 s4
s, ' 6
0.004 1.012 -0.001 -0.001 0.016 -0.022 0.024
-0.751 0.005 0.108 0.047 0.004 0.097 -0.212
-0.105 -0.003 -0.363 0.124 0.326 -0.126 0.112
0.034 -0.003 -0.001 0.154 0.967 -0.020 -0.107
SS 8 9
Q, 0.040 0.005 -0.038 0.074 0.019 0.684 -0.228
-0.001 0.025 -0.250 0.153 0.282 0.245
-0.001 0.001 -0.006 -0.072 0.1 78 -0.152 -0.305
Q, -0.065 1.150
1.036 0.002 -0.042 -0.043 -0.029 -0.046 0.136
0.002 -0.726 0.013 -0.002 -0.056 0.034 -0.039
Q3 -0.001 0.027 0.376 -0.111 -0.386 0.123 -0.155
-0.015 0.014 -0.024 -0.085 -1.311 0.019 0.064
0.040 0.009 -0.045 0.203 0.077 0.328 -0.384
-0.023 0.002 0.010 -0.223 0.117 0.389 0.044
-0.002 0.001 -0.006 -0.047 0.134 -0.218 -0.277
Q9 -0.077 0.921
s5 ' 6
1.035 -0.002 -0.036 -0.055 -0.042 0.055 0.138
Q, SS s9
Q, -0.002 -1.012 -0.001 0.003 0.019 0.021 0.023
-0.012 -0.003 0.376 -0.089 -0.336 -0.178 -0.165
-0.020 -0.005 -0.007 -0.077 -1.336 0.023 0.059
9, -0.038 0.005 0.052 -0.126 -0.028 0.701 0.214
-0.052 0.000 0.027 -0.269 -0.045 -0.252 0.285
0.011 0.001 0.000 0.097 -0.121 -0.148 -0.303
Sl sz 8 3
s4 8 5
0.002 -1.011 -0.001 0.003 0.016 0.021 0.023
-0.752 -0.003 0.096 0.068 0.027 -0.105 -0.213
0.084 -0.003 0.366 -0.107 -0.311 -0.157 -0.122
0.049 0.002 -0.017 0.151 0.974 -0.148 -0.130
0.038 -0.005 -0.044 0.068 -0.186 -0.701 -0.158
0.060 0.000 -0.026 0.249 -0.072 0.205 -0.276
0.010 0.001 0.000 0.096 -0.132 -0.145 0.300
Vibrational Spectrum of HCOSH
The Journal of Physical Chemistry, Vol. 84, No. 14, 1980
TABLE IX (Continued) cis-HCOSD
SZ s 3
s, 8 6
11.035 0.000 -0.0 36 -0.055 -0.042 0.051 0.138
0.726 0.010 -0.006 -0.051 -0.033 -0.037
Q3 -0.013 -0.020 0.376 -0.090 -0.337 -0.142 -0.162
0.019 0.014 0.009 0.076 1.334 -0.006 -0.059
-0.038 -0.004 0.005 -0.174 0.006 -0.393 0.073
-0.010 -0.002 0.001 -0.086 0.117 0.186 -0.296
0.052 -0.245 -0.064 0.349 0.355
TABLE X: Torsional Potential Function of HCOSH'" V(e)= l / z V , ( l - c o s e ) t V z ( 1 - c o s 2 e ) t v,(i - COS 3e)
228.9(8.0)b 3408.3( 13.0)
239.4 3429.3 (trans), 3387.3 (cis) 3408.3
239.3(4.7)b 3412( 28)
10.5( 8.0) 90.83 3529
O(5) 91.00 3533
a I: Anharmonic correction included. Structures from ref 4 used. 11: As I, omitting V3. Structures from ref 4 used. 111: Matrix diagonalization method. Structure ]Errors reflect only contributions of from ref 2 used. experimental uncerLainties.
larger, 1365 cm-'. Even if the same high-barrier, two-term model should apply as well as in the case of HCOSH, the value of V2 determined must be too high by 50 cm-l or more; the predicted value of v, would then be too high by 3 cm-' or more. It is difficult to transfer significant aspects of the vibrational assignment and force field calculation for the two rotamers to any other molecule, in particular to HCOOH. Hisatsune and Heickleng have tentatively assigned two bands in the spectrum of the products of a gas-phase ozonolysis of 1,2-dichloroethyleneto cis-HCOOH. The carbonyl CO stretching band, according to their assignment, is shifted down about 31.5 cm-l, while the other CO stretching band is shifted up by 19.2 cm-l relative to the analogous trans-HGOOH bands. The latter shift would be qualitatively corcsistent with the spectrum of HCOSH, but the large shift of the carbonyl band would not. If the assignment of Hisatsune and Heicklen is correct, then the conformational changes in the two CO bond strengths in HCOOH must be considerably larger than the analogous changes in HCOSII. Indeed, the structure recently determined by Bjarnov and Hocking2' for cis-formic acid from the rotational spectrum indicates a change of -0.007 8, in r(C=O) and 0.009 8, in r(C-0) from the trans rotamer, whereas the corresponding changes in HCOSH are only -0.0015 and 0.003 A, respectively. The direction of these changes, however, is such as to induce an upward shift in the carbonyl CO stretch and a downward shift in the other CO stretch, which is opposite to the effect cited by Hisatsune and Heicklen. The two rotamers of HONO, which are isoelectronic with HCOOH, show much more drastic differences in their spectra and force than those of HCOSH, and a comparison indicates mainly the more limited effect of conformation on the bonding of HCOSH. A striking similarity is observed between the v1 bands
v Figure 8. The one-dimensional torsional potential function of rnonothioforrnic acid, V(8) = '/,(239.4)(1 - cos 8) 4- '/,(3408)(1 - cos 28), in cm-'.
of HCOC1, reported by Hisatsune and Heicklen,15 and HCOSH. The analogy between spectra of molecules with the C1 and SH groups has been noted by Sheppard30and Crowder31for CH3COSH and CF3COSH,respectively. In the present case the similarity of the C-H stretching bands is due to the similar rotational constants of the two molecules and to the nearly identical orientation of the principal axes relative to the HCO g r o ~ p . The ~ , ~form ~ of the v1 band of HCOCl in Figure 1of ref 15 has exactly the form of the band in Figure 3 for HCOSH, except that the satellites due to the weaker rotamer are missing in HCOC1. However, the vl band of HCOCl lies 90 cm-' higher than in HCOSH and the values of the remaining fundamental frequencies are only roughly analogous to those of HCOSH. The similarity of force constants observed by Sheppard30 and Crowder31 is not as close in the present case. Differences in the s t r u c t ~ r e s ~ are s ~consistent ~ with the differences in the fundamental frequencies. A closer analogy for the formyl group fundamentals, including the formyl-H out-of-plane mode, is found in the spectrum of HCOSCH3, methyl thi0f0rmate.l~In particular, the differences found between the spectra of methyl thioformate and methyl formate33are nearly identical with those found between the spectra of monothioformic acid and formic acid.8-10 The sulfur substitution results in a lengthening of the C-H and C=O bonds of the formyl group, and a corresponding drop in the associated fundamental vibrations of 105 cm-l [v(C-H)], 56 cm-l [u(C=O)], and 112 cm-l [r(H-COX)] for methyl formate, and 100
The Journal of Physical Chemistry, Vol. 84, No. 14, 1980
cm-l [v(C-H)], 54 cm-' [v(C=O)], and 109 cm-l [.rr(HCOX)] for formic acid. In both sulfur-substituted molecules, the formyl-H out-of-plane mode is stronger than in the unsubstituted molecules. The only other molecules containing the COSH group whose gas-phase vibrational spectra have been studied are CH3COSH12J3and CF3COSH.31 There is general agreement on the assignment of the carbonyl stretching and HSC bending modes, but it is surprising that for CH3COSH the CS stretching and OCS bending modes, as assigned in ref 13, show no shift at all upon deuteration on the sulfur. The torsional band, on the other hand, shows an excessive shift upon deuteration, from 451 to 299 cm-l, compared with the present results for HCOSH. Only one conformer of CH3COSHis observed.34 Unfortunately, the torsional band for CF3COSH was not assigned. In the latter molecule the 0-trans rotamer is stabilized by an interaction between the hydrogen and the in-plane fluorine atom, and both the 0-cis and 0-trans rotamers are observed in the liquid phase. A similar stabilization of the cis (0-trans) rotamer of HCOSH occurs in solution, such that NMR measurements yielded a cis-trans ratio of l . l l : l . 5 The potential barrier of 43.2 (1.8) kJ/mol, considering the solvent effects, is in agreement with the gasphase barrier determined in the present work. The vibrational spectrum of vinylmercaptan, CH2CHSH, which is isoelectronic to HCOSH, has been measured by Owen and McDonald.16 For this molecule a trans rotamer and a gauche rotamer have been established from rotational ~ p e c t r a , ~ ~ and - ~ 'the vibrational spectrum is rather different from that of HCOSH in the region of the CSH-group vibrations. The presence of the gauche rotamer indicates a large V, term in the torsional potential, suggesting a closer analogy with butadiene and acrolein then with HCOSH.38 Data obtained so far for dithioformic acid, HCSSH,39!40 indicate that the torsional potential function is similar to that of HCOSH. Structural data for HCSSH allow a good estimate of the structure of the thion form, HCSOH. A semiempirical calculation of the relative energies of cis and trans, thiol and thion isomers of HCOSH and CH3COSH41 led to ambiguous results. However, a careful search of both the vibrational and pure rotational spectra have yielded no trace of the thion form, HCSOH. A lower limit for the ground state of HCSOH may be given as 1200 em-l above the ground state of trans-HCOSH.
Acknowledgment. The isotopically substituted species of formic acid used in the preparation of HCOSH were purchased through the grants to Dr. Gisbert Winnewisser, Max Planck Institut fur Radioastronomie, Bonn. The Perkin-Elmer 225 was made available by the Institut fur Organische Chemie, Justus-Liebig-Universitat Giessen. We are grateful to Chemical Laboratory V, University of Copenhagen, for the use of the RIIC interferometer, and to Dr. F. Nicolaisen for help in using the instrument. Drs. G. 0. Sorensen and N. W. Larsen of the same laboratory and Dr. C. J. Nielsen, Department of Chemistry, Univer-
Winnewisser and Hocking
sity of Oslo, are thanked for making their programs available. We thank Polytec GmbH and Bruker Physik AG for the opportunity to record spectra on their interferometer systems. Lastly, B. P. W. thanks Chemical Laboratory V of the University of Copenhagen for the opportunity to carry out part of this work in that laboratory.
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