8336
J. Phys. Chem. 1992, 96, 8336-8339
Christiansen, P. A.; Ross, R. B.; Atashroo, T.; Ermler, W. C. J . Chem. Phys. 1987.87.2812-24. (d) Ross. R. B.: Powers. J. M.: Atashroo. T.: Ermler. W. C.; LaJohn, L. A,; Christiansen, P. A. J . Chem. Phys. 1990, 93, 6654-70. (22) Raffenetti, R. C. J . Chem. Phys. 1973.58, 4452-8. (23) Dupuis, M.; Rys, J.; King, H. F. J . Chem. Phys. 1976, 65, 111-6. (24) (a)-McMurchie, L. E.; Davidson, E. R. J . Comput. Phys. 1981,44, 289-301. (b) Pitzer, R. M.; Winter, N . W. J . Phys. Chem. 1988,92,3061-3. (25) Roothan, C. C. J . Reo. Mod. Phys. 1960, 32, 179-85. (26) Mulliken, R. S. J . Chem. Phys. 1955, 23, 1833-40, 1841-6. (27) (a) Arbusow, A . E. J . Russ. Phys. Chem. SOC.1906,38ii, 293. (b) Mann, F. G.; Purdie, D.; Wells, A. F. J . Chem. SOC.1936, 1503. (28) (a) For copper metal, Cu-Cu bond length = 2.551 A: Lide, D. R. CRC Handbook of Chemistry and Physics, 71st ed.; CRC Press: Boca Raton,
FL, 1990; 9-20. (b) For CUI. crystallographic bond lengths: Cu-I = 2.62 Haas, A.; Helmbrecht, J.; Niemann, U.;Brauer, G. In Handbuch der Praeparatiuen Anorganischen Chemie; Ferdinand Enke Verla : Stuttgart, 1975. (c) For I, crystallographic bond lengths: Cu-I = 2.70 C u C u = 2.69 A; 1-1 = 4.51 A; sce ref 1la. (29) (a) Moore, C. E. Atomic Energy Levels; 1971; Nat. Bur. Stand. US. Circ.; vol. I-III,467. (b) Cotton, F. A.; Wilkinson, G . Advanced Inorganic Chemistry, 5th ed.; Wiley-Interscience: New York, 1989. (30) Rosenstock, H . M.; Sims, D.; Schroyer, S. S.; Webb, W. J. Ion Energetic Measurements. Part 1,1971-1973, in National Standard Reference Data System, Sept 1980. (3 1) Vanquickenborne, L. G.; Coussens, B.; Postelmans, D.; Ceulemans, A.; Pierloot, K. Inorg. Chem. 1991, 30, 2978-86.
A; C u C u = 1-1 = 4.28 A.
1;
A Theoretical Study on the Assignment of Fundamental Frequencies of o-Benzyne Ruifeng Lh,* Xuefeng Zhou, and Peter Pulay Department of Chemistry and Biochemistry, University of Arkansas, Fayetteville, Arkansas 72701 (Received: May 4, 1992)
The geometry and quadratic force field of o-benzyne are calculated by the recently developed unrestricted Hartree-Fock natural orbital complete active space (UNO-CAS) method. The force field, after an empirical scaling by scale factors of the UNO-CAS force field of benzene, satisfactorily reproduces the matrix IR frequencies of o-benzyne and its deuterium and I3Cisotopomers. On the basis of the calculations, earlier assignments of the fundamentalsof o-benzyne, o-benzyne-d4, and 1,2-I3C2C4H4 are discussed. The conclusion that the frequency of the formal triple bond stretching is at around 1860 cm-I instead of 2080 cm-l is confirmed. The matrix IR frequencies at 1627, 1607, 1598, 1596, 1307, 1271, 1055, and 838 cm-' are concluded to be. not fundamentals of o-benzyne, those at 1411, 1198, 1112, 1029, 679 and 616 cm-I are concluded to be not fundamentals of o-benzyne-d4,and those at 1298, 1266, 1040, and 835 cm-l are concluded to be not fundamentals of 1,2-I3C2C4H4.Reassignments on some of the normal modes are proposed.
Introduction Since the first matrix infrared (IR) identification of obenzyne,'J IR studies on this molecule have been conducted in several group^.^" However, only a small number of frequencies have been recorded and many questions were raised in the vibrational assignments. Representative of these is the assignment of the formal carbon-carbon triple bond stretching frequency. Early studies unambiguously assigned a strong band at 2080 c m - I to this vibrati~n.l-~It was challenged seven years ago by a gas-phase photodetachment study which assigned 1860 cm-' to this vibration.' Theoretical calculations6.*-" with both semiempirical and ab initio methods including MNDO, restricted Hartree-Fock (RHF), two-configuration SCF (TC-SCF), and second-order Moller-Plesset perturbation (MP2) resulted in frequency of this vibration in the range 2190-1930 cm-I. On the basis of results of their calculations at several levels of theory, Schaefer et a1.I0 concluded that this frequency cannot be higher than 2010 cm-I. Thus, the photodetachment conclusion is in line with theoretical results. However, because of strong electron correlation and basis set truncation errors, none of the pure ab initio studies successfully reproduced observed frequencies quantitatively. For example, the recent study of Scheiner and Schaefer" used MP2 in conjunction with triple [ plus two sets of polarization functions (TZ2P) and obtained a frequency 1943 cm-l for the CC triple bond stretching vibration.'l The size of their calculation is perhaps the largest at this level, but the result is still about 100 cm-' higher than the photodetachment result.' Recently, the conclusion of the photodetachment study was confmed experimentally. In a neat matrix 1R study, a weak band at 1846 an-'was detected and attributed to this vibration: The origin of the frequencies at around 2085 cm-I in the matrix IR spectra of o-benzyne was also found. Laboratory studiesI2J3 concluded that cyclopentadienylideneketene has a strong IR absorption at 2085 cm-I. This molecule or molecules with similar structural units are believed to be byproducts or unstable intermediates in the reactions generating o-benzyne in matrices.I"
Although the controversialassignments of the stretching vibration is apparently resolved, the assignment and interpretation of the experimental IR spectra are still not complete; e.g., results of the most recent matrix IR study6 differ in several aspects from previous experimental studies. To clarify the remaining problems, we used an empirically corrected ab initio technique in this study. On the basis of the results of our calculation, detailed discussions on the assignment of the matrix IR frequencies of o-benzyne, o-benzyne-d,, and 1,2J3C2C4H4are given.
Method For o-benzyne, the simple restricted HartreeFock (RHF) method is apparently not appropriate because of the presence of strong (nondynamic) electron correlation. The most straightforward way to treat strongly correlated systems is multiconfiguration SCF (MC-SCF) method, i.e., the optimization of molecular orbitals in a limited configuration interaction (CI) wave function. It is now generally agreed that the most satisfactory MC-SCF wave function should include all possible configurations in the active space, i.e., the space of strongly correlated orbitals. This FORS (full optimizul reaction space) concept was introduced by Ruedenberg and co-~orkers'~ and further developed by Roos et al.Is as the complete active space SCF (CAS-SCF). Up to now, the only multiconfigurational method applied to this molecule is two-configuration SCF (TC-SCF).9Jo Such a wave function can describe only the biradical nature of the formal triple bond. However, it has been our experience that, in conjugated radicals, the whole *-electron system is involved in resonance, leading to strong correlation effects. This predicts an eight-orbital active space, consisting of the bondingantibonding pair of the in-plane 7 orbitals on the formal triple bond, as well as the six out-of-plane .rr orbitals of the ring. Indeed, the unrestricted Hartree-Fock (UHF) natural orbital criterion16gives exactly this active space. To strike a compromise between computational expense and accuracy, an alternative to CAS-SCF, the recently developed unrestricted HartreeFock (UHF) natural orbital complete active
0022-3654/92/2096-8336%03.00/0 0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 8337
Fundamental Frequencies of o-Benzyne
TABLE I: Internal Coordinates of o-Benzyneg and Scale Factors of the UNO-CAS Force Field
no.
coordinate
RI, .-, R6
1-6 7-10
rl.
11 12
...,r4
6-1/2(al-a2+ay-a4+a3-a6)
1 2-’12(2al-a2-ay+2a4-as-a6) 2-I (a2-a3+a~-a6)
13 14 15 16 17-20 2 1-24
6-1/2(61-b2+63-64+65-66)
2-‘(6 1-63+64-66) 12-’/2(-61+262-63-64+26~-6~) BI = 2-1~2(cpI-cpl’),... B4 1
YI9
*..1
Y4
description
4-21G
scale factors 6-31G*
CC stretching CH stretching ring deformation ring deformation ring deformation ring torsion ring torsion ring torsion CH in-plane deformation CH wagging C C C C coupling
0.9423 0.8541
0.9001 0.8273
0.7984
0.8513
0.8522
0.8816
0.7875 0.8563 0.7400
0.8137 0.9034 0.7600
Osee Figure 1 for atomic numbering. aI is the angle of c6c2cI;61 is the c6cIc2c3 dihedral angle, and so on cyclically. cpI is the angle C2C3H7 and cpI’ is the angle C4C3H7,etc.; y l is the angle of the C3H7bond with the C2C3C4plane. All CH waggins are negative if the H atom moves toward us.
space (UNO-CAS)17method was used in this study. This method is based on the observation that UHF nautral orbitals approximate CAS-SCF orbitals very well. Thus, a full CI in the space of fractionally occupied UHF natural orbitals gives a good approximation to CAS-SCF wave function. If the orbital optimization step is omitted, the UNO-CAS method becomes considerably less expensive than CAS-SCF. Previous studies have shown that UNO-CAS potential energy surfaces are closely parallel to the CAS-SCF 0nes.17 Although the UNO-CAS energy is not fully variational, its gradient can be readily evaluated.” Complete geometry optimization for 0-benzyne has been carried out at the UNO-CAS level with the gradient technique18 and geometry DIIS algorithmIg working in internal coordinates. The internal coordinates are defined according to earlier proposalZo and presented in Table I. Both the 4-21GZ0and the 6-31GSZ’ basis sets are used. At the UNO-CAS/6-31G* equilibrium geometry, complete UNO-CAS/4-21G and UNO-CAS/6-3 1G* force fields are obtained by numerical differentiation of the energy gradients. To correct for the systematic errors due to dynamical electron correlation and basis set incompleteness, the ab initio force fields are empirically scaled by the scaled quantum mechanical (SQM) force field procedureZ2 F,j
= FijyCiC,)’/2
where Fij is the scale force constant; Fi,’ is the ab initio force constant; ci and cj are scale factors of coordinate i and j . Scale factors are normally obtained from fitting the fundamentals of vibrationally well-characterized molecules and are found to be transferable among molecules of similar bonding units.23 In the present study, we use the scale factors obtained for the UNO-CAS force fields of benzene.24As expected, the UNO-CAS active space of benzene consists of the six valence A orbitals. It is worth pointing out that, although benzene is not a very strongly correlated system, the UNO-CAS results are significantly superior to the RHF ones. The vibrational frequencies are calculated by diagonalization of Wilson’s GF matrix.25 Characterization of the normal mode is based on the total energy distribution (TED) criterionZ6 where i refers to a normal mode and p to an internal coordinate.
Results and Discussion Figure 1A shows the optimized geometrical parameters of o-benzyne. Since there are no experimental results to compare with, the UNO-CAS/6-3 lG* and microwaveZ7structural parameters of benzene are also presented in Figure 1B. The C-C distance for the latter is very well reproduced at the UNOCAS/6-31G* level of theory. The optimized formal triple bond length of o-benzyne at the same level is 1.262 A, in agreement with the GVB result 1.260 A of Hill, et ai? and is significantly longer than SCF results.28s29The results of single-reference MP2 with DZP and TZ2P basis sets are 1.2751° and 1.259 &I1 respectively.
H I 1.076
H7 11.073
1.076
125.9 ,262
1.420
10
(A)
0-benzyne
H
(8) B e n z e n e
Figure 1. UNO-CAS/6-31GS geometries of (A) o-benzyne and (B) benzene (the numbers in parentheses are the microwave results). TABLE II: Eaergies and Active Orbital Occupancies of o-Benzyne at UNO-CAS/QJlC* Geometry 4-21G energies: E R H F = -228.915732 au; E U H F = -228.964126 au; EuNocAs= -229.06091 1 au occupation numbers UHF NO: 1.957, 1.839, 1.812, 1.503, 0.497, 0.188, 0.161, 0.043 UNOCAS: 1.954, 1.895, 1.883, 1.781, 0.220, 0.118, 0.105, 0.044 6-31G* energies: E R H F = -229.383136 au; E U H F = -229.426423 au; EuNocAs = -229.519653 au occupation numbers UHFNO: 1.962, 1.854, 1.827, 1.508, 0.492, 0.173, 0.146, 0.038 UNOCAS: 1.957, 1.901, 1.890, 1.787, 0.214, 0.112, 0.100, 0.041
A good check on the quality of the theoretical geometry is the agreement between the calculated rotational constants of the optimized geometry and the observed results. The former are 6905.8, 5739.6, and 3134.5 MHz, and the latter are 6990, 5707, and 3 140 MHzM The relative differences are 1.2,0.6, and 0.2% respectively. A significant fraction of the differences, however, should be attributed to the fact that the experimentalresults are of vibrationally averaged instead of the equilibrium geometry. The total energies of RHF, UHF, and UNO-CAS with the 421 and 6-31G* basis sets at the 6-31G* UNO-CAS optimized geometry are presented in Table 11. This table also contains the fractionally occupied (occupancy between 0.02 and 1.98) UHF natural orbital occupation numbers and the occupation numbers of the UNO-CAS active orbitals. The expectation values of ( S ) of the UHF wave function with 4-21G and 6-31G* basis sets are 1.500 and 1.430, respectively. The theoretical value is 0 for a singlet state. This indicates the UHF wave functions are severely contaminated by higher spin states, so that the UHF method, although it recovers electron correlation in a limited way, is not appropriate for studying this system. Tables 111 compares the calculated frequencies and IR intensities of 0-benzyne, ebenzyne-d,, and 1,2-I3C2C4H4 with the most recent experimental results of Radziszewski, H a , and Zahradnik
8338 The Journal of Physical Chemistry, Vol. 96, No. 21, 1992
Liu et al.
TABLE III: Comparison of Calculated and Experimental' Frequencies of o - h z y n e GH4 calc sym Y 421G 631G' a, I 3097 3099 2 3068 3067 3 1861 1816 1 1446 1463 5 1342 1350 6 1157 1 I43 7 1037 1028 974 8 979 9 604 598 a2 I O 973 967 I1 844 850 12 637 606 13 446 425 b, 14 926 920 15 727 737 16 396 396 b2 17 3093 3097 18 3051 305 1 1526 19 1511 20 1401 1405 21 1229 1234 22 1106 I100 885 23 904 528 24 567 ~~
C6D4 EAS"
16 4.7 1.6 1.6 1.0 1.4 0.6 19.4 4.3 0.1 0.0 0.0 0.0 0.0 0.0 85.3 6.3 9.5 0.3 1.5 9.0 0.0 0.9 12.8 13.6
Y
3094 3071 1846 1415 1271 1055 1039 982 589
838 737 388 3086 3049 1451 1394 1307 1094 849 472
calc I PAY 421G 631G' 5.7 2297 2296 2266 2267 0.9 2.0 1856 1811 0.1 1451( I368 1376 1.3 135Sd 1256 I258 7.4 ? 834 830 10.4 973 964 5.2 793 793 0.1 586 579 790 780 656 659 563 552 417 405 745 737 0.3 ? 47.4 585 570 347 4.2 344 2292 2293 9.1 2251 2252 0.6 9.1 ? 1469 1477 5.5 1283 1284 0.2 ? 976 979 1.3 883 869 824 24.8 816 81.0 557 520
EASO Ib
Y
4.8 0.1 1.0 2.2 2.8 0.3 5.7 9.2 0. I 0.0 0.0 0.0 0.0 0.3 41.4 7.1 8.4 0.0
2311 2295 1844 I364 1198 853 995 792 579
0.0
4.0 0.4 2.2 13.0 12.0
679 57 1 336 2314 2285 1411 I293 1112 875 790 469
calc I PAY 421G 631G* 4.7 3097 3099 0.3 3068 3067 0.4 1792 1751 1 .O 1443 1459 2.6 ? I340 1348 3.9 1157 1143 5.9 I023 1015 4.3 977 970 0.I 591 598 967 973 844 850 601 63 I 435 413 0.1 920 926 726 23.5 137 393 393 4.2 5.8 3093 3097 0.1 3051 3051 3.0 1483' I508 1524 2.5 1394 1398 0.2 ? 1216 1220 0.1 I IO4 1098 879 26.4 896 79. I 551 513
I ,2-IJC2C4H, EAS' Ib
4.7 1.6 1.7 0.8 1.5 0.7 19.0 3.9 0.1 0.0 0.0 0.0 0.0 0.0 86.2 5.9 9.5 0.3 1.9 8.8 0.1 0.7 11.6 13.2
Y
3093 3070 1793 1414 I266
Io40 I024 98 1 586
835 736 388 3085 3049 1450 1385 1298 1092 846 457
I PAS' modcdcJcrutn 5.1 CH(D) str 0.8 CH(D) str 1.8 CHC str 0.1 1450 CC str-+ CH(D) def 1.9 ? CC str t CH(D) dcf 7.0 ? CH(D) def 9.5 CC str 5.5 CC str 0.1 ring del CH(D) wag CH(D) wag ring tor ring tor 0.3 ? CH(D) wag 43.7 CH(D) wag 4.0 ring tor 8.6 CH(D) str CH(D) str 0.3 11.2 CC str 4.9 CH(D) def + CC str 1.0 ? CH(D) def CC str 1.1 CC str 23.8 ring dcf 77.2 ring dcf
+
"Experimental assignments from a recent matrix IR sudy by Radziszewski et al., ref 6. bMP2/TZ2P IR intensities of Scheiner and Schaefcr, ref 1 I . 'See text. dMatrix IR frequency of Nam and Leroi, ref 4. cMatrix IR freipency of Dunkin and MacDonald. ref 3. 'Proposed assignment on the basis of the scaled ab initio calculations.
(RHZ)? The IR intensities are not calculated in the present study. For the ease of interpretation and assignment of the observed frequencies, the MP2/TZ2P intensities of Scheiner and Schaeferl are included in these tables. Most of these calculated intensities are within a factor of 2-3 of the observed results.6 All the calculated strong IR bands are observed to be strong. Most of the calculated frequencies are also in good agreement with the observed results; for example, all the calculated CH stretching modes are within 10 cm-l of the observed results. However, there are some differences between our calculated and observed results. Detailed discussions on the origins of these discrepancies are given below. For the convenience of discussions, the 24 normal modes are arbitrarily numbered as given in Table 111. a1 Modes. The most disputed CC triple bond stretching mode u3 of o-benzyne-h, is calculated to be at 1861 cm-l (4-21G basis set) and 1816 cm-I (6-31G* basis set). The two experimental results are 1860 (ref 7) and 1846 cm-I (ref 6). Since it is not a strong infrared band and it is in the region of intense carbonyl absorptions, this band was either ignored or obscured in earlier matrix IR studies which attributed the strong band at about 2080 cm-l to this m ~ d e . l -The ~ calculated deuterium and I3C isotope shifts of this mode, 4 and 65 cm-' (6-31G* basis set), agree reasonably with the observed results 2 and 53 cm-l. Considering both the experimental difficulty in determining the exact positions of this mode and the theoretical difficulty in deriving accurate force field for this highly correlated molecule, this agreement is adequate and confirms the new matrix IR observation. Relatively large differences between the calculated and R H Z s assignment of the totally symmetric modes are found for u4, us, and Y6. RHZ's assignment of u5 and Y6 was less confident than the rest of the a1 modes. They suggested that the band at 1055 an-',which was assigned to Y6, might be due to Fermi resonance. Indeed, this band was observed to have exactly the same I3C isotope shift as u,, and the sum of the observed intensities of the two bands, 17.8 km/mol, is very close to the calculated intensity of u7, 19.4 km/mol. Our calculated frequency of Y6, 1143 cm-l, is almost 100 cm-'higher than their assignment, 1055 an-'. The calculated frequency of the same mode in o-benzyne-d,, 830 cm-I, is, however, in much better agreement with their assignment, 853 cm-'. On the basis of these results, we believe the mode Y6 in o-benzyne is at around 1150 cm-I. The band at 1055 cm-I originates from a combination or overtone getting intensity by Fermi resonance with the fundamental u7. The calculated frequency of us, 1350 cm-I, is about 80 cm-' higher than R H Z s assignment, 1271 cm-l. Difference of this magnitude is larger than we anticipated. The calculated result is supported by a matrix IR study of Nam and Leroi4who reported
a band at 1355 cm-l and attributed it to o-benzyne. RHZ's assignment of u4, 1415 cm-I, is 48 cm-l lower than the calculated result, 1463 cm-I. The calculated intensity of this mode, 1.0 km/mol, is about 10 times of the observed result. For obenzyne-d4, both the calculated frequency (1376 cm-I) and intensity (2.2 km/mol) are in much better agreement with the experimental results (1364 cm-I and 1.O km/mol). Since calculated isotope shift is generally more reliable than calculated frequency itself, based on the observed frequency of the deuterium substituted isotopomer and the calculated isotope shift, the position of this mode in the parent molecule is predicted at 1364 (1463 - 1376) = 1451 cm-l. Indeed, an intense absorption (observed IR intensity 9.1 km/mol) was observed at 1451 cm-I, but it was assigned to the b2 mode ~ 1 9 .Since this absorption is observed to be much more intense than the calculated result of u4, we believe u4 of o-benzyne is either at 1451 cm-l or very close 1451 cm-I and is therefore obscured by the intense absorption at 1451 cm-I. b, Modes. For the three bl modes, the calculated frequencies and intensities of the very strong and medium intense modes vlS and are in very good agreement with the observed results of all three isotopomers. The calculated very weak mode ~ 1 is, 4 however, almost 100 cm-l higher than RHZ's assignment. The very weak nature of this mode reveals the Wiculty in experimental determination of its position. On RHZ's infrared spectrum of o-benzyne, there are very strong and broad absorptions at about 920 cm-l which are attributed to byproducts in the matrix. Our calculated frequencies of ~ 1 for 4 both the o-benzyne-h4 and 1,2I3C2C4H4are in this region, and therefore we believe they are obscured by the intense byproduct absorptions. 9 Modes. Of the eight 9modes, the largest difference between the calculated and RHZ's assignment is found for uzl. This mode is predicted to be the weakest among the three b2 symmetry ring stretching coupled with CH(D) in-plane bending modes. Since our calculated results for the other two similar but more intense modes, u20 and u22, agree very well with the assignment of RHZ, we believe the assignment of this mode to the band at 1307 cm-' is not conclusive. Significant discrepancia are also found for ul% uar and vu. For all three isotopomers, our calculated frequencies of ~ 1 are 9 about 70 cm-I higher than RHZ's assignment. The MP2/TZ2P IR intensities of this mode are significantly lower than the observed results of RHZ. For o-benzyne-d4, Dunkin and MacDonald3 observed a band at 1483 cm-l which was assigned by Ham and Leroi to a CC stretching vibration. This band is only 6 cm-I higher than our calculated frequency of ~ 1 9 ,Therefore, we believe the mode ~ 1 of 9 tetradeuteriobenzyne is more likely to be at 1483 cm-l instead of 1411 cm-l.
+
Fundamental Frequencies of o-Benzyne Our calculations overestimated the two b2 ring deformation modes u ? and ~ u--. ? ~esDeciallv .. with smaller 4-21G basis functions. Since &ih of the two modes are calculated and observed very strong, there should be no doubt concerning the experimental assignment. Two s o u m may be responsible for the overestimation by theoretical calculation: anharmonicity of the observed frequencies and inadequate description of ring strain by the theoretical model. The latter is evident from the fact that results obtained with the 6-31G* basis set, which includes higher angular momentum d polarization functions and therefore gives a better description of the ring strain effect, are in much better agreement with observed results than those obtained with the 4-21G basis set. a2 Modes. There are four a2 modes in o-benzyne. They are symmetry forbidden and, therefore, cannot be observed in IR spectrum in free molecule state. Nevertheless, these frequencies are important in calculating thermodynamic functions. Since the az modes are treated in the same way as symmetry-allowed modes in our calculation, we believe they are predicted with the same accuracy. Frequencies Not Belonging to the Fundementahof o-Benzyne. There are several matrix IR bands other than those at about 2080 cm-I which do not agree either with our calculated results or with RHZ's experiment. For o-benzyne-h4, they are at 1627 and 1607 cm-' reported by Chapman et a1.,'*21596 cm-'reported by Nam and Leroi? and 1598 cm-l reported by Dunkin and MacDonald? for o-benzyne-d4, they are at 1029 and 616 cm-I reported by Dunkin and Ma~Donald.~ On the basis of results of our calculation and RHZs recent experiment, we believe that these frequencies are not fundamentals of the subject molecules.
Conclusion Throughout this study, the only approximation made beyond the ab initio method is that the scale factors of benzene are applicable to o-benzyne. No empirical parameters of o-benzyne itself were used. In this sense, this is a priori prediction. Excluding the symmetry-forbidden az modes and v4, us, &,~ 1 4 , u19, and uzl, for which reassignment may be necessary, the mean deviation between the calculated and RHZ's assignment of 42 frequencies is 15.7 cm-'. Since all the normal modes are calculated in the same way, we believe this mean deviation is also valid for the IR-inactive a2 modes. For molecules of this size, the same accuracy cannot be attained either by empirical normalaordinate analysis or by pure ab initio calculation. For the former, the number of distinct force constants exceeds the number of observed frequencies, and, therefore, results of empirical fitting procedure cannot be conclusive; and for the latter, it is just too expensive to recover enough electron correlation and basis set truncation errors with the contemporary computing facilities. Therefore, we believe the present scaled UNO-CAS force field is the most reliable one for this molecule. The results confirmed that the frequencies at around 2080-2090 cm-l are not fundamentals of o-benzyne and o-benzyne-d4. The agreement between the calculated and experimental results suggests that the observed frequencies at 1627, 1607, 1598, 1596, 1307, 1055, and 838 cm-l are not fundamentals of o-benzyne, frequencies at 1411, 1198, 1112, 1108, 1029, and 679 cm-l are not fundamentals of o-
The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 8339 benzyne-d4,and frequencies at 1298, 1266, 1040, and 835 cm-l are not fundamentals of unperturbed 1,2-I3C,ClHd. Acknowledgment. This research was supported by the US. National Science Foundation, Grant CHE-8814143. The IBM Co. is acknowledged for the donation of an E 6 0 0 0 workstation to the Chemistry Department of the University of Arkansas at Fayetteville on which most of the calculations were carried out. We thank Dr. J. G. Radziszewski and Prof. B. A. Hess for a copy of their table of results prior to publication.
References and Notes (1) Chapman, 0. L.; Mattes, K.; McIntosh, C. L.; Pacansky, J.; Calder,
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