4348
J. Am. Chem. SOC.1984, 106, 4348-4352
t
220
i
l i
system, one sees that the points for 2,6-DTBP deviate from the linear relationships found for the other pyridines in this study by 1.5 kcal mo1-l for AH,' and by 3.0 kcal mol-] for AG,'. Similar plots for the data in 40.9% ethanol-water have deviations of 2.5 kcal mol-' in AH,' and only 2.0 kcal mol-' for AG,'. In pure methanol the point for 2,6-DTBP deviates nearly 4.8 kcal mol-' from the linear trend found for PA vs. AG,', whereas the point for 2,6-diisopropylpyridine deviates from the linear trend by 1.3 kcal mol-'. W e note, just as Hopkins and Ali9 did earlier, that the abnormally low basicity of 2,6-DTBP in these solvents is due apparently to both enthalpy and entropy effects. Again one is tempted to conclude that the specific solvation of the 2,6-DTBPH+ cation, via hydrogen bonding of a solvent molecule to the pyridine nitrogen, has ceased or a t least been reduced substantially. Nevertheless, we easily constructed from CPK models methanol and ethanol hydrogen-bonded complexes for 2,6-DTBP and the 2,6-DTBPH+ cation. In the 2,6-DTBPH+ cation-ethanol complex, steric crowding is much greater than for either the water or methanol complex, which could account for the larger enthalpy effect in the 40.9% ethanol-water mixture. There is, however, uncertainty about which one of the two types of solvent molecules is present in the specific solvation complexes in these mixtures. Actually, both types of hydrogen-bonded complexes could exist in the alcohol-water mixtures for both the neutral pyridines and their cations; thus, there might be different fractions of each type of complex for each of the tert-butyl-substituted pyridines. Consequently, further studies must be performed before one can complete a detailed analysis of the basicities of these pyridines in the alcohol-water solvents.
i Pyridine
5 a n d AH', (kcal/rnol) plotted vs. AGpo (0)and AHp"( 0 )in AGO,
Figure 3. PA 90% methanolwater for a series of tert-butyl-substituted pyridines.
for the unusually low basicity of 2,6-DTBP in aqueous solutions. correlation of PA and the Basicities in AlcohoLWater Mixtures. Our conclusions derived from the data for the gas phase and aqueous phase can now be compared to a similar analysis of the basicities of tert-butyl-substituted pyridines in 90% methanolwater and 40.9% ethanol-water mixture^.^ Since in these solvent mixtures only pK, and AH,' values are available for these compounds, we are restricted to an analysis in which the variations in the basicities in these solvent systems are compared to the corresponding ones in the gas phase. In Figure 3, where PA is plotted vs. both AG,' and AH," for the 90% methanol-water
Registry No. 2-TBP, 5944-41-2; 4-TBP, 3978-81-2; 2,4-DTBP, 29939-31-9; 2,6-DTBP, 585-48-8; 2-TBP.H+, 62907-59-9; 4-TBP.H+, 40569-37-7; 2,4-DTBP.H+, 62907-60-2; 2,6-DTBP.H+, 62907-61-3; pyridine, 110-86-1; pyridineH+, 16969-45-2.
Ab Initio Theoretical Frequencies and Intensities in the Interpretation of Infrared Spectra B. Andes Hess, Jr.,* L. J. Schaad,* and Prasad L. Polavarapu* Contribution from the Department of Chemistry, Vanderbilt University, Nashville, Tennessee 37235. Received January 3, 1984
Abstract: A comparison of the ab initio theoretical vibrational spectra with the experimental IR spectra of ethylene oxide and its tetradeuterio derivative shows that such calculated spectra can be of use in interpreting experimental results. However, it is crucial that relative intensities be calculated as well as frequencies.
It has been found that a b initio vibrational calculations can be useful in identifying unstable organic species.' The comparison of and experimental spectra of cyclobutadiene and its deuterated derivatives has been useful in resolving the question of its structure (square or rectangular). Similarly, computed IR spectra of thiirene617have helped confirm its presence in an argon (1) Hess, B. A,, Jr.; Schaad, L. J.; h s k y , 55, 253.
P.,Pure Appl. Chem. 1983,
(2) Kollmar, H.; Staemmler, V. J . Am. Chem. SOC.1978, 100, 4304. (3) Schaad, L. J.; Hess, B. A., Jr.; Ewig, C. S . J . Am. Chem. SOC.1979, 101, 2281. (4) Schaad, L. J., Hess, B. A., Jr.; Ewig, C. S. J . Org. Chem. 1982, 47, 2904. (5) Hess, B. A., Jr.; &sky, P.; Schaad, L. J. J . Am. Chem. SOC.1983, 105. 695. 0002-7863/84/1506-4348$01.50/0
matrix. Since computed frequencies can be in error by as much as a few hundred wavenumbers at short wavelengths, they alone were not sufficient, but when frequencies were combined with computed intensities, fairly definite assignment of observed bands was possible. In the two cases mentioned the primary purpose of the theoretical work was to aid in picking bands of the molecule sought from others in a reacting mixture. However, theoretical vibrational spectra can also help in interpreting I R bands of pure and otherwise well-characterized molecules. As an example we consider (6) Hess, B. A., Jr.; Schaad, L. J.; Ewig, C. S. J . Am. Chem. SOC.1980,
102, 2501. (7) Cirsky, P.; Hess, B. 105. 396.
A,, Jr.; Schaad, L. J. J . Am. Chem. SOC.1983,
0 1984 American Chemical Society
J . Am. Chem. Soc., Vol. 106, No. 16, 1984 4349
Ab Initio Theoretical Frequencies Table I. Symmetry Coordinates'ib species coordinate AI SI = d s2 = 2-lI2(rl + r2) s3 = I/2(tl + t2 + c3 s4
Bl
B2
+ a2 + a3 +
= 1/2(aI
s5 =
+ r4)
1/2(P1
CY4)
+ 62 + 83 + 8 4 )
s9 = 2-112 (rl - r2) sIo= 1/2(tl + t2 - t3 - t4) SI1 = I/2(a, + a 2 - a3 - 014) 312 = 1/2(61+ 82 - 83 - 64) s13 = 1 / 2 ( f 1 - t2 - f 3 + t4) s14 = '/2(aI - a2 - a3 + a4) s15 = I/2(61 - 82 - 83 + 84)
See Figure 1 for definition of internal coordinates. Here, as in ref 8, symmetry species subscript 1 or 2 is determined by symmetry or antisymmetry, respectively, in the plane of the three-membered ring.
H'
"
Figure 1. Definition of internal coordinates of ethylene oxide.
Table 11. Comparison of Calculated Geometry' with Experimentb parameter exptl STO-3G 4-31Gc 6-31G r 1.436 1.433 1.459 1.459 d 1.472 1.483 1.461 1.464 t 1.082 1.088 1.069 1.071 a 114.2 116.6 114.5 114.5 6 119.4 119.5 119.8 119.8 "Bond lengths are in 8, and angles are in Reference 9.
of Ethylene Oxide 6-31G* 6-31G**C 1.402 1.399 1.453 1.452 1.077 1.078 115.2 115.4 119.9 119.8 deg. bReference l b
Table 111. 6-31G* Force Constants of Ethylene Oxide" species constant value suecies constant value 6.504 5.346 AI Fl,l Bl F9%9 5.710 6.194 F2.2 FI0,lO 6.199 1.300 F3,3 Fll,ll 1.411 1.395 F4.4 F12.12 1.516 0.508 F5,5 F9,10 0.655 -0.239 FL2 F9.11 0.139 -0.298 F1,3 F9.12 -0.189 -0.080 F1,4 FIOJI 0.447 -0.166 F1,5 Fl0,12 0.199 -0.080 F2.3 FlI,l2 0.61 1 6.102 F2.4 B2 F13,13 -0.072 0.989 F14.14 F2,5 -0.098 0.633 F3,4 F15,15 -0.003 -0.150 F3,5 F13,14 -0.175 0.094 F4.5 F13,15 -0.282 F,, ,-.,, "Stretching force constants are in mdyn 8,-',bending force constant> in mdyn 8, rad-2, and stretch-bend interaction constants in rndyn rad-'. These force conslants are for the symmetry coordinates of Table I . 1
