J. Phys. Chem. 1083, 87,3433-3441
given in Table V. Such a procedure probably underestimates the AZPE term, while use of the unscaled values will overestimate this correction. The AZPE correction terms can be combined with the MOelec (SCF) values and the temperature term (at 298 K) to yield the corrected proton affinities in Table IV. The proton a f f ~ t i efor s protonation at oxygen range from 114.6 kcal/mol for OF2 to 310.1 kcal/mol for 0Li2 at the corrected Hartree-Fock level. For comparison, the calculated proton affinity of H 2 0 is 169.0 kcal/mo12. The range of proton affinities a t divalent oxygen thus extends over a range of -200 kcal/mol, significantly more than for any other basic center. The proton affinity of OF2is extremely low, comparable to that of HF33while the proton affinity of 0Li2 is the highest known for any neutral compound.6 In order to confirm that PA(OLi2) is indeed as large as our calculations suggest, we determined the correlation correction for this value. The correlation correction at the all single and double excitation CI level is 7.8 kcal/mol favoring the unprotonated form, which lowers the proton affinity. Although this is the largest reported correlation correction for a proton a f f i n i t ~it , ~is still very small in relation to the absolute magnitude of the proton affinity. Thus, the calculated proton affinity for 0Li2 is 302.3 kcal/mol. The calculated corrections for the other two bases are probably small and comparable to the value for H20, 1.5 kcal/m01,~and thus we have not employed any correlation corrections for these values. (33)(a) Foster, M. S.;Beauchamp, J. L. Znorg. Chem. 1975,14,1229. (b) Ng, C. Y.; Trevor, 0. J.; Tiedemann, P. N.; Ceyer, S.T.; Kronebwh, P. R.; Mahan, B. H.; Lee, Y. T. J. Chem. Phys. 1977,67, 4235.
3433
The proton affinity of a base, B, is defined by a thermodynamic cycle to be PA(B) = HA(B) + IP(H) - IP(B)
(2)
where IP is the appropriate ionization potential and HA is the hydrogen affinity defined as -AH for the reaction BH+
-
B+
+H
(3) The hydrogen affinities determined from the experimental ionization potentials% and the calculated proton affinities are given in Table IV; we have also included the values for the simple base H20. The results show that the difference in proton affinity between H20and 0Li2can be accounted for solely on the difference in ionization potentials, i.e., the hydrogen affinities are equal. The hydrogen affinities for the two halogenated species are 40-50 kcal/mol lower than that of H20. This, combined with the differences in ionization potentials makes PA(OC12)N PA(H20)and PA(OF,) much less than PA(H20).
Acknowledgment. D.A.D. acknowledges partial support of this work by NSF Grant No. CHE-7905985 and thanks the Camille and Henry Dreyfus Foundation for a Teacher-Scholar Award (1978-83). D.S.M. acknowledges partial support of this work by the Robert A. Welch Foundation, Grant Y-743, and by the Organized Research Fund of the University of Texas at Arlington. Registry No. 0Li2,12057-24-8;OFz,7783-41-7;0C12,7791-21-1; H, 12385-13-6. (34)Rosenstock, H. M.; Draxl, K.; Steiner, B. W.; Herron, J. T. J. Phys. Chem. Ref. Data, Suppl. 1977,6.
The CH-Stretching Overtone Spectra of Nitre and Halo-Substituted Benzenes: A Local-Mode Investigation of Substituent Effects Kathleen M. Gough and Bryan R. Henry' Unhwslty of Mannobe. Winnipeg, Mennoba, Canada R3T 2N2 (Received: August 17, 1982; In Final Fonn: December 8, 1982)
The overtone spectra of 20 nitro- and halo-substituted benzenes are measured in the spectral region of the pure local-mode overtones corresponding to AVCH= 2-5,6, or 7. The spectra are interpreted in terms of the local-mode model. The doublet structure observed in the nitrobenzene spectra is assigned to contributions from the ortho and from the meta-para CH bonds. The overtone spectra of the halo-substituted benzenes do not show resolution of the contributions from inequivalent CH bonds. This result is taken to indicate the near equality of the CH bond lengths in these molecules. The fwhm of the overtone transitions are correlated with the number of inequivalentCH bonds. Local-mode frequenciesOCH and diagonal local-mode anharmonicities X C H are obtained from an analysis of the spectra. The relationship of XCH to steric hindrance is discussed. The shifts in the positions of the overtone band maxima relative to benzene, as well as the shift in uCH, are correlated with the Hammett UI at each overtone. Although the general correlation is good, various specific effects are noted. In particular, the relative roles of through-space and through-bond contributions to uI are discussed.
Introduction The higher overtones of CH-stretching vibrations can be understood as transitions to nonstationary states where all of the excitation quanta are essentially localized in a single CH oscillator.lg The spectra are characteristic of (1)B.R. Henry, "VibrationalSpectra and Structure",Vol. 10,J. Durig, Ed.; Elsevier, Amsterdam, 1981,p 269. (2)I. A. Wataon, B. R. Henry, and I. G. Roes, Spectrochim. Acta, Part A , 37,857 (1981).
the individual bonds and distinguish between both chemically inequivalent CH oscillators4-6and conformationally inequivalent CH The positions of the ov(3)0.S.Mortensen, B. R. Henry, and M. A. Mohammadi, J. Chem. Phys., 75,4800 (1981). (4)W. R. A. Greenlay and B. R. Henry, J. Chem. Phys., 69,82(1978). (5)H. L.Fang and R. L. Swofford, J. Chem. Phys., 73,2607 (1980). (6)J. S. Wong and C. B. Moore, J. Chem. Phys., 77,603 (1982). (7)B. R. Henry and W. R. A. Greenlay, J. Chem. Phys., 72,5516 (1980).
0022-3654f83f2087-3433$Q1.50/0 0 1983 American Chemical Society
3434
The Journal of Physical Chemistry, Vol. 87, No. 18, 1983
ertone band maxima, corresponding to a single type of CH bond, fit the equation for a diatomic anharmonic CH oscillator, i.e.
AE
=
WCHU
+ xCHv2
(1)
where u C H is the local-mode frequency in cm-l, X c H is the diagonal local-mode anharmonicity constant, and AE is the frequency, in cm-l, at the band maximum of the (v - 1)th overtone. These local-mode parameters contain information concerning the bond strength and the local physical environment of the CH oscillator. Recently a local-mode analysis has been used to understand nonbonded steric interactions in alkanes.'&12 Because of the bond specificity of local-mode excitation, it had been noted some time ago that high-energy overtone spectra could provide the same type of information as NMR.13 In fact, because of the time scales involved, local-mode overtone spectroscopy can provide conformational information inaccessible to NMR.69 One area in which both NMR and vibrational spectroscopy have jointly provided information is in the study of substituent effects in aromatic molecules. The fundamental IR spectra of many substituted benzenes have been investigated thoroughly, and are reasonably well understood in terms of substituent effects on the parent However, these fundamental spectra are governed largely by normal-mode characteristics. In particular the role of substituent mass and the strong couplings that are involved obscure the purely electric nature of the substituent effect. Two experimental approaches have been used to surmount this difficulty. McKean and co-workers have studied fundamental CH-stretching frequencies in molecules where all but one hydrogen have been replaced by de~terium.'~ They ~ ~ have obtained very good correlations of such "isolated" CH-stretching frequencies with CH bond lengths and dissociation energies in a wide variety of molecules. Secondly, there has been a great deal of work in the correlation of Taft's uI,uR dual substituent parameter scale21with NMR 13C substituent chemical In contrast to studies in the fundamental region, the localized nature of CH-stretching overtones ensures that changes relative to a parent molecule like benzene reflect primarily the electric nature of substituent effects. It fact it has long been known that the positions of the overtone band maxima for substituted benzenes are shifted relative (8)B. R.Henry, I. F. Hung, R. A. MacPhail, and H. L. Straws, J.Am. Chem. Soc., 102,515 (1980). (9)J. S. Wonrr. R. A. MacPhail, C. B. Moore. and H. L. Straws, J. Phys. Chem., 86;'1478 (1982). (10)B. R. Henry and R. J. D. Miller, Chem. Phys. Lett., 60,81(1978). (11)M. A. Mohammadi and B. R. Henry, Proc. Natl. Acad. Sci. U. S A . , 78,686 (1981). (12)B. R.Henry, M. A. Mohammadi, and J. A. Thomson, J. Chem. Phys., 75,3165 (1981). (13)R. J. Havward and B. R. Henrv. Chem. Phvs.. 12. 387 (1976). R. T. C. Brownlee and R. D. Topsom, SpecGochim. Acta, Pait 1677 (1975). R. T.C. Brownlee, J. Di Stefano, and R. D. Topsom, Spectrochim. Acta, Part A, 31, 1685 (1975). (16)E. D. Schmid and J. Bellanato, 2.Electrochem., 65,362 (1961). (17)E.D. Schmid, 2.Electrochem., 66,53 (1962). (18)E. D. Schmid, Ber. Bumenges. Phys. Chem., 67,39 (1963). (19)D. C. McKean, J. L. Duncan, and L. Batt, Soectrochim. Acta, Part A , 29, 1037 (1973). (20)D. C.McKean, Chem. Soc. Reu., 7,399 (1978). (21)S.Ehrenson, R. T. C. Brownlee, and R. W. Taft, Prog. Phys. Org. Chem., 10, 1 (1973). (22)J. Bromilow, R.T. C. Brownlee, R. D. Topsom, and R. W. Taft, J. Am. Chem. SOC.,98,2020 (1976). (23)J. Bromilow, R. T. C. Brownlee, D. J. Craik, M. Sadek, and R. W. Taft, J. Org. Chem., 45,2429 (1980). (24)W. F. Reynolds, P. Dais, D. W. MacIntyre, G. K. Hamer, and I. R. Peat, J. Mag. Reson., 43,81 (1981). (25)W. F. Reynolds, J. Chem. SOC.,Perkin Trans. 2, 985 (1980).
Gough and Henry
to benzene. Very early investigations attributed this phenomenon to the electronegativity and dipole moment of the s u b s t i t ~ e n t .Recently ~ ~ ~ Katayama and ceworkers have determined the frequency shifts of 30 monosubstituted benzenes33and 15 di- and trisubstituted benze n e at ~ the ~ ~fifth overtone level using thermal-lensing spectroscopy. They have observed a very good correlation of these shifts with uI,the inductive part of the Hammett u. They have also observed additivity of the frequency shifts for para-dihalosubstituted benzenes.34 In this paper we extend the earlier work of Katayama to a study of the full overtone spectra (AucH = 2-7) of 20 substituted benzenes ranging from mono to penta substitution with either halo or nitro substituents. We determine local-mode parameters and examine other localmode characteristics of the spectra. In particular we examine the correlation between spectroscopic parameters and substituent effects at each overtone level from A v c H = 2 to A u C H = 7. The results provide further insight into the mechanism of the substituent effect, particularly in the case where inequivalent CH oscillators are resolved. Finally, the current work by Taft, Reynolds, Topsom, and c o - ~ o r k e r son ~ defining ~ * ~ ~ ~the ~ various substituent parameters more fully is considered and their reinterpretation of uI is used to help explain the observed frequency shifts.
-
-
Experimental Section All spectra were taken on either a Cary 14 (Av = 2, 3, 4) with a 0-2 or 0 4 . 2 absorbance slidewire, a Cary 219 (Av = 5, 6, 7) with scale expansions from 0-0.5 to 0-0.01, or on a Beckman 5270 (Av = 2-7) with scale exphsions from 0-3 to 0-0.01. Sample cells of various lengths from 0.1 to 10 cm were used. Gas-phase spectra were recorded with a variable path length gas cell (Wilks Scientific Corp., South Northwalk, CT, Model 5720). The samples used were all of commercial spectral grade or comparable quality, with the following exceptions. 1,4-Dichlorobenzene, 1,3,5-trichlorobenzene, and 1,3,5tribromobenzene were purified by recrystallizing twice from spectral grade carbon tetrachloride. Nitrobenzene was first passed through a column of Woelm alumina, and then fractionally distilled at reduced pressure. The third fraction, boiling at 149.5-150.0 "C, was used. Iodobenzene was fractionally distilled at reduced pressure and the fraction boiling at 105-107 "C was used. The spectra of the solids were obtained from solutions of each compound in spectral grade carbon tetrachloride. It was anticipated that, in the case of the unsymmetrically substituted benzenes, the observed spectral bands would contain several peaks due to excitation of the various inequivalent CH oscillators. In general, this was apparent only as asymmetry in the bandshape and in increased full-width at half-maximum (fwhm) (vide infra); therefore each of the overtone bands was digitized and deconvoluted. As the experimental bands were linear in wavelength, the digitized bands were first converted to an energy scale
..
\__,
(26)R. Freymann, Ann. Phys., 20, 243 (1933). (27)G.Allard, C.R. Acad. Sci., 190, 1497 (1932). (28)P. Barchewitz, C.R. Acad. Sci., 206,512 (1938). (29)H. Kempter, 2. Phys., 116, 1 (1940). (30)R. Suhrmann and P. Klein, 2.Phys. Chem., 50,23 (1941). (31)R. Suhrmann, Angew. Chem., 62,507 (1950). (32)P. Barchewitz and R. Chabbal, J.Phys. Radium, 12,42 (1951). (33)Y. Mizugai and M. Katayama, J. Am. Chem. Soc., 102, 6424 (1980). (34)Y.Mizugai, M.Katayama, and N. Nakagawa, J.Am. Chem. SOC., 103,5061 (1981). (35)W.F. Reynolds, P. G. Mezey, and G. K. Hamer, Can. J. Chem., 55, 522 (1977). (36)R. D. Topsom, Prog. Phys. Org. Chem., 12,1 (1976). (37)W.F. Reynolds, P. Dais, R. W. Taft, and R. D. Topsom, Tetrahedron Lett., 22,1795 (1981).
CH-Stretching Spectra of Substituted Benzenes
The Journal of Physical Chemistry, Vol. 87, No. 18, 1983 12,000 I
9000
8800 ij
11,800
11,400
11,600
I
I
I
I
I
3435
11,2 IO
I
I
8600
(cm-')
Figure 1. The overtone spectra of the four monohalobenzenesIn the liquid phase at room temperature in the region of Av, = 3; 1 cm pathlength. The bromo-, chiore, and Ruorobenzene absorbances have been offset by 0.2, 0.4, and 0.6 absorbance units, respectively.
(cm-I). The data were then entered into a Nicolet 1180 data system and deconvoluted with a standard curve analysis program (CAP), which fitted Lorentzian peaks to the experimental band. It was possible to include up to 100% Gaussian character in the calculated peaks but it was found that the inclusion of up to 25% Gaussian character did not improve or alter the results. CAP includes a baseline parameter so that a linearly sloping baseline could be subtracted. The experimental and calculated band envelopes were plotted with the Bruker WH-SODS plotter and compared to check the quality of the deconvolution fit.
Results For all of the molecules investigated, with the exception of nitrobenzene and 1,2-dichlorobenzene, the principal contribution to the band envelope for each overtone from Av = 3-7 was clearly a single peak. The peaks were often asymmetric and, at Av = 3, small shoulders were frequently present. As typical examples, in Figure 1the spectra for fluoro-, chloro-, bromo-, and iodobenzene are presented in the region of AuCH = 3. For Av = 4-7, we interpret the principal contributions to these peaks as local-mode transitions involving the unresolved excitation of the various inequivalent aryl CH oscillators. The occurrence of a Fermi resonance type interaction at Av = 3 was not uncommon. The band in 1,2-dichlorobenzene was split into two large overlapping peaks and those of 1,3-dichloro-,1,3-difluoro-, 1,4dichloro-, and 1,3,5-trichlorobenzeneall had small shoulders. These features were absent in the higher overtones. The likely origin of these secondary features a t Au = 3 involves two quanta of CH stretching coupled with the excitation of lower frequency normal modes. In sevkral other molecules, such states have been identified as stealing intensity from pure CH-stretching local-mode (38) H.L.Fang and R. L. Swofford, J. Chem. Phys., 72,6382 (1980).
Figure 2. The calculated and experimentally observed overtone spectra of nitrobenzenecorrespondingto Avw = 3 (lower curves) and AvCH= 4 (upper curves). The calculated band envelopes (the lower of each of the pair of curves) represent the sum of Lorentzian peaks obtained from a computergssisted &convolution of the experimentally observed overtone band. The experimental spectra were obtained In the liquid phase at room temperature. Ordinate: arbitrary llnear absorption units. 17,000
16.2(
16,600
I
I
I
I
I
I
v a 00
l
l
14,500
1
I
I
14,250
I
14,000
,
.I
13,75C
5 (cm-'
Figure 3. The calculated and experimentally observed overtone spectra of nitrobenzenecorrespondingto Avw = 5 (lower curves) and Avm = 6 (upper curves). The calculated band envelopes (the lower of each of the pair of curves) represent the sum of Lorentzlan peaks obtained from a computer-assisteddeconvolutln of the experimentally observed overtone band. The experimental spectra were obtained In the liquid phase at room temperature. Ordinate: arbitrary llnear absorption units.
Each of the nitrobenzene overtone bands was a partially resolved doublet (Figures 2 and 3). A t the second overtone, the ratio of the areas of the low-frequency and high-frequency peaks was -3~2, and partly on this basis they were assigned to the three CH bonds meta and para to the substituent, and to the two ortho to the substituent, (39) B.R.Henry and M. A. Mohammadi, Chem. Phys., 55,385 (1981).
3436
The Journal of Physical Chemistry, Vol. 87, No. 18, 1983
Gough and Henry
TABLE I: Parameters from the Curve Analysis Program for Nitrobenzene and the Monohalobenzenes molecule auCH peak width, cm-' int freq, cm-' nitrobenzene
3 4
82 100 124 188 163 237 218 289 220 69 128 45 29 68 105 42 35 75 106 63 49 29 37 42 65 90 95 51 59
A
B C A B
5
A
6
A
B B fluoro benzene
3
A
B chlorobenzene
3
A
B C D E bromobenzene
3
io do benzene
3
A B C D E F A
B C
D E F G
30 237 325 267 271 307 316 239 210 71 341. 14 14 64 229 12 18 115 314 14 8 7 1 14 62 23 7 17 7 7
8986 8898 8814 11634 11515 14274 14112 16795 16596 8872 8818 8939 8887 8844 8791 8684 8921 8838 8787 8689 8579 8528 9056 8905 8823 8772 8676 8558 8481
re1 area 3.7 35.5 60.7 53.0 47.0 51.5 48.5 59.9 40.1 10.2 89.8 2.0 1.3 14.5 80.2 1.6 1.4 19.6 75.5 2.0 0.8 0.4 0.1 2.0 14.3 75.0 5.6 1.2 1.4
TABLE 11: Fwhm (cm-' ) for Some Halo-Substituted Benzenes AUCH
substituent
2
1,2-difluoro1,2-dichloro1,2-dibromo1,3-difluoro1,3-dichloro1,3-dibromo1,4-difluoro1,Q-dichloro1,4-dibromo1,3,5-trifluoro1,3,5-trichloropentafluoro Resolved doublet.
63i 1 58i 1 73 t 1 47? 1 31' 26' 49+ 1 4 7' 46 f 1
3 130 i 2 125 t 1 123 t 2 137 = 1 126 F 1 139 t 1 108 t 2 116 = 1 112 i 1 79: 2 101 = l b 82 I2
4 174 t 1 164 t 1 163 t 2 205 ? 3 178 i 2 181 + 2 158 I1 141 i 2 141 * 2 151 5 2 115t 1 154 i 5
5 225 t 214 F 210 i 258i 229 t 227 t 1922 180 t 186 + 176 i 162 t
6 5 2 2 2 3 8 2 8 8 2 6
284 250
t t
8 4
309
t
8
243 t 8 231t 8 245
t
8
Unresolved shoulder.
respectively. However, the ratio of the areas was not constant throughout the overtone spectrum. The higher frequency peak gained in relative intensity with increasing u. This result is not surprising since liquid-phase overtone spectra typically show increased asymmetry to the highenergy side, due, in part, to unresolved local-mode combinations.' Furthermore, the baseline at Au = 5 and 6 sloped slightly, and the calculated band areas were quite sensitive to changes in the estimated position and slope. Our assignment of the two peaks to ortho and meta-para CH bonds is subject to uncertainty if hydrogen bonding is significant, since such hydrogen bonding could markedly affect relative intensities. However, hydrogen bonding is unlikely to be important here. The barrier to nitro internal rotation, as measured by microwave spectroscopy, is relatively small.40 Moreover a recent reinterpretation of NMR and theoretical results by Lipkowitz has suggested that most of the negative charge withdrawn from the benzene ring by the nitro group is concentrated on nitrogen (40) T.Correll, N. W. Larsen, and T. Pedersen, J.Mol. Struct., 65,43 (1980).
with little change in the electron density at the oxygen^.^^ It should be noted that the assignment in nitrobenzene was not based solely on the relative areas. Confirmation is provided by the relative shifta (Av)and by the value of XcH (vide infra). All of the overtone spectra were analyzed with the CAP program. Except for the nitrobenzene spectra, the results were not readily analyzable in terms of inequivalent hydrogens. For example, the spectra of the four monohalobenzenes each show one or more high-energy shoulders in the Au = 3 band; however, these shoulders make a rather small contribution to the overall band. Their likely origin is either local-mode combination bands, for the shoulders about 150-200 cm-l from the band maxima, or mixed local-mode-normal-mode combination bands of the type referred to above for the shoulders closer to the band maxima. The spectra of the more highly substituted benzenes were similarly unresolvable. In Table I, we have listed the parameters obtained from the CAP procedure for (41)K. B.Lipkowitz, J.Am. Chem. Soc., 104, 2647 (1982).
CKStretching Spectra of Substituted Benzenes
The Journal of Physical Chemistty, Vol. 87, No. 18, 1983 3437
TABLE 111: Frequency of Band Maxima (cm-') at Each Overtone AV
molecule fluoro benzene chlorobenzene bromobenzene iodo benzene nitrobenzene ( 0 ) (TP) 1.2-difluorobenzene 1;3-difluorobenzene 1,4-difluorobenzene 1,2-dichlorobenzene 1,3-dichlorobenzene 1,4-dichlorobenzene 1,2-dibromobenzene 1,3-dibromobenzene 1,4-dibromo benzene 1,3,5-trifluorobenzene 1,3,5-trichlorobenzene 1,2,4-trichlorobenzene 1,3,54ribromobenzene 1,2,4,5-tetrachlorobenzene pentafluorobenzene benzenea From ref 43.
2
6057 6040 6016 5990 6004 6023 6091 6050 6025 6077 5983
3
4
5
6
7
8824 8798 8785 8771 8898 8815 8854 8891 8875 8817 8855 8839 8815 8830 8822 8943 8880 8850 8887 8900 8949 8760
11543 11 515 11501 11477 11635 11514 11563 11617 11598 11528 11569 11558 11513 11552 11 546 11708 11631 11585 11620 11609 11694 11443
1 4 136 1 4 097 14 078 14 045 14 274 14 112 1 4 174 1 4 249 14 217 14 129 14 184 14 164 14 100 14 163 14 150 14 347 1 4 272 14 186 14 248
1 6 633 16 582 16 559 1 6 507 16 795 1 6 595 16 661 16 759 16 711 16 606 16 667 1 6 644 16 570
1 9 004
19 139 19 106 1 8 975
1 6 880 16 683
14 338 14 015
16 467
18 810
TABLE IV : Diagonal Local-Mode CH-Stretching Anharmonicity Constants and Local-Mode CH-Stretching Frequencies Calculated from the Peak Maxima of Table I11 molecule
a
AUCH
UCH,
cm-'
fluorobenzene 3-7 3112i 1 chlorobenzene 3-6 3104 t 3 bromo benzene 3-6 3099 t 3 iodo benzene 3-6 3098 i 3 3-6 3132 i 2 nitrobenzene ( 0 ) (mlP) 3-6 3109 i 3 1,2-difluorobenzene 3-6 3124 i 3 1,2-dichlorobenzene 3-7 3111 i 1 1,2-dibromobenzene 3-6 31121 1 1,3-difluorobenzene 3-7 3135 * 2 1,3-dichlorobenzene 3-6 3124i 3 1,3-dibromobenzene 3-5 3109.6 i 0.5 1,4-difluorobenzene 3-7 3129i 1 1,4-dichlorobenzene 3-6 3119 i 2 1,4-dibromoben~ene~ 3-5 3107 i 3 l13,5-trifluorobenzene 3-6 3151 i 2 1,3,5-trichlor~benzene~ 3-5 3119 t 1 1,3,5-tribromoben~ene~ 3-5 3130 i 2 1,2,4-trichlorobenzene 3-6 3121 i 3 1,2,4,5-tetrachloroben~ene~ 2-4 3126i 3 pentafluorobenzene 2-5 3153 i 4 benzeneb 4-9 3091 Confidence less than 0.001 (see text). From ref 43.
nitrobenzene and the monohalobenzenes. In Table 11,we have listed the fwhm for the di-, tri-, and pentasubstituted molecules for the overtones from Av = 2 to Av = 6. We have calculated local-mode parameters, wCH and X C H , on the basis of eq 1 and the positions of the band maxima tabulated in Table 111. In general, the values in Table I11 are simply the positions of the absorbance maxima for the overtones. However, for nitrobenzene, the resolved deconvoluted values for the ortho and the metapara hydrogen peaks were taken from the CAP program. For l,Zdichlorobenzene, the band center is given for the peak at Av = 3. In some cases we were able to measure the Av = 7 transition. For tetrachlorobenzene and pentafluorobenzene, data from Av = 2 were also used in order to make a meaningful determination of the local-mode parameters. The local-mode parameters are listed in Table IV. The uncertainties and the correlation coefficients r indicate an excellent fit for all of the molecules except 1,2,4,5-tetrachlorobenzene.The significance of the cor-
XCH,cm-' -56.6 -56.7 -56.6 -57.8 -55.5 -57.3 -57.8 -57.1 -58.8 -57.1 -57.6 -55.4 -57.3 -57.4 -55.4 -56.3 -52.9 -56.0 -56.6 -55.0 -57.2 -57.6
i
t t t i t i
* t
t t i
* *
i
i t
*
f
i t
0.3 0.7 0.7 0.7 0.5 0.5 0.5 0.2 0.3 0.5 0.6 0.1 0.3 0.3 0.7 0.5 0.3 0.6 0.7 1 1
r
-0.999 -0.999 -0.999 -0.999 -0.999 -0.999 -0.999 -0.999 -0.999 -0.999 -0.999 -0.999 -0.999 -0.999 -0.999 -0.999 -0.999 -0.999 -0.999 -0.995 -0.999
97 85 87 84 92 91 91 99 97 90 90 99 96 97 93 93 98 95 84 3 91
relation coefficient depends on the number of points used in the correlation. For all of the molecules listed in Table IV, except for the four marked with superscript a, P (the probability of obtaining the same r value from random is ortho disubstituted >> para disubstituted, 1,3,5-tri- and pentasubstituted. The (45) E. R. Lippincott and R. Schroeder, J. Chem. Phys., 23, 1131 (1955). (46) R. W.Taft, "StericEffecta in Organic Chemistry",M. S. Newman, Ed., Wiley, New York, 1956, pp 594-7.
20c-
00-
, /
,
,
2o
1
33
VI
Flgwe 4. The correlation between the frequency shift of the overtone band maxima at Avw = 5 and 6,. The line represents a leastmean-squares fit of the data. The points corresponding to the ortho CH bonds of nitrobenzene and to pentafluorobenzene have been omitted in the least-mean-squares fit.
number of inequivalent CH oscillators is three for meta disubstituted and two for ortho disubstituted, while the rest have only a single type. Where inequivalent CH bonds are present, the inequivalence for halo-substituted benzenes would be expected to be greatest for fluoro substituents since these are the most polar. This expectation is again consistently reflected in the data of Table I1 for the overtones from Av = 3-6. The fwhm of the overtone transitions in pentafluorobenzene are of interest. Swofford et aL4' provided early evidence for the local-mode model when they observed that the fwhm in this molecule, at Au = 6, is equal to that of benzene. The transitions at Av = 2 and 3 in benzene are structured, with contributions from local-mode and combination states.43 However, at Av = 4 the liquid-phase benzene overtone displays near Lorentzian character with a band width43 close to that observed here for pentafluorobenzene. This near equality provides further evidence that the local-mode character of the overtone spectra is firmly established by Av = 4. The lack of resolution of contributions from inequivalent CH bonds in the halobenzenes implies that the variation in bond length for the inequivalent CH bonds of a given molecule must be quite small. McKean et al.l9have established an excellent correlation between frequency shift, at the fundamental level, and change in CH bond length for a wide variety of CH bond types. They have found that a frequency shift of 10 cm-l in the fundamental corresponds to a change in bond length of 0.001 A. For a given difference in bond length, frequency shifts are much larger for the higher overtones. Mizugai and Katayama have correlated frequency shifts at Av = 6 with bond length changes for heterocyclic molecules.48 Wong and Moore have made a similar correlation for a series of alkanes and alkenes.6 In fact, they find that bond length changes of 0.001 A correspond to a frequency shift of 69 cm-l at Av = 6.6 From these results, we can conclude that the variation in bond lengths for the CH bonds of any given halobenzene is certainly less than 0.003 A. For nitrobenzene, the observed separation between the peaks associated with the ortho and the meta-para hydrogens corresponds to a (47) R.L.Swofford, M.S. Burberry, J. A. Morrell, and A. C. Albrecht, J . Chem. Phys., 66,5245 (1977). (48) Y. Mizugai and M. Katayama,Chem. Phys. Lett., 73,240 (1980).
CH-Stretching Spectra of Substituted Benzenes
The Journal of Physical Chemistry, Vol. 87, No. 18, 1983 3439
TABLE VI: Shifta in Position of Band Maximum (cm-' ) at Each Overtone, and o b for Halo- and Nitro-Substituted Benzenes molecule A w ru 2 fluorobenzene 21 chlorobenzene 13 bromobenzene 9 iodobenzene 8 nitrobenzene (0) 41 (m,P) 18 1,2-difluorobenzene 33 1,3-difluorobenzene 44 74 1,4-difluorobenzene 38 57 1,2-dichlorobenzene 20 1,3-dichlorobenzene 33 33 1,4-dichlorobenzene 28 1,2-dibromobenzene 21 7 1,3-dibromobenzene 19 21 1,4-dibromobenzene 16 40 1,3,5-trifluorobenzene 60 108 1,3,5-trichlorobenzene 31 1,2,4-trichlorobenzene 30 1,3,5-tribromobenzene 39 67 1,2,4,5-tetrachlorobenzene 35 42 pentafluorobenzene 62 96 Shift relative to benzene as reported by Patel, Tam, and
3 64 38 25 11 139 55 94 131 115 57 95 79 55 70 62 183 120 90 127 140 189 Ker1.43
TABLE VII: Correlationa between Frequency Shift and A W C H (cm-I) with a1 a t Each Overtone no. of data A V C H points 2 3 4 5 6 7 AWCH
9 19 19 19 14 5 19
slope 60.7 i 0.8 91.4 i 0.5 125.5 i 0.8 167.5 i 0.9 222i 1 238i 4 26.6 i 0.5
intercept -17.8 i -10.6 i -7.0 f -15.0 t -21.7 i 14.6 ? -1.2 t
0.7 0.5 0.7 0.8 0.9 0.9 0.5
r
0.80268 0.87932 0.89288 0.894 29 0.88768 0.894 72 0.84160
Does not include data for 1,2,4,5-tetrachlorobenzene, pentafluorobenzene, or the ortho H's from nitrobenzene. a
difference of 0.002 to 0.003 A with the ortho bonds as the shorter.49 On the basis of a 13C satellite proton NMR study of chlorobenzene in nematic phases, Diehl and Jokisaarim have predicted bond length differences in the inequivalent CH bonds of up to 0.008 A. Such a prediction is clearly inconsistent with our spectral data. It is possible that the necessity of correcting for harmonic vibrations decreases the accuracy of the NMR bond length results. On the other hand, a similar study by Jokisaari et al.51predicted virtually identical values for the CH bond lengths of fluorobenzene dissolved in a given nematic phase. The predicted bond length differences were 0.001 A or less which is consistent with our overtone spectral data. Diagonal Local-Mode Anharmonicities and Dissociation Energies. The diagonal local-mode anharmonicity constant, XCH,was found to vary slightly for the molecules studied here (Table IV). This parameter has been shown to be sensitive to changes in the environment of the CH oscillator. Steric crowding in methyl-substituted alkanes has been shown to inhibit large amplitude CH vibrational motion.'&12 As a result the local CH potential is made more harmonic and the sterically hindered molecules display a lower magnitude for XCH.It was not possible (49) The relative length of the different bond types given here is, of course, subject to the correctness of our assignment which, as we have noted above, is to some degree uncertain because of the possible effects of hydrogen bonding on peak intensities. (50) P. Diehl and J. Jokisaari, J.Mol. Struct., 53, 55 (1979). (51) J. Jokisaari, J. Kuonanoja, A. Pulkkinen,and T. Vaananen, Mol. Phys., 44, 197 (1981).
4
100 72 58 34 192 71 120 174 155 85 126 115 70 109 103 265 188 142 177 166 251 a1 from ref
5
6
7
121 82 63 30 259 97 159 234 202 114 169 149 85 148 142 332 257 171 233
166 115 92 40 328 128 194 29 2 244 139 200 177 103
194
3 23 46.
413 216
329 296 165
(Sr
b
0.56 0.51 0.50 0.43 0.64 0.64 1.12 1.12 1.12 1.02 1.02 1.02 1.00 1.00 1.00 1.68 1.53 1.53 1.50 2.04 2.80
to calculate individual anharmonicities for asymmetrically substituted benzenes, so the values listed in Table IV represent averages for these molecules. In general, those molecules in Table IV where the CH bonds are most sterically hindered have XCHvalues lower in magnitude, Le., the molecules 1,3- and 1,4-dibromobenzene, 1,3,5-trichlorobenzene, 1,3,5-tribromobenzene, and 1,2,4,5-tetrachlorobenzene. Also in keeping with this generalization, in nitrobenzene, the magnitude of the anharmonicity is significantly lower for the ortho CH bonds than for the meta-para CH bonds. Since the uI parameters should be directly related to bond strength, it might have been expected that a correlation of uI with changes in the dissociation energies of the local CH oscillators might be even better than that between UI and frequency shifts. However, the correlation between the dissociation energies, calculated from eq 2 or eq 3, and UI were markedly worse than those based on frequency shifts, and summarized in Table VII. The reasons for the poorer correlations are evident from the uncertainties listed in Tables IV and V. The percentage error in ucH is typically less than 0.1%, whereas the average percentage error in XCH is -0.9%. The dissociation energies are sensitive to small changes in XCH. The uncertainties in XCHlead to uncertainties in the calculated dissociation energies of the same order as their differences from benzene. There is an additional uncertainty introduced into dissociation energies calculated from the LippincottSchroeder potential. Although this potential yields more accurate values of it does not lead exactly to the simple two-term equation for the energy levels (eq 1). However, the error introduced by the approximations leading to eq 3 is at most of the order of 5%.45 Correlation of Frequency Shifts with uI. Before we examine more closely the correlation of frequency shifts with uI,it is worthwhile to briefly review some of the relevant concepts from the very large number of papers that have discussed substituent parameters. While the u parameters have generally been derived from ionization equilibria, they are interpreted as a measure of the change in electric charge distribution. The two chief mechanisms by which an alteration can be effected, resonance and induction, have been intensively studied, and parametrized as uR and uI.& The latter effect has been proposed to arise
3440
The Journal of Physical Chemistry, Vol. 87,No. 18, 1983
Gough and Henry
from several different sources.36 In particular, there has been an attempt to distinguish between a “through-bond” withdrawal or donation of electrons proportional to the electronegativity of the substituent, and a “through-space” field effect, i.e., the interaction between an electric dipole and some site elsewhere in the molecule. Ab initio STO 3G calculations on interactions between isolated molec u l e ~on , ~point-charge ~ perturbed substituted and on variations in charge densities on 4-substituted as well as correlations between substituent-induced chemical shifts and substituent parameters,2s indicate that the uI parameter is well modeled as essentially a field effect, dependent on substituent polarity. A stronger short-range withdrawal or donation of electrons, where the substituent is bonded directly to the ring, is also indi~ated.~ In~practice, ,~~ uI is measurable only for the meta and para positions, and therefore is associated with the through-space effect. A CH bond ortho to a substituent would experience both effects. Moreover the ortho through-space effect would not be expected to be the same as that measured for the meta and para positions. Both these effects are usually dealt with separately from the resonance effects, and it would be anticipated that the CH bonds would reflect primarily the changes induced in the u-bond framework. If UR is also involved, the analysis is much more complex, especially at higher levels of substitution, where the response may be n ~ n l i n e a r . ~ ~ J ~ The correlation of frequency shift with uI observed in our work, with the assumption of simple additivity of uI up to trisubstitution, is quite good (Figure 4, Table VII). A poorer correlation is expected at the lower overtones, Av = 2 and 3, since at Av = 2 splittings between local-mode states still O C C Uand ~ , ~at both Av = 2 and 3 interference from combination bands is c0mmon.l The results confirm the assumption that the change in CH frequency is a direct manifestation of the change in CH bond strength due to the electrical effect of the substituent. However, it is also apparent that the correlation is good only as a first approximation. We can identify four principal difficulties: 1. There are small but significant differences in the local-mode anharmonicity constants which contribute slightly to the observed shifts (Table IV). 2. The asymmetrically substituted halobenzenes have inequivalent CH bonds whose spectral contributions are unresolved. The measured frequency shift is thus simply a band shift which masks individual variations. 3. The assumption of simple additivity would appear to apply only in a gross fashion. This shortcoming is most readily apparent in the frequency shifts observed for the disubstituted benzenes. This shifts occur consistently in the order ortho
