Vibrational Spectrum, Force Field, and Torsional Potential Function of

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.

1771

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

1772

Winnewisser and Hocking

The Journal of Physical Chemistry, Vol. 84, No. 14, 1980

TABLE I: Fundamental Vibrations (in em-') Observed for Monothioformic Acid HCOSH

HI3COSH

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

924.2 400.3

912.3 398.0

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

DCOSH

HCOSD

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

921.gb 399.0

772.0 392.0

917.0 319.5

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'

912.3' 382.0

921.gb 383.0

772.0c 377.3

917.0' 299.1

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

--

HC'*OSH

HVOSH

HCOSH

DCOSH

HCOSD

__.--

vlcm-'

a

v/cm-'

assignmt

assignmt

u/cm-'

assignmt

u/cm-'

assignmt

u/cm-'

assignmt

Superscripts specify cis or trans rotamer, and lack of superscript indicates both rotamers.

I

4000

3000

"000

1500

1000 '

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%.

1774


Winnewisser and Hocking

100

-

-s 100o W 0

z < c i-

P

w

z

o

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.

2900 80,

I

I

I

I

2800 cm-l I

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

\M’’\/!U’ 5

o r

I

,

,

,

.

’

Tom -1


Vibrational Spectrum of HCOSH

: E""-

1

lL00

I

I

HCOSH

W

1775

I

I

I

I 1350

I

I

I

1

I

1300

-

E M

I n z

Y

HCOSH, HPOSH

l t ( r

10 TORR

38 TORR

i

80

z U

a

-

t

L

DCOSH I 1100

I 1050

I

I

1 crn-1

I 10001

Flgure 5. The region of the v, absorption band of HCOSH and DCOSH.

Ln

z I

Ht3COSH 0

700

650

LJJ 1 20 T O R R

'1

7b0

1 650

'

1

,

.

,

1

6oo

10 TORR

1

12 TORR 101

'

'

I

650

Figure 7. The region of the species studied.

I

900

850

800

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

600

,

,

/

1 ~

/

cm-1

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

1776


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

trans

cis

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' '

a'

s,

S, = 6rCH s, = 6rSH s, = 6rc0 S,=Sr

s,=

= 'TH-COS 8, = ' / z ( A 7 0 C S H

+

+

A~HCSH)

(l?$/')(SY,

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.

- ST,)

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

v3 v4

VS 6'

v7 V8

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

(0.0)

(0.0)

HCOSD (2.5)d

(2.5)

(0.0)

(0.0) (0.0)

-14.6 -44.0

(0.0)

14.7

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

15.9

DCOSH



TABLE V: Centrifugal Distortion Constants (in kHz) of the Two Rotamers of Monothioformic Acida

--

HCOSH~

HWOSHC

HC’*OSHC

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)

HCO~SH~

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)

DCOSH~

HCOSD~

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

cis

trans-cis

a’

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)

a’’

F & J (mclyn A /radz) F,,,/(mcl?jn A/radz)

0.36565(89) 0.07290(31)

0.37258(101) 0.06998(48)

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,

+

1778


Winnewlsser and Hocking

TABLE VII: Deviations (Obsd - Calcd) for the Force Fields Given in Table VI HCOSH Vl V2

v3 v4

v5 '6

v7 V8

v9

V 8

v9

HL3COSH

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

1.3 0.1

1.2 -0.6

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

0.2 1.7

-0.5 0.8

HC"0SH Trans (in cm-l) -3.8 -0.0' -0.6 -0.1 2.1 0.9 10.Bb 0.6' 0.2

DCOSH

HCOSD

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

2.8 -0.4

-4.8 0.1

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

6.8 -1.7

-5.5 -0.4

-0.8' 1.6

HCO%H

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

HCOSD

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

0.9566 0.9429

0.5265 0.5168

0.014

0,010

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



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

Vibrational Spectrum, Force Field, and Torsional Potential Function of

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