J. Phys. Chem. 1987, 91, 5573-5577 at 2090 cm-I. Therefore, it is likely that the 2092-cm-’band arises from decomposition of ferricyanide during oxidation of ferrocyanide. Conclusion
Within the limits of the model described above we conclude that adsorption of ferricyanide and ferrocyanide on metal electrodes is an important step in the heterogeneous electron-transfer reaction. It appears that ion pairing with alkali-metal cations may stabilize particular surface-adsorbate orientations. These orientations explain the nature of the spectra of the adsorbed species observed by Raman and infrared spectroscopies and the behavior of the spectra with changes in cation and electrode potential. The
5573
simplicity of the model should be noted. Actual surfaceadsorbate interactions may be much more complex; thus, this model does not account for large changes in electronic structure which must occur upon adsorption and which must be important in determining the kinetics of the ferri/ferrocyanide redox reaction. However, the model can be used effectively to assess qualitatively the nature of the intramolecular interactions.
Acknowledgment. This research was supported by contracts with the Office of Naval Research, Arlington, VA. C.K. thanks Dr. J. K. Foley and H. L. Taylor for many helpful discussions. Registry No. Ferricyanide, 13408-62-3;ferrocyanide, 13408-63-4.
Quantitative Relationship between Bond Dissociation Energles, Infrared Stretching Frequencies, and Force Constants in Polyatomic Molecules Andreas A. Zavitsas Department of Chemistry, Long Island University, Brooklyn, New York 11201 (Received: December 4, 1986)
Uncoupled infrared stretching frequencies are related to bond dissociation energies in polyatomic molecules. The “pure” where the bond dissociation energy, D, is in kcal/mol and cI is stretching frequency, in cm-’, is given by 143.3(D - c~)’/~, characteristic of the bonded atoms, irrespective of the multiplicity of the bond; c1 = 39.7 for carbon-carbon bonds, 26.7 for carbon-nitrogen, 33.8 for carbon-oxygen (alcohols, carbonyls), 24.2 for carbon-alkoxy (ethers, esters), 5 1.4 for carbon-fluorine, 42.6 for carbon-chlorine, and 40.6 kcal/mol for carbon-bromine. Stretching force constants are calculated as a function of bond dissociation energies and agree with scaled quantum mechanical values. Some applications are shown for infrared assignments and for the estimation of bond dissociation energies from stretching frequenciesor from force constants.
Chemical intuition suggests that a correlation should exist between bond dissociation energies and stretching force constants or “pure” infrared stretching frequencies. Stretching frequencies have been used to determine “spectroscopic” bond dissociation energies in diatomic species.’ However, the limitations of such procedures are well-known. As noted by Gaydon’ in his monograph which reviews the topic, “attempts to correlate the dissociation energy with stretching frequency do not seem very promising”, even for diatomic species. Nevertheless, it has been noted that force constants for the hydrogen halides are linearly related to bond dissociation energies with a nonzero intercept.2 Beyond diatomics, an adequate understanding of the complete infrared spectrum becomes a difficult task.3 A linear dependence of the square of the stretching frequency on bond dissociation energy, D, is implied by known’ relationships such as D = w2/4(wx) and DO2 = k / 2 , where w is the “equilibrium” frequency, (wx) is a measure of the anharmonicity of the vibration, p is the “spectroscopic” constant of the Morse function, and k is the force constant. We find that plots of the square of the frequency vs. D for polyatomic molecules are indeed linear. However, bonds between different atoms define different, although parallel, straight lines. While the above relationships require zero intercepts, the data for actual molecules show that the D axis is crossed at values significantly different from zero, ranging between 24 and 52 kcal/mol. Early works on such relationships suffered from lack of good thermodynamic data a t the time. We report here the observed quantitative relationship between dissociation energy of a bond (1) (a) Gaydon, A. G. Dissociation Energies and Spectra of Diatomic Molecules; Chapman and Hall: London, 1968. (b) Karplus, M.; Porter, R. N. Atoms and Molecules; W. A. Benjamin: New York, 1970. ( 2 ) Nakamoto, K. Infrared and Raman Spectra of Inorganic and Coordination Compounds; 3rd ed.; Wiley: New York, 1977. (3) Wiberg, K. B.; Walters, V. A. J . Am. Chem. SOC.1985, 107, 4a60-4867.
0022-365418712091-5573$01.50/0
and its infrared stretching frequency, when the latter is not mixed extensively with other vibrational modes, and a corresponding relationship between bond dissociation energy and stretching force constant. Since frequencies are observable quantities, they will be treated first. Stretching Frequencies
Observed uncoupled stretching frequencies, v in cm-’, are related to bond dissociation energies, D in kcal/mol, by eq 1. The v = 143.3(D - cI)’/~
(1)
constant c, is characteristic of the two bonded atoms and is not dependent on the multiplicity of the bond. For carbon-carbon bonds, c1 = 39.7 kcal/mol; for carbon-nitrogen, 26.7; for carbon-oxygen (alcohols, carbonyls), 33.8; for carbon-alkoxy (ethers, esters), 24.2; for carbon-fluorine, 5 1.4; for carbon-chlorine, 42.5; and for carbon-bromine, 40.6. The relationship of eq 1 was established by examining reported values of v and D in a high-quality data base; generally, molecules examined are those included in both sources 1 and 2 as follows: (1) For stretching frequencies, the compilations of Shimanouchi: adopting his designation as “stretching” under the heading “approximate type of mode”, or those given in the J A N A F Thermochemical table^;^ (2) For bond dissociation energies, the compilations of Kerr,6 of Benson,’ and of the J A N A F table^,^ (4) (a) Shimanouchi, T. Tables of Molecular Vibrtational Frequencies. Consolidated Volume 1 ; NSRDS-NBS 39; National Bureau of Standards, US.Government Printing Office Washington, DC, 1972. (b) Shimanouchi, T. J . Phys. Chem. ReJ Data 1977, 6, 993-1 102. ( 5 ) Stull, D. R.; Prophet, H. JANAF Thermochemical Tables, 2nd ed.; NSRDS-NBS 37; National Bureau of Standards, US.Government Printing Office: Washington, DC, 1971. (6) Weast, R. C., Ed. Handbook of Chemistry and Physics, 66th ed.; CRC Press: Boca Raton, FL, 1985-1986. (7) Benson, S . W. Thermochemical Kinetics, 2nd ed.; Wiley: New York,
1976.
0 1987 American Chemical Society
5574 The Journal of Physical Chemistry, Vola91, No. 22, 1987 TABLE I: Bond Dissociation Energies, Observed Stretching Frequencies, and Frequencies Calculated by Eq 1 molecule D, kcal/ u(obsd), v(calcd), and bond 1
2 3 4 5 6 7 8 9*g
10 11
12 13 14 15 16 17 18 19 20* 21 22 23 24 25 26 27* 28 29 30 31 32 33* 34 35 36 37 38 39* 40 41 42 43 44 45* 46 47 48 49 50 51* 52
CH,=CHCH,-CHq C - C ~ H(C-Cj I~ C2H5-C2H5
CH3OCH2-CH3 CH3-CH2OH CH3-CzH5 CH3-CHzCl CH3-CH2COCH3 CH3-CH3 CH2=CH--C2HS CH,=CH(CH3)-CH! C H 3-C F3 H2C=CH-CH=CH2 H2C=CH2 C2- (negative ion) CH=CH (CHJ2N-CH3 CH3NH-CH3 CH,-NH2 Ar-NH2 HC=N CH3-OH CH3CO-OH Ph-OH (CH 3) 2C=O H2C=O CEO CH3-OCOCH3 CH3-OCH3 CH,=CH-OC2HS HCO-OCH3 CH3GCOCH3 Ph-OCH3 CCI3-F CH3-F CC12F-F CBrF2-F CCIF2-F Ph-F C-F (diatomic) CBrCI2-C1 CBr3-C1 CH2=CHCH2-CI CFCI2-CI C-Ci (diatomic) Ph-CI CClBr,-Br PhCH2-Br CHBr2-Br CH3COCH2-Br C-Br (diatomic) CF3-Br
mol
cm-I
cm-’
74.5 82.3 83 83.3 84 85 85 87 88 96 96 99 1IO 172 195.8 230 78.3 83.5 85 104 223 f 3 91 106 110 179 179.2 257.3 80 81 95 96 97 99 106.9 108 f 3 110 f 6 116 f 6 117 f 6 125 132 70 70 71 73 3 80 5 95 f 5 55.5 58 60 62.5 67 f 5 70.6
850“ 921 954 937“ 946” 966 974 997 995 1068 1069 1090“ 1 I96 1623 1781 1974 1049b 1035b 1044 126OC 201 1 1033 1226 1223‘ 1731 1746 2143 1060 1019 1205 1207 1248 1240d 1085 1049 1130 1167 1177 1230d 1295 756 747 752e 757 876 1085d 583 602“ 629 669’ 736 76 1
844 937 942 945 954 964 964 985 995 1075 1075 1IO3 1201 1647 1790 1977 1029 1079 1093 1260 2009 f 22 1084 1218 1251 1727 1729 2143 1071 1080 1206 1214 1223 1240 1068 1078 f 28 1097 f 55 1152 f 52 1161 f 52 1230 1287 750 750 764 790 f 39 876 1037 f 47 553 597 63 1 670 736
* *
785
“Reference 34. bAverage from the PED distribution of ref 31. ‘Characteristic frequency, ref 29. dReference 23. Barnes, A. J.; Holroyd, S.; George, W. 0.;Goodfield, J. E. Specrrochim. Acta, Part A 1982, 38A, 1245-1251. fCrowder, G. A.; Cook, B. R. J . Chem. Phys. 1967, 47, 367-371. gSee text for explanation of the asterisk.
including heats of formation given therein. This choice of a well-defined data base helps avoid the pitfall of selecting values to fit from the very extensive and occasionally contradictory data available in the literature, even though it restricts the number of molecules. Table I lists bond dissociation energies, corresponding observed stretching frequencies, and frequencies calculated by eq 1. The general agreement between calculated and observed values is remarkably good. The value of c, for each type of bond was calculated by eq 1 from the known u and D of a single molecule, shown with * following the entry number in Table I. The specific molecules in Table I were chosen to span a large range of dissociation energies and are often the simplest representative of each bond type, to minimize the number of fundamentals and hence the probability of extensive vibrational mixing.
Zavitsas The combinations of bonded atoms examined were selected because they are represented sufficiently in the data base. For example, with carbon-carbon bonds, the range of D is from 74.5 to 230 kcal/mol and includes triple, double, and single bonds of various hybridizations. The average deviation between calculated and observed frequencies in this group is f 9 cm-l. No correlation between u and D can possibly remain valid for observed frequencies that are not essentially pure stretching modes. As a result, among the molecules for which both carbon-carbon stretching frequency and bond dissociation energy are available in the defined data base, six frequencies are not correlated reasonably well with the dissociation energy by eq l: CH3-CHO, CH3-CN, CH2=CH-CHO, CF3-CF,, CH3-COOH, and CH3-COCH3. For these molecules, the frequency designated as stretching appears to be a mixed mode (see following section): two or more local symmetry coordinates are often coupled strongly in a normal coordinate, and the “approximate type of mode” given has limited significance in such a casee4 Values of D in Table I that show no error limits are reported to be known within 2 kcal/mol; greater uncertainties are specified. An error of 1 kcal/mol in D generally results in an uncertainty of about 10 cm-’ in the calculated frequency. The overall average deviation between calculated and observed frequencies is 13 cm-I, excluding entries that show uncertainties in D greater than 2 kcal/mol. Some entries show frequency deviations greater than can be accommmodated by reasonable errors in D;evidence of vibrational mixing in several such molecules is given in the Data section. D values in Table 1 range from 55 to 257 kcal/mol and u values from 583 to 2143 cm-’. A statistical comparison of calculated and observed frequencies gives a slope of 1.002 with a standard deviation of 0.009 and a correlation coefficient of 0.992; this is based on 45 entries from Table I, excluding entries showing a f in the column u(ca1cd). The correlation would be improved even further if c1 were determined by all entries for each type of bond, instead of the single molecule used for simplicity and for easy extension of this approach to other bonds.
Force Constants Equation 1 implies a linear relationship between the stretching force constant, k in mdyn/& and the corresponding D,through eq 2 , where p denotes the reduced mass in amu. u
= 1303(k/p)1/2
(2)
Substitution of eq 2 into eq 1 gives k’/p = 0.0121(0 - c,)
(3)
In principle, eq 3 may be considered a better choice for testing this type of correlation since vibrational mixing does not affect k . However, eq 3 cannot be tested in as straightforward a manner as eq 1 for two principal reasons: (1) force constants are not observable quantities; (2) the effective reduced mass in asymmetric polyatomic molecules is not defined simply or unequivocably. Each obstacle is addressed below. The value of force constants calculated from observed spectra depends on the method used. For example, the assumption of “central forces” leads to values quite different from those obtained from “valence forces“;8 in more elaborate treatments, the assumption of a generalized valence force field (GVF) leads to values different from those obtained from the Urey-Bradley force field (UBF).’ Also, “emprical” force field methods consist essentially of adjusting force constants to fit observed fundamental frequencies for the molecule and isotopically substituted a n a l o g ~ e ssubject ,~ to reasonable judgment on the magnitude of the force constants. As a result of all of the above, sets of force constants reported for one molecule can be quite different, even though they all reproduce the observed spectrum quite well.’O Even within the (8) Herzberg, G . Molecular Spectra and Molecular Structure. 11, Van Nostrand: Princeton, NJ, 1945. (9) For an example see: Cossart-Magos, C. Spectrochim. Acta, Parr A 1978, 34A, 415-421.
The Journal of Physical Chemistry, Vol. 91, No. 22, 1987 5575
Stretching Frequencies and Bond Energies
TABLE II: Comparison of Reported Stretching Force Constants (kF)with Those Calculated in This Work (k’and kD),in mdyn/A kF, (lit.) molecule and bond s (eq 4) kD = sk’ D, kcal/mol k‘ (eq 3) 1.92 3.94 f 0.07 3.97 f 0.04 68.4 f 2 2.01 0.14 HCO-CHO 4.45 82.5 f 2 3.10 f 0.15 1.42 4.39 f 0.06 c-C6H12 4.63 3.14 f 0.14 1.40 4.40 f 0.04 83 f 2 CHj-CHO
CH3-CH2C1 CH3-CH3 H,C=CH-CHO HZC=CH-CH3 Ph-CH3 H&+CH-CH=CH2 CHj-CN HZC=CH2 C2- (neg ion) HC=CH CHj-OH HCO-OH H2C=O CEO CC13-CI CF3-F
85 f 2 88 f 2 96 f 2 99 f 2 100 f 2 110 f 2 122 f 2 172 f 2 196 f 2 230 f 2 91f2 107 f 2 179 f 2 257 f 2 70 f 2 129.5 2
*
3.28 f 0.15 3.50 f 0.15 4.08 f 0.15 4.30 f 0.15 4.37 f 0.15 5.10 f 0.14 5.98 f 0.13 9.60 f 0.15 11.34 f 0.15 13.81 f 0.15 4.75 f 0.17 6.08 f 0.17 12.08 f 0.15 18.55 f 0.17 3.02 f 0.22 6.95 f 0.18
1.35 1.29 1.15 1.11 1.10 1.oo 0.94 0.94 1.oo 1.12 1.09 1.06 1.oo 1 .oo
ref 14 3 15 15 15 14 15 15 14 15 14
4.42 4.45 4.73 f 0.04 4.66 4.68 5.09 f 0.05 5.26 8.95 f 0.05 11.22 15.59 5.27 6.17 12.28 f 0.02 18.51 3.08 7.02
4.45 f 0.04 4.52 f 0.04 4.71 f 0.05 4.78 f 0.05 4.81 f 0.05 5.08 f 0.07 5.60 f 0.09 8.99 f 0.18 11.34 f 0.24 15.44 f 0.27 5.19 f 0.16 6.42 f 0.16 12.09 f 0.15 18.58 f 0.19
U
16 19 18 14 17 b C
‘k F calculated from eq 2. bAndrews,L. J. Chem. Phys. 1968,48,972-982. Jeannotte, G . A.; Marcott, C.; Overend, J. J . Chem. Phys. 1978,68, 2076-2086; also, a quadratic force constant of 6.97 is reported by Duncan, J. L.; Mills, I. M. Spectrochim. Acta, Part A 1964, 20A, 1089. same calculational procedure, the uniqueness of any particular set of force constants can be a source of concern.” Force constants derived from quantum mechanical calculations were chosen to test eq 3. Calculations at the level of ab initio Hartree-Fock are feasible now, using double { basis sets, for molecules as complex as cyclohexane3 and naphthalene.’* The values of the calculated force constants generally are too high by 10-25%. The use of ab initio values, scaled down to match observed fundamental frequencies shows p r ~ m i s e . ’ ~This approach, based on scaled quantum mechanical (SQM) force fields, shows that, even though force constants are found not to be “transferable” between similar molecules, the scaling factors (with the same basis set) are transferable with greater S U C C ~ S S . ’ ~The SQM values of Pulay14 were chosen as one self-consistent group of carbon-carbon force constants. A second self-consistent group was obtained from the selected values of Ka~nienska-Trela,’~ which were found to correlate with 13C-13C spin-spin NMR coupling constants, an observable quantity. The values from both groups are listed in Table I1 under the heading kF. The problem of the appropriate effective reduced mass to be used with eq 3 was solved by defining p in terms of the two directly bonded atoms only; e.g., p is taken as 6.005 for all carbon to carbon bonds. This unequivocal, even though arbitrary, definition of p was used to calculate force constants by eq 3. These force constants, denoted k’, were then compared to literature values of kF (Table 11). The absence of agreement between kF and k’ values is not surprising in view of the necessarily elaborate nature of force field calculations relative to the simplicity of eq 3 and of the minimalist definition of p adopted here. It is also not surprising that the two types of force constants are related quantitatively. A plot of their ratio, s = kF/k‘,vs. D is shown in Figure 1. The curve can be described adequately by a function such as
, , , , , : : :
s = P[(Q/D) - (Q/D)’I2]
+R
(4)
(IO) E.g., the C-C stretching force constant in glyoxal (HCO-CHO) is reported as 4.70 in ref 9 and 3.973 in ref 14. Both sets of reported force constants reproduce the frequencies adequately. The difference in the value of the stretching force constant appears to be compensated mainly by differences in the value of the force constant for the CCO deformation.
(11) Crowley, J. I.; Balanson, R. D.; Mayerle, J. J. J. A m . Chem. SOC. 1983, 105, 6416-6422. (12) Sellers, H.; Pulay, P.; Boggs, J. E. J . Am. Chem. SOC.1985, 107,
6487-6494. (13) (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. (14) Pulay, P.; Fogarasi, G.; Pongor, G.; Boggs, J. E.;Vargha, A. J . Am. Chem. Soc. 1983, 105, 7037-7047. (15) Kamienska-Trela, K. Spectrochim. Acta, Pur2 A 1980,36A, 239-244. The internal consistency is obtained through a useful correlation with NMR coupling constants.
0.2
80
100
120
140
160
180
200
220
D kcal /mole I
Figure 1. Plot of the ratio of literature values of force constants to those
calculated by eq 3 ( k F / k ’ vs. ) the bond dissociation energy, for carbon to carbon bonds. The curve drawn is the scaling function of eq 4. Data from Table 11. The values of the constants for carbon to carbon bonds are P = 20, Q = 36, and R = 5.9, irrespective of the multiplicity of the bond. In essence, s is a scaling factor correlating SQM force constants to those obtained from bond dissociation energies. Scaling factors applied to ab initio force constants have no theoretical basis,14 as is the case also with the scaling factor of eq 4. Table I1 lists values of kD = sk’. There is very good agreement between kD calculated from bond dissociation energies and kF reported from force fields, throughout the large range of D covered (68-230 kcal/mol). The agreement with the SQM values of Pulay14 is particularly good, with an average deviation of only 0.025 mdyn/A between kD and corresponding k F values. Agreement is also good with the kFvalues of Kamienska-Trela’’ and with the value calculated by Colby for acetylene,I6 the SQM value of Wiberg for cy~lohexane,~ and the force constant for diatomic carbon negative ion obtained from the reported frequency’ and eq 2. A statistical analysis of a plot of kDvs. kFresults in a slope of 1.007, with a standard deviation of 0.011; the correlation coefficient is 0.9992. The fact that stretching vibrations of strong bonds are known to be relatively independent of the rest of the molecule2is reflected in the scaling factor of eq 4 which is a function of bond dissociation energy and is within 10% of unity for D > 100 kcal/mol. The group of force constants from Pulay14 and KamienskaTrelaI5 (Table 11) happens to include three of the molecules whose frequencies assigned as approximately “C-C ~ t r e t c h i n g ”were ~ (16) Colby, W. F. Phys. Reu. 1935, 47, 388
5516
The Journal of Physical Chemistry, Vol. 91, No. 22, 1987
noted to deviate severely from eq 1. Values of kD for the c-c bonds in CH3-CHO, CH2=CH-CHO, and CH3-CN are in good agreement with reported kF values. Evidently, the frequencies in question are coupled extensively with other vibrational modes and eq 1 fails, while eq 3 and 4 remain valid since coupling does not affect the value of force constants. Large groups of S Q M values of stretching force constants derived in a consistent fashion for bonds other than carbon to carbon do not appear to be available. Table I1 includes some carbon to oxygen bonds (alcohols, carbonyls): force constants for carbon m ~ n o x i d e , and ’ ~ SQM values for f~rmaldehyde,’~ formic acid,l8 and methan01.l~ From this small group, constants for eq 4 can be estimated approximately as P = 1.2, Q = 5 5 , and R = 1.3. Table I1 gives values of k’(from eq 3 with p = 6.86 and cl = 33.8) and scaled kD = sk’; the latter are in good agreement with the reported kF values. As seen in Table 11, the value of the s function now is much closer to unity, compared to C-C bonds, since the minimalist definition of p affects essentially only one terminus of the bond in alcohols and carbonyls. With carbon tetrafluoride and carbon tetrachloride also, the values of the force constants obtained from eq 3 are the same as those obtained from GVF field calculations (Table 11). Estimation of Bond Dissociation Energies
Equation 1 may be used to estimate otherwise unavailable D values from observed stretching frequencies, when there is confidence that the stretch is fairly “pure”, as judged from normal-coordinate analysis, spectra of many isotopically substituted analogues, or other factors. Methylenimine provides a good example; its C-N stretching frequency near 1638 cm-I is confirmed to be relatively pure by isotopic studies.20 The D value for the bond is not available in the data base. Equation 1 gives D(H,C=NH) = (1638/143.3)2 -+ 26.7 = 157 kcal/mol. Recently, the C-C stretch in ethyl radical was found to be at 1175 cm-’, indicated to be essentially pure stretching by examination of isotopic analogues.21 Applications of eq 1 gives the interesting result that D(CH3-CH2’) = 107 kcal/mol significantly stronger than a usual C(sp2)-C(sp3) bond (100 kcal/mol), but weaker than a single bond between sp2 carbons 110 kcal/mol). The bond dissociation energy for the C-F bond in allyl fluoride is not available in the data base or in other similar compilations. From the assigned22stretching frequency of 972 cm-’, eq 1 gives D(CH2==CHCH2-F) = 97.4 kcal/mol, a reasonable value in view of the known D(iPr-F) = 106 kcal/moL6 Similarly, from v(PhCH,-F) = 985 cm-1,23eq 1 gives D = 98.6 kcal/mol for the C-F bond in benzyl fluoride, another unavailable value. It is reemphasized that observed frequencies cannot be used to estimate reliable values of D in the absence of assurance that the absorption is not due to a mixed mode. Estimates of D can be made much more reliably by use of the appropriate force constant, which is independent of coupling. For example, from the SQM value of kF = 4.73 f 0.04 mdyn/A for the single bond in a ~ r o l e i n and ’ ~ by an iterative solution of k‘s = kF, the bond dissociation energy can be calculated to be 96.7 f 1.4 kcal/mol. This is in excellent agreement with the observed value of D(C= 96 kcal/mol (Table 11). H2=CH-CHO) ~
~
~~~~
~~~
(17) Pariseau, M. A,; Suzuki, I.; Overend, J. J . Chem. Phys. 1965, 42, 2335-2344. (18) Average of 6.1 and 6.23. (a) Davis, R. W.; Robiette, A. G.;Gerry, M. C. L.; Bjarnov, E.; Winnewisser, G. J . Mol. Spectrosc. 1980, 81, 93. (b) Ha, T. K.; Meyer, R.; Gunthard, Hs. H. Chem. Phys. Lett. 1978, 59, 17. (19) (a) Blom, C. E.; Otto, L. P.; Altona, C. Mol. Phys. 1976, 32, 1132-1149. (b) Blom, C. E.; Altona, C.; Oskam, A. Mol. Phys. 1977, 34, 557-571. (20) (a) Hamada, Y.; Hasiguchi, K.; Tsuboi, M. J. Mol. Specrrosc. 1984, 105, 70-80. (b) Duxbury, G . ;Le Lerre, M. L. J . Mol. Spectrosc. 1982, 92, 326-348. (21) Pacansky, J.; Dupuis, M. J . Am. Chem. SOC.1982, 104, 415-421. (22) Durig, J. R.; Zhen, M.; Heusel, H. L.; Joseph, P. J.;Groner, P.; Little, T. S . J . Phys. Chem. 1985, 89, 2877-2886. (23) Sadtler Standard Spectra, Sadtler Research Laboratories, Philadelphia, PA.
Zavitsas
/
1 2 c
D , kcal/mole
Figure 2. Plot of literature force constants vs. the bond dissociation energy, for carbon to carbon bonds. The curve is eq 3 multiplied by eq 4 ( k , = sk?. Data points from Table 11.
The dependence of the stretching force constant on dissociation energy is shown graphically in Figure 2 for carbon to carbon bonds. The internally consistent group of kF (mdyn/A) values of Kami e n ~ k a - T r e l a ’includes ~ the C-C bonds in methylacetylene (CH3-CCH, 5.50), N,N-dimethylacetamide (CH,-CON(CH,),, 5.17), and propionamide (CH,-CH2CONH2, 4.53). Bond dissociation energies for these bonds are not available in the data base. Using Figure 2, or eq 3 and 4, allows the estimation of D = 120, 111, and 88 kcal/mol, respectively. SQM values of kF exist for cyclobutane: 3.9024 and 3.85 m d ~ n / A from ; ~ ~ these values D(C-C) can be estimated as 65.5 f 2 kcal/mol. This can be compared with an estimated value of E , = 63.2 kcal/mol for the diradical ring opening of cyclobutane.26 SQM values for kF for benzene and naphthalene also are available as an internally consistent group.’* From kF = 6.58 mdyn/A for benzene, Figure 2 allows an estimate of D(C-C) = 140 kcal/m01.~’ From the force constants for naphthalene, bond dissociation energies estimated similarly are 125 kcal/mol for the bond between the carbons common to both rings, 126 for the bond between a common carbon and the a-carbon, 153 for the bond between the a- and @-carbons,and 130 for the remaining bond. The force constants and the D values reflect the usual resonance concepts of double bond localization in such systems. Assignments of Frequencies
Occasionally eq 1 can be helpful as a guide to assignment of frequencies, along with other tools, such as normal-coordinate analysis, Raman spectra, etc. Some examples are given below. The infrared spectrum of benzyl chloride exhibits two strong absorptions in the region of C-Cl stretching frequencies, at 767 and 679 cm-l. The lower frequency was chosen to be assigned to the C-CI stretching fundamentaL2* However, from the known D(PhCH,-Cl) = 72 kcal/mol, eq 1 gives v(ca1cd) = 776 cm-’. In the absence of any strong evidence to the contrary, the higher frequency is a better choice for the C-C1 stretch. Characteristic stretching frequencies for Ar-Br generally are not available in infrared “correlation charts”,6 or tables of characteristic f r e q ~ e n c i e s . With ~ ~ D(Ph-Br) = 80 kcal/mol, eq (24) Banhengyi, G.;Fogarasi, G.;Pulay, P. J . Mol. Strucr. 1982,89, 1-13. (25) Annamalai, A.; Keiderling, T. A. J. Mol. Spectrosc. 1985, 109, 46-59. (26) Benson, S. W.; O’Neal, H. E. Kinetic Data of Gas Phase Unimolecular Reactions; NSRDS; National Bureau of Standards, U.S. Government Printing Office: Washington, DC, 1970. (27) Not all SQM force fields yield the same value of k F . The value depends critically on molecular geometry and type of basis set used, choice of internal coordinates, scaling factors, etc. (28) Ribeiro-Claro, R. J. A.; Rocha-Gonsalves,A. M. D’A.; Teixeira-Diaz, J . J. C. Spectrochim. Acta, Part A 1985, 41A, 1055-1062 (29) Bellamy, L.J. The Infra-red Spectra of Complex Molecules; 2nd ed.; Wiley: New York, 1958.
Stretching Frequencies and Bond Energies 1 gives 899 cm-I for the stretching frequency. The spectrum of bromobenzene exhibits a medium absorption at 903 cm-l, consistent with the stretching mode. Methallyl chloride (3-chlorobut- 1-ene) in our hands exhibits three strong absorbances below 1000 cm-I, at 904,749, and 661 cm-’. The highest frequency is typical of CH2=CHR;29 from = 69 an approximate value of D(CH,=CHCH(CH,)-Cl) kcal/mol, eq 1 gives v(ca1cd) = 736 cm-I. Evidently, the observed strong absorption at 749 cm-’ is attributable primarily to the C-Cl stretch. The spectra of methyl chloride and methyl bromide show absorbances at 732 and 61 1 cm-’, respectively, assigned as being approximately the carbon-halogen stretching modes4 On the basis of the known D values of the bonds, eq 1 gives 922 and 777 cm-’, respectively. Isotopic substitution studies have shown that none of the observed frequencies in simple aliphatic chlorides and bromides can be assigned principally to a carbon-halogen stretch;30 the large discrepancy between calculated and observed frequencies confirms this conclusion. The uncoupled C-Br stretch can be seen in equatorially substituted cyclohexanes and steroids in the 750cm-l region, as a “characteristic” frequency;29with D(C6Hl1-Br) = 68 kcal/mol, eq 1 gives v = 750 cm-’. Equation 1 is not useful for describing frequency shifts caused by isotopic substitution adjacent to the bond of interest (e.g., CH3-CHO vs. CH3-CDO), because of the minimalist definition of 1.1 employed. The force constant is changed very little by such isotopic substitution.
Data Whenever available, the observed frequency, v, and dissociation energy, D, were used, rather than the “harmonic” values. Vapor-phase frequencies were used, when available. The single molecule used to set c1with eq 1 was selected because the frequency appeared to be fairly pure stretching and D was known accurately. For the C-Cl and C-Br bonds, cl was determined from the diatomic species to eliminate complications from reported mixings with C-H modes.30 The value of D(C-Cl) = 80 f 5 is from the J A N A F table^,^ while ref 6 gives 95 f 7 kcal/mol. If the higher value is used to set cl, hardly any other C-Cl frequencies would be accommodated. Similarly, despite the large uncertainty in diatomic D(C-Br) = 67 f 5 kcal/mol, the value of c1 obtained from it allows accurate estimation of a whole series of typical C-Br frequencies in Table I. For molecules exhibiting more than one stretching frequency (symmetric-asymmetric, symmetric-degenerate), the value of v(obsd) listed in Table I is an estimated average consistent with the usual normal-coordinate calculations. For molecules that can ~, be approximated as XY,, v(obsd) = [(1/2)(v: + v , ~ ) ] ’ / entries 2, 6, 11, 18, and 36. For molecules that can be approximated as XY3, v(obsd) = [(1/3)(7: + 2 u ~ ~ ) ] ’ entries / ~ , 17, 37, 38,41, 44, 47, and 49. Averaging in this fashion tends to minimize the effects of the ”interaction” force constant between the two stretching modes. Table I contains some values of v(obsd) that are known to be somewhat coupled to other vibrations, as follows. The value of v(obsd) = 201 1 cm-’ for HC-N is the average of 1925 (DCN) and 2097 (HCN).4 The latter band is somewhat (30) Williams, R. C.; Taylor, J. W. J . Am. Chem. SOC.1963, 95, 1710.
The Journal of Physical Chemistry, Vol. 91, No. 22, 1987 5577 coupled to a C-H mode,29and Herzberg* reports a “zero-order” frequency (wo, at zero amplitude of vibration) of 2001 cm-’, in good agreement with the calculated value of 2009 cm-I. The frequency of 1044 cm-’ attributed primarily to the C-N stretch in methylamine4 is considerably lower than tlie calculated value of 1093 cm-’. Examination of the spectra of deuteriated analogues3’ indicates that the observed frequency is somewhat mixed. The mean corresponding frequency of CH3-ND2 is near 1051 cm-’, and of CD3-NDz near 1065 cm-’. In the absence of mixing, the deuteriated compounds would be expected to exhibit lower C-N frequencies, rather than the increasingly higher values observed. The value from the d5 compound is in excellent agreement with the calculated frequency of 1093 cm-’ for CH3-NH2. The frequency of 1033 cm-’ attributed4 primarily to C-0 stretching in methanol is also considerably lower than the calculated value. Some mixing is apparent from an analysis of the spectra of deuteriated analogues:32 the average of the two observed frequencies with a major C-0 component in CD3-OD is 1069 cm-’ in excellent agreement with the calculated value of 1082 cm-’ for CH3-OH. The value of v(obsd) = 1226 cm-l for CH3CO-OH is the average of 1182 cm-I from the natural compound and 1270 cm-’ from CH3CO-OD;4 this upward shift on deuteriation is evidence of some vibrational mixing in either or both compounds. The data base for D values in Table I1 has been augmented by the compilation of McMillen and Golden.33 The D values for benzylic bonds in Tables I and I1 are based on a heat of formation of 48 kcal/mol for the benzyl radical, consistent with our long~*~~ standing suggestion that D(PhCH,-H) = 88 k c a l / m 0 1 , ~ which now appears to have been a ~ c e p t e d . ~ ~ , ~ ~
Acknowledgment. Part of this work was supported by a grant from the Committee on Research of the Brooklyn Campus of Long Island University. Registry No. CH2=CHCH2CHg, 106-98-9; c-C6HIZ,110-82-7; CZHSC2H5, 106-97-8; CHgOCH2CH3, 540-67-0; CH3CH20H, 64-17-5; CH3CzH5, 74-98-6; CHpCH2C1, 75-00-3; CH3CH2COCH3, 78-93-3; CH3CH3, 74-84-0; HCOCHO, 107-22-2; CH2=CH(CHI)CHI, 11511-7; CHgCFg, 420-46-2; H2C=CHCH=CH2, 106-99-0; HZC=CH2, 74-85-1; Cy, 12595-78-7; H C E C H , 74-86-2; (CH3)2NCHg, 75-50-3; CHgNHCH3, 124-40-3;CH3NH2, 74-89-5; CH$HO, 75-07-0; H C E N , 74-90-8; CH,OH, 67-56-1; CH,COOH, 64-19-7; PhOH, 108-95-2; (CH,),C=O, 67-64-1; H2C=O, 50-00-0; C a , 630-08-0; CH3OCOCHg, 79-20-9; CHjOCH3, 1 15-10-6; CH2=CHOC2Hs, 109-92-2;HCOOCH3, 107-31-3;H 2 C = C H C H 0 , 107-02-8;PhOCHg, 100-66-3;CClgF, 75-69-4; CH,F, 593-53-3;CC12F2,75-71-8; CBrF3, 75-63-8; CCIFg, 7572-9; PhF, 462-06-6; CF, 3889-75-6; CBrCl,, 75-62-7; CBr3CI, 594-15-0; CH2XCHCH2C1, 107-05-1; H2CxCHCH3, 115-07-1; CC1, 3889-76-7; PhC1, 108-90-7;PhCH2Br, 28807-97-8; CHBr3, 75-25-2; CH3COCH2Br, 598-31-2; CBr, 3889-77-8; PhCHg, 108-88-3;CH3CN, 75-05-8; HCOOH, 64-18-6; CCI,, 56-23-5; CF4, 75-73-0. (31) Dellepiane, G.; Zerbi, G. J . Chem. Phys. 1968, 48, 3573-3583. (32) Timidei, A.; Zerbi, G. Z. Naturjorsch. A . 1970, 25, 1729-1731. (33) McMillen, D. F.; Golden, D. M. Annu. Rev. Phys. Chem. 1982, 33, 493-532. (34) Zavitsas, A. A. J. Am. Chem. SOC.1972, 94,2779-2789. Zavitsas, A. A,; Mellikian, A. A. J . Am. Chem. SOC.1975, 97, 2757-2763. (35) Zavitsas, A. A.; Fogel, G.; Halwagi, K. E.; Legotte, P. A. M. J. Am. Chem. SOC.1983, 105, 6960-6962. (36) Lossing, F. P.; Holmes, J. L. J . Am. Chem. SOC.1984, 106, 691 7-6920.
