12422
J. Phys. Chem. 1995,99, 12422-12433
Methyl Group Internal Rotation in 2,6-Difluorotoluene (SI) and 2,6-Difluorotoluene+ (Do) Robert A. Walker, Erik C. Richard? Kueih-Tzu Lu: and James C. Weisshaar* Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706-1396 Received: March 16, 1995; In Final Form: June 9, 1995@
For 2,6-difluorotoluene (2,6-DFT), we determine the 6-fold potential for intemal methyl rotation in the first excited singlet state SI and the cation ground state Do. The sample is cooled internally by expansion in Ar from a pulsed nozzle. The &-SO absorption spectrum recorded by resonant two-photon ionization (R2PI) yields the effective rotational constant F ' = 5.1 f 0.1 cm-I and the potential parameter V6' = -10.5 f 2.0 cm-' (staggered minimum) in S I , We find clear evidence of potential energy coupling in S I between torsion and a low frequency out-of-plane bending mode b of a*'' symmetry under Gl2. In S I the unperturbed bending fundamental lies at only 78 cm-I; the magnitude of the torsion-bend coupling matrix element between the zeroth-order pure rotor state m4 and the combination b'ml is 7 cm-I. Threshold photoionization spectra detected by pulsed field ionization (PFI) through a number of SI intermediate states corroborate the SI-SO assignments and yield the rotor constants = 5.2 f 0.1 cm-' and v6+ = +15 f 2.0 cm-I (eclipsed minimum) in the ground state cation Do. The adiabatic ionization energy is 73 674 f 5 cm-l. We also present a b initio calculations indicating that for both 2,6-difluorotoluene (SO) and 2,6-dichlorotoluene (SO),the preferred conformation is eclipsed, which is unusual in SO. The calculated vibrationally adiabatic torsional potential parameter V/ is +14 cm-I in 2,6-difluorotoluene and +52 cm-' in 2,6-dichlorotoluene. In other words the calculated energetic preference for the eclipsed geometry increases from the difluoro to the dichloro species. At the same time, the optimized geometries vs rotor angle a show increasing in-plane methyl and halogen wagging from the difluoro to the dichloro species, consistent with stronger in-plane steric repulsion. This apparent paradox in the vibrationally adiabatic torsional potential can be explained by a simple model comprising free rotation coupled by the potential energy to in-plane and out-of-plane bending vibrations, with the in-plane coupling stronger.
I. Introduction
Six-fold barriers to intemal rotation of methyl or silyl groups are invariably small, typically less than 25 cm-I.' Well-studied examples include h3-t0luene?-~d3-toluene,6s7p-fluorotoluene, lo p-toluidine @-aminotoluene),'I and phenyl~ilane.'*-'~Most of these molecules have now been studied in the neutral ground state (SO),the first excited singlet state (SI), and the doublet cation ground state (Do). The magnitude of the barrier height lv6l in SO can often be obtained from microwave spectrosc ~ p y . ~Laser . ' ~ absorption spectroscopy of jet-cooled molecules in the near-UV, detected by either laser-induced fluorescence or resonant two-photon ionization (R2PI), provides lV6l in SI. Most recently, the new threshold photoionization technique of pulsed field ionization (PFI) yields lv6l in DO.^.'.'^ In addition the conformation of minimum energy in SI can be determined unambiguously from relative intensities of certain forbidden bands in the S I-SO absorption spectrum.' Dispersed fluorescence spectra can then determine the preferred SO conformation,' and PFI spectra can determine the preferred conformation in D ~ . ~ J ~ This substantial body of 6-fold barriers and conformational preferences shows clear patterns. For most molecules the SO barrier is the smallest, usually ' under G12). The simple Huckel form of these orbitals, which form a degenerate pair in SO benzene, is shown in Figure 8. In Do, the ring has two long CC bonds and four short CC bonds, 'with the pair of long bonds lying parallel to the methyl rotor axis (Figure 9, left). We can easily understand this in terms of removal of an a2 electron from neutral 2,6-DFT, since the a2 orbital is bonding between c2-c3 and CS-CS. Thus, the calculated ground state Do has 2A2 electronic symmetry under C2,, (2A2' symmetry under Gl2). The actual LUMO from the UHF/6-3 lG* calculation bears a striking resemblance to the a2 Huckel orbital.
Methyl Group Internal Rotation In addition to Do, we fortuitously discovered the first excited state of the cation DI ( 2 B ~symmetry under CzV,2A2" under G I ~ ) , whose optimized geometry with a = 90" is shown at the right in Figure 9. In fact, the UHF calculation initially converged to this stationary point, which lies some 1300 cm-I above Do. When we rotated a to 0", the calculation collapsed onto the Do surface. We could not converge to a stationary point on the DI surface with a = 0", so we do not know the calculated value of v6 in D1. The pattern of ring CC bond lengths is completely different in Do and in D I . In DI the ring has two short CC bonds (parallel to the C2 axis) and four long bonds. This picture is in complete accord with expectations based on removal of a bl electron from neutral 2,6-DFT (Figure 8). The actual LUMO for DI bears a striking resemblance to the bl Huckel orbital. According to the UHF/6-3 lG* calculations, the electronic symmetries of Do and DI are reversed in 2,6-DFT compared with other 6-fold symmetric cases. In fluorobenzene+,toluene+, and p-fluorotoluene', DOhas 2 B ~symmetry (2A2" under G12) and two short ring CC bonds parallel to the methyl axis.Is We expect the charge on the cationic ring to be distributed roughly according to the amplitude of each atomic 2pn orbital (diameter of the circles in Figure 8) in the MO from which the electron is ionized. We earlierIs rationalized the fact that fluorobenzene+, toluene+, and p-fluorotoluene+ all have 2 B (*AT) ~ ground states by noting that in those molecules the bl molecular orbital has the largest amplitude at the point(s) of substitution, CI (and Cq for p-fluorotoluene+). This allows the methyl and fluoro substituents to partially stabilize the positive charge by n donation. Evidence of this stabilization can be seen clearly in the unusually short ring-substituent CC and CF bonds of these cations compared with their neutral counterparts.I8 In these same terms, the 2,6-difluorotoluene cation faces a compromise, which may help to explain the unusually small DO-DI energy gap. Removal of the bl electron places some positive charge at all three substituents but mostly at methyl. Removal of the a2 electron places greater positive charge at the points of fluorine substitution but a node near methyl. The latter choice is more favorable in the UHF/6-31G* calculations, presumably due to the greater n-donor capability of fluorine compared with methyl. The unusually khort CF bond lengths and the normal exocyclic CC bond length in Do provide direct evidence of this pattern of n donation. In DI,the exocyclic CC bond is much shorter (by 0.02 A) due to significant n donation by methyl; the CF bonds are longer than in Do, evidently because c6 and c:!are less positive in DIthan in Do. Steric repulsion between methyl and fluorines may also be less severe in Do than in D I . With a = 90", the distance between fluorine and the methyl carbon atom is 2.85 8, in Do compared with 2.80 A in D I . This occurs in spite of the shorter c6-cI and C I - C ~bond lengths in DI primarily because the CF bonds tilt away from methyl to a greater extent in Do than in DI (C1-Cs-F bond angle of 119.5" in Do compared with 116.3' in DI). This differential CF bond tilt relative to the ring is in accord with Bent's Rule,33which predicts that the larger of the two angles C1-Cs-F and C5-C6-F will lie opposite the ring CC bond of larger bond order, as we have discussed previously.Is Finally, we emphasize that our discussion has focused on the Do and DI electronic wave functions as calculated by the UHF/ 6-3 lG* level of theory, which is a single-electron-configuration technique. Strong vibronic coupling and further in-plane distortion could occur due to the energetic proximity of Do and D I. Perhaps only a multireference configuration technique can properly describe this effect. The good agreement between experimental and calculated barriers and the out-of-plane
J. Phys. Chem., Vol. 99, No. 33, 1995 12431 bending frequency is encouraging, but we lack experimental data that independently determine the electronic symmetry of Do or DI. VI. Discussion
A. Forbidden Band Intensities. In the S I-SO spectrum, we find a rough hierarchy of band intensities. The electronically allowed type A bands with large Franck-Condon factors, 0; and mi, together have 20 times the intensity of any other single band in the first 250 cm-I above the origin. At roughly 5% of the origin band intensity, we find the combinations and overtones including b b i , bAmi-, bAm:, b&:, and b&i. These features are also electronically allowed type A bands. The combination bands bAmi, b$ni-, and b$n: would have vanishing Franck-Condon factors if torsional and vibrational motion were truly separable. Significant intensity in the overtone bands b&: and b&: presumably arises from the dramatic change in out-of-plane bending frequency from a calculated 162 cm-I in SO to the measured 78 cm-I in SI. This shift gives the totally symmetric b2 state in SI some overlap with bo in SO. The reason for this remarkable softening of the out-of-plane bend on electronic excitation to S I remains unclear, but the phenomenon appears to be quite general for toluene derivatives. We inferred a 91 cm-' out-of-plane bending mode in S I phenyl~ilane,'~ and Parmenter .and co-workers have observed a 138 cm-I feature in S I p-fluorotoluene.' Vibronic coupling cannot artificially suppress the b1 frequency; no valence n-electronic states have the proper symmetry to couple to S I via the out-of-plane bend. At roughly 1-2% of the origin intensity, we observe the electronically forbidden, pure torsional transitions mi, m?, and m:. In separate work we have shown that the relative intensities of these bands are quantitatively consistent with the cos 3 a dependence of the b axis component of the S I-SO electric dipole transition moment. We believe the very small miintensity arises from weak mixing of 13-) and 13+) due to torsion-overall rotation coupling term BPbpa in the torsionrotational Hamiltonian of eq 3. The nominal bAml band arises from the strong mixing of the S I states blml and m4. The coupling matrix element of 7 cm-I is a form of potential energy coupling analogous to anharmonic coupling between zeroth-order vibrational states. The magnitude of the coupling is quite similar to torsion-vibration coupling matrix elements inferred previously in SO and S Ip-fluorotoluenel and in S I phenylsilane and its ground state cation.I5 B. Staggered vs Eclipsed Minima of 6-Fold Molecules. In Table 4 we collect the known experimental values of the rotor constant F and the potential parameter v 6 in the SO,S I , and DO electronic states of six 6-fold symmetric molecules: toluene, d3-toluene, p-fluorotoluene, 2,6-difluorotoluene, phenylsilane, and p-toluidine. Despite the generally small magnitude of v6, patterns appear in the data. In SOv6 is typically quite small with all experimentally determined magnitudes below 6 cm-l. Only for p-fluorotoluene is the minimum energy conformation known experimentally; it is staggered, with v6 = -5 cm-'. The ab initio calculations at different levels of theory predict staggered minima in toluene, p-fluorotoluene (in agreement with experiment), and phenylsilane. When the calculations find staggered So minima, they also find greater out-ofplane tilt angle AB than in-plane tilt angle A y (Table 5). In contrast, the calculated values of 14 cm-I for 2,6-difluorotoluene and +52 cm-I for 2,6-dichlorotoluene are unusually large and indicate an eclipsed minimum. For these two cases, the inplane tilt of the methyl rotor axis is larger than the out-of-plane tilt. We return to this result below.
+
12432 J. Phys. Chem., Vol. 99, No. 33, 1995
Experiments on 6-fold symmetric molecules have shown Vs to be negative in SI (staggered minimum) and often larger in magnitude than in SO or Do. Again, the case of 2,6-difluorotoluene stands apart. The SI barrier in 2,6-DFT is roughly 3 times smaller than for the other molecules. The fact that v6 in SI is always 20-30 cm-I more negative than v6 in SO hints at an additivity effect, as if the S I barrier is the sum of a steric contribution (present in both SO and S I ) plus a contribution arising from electronic excitation. The best evidence for this additivity comes from 2,6-DFT itself, whose unusually large and positive (calculated) v6 in SOseems to cancel much of the apparent effect of S I excitation to yield an unusually small but still negative v 6 in S I . The reason for this subtle electronic effect remains unclear. With the possible exception of p-fluorotoluene+, the cations share consistently positive values of v6 (+I2 to +I9 cm-I), indicating the eclipsed minimum. We suggest that the sign of v6 in the 6-fold cation ground states Do may be determined by the inevitable proximity of the D1 excited state. In a crude adiabatic representation of the DO and DI electronic wave functions, the strong, forbidden Am = f 3 PFI bands arise from torsion-electronic coupling of the form VOI cos 3 a between levels of DO and D I , analogous to vibronic coupling.’ This couples the zeroth-order torsional state 13+) in DOwith both 10) and 16+) in DI.At the same time, IO) in DOcouples only to 13+) in D I , and 13-) in Do couples only with 16-) in D I . The result is a difSerenria1 shift of the crude adiabatic levels 13+) and 13-) in DO, with the 13+) state pushed further downward than 13-). This effect may always be large enough (about 20 cm-I) to push the adiabatic 13+) level below the adiabatic 13-) level, as observed in the consistently positive experimental values of v6 in Do. If so, then the adiabatic potential for DO may always favor the eclipsed geometry because of the close proximity of DI rather than because of some subtle ring-rotor interaction. This idea predicts the opposite effect in DI, in which the DoD1 coupling must differentially push 13+)higher in energy than 13-). We would thus expect unusually large, negative v6 in DI (staggered minimum), a suggestion subject to experimental test in future work. C. Vibrationally Adiabatic Torsional Potential. The a b initio calculations on the SOstate of 2,6-difluorotoluene and 2,6dichlorotoluene make a clear prediction that the minimum energy conformer is eclipsed (v6 = +I4 and $52 cm-I, respectively). The effect is larger for chlorine than for fluorine, which suggests that greater in-plane steric interaction leads to a deeper potential well favoring the eclipsed conformation! We can understand this counterintuitive result with a simple model involving a free internal rotor, in-plane and out-of-plane bending vibrational modes, and potential energy coupling between torsion and the bends. Our simple model highlights the meaning of the vibrationally adiabatic34 ab initio torsional potential generated by optimizing all internal coordinates at each fixed value of the rotor angle a. For simplicity, we include only two vibrational modes, an in-plane bend QI (al” vibrational symmetry under G12) and an out-of-plane bend 4 2 (a2” symmetry). In the simplest case these might be the in-plane and out-of-plane wag of the methyl group. We write the model potential as
Here, Ql and Q2 are (mass-weighted) normal coordinates. We include no explicit term in cos 6 a , since the zeroth-order rotor
Walker et al. is assumed to be unhindered. The “anharmonic coupling” parameters Cl and C2 describe the strength of the leading term in the potential energy coupling between internal rotation and the in-plane and out-of-plane bend, respectively. The a dependence is determined by the requirement that the overall potential energy be totally symmetric under G12. That is, QI and cos 3 a both transform as al”, and Q2 and sin 3 a both transform as a2”. The ab initio procedure minimizes the potential energy with respect to variations in all other internal coordinates at each fixed value of a. Within the simple model, we can solve for the dependence of the optimal (adiabatic) values of QI and Q2 on a by setting 8Vl8Qi = 0. The results are Q~~~=
-(c,/w12) cos 3a
Qtd = -(C,/W,~) sin 3 a We insert these values into V(a,Ql,Qz) to obtain the adiabatic potentia1:
= const
+ [C22/4w22- C12/40,2]cos 6 a
(6)
Since the traditional spectroscopic effective potential for internal rotation takes the form V(a) = const - (Vd2) cos 6 a (eq l), the adiabatic model potential parameter becomes
v, = [c,2/2w,2- c22/2w22]
(7)
In the adiabatic picture both the frequencies and coupling parameters of the in-plane and out-of-plane modes influence v6. If the adiabatic motion of all the atoms contained only the two normal coordinates QIand Q2, as in the model, we could obtain the coupling constants CI and C2 from the ab initio harmonic frequencies W I and w2 and the calculated adiabatic displacements and Q2ad. However, the actual adiabatic motion contains many normal coordinates. All modes of at’’ symmetry contribute to the cos2 3 a term of eq 6, and all modes of a2” symmetry contribute to the sin2 3 a term. We could generalize the model to include all the normal coordinates that can couple to internal rotation by symmetry. It would then be possible to decompose the adiabatic motion into a sum of amplitudes of different normal coordinates and perhaps gain quantitative insight into the nature of the overall 6-fold barrier. In the ab initio calculations on SOtoluene and p-fluorotoluene, the adiabatic motion looks qualitatively like a precession of the methyl axis, which is a superposition of in-plane and out-ofplane bending motions. The out-of-plane tilt AB exceeds the in-plane tilt A y , and the adiabatic minimum is staggered. This correlation is in qualitative accord with the simple model. In SO of such substituted benzenes, the out-of-plane substituent bending frequencies are always substantially smaller than the in-plane bending frequencies, typically about 200 cm-l vs 300400 cm-1.35 This difference provides a simple qualitative explanation of the preference for the staggered conformation in SO of most 6-fold molecules. In contrast, for SO 2,6-difluorotoluene and 2,6-dichlorotoluene, the calculations show that the adiabatic in-plane tilt Ay exceeds the out-of-plane tilt AB and the adiabatic potential minimum is eclipsed (Table 5). Once again the calculation is consistent with the model. Qualitatively, in 2,6-difluorotoluene the in-plane
elad
Methyl Group Intemal Rotation motion looks like the 297 cm-’ in-plane bend 436 in Figure 4. The out-of-plane motion resembles the 307 cm-’ mode 4 35 more than the 162 cm-’ out-of-plane bend 4 3 8 . Within the context of the model, this suggests that the strongest out-of-plane coupling is to the higher frequency mode Q35 rather than the methyl bend. Meanwhile, the coupling to the in-plane bend is enhanced by steric repulsion, as judged by the larger in-plane tilt in 2,6-difluorotoluene compared with toluene itself. The in-plane contributions to eq 7 win out in 2,6-difluorotoluene so that the adiabatic potential favors the eclipsed conformation. The effects are similar but even stronger in 2,6-dichlorotoluene. Finally, we should include an “intrinsic” 6-fold potential term of the form V,(O)cos 6 a in eq 4. This term would correspond conceptually to the rigid-frame, rigid-rotor potential typically written by molecular spectroscopists. Further ab initio calculations with a rigid frame and a rigid methyl rotor might shed light on the magnitude of this contribution to the overall 6-fold potential. Acknowledgment. J.C.W. thanks the U.S. Department of Energy, Division of Chemical Sciences, Office of Basic Energy Research (No. DE-FG02-92ER14306) for generous support of this research. The IBM Corporation generously donated two RS6000 workstations under the IBM-SUR program. We thank Frank Weinhold for instruction in the art of ab initio quantum mechanics. References and Notes (1) Zhao, Z.-Q.; Pmenter, C. S.; Moss, D. B.; Bradley, A. J.; Knight, A. E. W.; Owens, K. G. J. Chem. Phys. 1992, 96, 6362. (2) Breen, P. J.; Warren, J. A.; Berstein, E. R.; Seeman, J. I. J. Chem. Phys. 1987, 87, 1917. (3) Lu, K.-T.; Eiden, G. C.; Weisshaar, J. C. J. Phys. Chem. 1992, 96, 9742. (4) Murakami, J.: Ito, M.; Kaya, K. Chem. Phys. Lett. 1981, 80, 203. (5) Rudolph, H.; Dreizler, H.; Jaeschke, A.: Wendling, P. Z. Naturforsch., A 1967, 22, 940. (6) Lu, K. T. Ph.D. Thesis, Department of Chemistry, University of Wisconsin-Madison, Madison, WI, 1993.
J. Phys. Chem., Vol. 99, No. 33, 1995 12433 (7) Walker, R. A.; Richard, E. C.; Lu. K. T.; Weisshaar. J. C. J. Chem. Phys. 1995, 102, 8718. (8) Takazawa. K.: Fuiii. M.: Ito. M. J. Chem. Phvs. 1993. 99. 3205. (9) Ito, M.; Takazawa, K.; Fujii, M. J. Mol. Srruft. 1993, ‘292. (IO) Okuyama, K.; Mikami, N.; Ito, M. J. Phys. Chem. 1985, 89,5617. (11) Tan, X.-Q.; Pratt, D. W. J. Chem. Phys. 1994, 100, 7061. (12) Phillis, J. G. Chem. Phys. Lett. 1990, 169, 460. (13) Ioannidou-Philis, A.; Philis, J. G.; Christodoulides, A. A. J. Mol. Spectrosc. 1987, 121, 50. (14) Ishikawa, H.; Kajimoto, 0.;Kato, S. J. Chem. Phys. 1993, 99, 800. (15) Lu, K.-T.; Weisshaar, J. C. J. Chem. Phys. 1993, 99, 4247. (16) Caminati, W.; Cazzoli, G.; Mirri, A. M. Chem. Phys. Lett. 1975, 35, 475. (17) Walker, R. A.; Lu, K. T.; Richard, E. C.; Weisshaar, J. C. In preparation. (18) Lu, K.-T.; Weinhold, F.: Weisshaar, J. C. J. Chem. Phys. 1995, 102, 6787. (19) Okuyama, K.; Mikami, N.: Ito, M. Laser Chem. 1987, 7, 197. (20) Muller-Dethlefs, K.; Schlag, E. W. Annu. Rev. Phys. Chem. 1991, 42, 109. (21) Wiley, W. C.: McLaren, I. H. Rev. Sci. lnstrum. 1955, 26, 1150. (22) Braunstein, M.; McKoy, V.; Dixit, S. N.; Tonkyn, R. G.; White, M. G. J. Chem. Phys. 1990, 93, 5345. (23) Chupka, W. A. J. Chem. Phys. 1993, 98, 4520. (24) Lin, C. C.; Swalen, J. D. Rev. Mod. Phys. 1959, 31, 841. (25) Gordy, W.; Cook, R. L. Microwave Molecular Spectra, 3rd ed.; Wiley Interscience: New York, 1984. (26) Longuet-Higgins, H. C. Mol. Phys. 1963, 6, 445. (27) Bunker, P. R. Molecular Symmetty and Spectroscopy; Academic Press: New York, 1979. (28) Wilson, E. B. Chem. Rev. 1940, 27, 17. (29) Zare, R. N. Angular Momentum; John Wiley & Sons: New York, 1988. (30) Eiden, G. C.; Weinhold. F.; Weisshaar, J. C. J. Chem. Phys. 1991, 95, 8665. (31) Lawrance, W. D.; Knight, A. E. W. J. Phys. Chem. 1990,94, 1!249. (32) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.: Gill, M. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomparts, R.; Andres, J. S.; Raghavachari, K.; Binkley, J. S.; Stewart, J. J. P.; Pople, J. A. GAUSSlAN 92; Gaussian, Inc.: Pittsburgh, PA, 1992. (33) Bent, H. A. Chem. Rev. 1961, 61, 275. (34) Carrington, T.; Miller, W. H. J. Chem. Phys. 1986, 84, 4364. (35) Varsanyi, G. Vibrational Spectra of Benzene Derivatives; Academic Press: New York, 1969; pp 430. JP950749+
