6528
J . Phys. Chem. 1988, 92, 6528-6536
Vibrational Spectra and Scaled ab Initio Harmonic Force Field for Thietane and Several Deuterlated Isotopomers R. Anthony Shaw, Cristina Castro, Nan Ibrahim, and Hal Wieser* Department of Chemistry, University of Calgary, Calgary, Alberta, Canada T2N 1 N4 (Received: December 29, 1987; In Final Form: April 26, 1988)
The vibrational spectra are reported for thietane and four deuteriated isotopomers, and a harmonic force field derived by scaling 3-21G ab initio force constants to fit the observed fundamental transition frequencies. Of the 115 calculated transitions (excluding the highly anharmonic puckering mode), 97 are assigned in the experimental spectra, and the observed frequencies reproduced by the force field with an average error of 8.8 cm-' (6.4 cm-I excluding the C-H stretches). The scaling factors are compared to those previously derived for oxetane following the same procedure, and their transferability is discussed.
Introduction Ab initio methods have been demonstrated to be invaluable in determining the vibrational force fields for a number of molecules with a degree of accuracy unattainable for any but the smallest using conventional empirical procedures.' While commonly used split-valence basis sets overestimate the diagonal force constants, yielding vibrational frequencies generally on the order of 5-1 5% higher than experimental values, the off-diagonal coupling constants, which are difficult or impossible to determine from experimental data alone, are calculated very accurately.'J The force field may be corrected by first evaluating the force constants for a nonredundant set of local symmetry coordinates, either directly or through appropriate transformation of Cartesian force constants, and then scaling down the ab initio values so as to optimize agreement between observed and calculated frequencieL2 One commonly used scaling procedure, which we have adopted for this study, adjusts the a b initio force constants Kij according where Ciand Cj denote scaling factors for to Fij = ( CiCj)1/2Kij, coordinates i and j , and Fij is the scaled force constanL3 Typically the vibrational coordinates are divided into groups according to type (e.g., C-C stretches, CH2 deformations, etc.), with separate factors assigned to each group. The scaling factors thus effectively replace the individual force constants as variables that must be specified in predicting and refining the calculated vibrational frequencies. Our experience for the 3-21G basis set parallels other reports for the 4-21G and 4-31G bases in that reasonably good transferability may be expected of optimized factors. For example, the scaling factors for the CH3 symmetric deformation mode refines to values of 0.77, 0.78, and 0.78 for the 3-21G basis set, as determined by independent refinements to fit the observed frequencies of propane, ethane, and dimethyl ether, re~pectively.~While such observations are encouraging, we have also encountered a number of instances for which the scaling factor for a given coordinate type may vary substantially according to chemical or geometrical influences upon the relevant moiety. For example, the factors refined individually for the (Y- and P-CH2 wagging modes of oxetane assume values of 0.814 and 0.753 r e s p ~ t i v e l y and , ~ the optimized factor for the out-of-plane deformation is 0.750 for propene5 and 0.663 for norbornadiene/norbornene.6 For full exploitation of the predictive ability of scaled ab initio force fields as a guide to assigning the spectra of moderately complex molecules, it is essential that such differences be recognized and accounted for in the selection of the initial scaling ( I ) (a) Fogarasi, G.; Pulay, P. Vibrational Spectra and Structure; Durig, J. R., Ed.; Elsevier: Amsterdam, 1984; Vol. 14, pp 125-219. (b) Fogarasi, G .; Pulay, P. Annu. Reu. Phys. Chem. 1984, 35, 191-243. (2) (a) Blom, C. E.; Slingerland, P. J.; Altona, C. Mol. Phys. 1976, 31, 1359-1376. (b) Blom, C. E.; Altona, C. Mol. Phys. 1976, 31, 1377-1391. (3) Pulay, P. Mod. Theor. Chem. 1977, 4, 153-185. (4) Shaw, R. A.; Ursenbach, C.; Rauk, A,; Wieser, H. Can. J. Chem. 1988, 66, 1318-1332. ( 5 ) Shaw, R. A.; Wieser, H., unpublished results. (6) Shaw, R. A,; Castro, C.; Dutler, R.; Rauk, A,; Wieser, H. J . Chem. Phys. 1988, 89, 716-731.
0022-3654/88/2092-6528$01.50/0
factors. This requirement in turn suggests the need for systematic evaluation of scaled force fields for a variety of molecules comprising or containing characteristic structural units, thus deriving scaling factors for transfer to more complex molecules that either contain or are closely related to those units. In this report we present a force field for thietane (Figure l), determined by scaling the 3-21G force constants to reproduce the observed spectra of the parent compound and four deuteriated isotopomers. Previous spectroscopic studies of thietane have focused primarily on the far-infrared region, where a sequence of transitions, corresponding to the fundamental of the inversion mode and several hot bands, is From these transitions a one-dimensional inversion potential function was derived, indicating that the molecule is nonplanar with a barrier to inversion of 272-274 cm-1.8-10 Combination bands involving sums and differences of the inversion mode with scissoring fundamentals have also been identified and assigned." The only previous attempt to assign the entire mid-infrared spectrum of the parent compound was by Scott et a1.I2 The present study confirms their assignments for the AI species ( C , symmetry was assumed in the original work) but differs significantly for the majority of other modes. No ab initio calculation of a harmonic force field for thietane has been attempted previously.
Experimental and Computational Details The syntheses of the deuteriated compounds were reported previously." The parent thietane was purchased from Aldrich Chemicals. The chemical purity of all compounds was verified by gas chromatography to be better than 95%. The infrared spectra were recorded by using a Nicolet 8000 FT-IR spectrometer. Vapor-phase spectra, displayed in Figures 2 and 3, were run at a nominal resolution of 0.12 cm-I, by using a Wilkes multipass cell, while the spectra of the neat liquids and solutions were run with the samples sandwiched between KBr plates or in a 0.1-mm cell (KBr windows), respectively. Typically 200-400 scans were accumulated for the vapor phase, and 500 scans for the solution and neat samples. The infrared spectra of the available neat liquids, displayed in Figure 4, are redrawn from the original plots. The Raman spectra of the neat liquids were run in capillary tubes by using a Jarrell-Ash triple monochromator and an Ar+ laser (Coherent Radiation) with 514.5-nm excitation. The spectra, displayed in Figure 5, also have been redrawn from the original plots. The measured peak positions for all spectra are summarized in Table I. (7) Durig, J. R.; Lord, R. C. J . Chem. Phys. 1966, 45, 61-66. (8) Borgers, T. R.; Strauss, H. L. J . Chem. Phys. 1966, 45, 947-955. (9) Wieser, H.; Duckett, J. A.; Kydd, R. A. J . Mol. Spectrosc. 1974, 51, 115-1 22. (10) Harris, D. 0.; Harrington, H. W.; Luntz, A. C.; Gwinn, W. D. J . Chem. Phys. 1966, 44, 3467-3480. ( 1 I ) Wieser, H.; Duckett, J. A. J . Mol. Spectrosc. 1974, 50, 443-456. (12) Scott, D. W.; Finke, H. L.; Hubbard, W. N.; McCullough, J. P.; Katz, C.; Gross, M. E.; Messerly, J. F.; Pennington, R. E.; Waddington, G. J . Chem. Phys. 1953, 75, 2795-2800.
0 1988 American Chemical Society
The Journal of Physical Chemistry, Vol. 92, No. 23, 1988 6529
Spectra and Scaled 3-21G Force Field for Thietane
23
d6 24
'9
a\
I
17 Figure 1. Atom numbering and coordinate definitions for thietane.
nII
6
I
I
I;
I
21
d6
i
'P
(16
a-d,
/1u 26
I
zdoo
26-75
ziso
2225 UFtVENUMBERS
URVENUMBERS
I
in
Figure 3. Infrared spectra in the C-H and C-D stretching regions of thietane and isotopomers in the vapor phase.
I
IO-,
-13
I1
I
d6 25 WRYENUMBERS
Figure 2. Infrared spectra from 400 to 1500 cm-I of thietane and isotopomers in the vapor phase.
The ab initio geometries were optimized, and Cartesian force constants evaluated by using the GAUSSIAN 82 program13 as implemented on the Cyber 205 supercomputer at the University of Calgary.I4 The subsequent steps, viz., transforming the Cartesian force constants to local symmetry coordinates and optimizing the scaling factors to reproduce observed frequencies, were achieved with programs written in our laboratory. For all refinements the u ~ ,weighted by observed frequency parameters, Xi = 4 7 ~ ~ 2were 1/X;(obsd). The optimized structural parameters and local symmetry coordinate definitions are listed in Tables I1 and 111, respectively, with the atoms defining the geometry and coordinate definitions numbered as in Figure 1.
a, a'
- d,
d
m
7
I7
B 'd,
Results and Discussion The optimized 3-21G structure is in accord with previous ex-
10
1
perimentalL5and molecular orbitalI6 studies of thietane, all in(13) Binkley, J. s.; Frisch, M. J.; DeFrees, D. J.; Raghavachari, K.; Whiteside, R. A.; Schlegel, H. B.; Fluder, E. M.; Pople, J. A. GAUSSIAN 82; Carnegie-Mellon University: Pittsburgh, 1983. (14) Rauk, A.; Dutler, R. J. Comput. Chem. 1987, 8, 324-332. (15) Karakida, K.; Kuchitsu, K. Bull. Chem. SOC.Jpn. 1975, 48, 1691-1695.
400
'
6b0
'
800 ' 1000 ' 12'00 ' l 4 b ' 1dOO
CM-' Figure 4. Infrared spectra from 400 to 1500 cm-' of thietane and isotopomers in the liquid phase (redrawn). Weak unlabeled features for the deuteriated species may be possible unidentified impurities.
6530 The Journal of Physical Chemistry, Vol. 92, No. 23, 1988
Shaw et al.
TABLE I: Observed Infrared and Raman Bands (in cm-I) of Tbietane and Deuteriated Isotopomers infrared assigned infrared peak” vaporb liquid Raman sym species peak” vaporb liquid Thietane a’ 14 1 529.0s 527.0s 528 vs, p 1182.5s 1190 S, sh 2 677.0s, B 672.3s 670 s a” 15 1224.1s 700.0s 699.5m 699 s, p a’ 16 1229.4s, B 1223.4s 3 4 734.4w 17 1232.3s 756.1 m 18 1281.2m, B 5 1271.6s 19 772.1m 1446.8s 1438.4s 6 7 841.3m 845 m,p a’ 20 1470.3m 845.1s 1459.9m 8 933.2w 936 (sh) 935 ws,p a’ 21 2875.5m 9 956.7m 22 2903.2w 2924.8m IO 975.3s 966.4s 974 m a’ 23 1006 sh a” 24 11 1010.8w 2946.0m 1087.8w 25 12 2971.5s 1164.7s, B 1165.9s 2994.1vs 13 a’’ 26
-
1
2 3 4 5 6 7 8 9 IO
11 12 13 1
2 3 4 5 6 7 8 9 IO 11 12 13 14
15
507.9s
508.6s
620.5s 638.0m, B 736.5m, B 763.5m
623.1m 637.7m 731.3m 755.0m
830.5m
828.5w
860.5m, B 994.5s, B 1025.8w 504.2s 627.2s 658.5s, B 722.4m 802.2m 831.4m, B 897.9w 957.1s 1076.7w,B,sh 1086.9s 1124.0m, B 1131.1 m
858.4s 990.0vs 1004.7w 1020.7m 505.2m 627.5m 656.9m 760.6s 787.6s 834.2m 898.7m 950.1m 1076.5m 1083.0m 1114.7m
509 s, p (589 ww) -630 m, sh, p 641 s
755 m,p 815 w,sh 829 ws,p 842 w,sh 859 w,sh 991 w 1020 w
505 s, p 628 m,p 656 m
Thietane-cr,a’-dp a’ 14 a” 15 a’ 16 a“ 17 a” 18 a‘ 19 a’ a” a” a’
Thietane-P-d2 a’ 16 a’ 17 a“ 18
729 w
a”
792 s, p 832 m 896 ws,p 922 w,sh
a’ a” a’ a” a’ a“ a‘ a”
1083 w,p
20 21 22 23 24 25 26
19 20 21 22 23 24 25 26 21 28 29 30
1057.9s 1091.1m,B 1123.6s 1130.6m 1184.4m, B 1272.9s, B 1454.9s 2151.8s, B 2191.5m 2248.7s 2880.4s 2946.3s 2972.7s
1048.6w 1084.5s 1 1 17.8m
1154.9s 1185.1vs, B 1220.6m 1467.4s 2119.1s 2133.6 s 2194.5 m 2230.5 s 2245.4s 2879.7s, B 2913.3w 2954.5 s, B 2957.2s 2981.8s 2989.4m
1148.6sh 1180.6m
1074.8s 1107.2w,B 1136.4w 2100.3w 2128.2m 2141.8sh 2161.3s, B 2170.0m 2190.2w 2238.2s 225I .7s
1182.5w 1264.7vs 1447.6m
1452.7m
Raman
assigned sym species
1181 w
a‘ a’
1226 w
a‘’
(1283 ww) 1439 m 1461 w 2891 m 2906 s
af’ a’ a’
2942 s -2970 m, sh
a’ a’ a’
1086 w Ill9 m, p 1180 w 1450 vw 2142 vs 2181 s 2240 m 2867 m 2939 s 2961 m, sh 1145 ww 1217 w w 1453 m 2117 s
a’
a’ a’‘ a’ a” a’’ a’ a” a’ a’ a‘ a’ a” a’ a‘ a‘
2191 w,br 2237 w a’
2875 m 2914 m
a’
2961 s
(a‘‘)
2990 m
a’
1067.7s
1062 w
1131.4m
1114vw 1130 p 2095 m
a‘ a” a’
Thietane-d, 1
2 3 4 5 6 7 8 9 10 11 12
470.6s 579.5s
476.7m 573.7m
645.7s, B 722.3s 741.7s
640.6m 719.1m 733.6m
814.4s
812.3w
965.4vs, B
1005.1s 1054.8m, B
959.5s 998.7m 1049.9m
481 w,p 574 s, p 598 vw,sh 641 m 122 m 732 m, p 766 w 813 ws, p 904 w 955 w 992 w,p
a‘ a’ a” a” a‘ a’ a’’ a‘ a” a” a’ a”
13 14 15 16 17 18 19 20 21 22 23 24
2123 w,sh 2133 m 2162 vs 2244 s 2274 w
a’ a” a’ a‘ a‘
Thietane-a-d2
1 2 3 4 5 6 7 8 9 IO 11
12 13
516.9s 631.0m 660.9m, B 703.2m 759.9m 827.5m 847.7s 952.1 w 975.9m 1011.7s, B 1105.2m, B 1126.8s 1187.0w
513 s, p 535 m, sh, p 653 s 696 w 753 m, p
840 vs, p 948 s, p 999 m 1098 m, p 1123 m (1195 vw)
14 15 16 17 18 19 20 21 22 23
24 25
1226.7s, B 1276.4s, B 1446.7s 2150.6s, B 2227.7m 2257.3s 2876.5s 2909.8vw 2946.5s 2970.6s 2992.6s
1222 w (1267 vw) 1442 m 1454 m, sh 2151 vs 2222 s 2257 m 2871 rn 2902 m 2941 vs 2966 m.sh
“Correspond to infrared or Raman bands labeled in Figures 2-6. bobserved band contours are A, C, or A / C hybrid, unless designated as B.
The Journal of Physical Chemistry, Vol. 92, No. 23, 1988 6531
Spectra and Scaled 3-21G Force Field for Thietane
TABLE 111: Local Symmetry Coordinate Definitions for Thietane
coord no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14
d6
a -d,
a,a'- d4
definition' C2-S1 C4-S1 C3-C2 C3-C4 C2-H5 C2-H6 C3-H7 C3-H8 C4-H9 C4-H10
+ + +
19 20 21 22 23
5a(5-2-6) y(1-2-3) 5a(9-4-10) y(3-4-1) p(1-2-5) @(1-2-6) - b(3-2-5) - fi(3-2-6) b(1-4-9) p(1-4-10) - p(3-4-9) o(3-4-10) a-CH, rock b(1-2-5) - p(1-2-6) p(3-2-5) - p(3-2-6) a-CH2 rock p(1-4-9) - p(1-4-10) b(3-4-9) p(3-4-10) a-CH2twist p(1-2-5) - p(1-2-6) - p(3-2-5) b(3-2-6) a-CH2 twist p(1-4-9) - @(1-4-10) - b(3-4-9) p( 3-4-1 0) @-CHIscissor 5a(7-3-8) y(2-3-4) @-CHIwag p(2-3-7) p(2-3-8) - b(4-3-7) - fi(4-3-8) P-CH2 rock p(2-3-7) - b(2-3-8) + b(4-3-7) - j3(4-3-8) P-CH, twist p(2-3-7) - p(2-3-8) - j3(4-3-7) p(4-3-8) ring y(2-1-4) - y(1-2-3) ~(2-3-4) - ~(3-4-1)
24
deformation ring pucker r(1-2-3-4)
15 16 17 18
P-d2
type C-S stretch C-S stretch C-C stretch C-C stretch a-CH stretch a-CH stretch 0-CH stretch 0-CH stretch a-CH stretch a-CH stretch a-CH, scissor a-CH2 scissor a-CH2wag a-CH2wag
+
+ +
+ +
+ +
+
+
- ~(2-3-4-1)
+ ~(3-4-1-2)
-
r(4-1-2-3) !I
il!II
'As suggested by: Pulay, P.; Fogarasi, G.; Pang, F.; Boggs, J. E. J . Am. Chem. SOC.1979, 101, 2550-2560. See Figure 1 for atom num-
bering and designation of angle deformations. TABLE I V 3-21G Scaling Factors
N
3 2 b ' 3dbo ' 2e'bo" 24bo ' 22bo ' 20W?600
1LOO
1200 low' BdO
'
600
'
4b0
CM-' (redrawn). TABLE II: Optimized 3-21G Structural Parameters for Thietane
c-s c-c
C2-H6 C2-H5 C3-H8
C3-H.7 S-C2-H6 S-C2-H5 C3-C2-H6 C3-C2-H5 HJ-C~-H~ C&-HS CZ-C3-H7 H&-Hs
c-s-c s-c-c c-c-c gr
electron diffractionb
4-4-21GC
3-2 1G
1.847 1.549 1.09 1.09 1.12 1.12
1.859 1.560 1.078 1.077 1.079 1.080
d d
e e e e
1.922 1.555 1.077 1.076 1.08 1 1.080 109.7 112.6 113.7 116.0 111.3 114.1 110.5 109.5 75.1 92.1 97.8 18.3
d
d 112 d d 114 76.8 90.6 95.6 26
rfnmnt
2nd rfnmnt
oxetaneb
1.057 0.968 0.792 0.812 0.802 0.798 0.853 0.796 0.786 0.767 0.810 0.773 0.742 O.97Oc
1.048 (11) 0.960 (12) 0.804 (5) 0.815 (6) 0.802 (9) 0.799 (7) 0.957 (20) 0.795 (10) 0.786 (10) 0.762 (10) 0.772 (19) 0.757 (12) 0.743 (1 1) 0.97oC
0.885 (C-O) 1.013 O.81Odve 0.810d-c 0.777 0.814 0.849 0.819 0.792 0.753 0.788 0.765 0.802 O.97Oe
1st
Figure 5. Raman spectra of thietane and isotopomers in the liquid phase
parametera
thietane ~~
109.9 e
e
108.9 77.7 13.3
a Bond lengths in angstroms, bond angles in degrees; atom numbering defined in Figure 1. Reference 15. Reference 16. Assumed to obey imposed constraints. Reported as equilibrium twisting, rocking, and wagging angles. 'Puckering angle defined as the angle between the CSC/CCC diagonals.
dicating that the ring adopts a puckered C, conformation. The normal coordinates thus divide into 14 a' and 10 a" modes, with the former anticipated to give rise to A/C and the latter B contours (16) Skancke, P. N.; Fogarasi, G.; Boggs, J. E. J . Mol. Strucf. 1980,62, 259-213.
coordinate transferred C-S stretch 1.04c C-C stretch 0.97 0.809 a-CH stretch 0.809 @-CHstretch a-CH2scissor 0.787 a-CH2 wag 0.76 0.80 a-CH2rock a-CH, twist 0.77 @-CHIscissor 0.787 P-CH, wag 0.76 0.80 p-CHz rock P-CH, twist 0.77 ring deformation 0.82 ring pucker 0.97
a Transferred from pr~pane,~ cy~lobutane,~ and o~etane;~ see text. bShaw, R. A,; Wieser, H., unpublished result^.^ See also ref 18 for a scaled 4-21G force field for oxetane. cAdjusted to fit the C-S (a") stretching frequency of thietane; see text. "The C-H stretching region was not included, and hence the scaling factor not optimized in that study. eScaling factor held fixed in refinement.
in the vapor-phase infrared spectra. The present 3-21G ab initio calculation indicates a dihedral angle of 18.3O, which falls between previous ab initio (13.3O) and experimental (26O) values. Probably the most serious deficiency of the 3-21G structure is the apparent overestimation of the C-S bond length, which must result from the neglect of polarization functions on sulfur. The assignment of the spectra was approached in three stages. The first two involved assigning the mid-infrared region on the basis of predicted and subsequently refined frequencies. The C-H and C-D stretching region was then analyzed separately. Mid-Infrared Assignments. The analysis of the mid-infrared spectra is complicated by the influence of the highly anharmonic puckering coordinate, which particularly affects the accuracy of calculated frequencies for the CH2 rocking and, to a lesser degree,
Shaw et al.
6532 The Journal of Physical Chemistry, Vol. 92, No. 23, 1988
TABLE V Observed and Calculated Frequencies (in cm-') of Thietane and Deuteriated Isotopomers U peak" obsdb calcd l C calcd 2d calcd 3' approx description' Thietane 1 2994.1 3024.0 2996.4 3017.1 0.88 stretch (b,) + 0.1 1 @-CHIstretch 26 2971.5 2968.3 stretch (b,) + 0.11 a-CH, stretch 25 2 2967.6 2977.1 0.87 2959.2 2946.0 24 3 stretch (a,) + 0.10 a-CH2 stretch 2934.0 2952.9 0.88 2922.5 4 2922.3 2932.7 2903.2 22 0.89 stretch (a,) + 0.09 P-CH, stretch 1469.2 0.67 1470.3 1476.2 1476.2 20 5 scissor + 0.33 @CH2 scissor 1444.4 0.69 1449.9 1449.8 19 6 1451.6 scissor + 0.33 a-CH2 scissor 1201.6 7 1224.1 1227.3 1227.1 15 a - c H , wag 1178.4 1197.1 1202.6 14 0.45 a-CH, twist + 0.15 a-CH2 rock 8 1182.5 10 0.37 a-CH2 rock + 0.34 a-CH2 twist 9 975.3 943.2 950.0 963.4 10 933.2 p 916.1 C-C stretch 8 928.1 930.6 11 818.7 0.32 C-S stretch + 0.26 @-CHIrock 7 845.1 p 813.2 814.1 12 701.2 3 0.44 C-S stretch + 0.36 @CHI rock 700.0 p 710.1 711.0 13 547.7 ring deformation 1 529.0 p 532.5 532.5 14 113.2 pucker 113.4 113.6 15 3020.3 a-CH, stretch (a,) (2994.1) 2988.2 3011.8 16 2959.7 a-CH, stretch (b,) 2926.4 2949.6 1440.4 17 1454.2 1454.3 a-CH2 scissor 1269.8 18 1281.2 B 1276.9 1274.3 18 @-CHIwag 1216.3 0.43 P-CH, twist + 0.28 o(-CH2wag 19 16 1229.4 B 1227.0 1223.5 1148.3 20 13 a-CH, wag 1164.7 B 1170.3 1169.2 1005.9 21 11 a-CH, twist 1010.8 1019.5 1017.1 22 C-C stretch 985.3 987.8 986.4 23 a-CH, rock 760.6 783.1 822.7 677.0 2 677.0 B 24 C-S stretch 682.3 679.3
.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
26 25 23 21 20 16 14 13 8 6
2972.7 2946.3 2248.7 (21 50.5)
3
620.5 507.9 p
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
30 26 24 20 19 18 16 13 11 9 7 3
1
23 21 19 18 15 11 10
5 4 2
1
1454.9 1123.6 p 1057.9 1025.8 830.5 p 756.5 p
(2248.7) 2151.8 B 1272.9 B 1184.4 B 1091.1 B 994.5 B 860.5 B 736.5 B 638.0 B
(589 R) 2989.4 2913.3 2245.4 2119.1 1467.4 1220.6 1154.9 1086.9 p 957.1 897.9 p 802.0 p 627.5 p 504.2 p
30
(2989.4) (2954.6 B)
17 14 12 10 8 5 3
1185.1 B
1124.0 B 1076.7 B 922 R 831.4 B 729 R 658.5 B
2970.0 2923.5 2249.0 2150.5 1460.0 11 14.2 1043.9 1013.2 823.6 740.8 690.8 617.2 521.4 99.0 2246.9 2145.5 1260.2 1179.1 1087.7 987.9 852.2 728.3 640.2 590.8
Thietane-a,a'-d, 2974.9 2981.3 2928.4 2934.6 2225.3 2242.7 2128.0 2144.6 1459.1 1458.7 1122.9 1121.7 1056.8 1054.7 1019.1 1018.6 83 1.7 830.0 742.3 739.2 698.8 711.7 626.8 632.5 510.4 512.2 99.2 99.5 2223.2 2240.6 2122.9 2139.5 1265.7 1262.0 1182.3 1173.5 1096.1 1095.2 994.6 992.8 867.4 867.1 740.5 741.0 646.0 644.5 609.0 640.6
@-CHIstretch (b,) P-CH, stretch (al) a-CD, stretch (b,) a-CD2 stretch (a,) P-CH, scissor 0.65 a-CD2 scissor 0.34 C-C stretch P-CH, rock 0.42 a-CD2 wag 0.30 a-CD2 scissor 0.38 C-C stretch 0.34 a-CD2 wag 0.35 a-CD, twist + 0.20 C-C stretch 0.37 a-CD2 twist + 0.36 a-CD2 rock 0.35 C-S stretch + 0.28 a-CD2 rock ring deformation pucker a-CD2 stretch (a,) a-CD, stretch (b,) P-CH, wag P-CH, twist 0.69 a-CD2 scissor 0.27 C-C stretch 0.43 C-C stretch 0.31 a-CD2 scissor a-CD2 wag a-CD2 twist C-S stretch a-CD, rock
3021.1 2959.9 2207.1 2125.9 1454.2 1198.5 1145.3 1085.6 904.3 891.4 793.1 623.5 522.2 103.2 3020.2 2957.9 1440.3 1 159.3 1111.9 1064.9 889.9 841.7 709.0 660.8
Thietane-P-d, 2989.0 3012.6 2928.4 2951.5 2210.8 2215.5 2129.4 2133.9 1467.8 1467.9 1223.9 1224.0 1163.1 1170.5 1086.9 1086.5 922.0 951.3 895.0 892.6 784.5 781.5 628.0 624.2 510.2 510.1 103.3 103.4 2988.2 3011.8 2926.4 2949.6 1454.1 1454.2 1187.0 1187.4 1118.4 11 19.8 1076.8 1075.8 903.3 922.2 845.8 844.9 721.5 734.8 666.2 664.1
a - C H 2 stretch (b,) a-CH2 stretch (a,) P-CD, stretch (b,) P-CD, stretch (al) a-CH2 scissor a-CH2 wag a-CH, twist P-CD, scissor 0.56 a-CH, rock + 0.35 a-CH2 twist C-C stretch 0.57 C-S stretch + 0.29 ring deformation 0.52 P-CD, rock + 0.26 C-S stretch ring deformation pucker a-CH2 stretch (a,) a-CH2 stretch (b,) a - C H 2 scissor a-CH, wag 0.38 C-C stretch 0.33 P-CD, wag 0.41 a-CH2 twist + 0.41 C-C stretch 0.46 a-CH2 rock + 0.29 a-CH2 twist 0.53 P-CD, wag + 0.21 C-C stretch 0.59 P-CD2 twist + 0.41 a-CH2 rock C-S stretch
+
+
+
+
+
+
(b,) (b,) (a,) (a,)
The Journal of Physical Chemistry, Vol. 92, No. 23, 1988 6533
Spectra and Scaled 3-21G Force Field for Thietane
TABLE V (Continued) U
peak"
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
23 22 20 18 15 13 11
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
obsdb 2251.7 2238.2 2170.0 2141.8 1136.4~ 1074.8 1005.0 p
8 6 5 2 1
814.4 p 741.7 p 722.3 579.5 p 470.6 p
23 19 14 12 10 9 7
(2251.7) 2161.3 B 1107.2 B 1054.8 B 965.4 B 904 R 766 R
4 3
645.9 B (598 R)
25 24 23 22 20 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
2992.6 2970.6 2946.5 2909.8 2257.3 2150.6 (1454 R) 1446.7 1276.4 B 1226.7 B 1187.0 1126.8 1105.2~ 1011.7 B 975.9 p 952.1 847.7 p 827.5 759.9 p 703.2 660.9 B 631 .O 516.9 p
calcd l e
calcd 2d calcd 3e Thietane-d6
2249.6 2206.3 2153.0 2123.2 1135.5 1068.3 987.8 955.9 807.3 718.0 687.5 578.1 479.4 91.5 2246.5 2145.5 1117.6 1045.6 946.0 901.9 768.7 71 1.7 636.2 570.2
2226.9 2209.0 2137.1 2120.2 1140.8 1069.3 998.2 970.4 8 12.0 721.9 694.7 577.1 475.4 91.7 2222.8 2122.8 1121.1 1053.7 961.3 908.5 776.8 722.2 642.1 585.7
3022.2 2968.9 2958.7 2922.9 2247.9 2148.0 1464.2 1442.8 1265.6 1210.9 1173.3 1121.6 1097.4 1001.5 965.7 938.0 839.5 785.6 753.2 682.8 650.8 613.6 53 1.6 106.1
2993.0 2970.6 2932.0 2923.6 2224.3 2125.4 1468.9 1450.9 1272.1 1225.2 1192.2 1133.7 1106.8 1007.0 969.7 952.7 848.5 794.7 760.0 692.0 657.0 626.2 519.9 106.4
3014.6 2979.0 295 1.4 2933.6 2241.7 2142.1 1468.7 1450.8 1269.4 1223.5 1191.3 1131.0 1106.0 1005.1 970.8 958.1 847.3 814.1 759.8 695.7 661.2 640.9 521.4 106.7
10.1 57
5.5 57
6.5 75
2243.7 2214.3 2149.1 2139.5 1139.4 1069.6 997.5 977.5 810.8 725.8 701.0 576.8 477.5 91.9 2240.3 2139.5 11 18.5 1052.7 960.4 909.6 776.3 720.9 641.9 610.3
Thietane-a-d2
overall av error/cm-' no. of assigned transitions
approx description'
+
0.96 a-CD2stretch (b,) 0.03 &CD2 stretch (b,) 0.97 P-CD2stretch (b,) 0.03 a-CD2 stretch (b,) 0.76 a-CD2stretch (a,) + 0.23 @-CD2stretch (a,) 0.77 @-CDzstretch (a,) 0.24 a-CD2stretch (a,) 0.40 a-CD2scissor 0.39 C-C stretch 0.54 /3-CD2scissor 0.43 a-CDz scissor
+ +
+ +
a-CD2 wag fi-CD2rock + 0.24 a-CD2 twist C-C stretch + 0.20 a-CD2wag a-CD2twist + 0.20 a-CD2rock a-CD2 twist + 0.20 ring deformation C-S stretch + 0.28 @CD2rock ring deformation + 0.33 j3-CD2 rock pucker a-CD2 stretch (az) a-CD2 stretch (b,) 0.65 C-C stretch + 0.33 a-CDz scissor 0.58 a-CD2scissor + 0.32 /3-CD2 wag o(-CDzwag P-CD2twist 0.33 (3-CD2wag + 0.27 a-CD2wag a-CDz twist C-S stretch o(-CD2rock
0.24 0.41 0.49 0.20 0.33 0.49
+ + + +
0.80 a-CH2 stretch (as) 0.20 &CH2 stretch (as) 0.82 j K H 2 stretch (as) 0.20 a-CH2 stretch (as) 0.56 @CH2stretch (s) 0.44 a-CH2 stretch (s) 0.56 a-CH2 stretch (s) 0.44 fi-CH2stretch (s)
CD2 stretch (as) CD2 stretch (s) 0.56 a-CH2scissor + 0.44 &CH2 scissor 0.58 j3-CHz scissor + 0.43 a-CH2scissor @-CHIwag 0.48 a-CH2 wag + 0.25 0-CH2 twist 0.49 a-CH2 wag + 0.20 8-CH2 twist 0.32 &CH2 twist + 0.24 a-CH2 twist 0.66 CD2 scissor + 0.25 C-C stretch (3) 0.31 CD2 wag + 0.31 C-C stretch (3) C-C stretch (4) 0.36 a-CH2twist + 0.29 C-C stretch (4) 0.39 CD2 wag + 0.31 C-C stretch (3) a-CH2rock 0.28 CD2 twist + 0.27 C-S stretch (2) 0.50 CD2 twist + 0.17 C-S stretch (2) 0.39 C-S stretch (2) + 0.28 CD2 rock 0.46 C-S stretch (1) + 0.30 CD2 rock ring deformation pucker excluding C-H and C-D stretching regions
#Correspond to infrared or Raman bands labeled in Figures 2-5. bVapor-phaseband positions unless otherwise indicated. R means that the band is observed in the Raman spectrum only. Frequencies in parentheses depict uncertain band positions. Italic type indicates transitions included in initial refinement of scaling factors; designations p and B, respectively, label transitions that give rise to polarized Raman lines or exhibit B contours in the vapor-phase infrared spectrum. Calculated with transferred scaling factors (cf. Table IV). dCalculated upon first refinement of scaling factors (cf. Table IV). eCalculated upon second refinement of scaling factors (cf. Table IV). 'As inferred from potential energy distribution. twisting modes. Previously published scaled 4-2 1G force fields for c y c l o b ~ t a n eand ' ~ oxetaneI8 demonstrate the importance of this influence. In each case the rocking mode belonging to the same symmetry species as the puckering mode is calculated with an unusually large deviation from experimental frequencies, Le., up to 40 cm-I, while the rocking modes belonging to other symmetry species are reproduced with the degree of accuracy normally expected. We anticipated therefore that the calculated frequencies for normal coordinates containing significant contributions from the CH2 rocking vibrations might be less accurate than others and that in fitting the observed band positions the associated scaling (17) Banhegyi, G.; Fogarasi, G . ;Pulay, P. J . Mol. Struct. 1982.89, 1-13. Pulay, P.; Fogarasi, G . Spectrochim. Acta, Part A
(18) Banhegyi, G.; 1983, 39A, 761-769.
factors might deviate significantly from the transferred values. The initial prediction of vibrational frequencies was accomplished by transferring scaling factors previously optimized for p r ~ p a n e cyclobutane? ,~ and oxetaneS (Table IV). In the initial set, the factors for cy- and /3-CH2 bending modes were assumed to be equivalent, as we have no a priori information about the effect of sulfur substitution in the ring. The factors we have chosen are those for the @-CHImodes of oxetane, with minor adjustments where suggested by comparison with the corresponding factors optimized for propane and cyclobutane. The C-H stretching factor of 0.809 was transferred from cyclobutane and is appreciably lower in magnitude than the same factors optimized for propane and ethane (-0.835). No scaling factor was available for the C-S stretching coordinate. As a starting point a value of 0.9 was chosen as an average
6534 The Journal of Physical Chemistry, Vol. 92, No. 23, 1988
of the values for the C-C and C-0 stretches in oxetane. The lowest frequency a” mode, u2+ of thietane corresponding to the asymmetric C-S stretch clearly gives rise to a prominent B contour in each isotopomer. The starting value of 0.9 was corrected by multiplying with the square of the ratio of observed (677.0 cm-’) 4 thietane (the to calculated (629.9 cm-I) frequencies for ~ 2 of results of the calculation using 0.9 for the C-S scaling factor are not included here). The resulting factor of 1.04, equal to 0.9(677.0/629.9)2, was then used to determine the first set of frequencies listed under calculation 1 in Table V. The two most helpful experimental guides in assigning the spectra were polarized Raman lines and vapor-phase infrared band contours. Specifically a number of B bands could be readily identified as a” vibrational modes. On this basis, 35 assignments could be confirmed immediately for thietane and the three symmetrically deuteriated isotopomers. These transitions are designated p (Raman polarized) or B (B contour) in Table V. Moreover, the positions of these bands calculated with the transferred scaling factors (calculation 1) were sufficiently accurate that the predicted frequencies for other modes could be used reliably as guides for further assignments, particularly for the a-d, isotopomer. All included, 57 observed bands were assigned with an error of 10.1 cm-l on the basis of the predicted frequencies alone. These vibrations are indicated by italic type in Table V. Following this stage the scaling factors were least-squares fit to the observed frequencies to enhance the reliability of predicted band positions for as yet unassigned modes. The average error was thereby reduced to 5.5 cm-I. The calculated frequencies appear in Table V under calculation 2, and the corresponding refined scaling factors in Table IV in the column headed first refinement. We have not attempted to reproduce the fundamental transition frequency for the puckering mode. The dominant term in the potential is known from the interpretation of the far-infrared spectra to be quartic, with a small negative quadratic term accounting for the inversion b a ~ ~ i e r The . ~ - remaining ~ assignments were largely based on their predicted positions for calculation 2 in Table V. They are discussed individually below. Thietane. For the A’ species, v7 is assigned as the lower frequency (1224.1 cm-I, peak 15 in Figure 2) of the two strong Q branches straddling the B contour at 1229.4 cm-l ( ~ 1 9 ,peak 16). The in-phase a-CH2 rock, ug, is assigned to the strong A/C infrared band at 975.3 cm-I (peak 10 in Figure 2) although the calculated position of 950.0 cm-I is, as anticipated, less than adequate. On the basis of the calculated frequencies alone it would be preferable to assign this feature as u2,; however, the distinctive band contour precludes that possibility. Neither uZ2nor u23 can be located in the spectra. The latter mode may be assumed simply to be of very low intensity as it involves predominantly the outof-phase a-CH2rocking symmetry coordinate, which would belong to the A, symmetry species for a planar (C,) molecule and hence be infrared forbidden. Finally, the weak feature at 1010.8 cm-I in the infrared spectrum of the neat liquid (peak 11 in Figure 4) is assigned to u2, solely on the basis of the good agreement with the calculated frequency for this mode. Thietane-a,a‘-d4. The only missing fundamentals are uI1 and v,~, which are predicted to lie in the vicinity of 700 and 600 cm-l, respectively. The latter is the out-of-phase C D , rock, which may be of low intensity in the infrared spectrum for the same reason as for the parent compound. The a’ mode v I I consists of a mixture of in-phase CD2 twisting and rocking displacements and may be tentatively assigned on the assumption that the infrared contour in the vapor phase at 720-770 cm-l is comprised of three fundamental transitions. The B gap at 736.5 cm-’ is u,, (peak 5 in Figure 2). A higher frequency transition, accompanied by a series of combination bands with the puckering mode, is resolved better in the spectrum of the neat liquid and represents ul0 (peak 6 in Figure 4). We can then assign uI1 as the lowest frequency feature in a series of Q branches extending from 725.2 to -740 cm-I, which does not clearly emerge in the condensed-phase spectra. Thietane-P-d2. All a’ modes are assigned readily on the basis of the predicted frequencies. The in-phase a-CH2rock, v9, which
Shaw et al. was not included in the initial refinement, is assigned as the strong A/C contour at 957.1 cm-’ (peak 11 in Figure 2). The similarity of this band shape to that assigned as ug for the parent compound serves to substantiate both assignments, in spite of the relatively large deviations from the calculated frequencies. Among the a” vibrations, the out-of-phase a-CH, scissor, ~ 1 7 is , absent in all spectra, as noted also for the parent compound. The modes u~~ and u23, predicted to lie at 903 and 720 cm-’, are assigned as weak features in the Raman spectrum at 922 and 729 cm-I, respectively (peaks 10 and 5 in Figure 5). An indistinct B contour at 1076.7 cm-I in the vapor-phase spectrum (peak 12 in Figure 2) is assigned to u20, while the calculated position for u I g suggests that of the apparent series of B gaps between 1104 and 1124 cm-l the most prominent at 1124.0 cm-’ (peak 14 in Figure 2) corresponds to the fundamental transition. T h i e 2 ~ n e - d ~For . the A’ species uI1, calculated at 695 cm-I, must correspond to the A/C band in the vapor-phase infrared spectrum at 722.3 cm-’, with analogous bands also present in both the infrared and Raman spectra of the neat liquid (peak 5 in Figures 2,4, and 5). The calculated position of 1121 cm-l suggests the weak B gap at 1107.2 cm-I to represent uI7 (peak 14 in Figure 2). The weak Raman bands at 904 and 766 cm-I (peaks 9 and 7 in Figure 5) are assigned as u20 and v 2 , , calculated at 909 and 4 difficult to locate in 777 cm-I, respectively. Both u2, and ~ 2 are all spectra, which may be due to the fact that both modes involve displacements of coordinates, namely, out-of-phase a-CD, twist and rock, that would be infrared forbidden for the planar C21, molecule. Thierane-a-d2. All six mid-infrared fundamentals omitted from the first refinement, namely, u7, us, u l I , Y ] 6 , uIsr and u,~, are readily identified on the basis of the refined frequencies. We note that the CH2 rocking mode, u l S , follows the same pattern as the a’ rocking modes of the h6 and P-d2 compounds in that the initial refined frequency is significantly lower than observed. The final refinement of the scaling factors, including all new assignments, yielded the set of calculated frequencies listed under calculation 3 in Table V. The optimized scaling factors are listed in Table IV under second refinement. This completes the assignment of the mid-infrared spectra. With the exception of the a-d, isotopomer, the final description of the normal modes is given in terms of the potential energy distribution in full symmetry coordinates. These are defined in Table VI. C-H and C-D Stretching Vibrations. For the parent compound and symmetrically deuteriated isotopomers, the C-H/C-D stretching modes are most conveniently described under the ClU point group, whereby there are two symmetry coordinates belonging to each of the AI and B2 representations and one to each of the A, and B2 species. The designation of each symmetry coordinate in C2, is included in Table VI. While in the C, symmetry point group the a, and bl coordinates may mix (a’), as may those in A, and B2 (a”), the force field shows that such mixing is minimal as indicated by the potential energy distribution and by the eigenvectors. In addition, a- and @CH2 coordinates of the same symmetry in C,, may also mix extensively and do so in most cases where deuteriation does not separate them. When a uniform scaling factor is used for both a- and P-CH, stretches, the highest frequency band predicted for the normal, P-d2, and a-d2 compounds is predominantly the b, a - C H 2 stretch (asymmetric a-CH, stretch for the a-d2 isotopomer), corresponding to absorptions near 2990 cm-l observed for all three. For thietane-a,a’-d, the P-CH, stretch (b,) was readily assigned near 2973 cm-’, which confirmed the assignments for bands observed in the same vicinity for both the normal and a-d2 compounds (peaks 25 and 24, respectively, in Figures 3 and 5). Separate scaling factors were then refined independently for the a- and P-C-H stretching coordinates to fit these assignments only, with the aim of optimizing the accuracy of the positions calculated for the remaining C-H stretching transitions. The resulting calculated frequencies are listed in Table V under the heading calculation 2, and the corresponding scaling factors in Table IV under first refinement. The accuracy of the positions predicted for the remaining modes is limited primarily by the
The Journal of Physical Chemistry, Vol. 92, No. 23, 1988 6535
Spectra and Scaled 3-21G Force Field for Thietane TABLE VI: Full Symmetry Coordinates for Tbietane A'
no. 1 2 3
4 5
6 7 8
9 10 11 12 13 14
description a-CH2(CD2)stretch P-CH2(CD2)stretch P-CH2(CD2)stretch a-CH2(CD2)stretch a-CH2(CD2)scissor P-CH2(CD2)scissor a-CH2(CD2)wag a-CH2(CD2)twist a-CH2(CD2)rock C-C stretch C-S stretch P-CH2(CD2)rock ring deformation ring pucker
LSC"
5-6 7-8 7
+ 9-10
+8
+ 6 + 9 + 10 11 + 12 19 13 + 14 17 + 18 15 + 16
5
A" Chb
no.
bl
15
bl
16
a1 a1 a1
17 18
a1
3+4
a1 bl bl a1
1+2
a1
21
23 24
19 20 21
22 23 24
description a-CH2(CD2)stretch o(-CH2(CD2)stretch a-CH2(CD2)scissor P-CH~(CDZ) wag P-CH2(CD2)twist a-CH2(CD2)rock a-CH2(CD2)twist C-C stretch a-CH2(CD2)wag C-S stretch
LSC" 5-6-9 + 10
+
C2ub a2
5 6-9-10 11-12
b2
20 22 15-16
b2
a2
b2 a2
17-18
b2
3-4
b2
13-14
b2 b2
1-2
bl
a1 bl
Local symmetry coordinates (Table 111) combined to define full symmetry coordinates. Designation of symmetry coordinate for the hypothetical planar (C2J molecule. (I
accuracy of the ab initio values for the CH/CH interaction force constants and, in the C-D stretching region in particular, by the assumption of harmonic behavior. In addition, some of the C-H stretching energy levels are likely perturbed by Fermi resonance, which we believe is responsible for the enhanced intensity of the band near 2880 cm-I in all spectra. The spectra of the a,a'-d4 compound clearly demonstrate that this is not a fundamental transition, as it is the third intense band in the C-H stretching region, where only two fundamental transitions are anticipated. A most helpful guide to further assignments is provided by the similarities between the spectra of the normal and the a-d2compound, in both the infrared and particularly the Raman. The very strong Raman bands at 2942 and 2941 cm-I for normal thietane and thietane-a-dz (peaks 24 and 23 in Figure 5) are readily assigned as the symmetric stretching combinations of all C-H stretches, calculated at 2934 and 2932 cm-I, respectively. The analogous band in the Raman spectrum of the a,a'-d4 isotopomer at 2939 cm-I (peak 25 in Figure 5) is the symmetric @-CH2stretch, calculated at 2928 crn-'. The remaining a' mode for the normal compound, calculated at 2922 cm-', is the out-of-phase combination of the two CH2 symmetric stretching (al) symmetry coordinates. The analogous mode for thietane-a-d2 is calculated at 2924 crn-'. These are assigned to the Raman lines at 2906 and 2902 cm-', respectively (peak 22 in Figure 5), corresponding in each case to very weak transitions in the infrared spectra. This completes the assignment of the a' modes of the parent compound and accounts for all C-H stretching fundamentals for the a-dz and a,af-d4isotopomers. The highest frequency afr mode for the normal and P-d2compounds belongs to A, in C,,, and hence low infrared intensity is anticipated. In addition, it is calculated within 10 cm-I of the intense b, mode in both cases. We assume that the two modes are nearly coincident in all spectra and cannot be resolved. The second a'I mode in each case is of Bzsymmetry under C,. Neither infrared spectrum exhibits a clear B contour, which would be expected for this mode, although peak 27 in the spectrum of the P-dZcompound (Figure 3) suggests the possibility of a B contour nearly coincident with another transition (peak 28). With no other plausible explanation for this band, we assign it tentatively as the bz fundamental, although the calculated position of 2926 cm-' is in poor agreement with that observed at 2955 cm-l. One possible explanation for the discrepancy is that the latter is shifted by Fermi resonance, the second band of the doublet occurring at 2880 cm-'. The observed B contour for the 2880-cm-' band suggests that it is not an overtone but rather a combination band of B2 symmetry and hence capable of Fermi resonance with the b2 C-H stretching fundamental. The most obvious possibility is a combination of the two a-CHz scissoring modes (a, plus b2). The assignment of the C-D stretches is generally straightforward in light of the observations noted for the C-H stretches. The final assignments are given in Table V. The assignment of the symmetric C-D stretching mode for the a-d2molecule deserves
particular mention. This vibration corresponds to the bz combination of the symmetric C-D stretches in thietane-a,a'-d4, Le. the dipole transition moment for this mode lies along the B axis. The strong B contour at 2151 cm-I for a-d2(peak 18 in Figure 3) is thus assigned as the symmetric CD2 stretch, accounting also for the strong Raman line at the same position (peak 18 in Figure 5). The absence of analogous bands in the C-H stretching region is due to the mixing of the a-with the P-CHz stretching coordinates, Le., there is no pure symmetric a-CH2stretching mode and hence no B contour at the corresponding position in the C-H stretching region. The final refinement of the C-H stretching scaling factors yielded the set of calculated frequencies listed under calculation 3 in Table V, while the complete set of optimized force constants is listed in Table VII.
Conclusion We have reported the infrared and Raman spectra for thietane and four deuteriated analogues. A scaled 3-21G force field has been derived by fitting 13 scaling factors to the observed positions for 98 of the total of 120 fundamentals with an average error of 8.8 crn-', or 6.4 cm-' excluding the C-H and C-D stretches. Comparison of the refined scaling factors with those previously optimized for oxetane5 support the notion that reproducible and physically significant differences exist among factors that are generally assumed to be identical. All observed transitions, the symmetry of which could be confirmed unequivocally by experimental evidence, were readily assigned, and their observed frequencies were reproduced very accurately. We believe, therefore, that the 3-21G force field for thietane presented here is essentially correct. The only missing fundamentals are those that might be expected to be of low intensity and/or overlapped by other more intense transitions. Evidentally, significant differences exist among the refined stretching scaling factors. The factors for the C-H, C-C, and C-S stretches refine to values of -0.8, 0.968, and 1.057, respectively. There can be little doubt that allowance must be made for such differences, correcting for what are essentially nonuniform deficiencies of the 3-21 G basis set in calculating force constants for different types of stretching coordinates. The a-CH, deformations invariably require higher scaling factors than their P-CH2counterparts. For example, the a- and 0-CH, wagging factors are 0.799 and 0.762, respectively, while the respective values for the twisting coordinates are 0.795 and 0.757. These may be compared to factors for oxetane that were derived previously by fitting to experimental frequencies for five isotopomers including the parent compound (Table IV). While we may expect differences in the refined factors for the a-CH2 deformations, reflecting the change in environment surrounding the methylene group, the @CH2 factors should be less sensitive to the substitution of sulfur for oxygen. This is confirmed, in that the refined P-CH, deformation factors for thietane assume values
6536 The Journal of Physical Chemistry, Vol. 92, No. 23, 1988 TABLE VII: Scaled 3-21G Harmonic Force Constants for Thietane" LSCb force constant LSCb force constant 1 3 5 6 7 8 11 13 15 17 19 20 21 22 23 24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3
1 3 5 6 7 8 11 13 15 17 19 20 21 22 23 24 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 4
2.889 4.009 4.898 4.868 4.838 4.797 0.711 0.688 0.511 0.620 0.7 19 0.671 0.492 0.655 1.270 0.062 -0.073 0.046 0.145 0.053 0.05 1 -0.015 -0.025 -0.017 -0.012 -0.151 -0.028 0.031 0.007 -0.012 0.017 -0.059 -0.001 -0.020 0.016 -0.026 -0.006 0.002 -0.026 0.047
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 7
0.040 0.050 0.077 0.078 -0.020 -0.005 -0.140 -0.018 -0.223 -0.001 0.030 0.008 0.051 0.000 -0.138 0.259 0.002 0.079 -0.035 0.036 0.041 0.014 -0.001 0.001 0.000 0.109 -0.002 -0.016 -0.002 0.050 0.006 -0.029 0.000 0.000 0.000 -0.01 1 -0.017 0.047 -0.006 -0.010
Shaw et al.
LSCb 6 8 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 6 21 6 22 6 23 6 24 7 8 7 11 7 13 7 15 7 17 7 19 7 21 7 23 7 24 8 11 8 13 8 15 8 17 8 19 8 21 8 23 8 24 11 12 1 1 13 11 14 11 15 11 16 11 17 1 1 18
force constant 0.015 0.002 0.106 -0.004 -0.025 -0.001 -0.059 -0.002 0.037 -0.001 -0.002 0.007 0.020 0.018 0.027 0.000 0.049 -0.001 -0.006 -0.019 0.024 0.084 0.092 -0.036 0.014 -0.001 -0.001 0.008 -0.012 0.095 -0.072 -0.067 -0.020 0.008 -0.014 -0.000 -0.001 -0.003 0.002 0.000
LSCb 11 11 11 11 11 11 13 13 13 13 13 13 13 13 13 13 13 15 15 15 15 15 15 15 15 15 17 17 17 17 17 17 17 19 19 19 20 21 21 23
19 20 21 22 23 24 14 15 16 17 18 19 20 21 22 23 24 16 17 18 19 20 21 22 23 24 18 19 20 21 22 23 24 21 23 24 22 23 24 24
force constant 0.007 -0.005 -0.003 -0.009 -0.025 -0.006 0.018 -0.004 -0.002 -0.03 1 0.003 0.004 -0.022 -0.006 -0.014 -0.020 -0.003 0.003 -0.035 0.003 0.003 -0.006 -0.014 -0.053 0.046 -0.052 -0.003 -0.006 0.016 0.050 0.054 -0.0 17 0.004 0.003 0.035 -0.01 1 0.046 0.047 0.065 0.012
Force constants for bond stretches in units of mdyn/A, for angle bends in mdyn A/rad2, and for stretch/bend interactions in mdyn/rad. Local symmetry coordinate defined in Table 111. within 0.01 of their counterparts for oxetane despite a range of 0.03-0.04 in the individual values. Thus, defining and refining these factors separately lead to values that are not only different from one another but also reproducibly so, implying that such differences, obtained by refining to a large number of carefully assigned experimental data, are not only statistically but also physically significant. The factors for the a-CH2 deformations for thietane are, as anticipated, quite different from the corresponding oxetane values. The a-CH2 rocking factor is exceptionally high for a bending mode, which undoubtedly reflects the influence of the puckering coordinate either through the harmonic constants coupling the two modes or due to the neglect of possibly important higher order interaction terms. A refinement was performed in which the puckering scaling factor was allowed to float, to assess the sensitivity of the a-CH2rocking factor (and hence the diagonal force constant) to changes in the diagonal and off-diagonal force constants involving the puckering mode. Virtually no change resulted in the fit to the rocking fundamentals, and the scaling factor emerged virtually unchanged in spite of a 30% increase in the puckering factor. Evidence supporting the validity of the refined
a-CH2 rocking factor is found when the refined scaling factors for thietane are transferred to the 3-21G force field for 2meth~1thietane.l~A complete assignment of the mid-infrared spectrum of that molecule is straightforward on the basis of the predicted frequencies, and in particular the analogous a-CH2 rocking transition is calculated to within 10 cm-' of observed. The scaled force field for 2-methylthietane will be reported separately.
Acknowledgment. R.A.S. gratefully acknowledges the award of a postdoctoral fellowship from the University of Calgary Grants Committee. We thank the Academic Computing Service and the Supercomputer Service of the University of Calgary for their assistance. This research program is supported by an operating grant from the Natural Sciences and Engineering Research Council of Canada. Registry No. Thietane, 287-27-4; thietane-d6,51760-01-1; thietanea-d2, 51759-98-9; thietane-a,a'-d,, 51760-00-0; thietane-&d2,5175999-0. (19) Shaw, R. A.; Ibrahim, N.; Wieser, H., unpublished results
