J. Phys. Chem. 1995,99, 8033-8037
8033
Isotope Effects on the One- and Two-Electron Reductions of Cyclooctatetraene. A Semiempirical Quantum Chemical Investigation Han Zuilhof and Gerrit Lodder" Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O.Box 9502, 2300 RA Leiden, The Netherlands Received: August 29, 1994; In Final Form: February 23, 1995@
The isotope effects (IEs) on the one- and two-electron reductions of cyclooctatetraene (COT) have been studied by using the semiempirical PM3 method. The one-electron reduction is calculated within the ROHF formalism to yield a nonplanar radical anion. The hydrogen compound is calculated to be preferentially reduced rather than the deuterium compound, as observed and calculated earlier for aromatic systems. This is in contrast with the experimental data for the one-electron reduction of COT but in line with the experimental IE on the addition of the second electron. Ion-pair formation and population of higher vibrational levels in the anions are discussed as possible causes for the deviation between theory and experiment, and the first of these is concluded to be the most important.
Introduction Recently a controversy has arisen on how isotopic substitution affects the electron affinity (EA) of aromatic compounds. Electron spin resonance (ESR) results showed for several aromatic hydrocarbons that the EA of the deuterated compounds was lower than that of their parent molecules with hydrogen atoms.',* These data were complemented experimentally by using ion cyclotron re~onance,~ mass spectrometric analysis: and cyclic ~oltammetry.~ Semiempirical quantum chemical calculations have been shown to represent molecular vibrations accurately,6as is needed in evaluating isotope effects (IEs).' From PM3 calculations both direction and magnitude of equilibrium deuterium IEs on electron transfer (AEA) to benzene and pyrene were successfully reproduced computationally. The cause of the AEA was shown to be a sum of a multitude of small, and often oppositely directed, vibrational changes.8 In contrast with this situation, the ESR data on the heavy atom AEA values reported for the reductions of nitrobenzene and ben~ophenone~,~ could not be reproduced theoretically with molecular mechanics.'0 Since standard isotope theory has been so successful in rationalizing measured IEs," this casted doubt on the interpretation of the ESR results as equilibrium IEs.Io This criticism was responded to on the methodological grounds that a technique which is viable to use for one kind of isotopomers should be accepted for use to obtain analogous results for other i s o t ~ p o m e r s . ~ ~ ' ~ Stevenson et al.I3 have recently also published ESR data on AEA for cyclooctatetraene (COT) and its perdeuterated isotopomer (COT-d8). These results show that for this compound the direction of AEA is opposite to that of the aromatic compounds studied up to now. The equilibrium of eq 1 lies to the left, in other words, the EA of COT-& is larger than that of COT-h8. We report here that PM3 calculations do not reproduce the experimental data on the deuterium IE,and causes of the deviation between theory and experiment will be discussed. Furthermore, data have recently become available for the thermodynamics of the equilibrium of eq 2. Stevenson, Reiter, and c o - ~ o r k e r shave ' ~ ~ reported a value of AG = -86 cal/mol @
Abstract published in Advance ACS Abstracts, April 15, 1995.
0022-365419512099-8033$09.00/0
in THF, as measured by ESR. This means that, in contrast to the attachment of the first electron, the second electron is added more easily onto the perhydrogen radical anion than to the perdeuterated species. PM3 calculations do reproduce the experimental data on this equilibrium. The results will be discussed in the light of the proposed relation between aromaticity and the direction of AEA.I3 Calculational Details All calculations were carried out on an IBM-compatible 486DX2166MHz PC. Geometries were optimized by using the PM3 parameter^'^ as implemented in the semiempirical calculation program MOPAC 6.0. RHF calculations were performed for both the neutral and the dianionic species; for the radical anions both restricted open-shell Hartree-Fock (ROHF) and unrestricted Hartree-Fock (UHF) calculations were used.I5 Calculations were started without symmetry constraints unless noted otherwise. If the optimization without symmetry constraints led to a geometry which clearly displayed symmetry, that symmetry was subsequently imposed in further reduction of the heat of formation and gradients. Optimizations were started with the BFGS algorithm,I6 in combination with the keyword PRECISE. After these optimizations were finished, the calculation was completed by using the eigenvector following method. Only with this procedure the gradient norm could be minimized to values smaller than 0.02. This was required to obtain accurate second derivatives of the energy with respect to the nuclear coordinates and proved to be important in both the UHF and ROHF calculations of the radical anion of COT (vide infra). Optimizations starting with the eigenvector following method before preoptimization with BFGS at geometries with high gradients sometimes yielded erroneous results for the geometries. All data were obtained by using the Born-Oppenheimer approximation, yielding identical electronic energies for different isotopomers, and the calculated IEs are therefore completely 0 1995 American Chemical Society
8034 J. Phys. Chem., Vol. 99, No. 20, 1995
Zuilhof and Lodder
(b)
(a)
Figure 1. (a) Bond-length- and (b) bond-angle-altemated D4h geometries of C O Y .
TABLE 1: Optimized Bond Distances (A), Angles (degrees), and Heats of Formation (kcaymol) for Several Geometries of COT Radical Anion, Obtained from PM3 Calculations method geometry CC dist CHdist LCCC LCCH AHf UHF planar D4h 1.387 1.099 134.2 112.9 49.63 (angle altem) 1.103 135.8 112.1 ROHF puckered D z ~ 1.357 1.101 133.7 112.0 52.20 1.417
ROHF planar D4h 1.357 (length altem) 1.414
1.101
135.0
114.2 112.8 52.49
due to differences in vibrational energy. All IE calculations were performed with the FWF/ROHF formalism.
symmetry; AHf = 52.20 kcaVmo1). Both species showed only positive values for the vibrational frequencies, and, when taken as a starting geometry, neither of them optimized to the other one, even with very tight gradient criteria. Therefore, both are definite minima on the PM3-ROHF surface. Using ROHF theory the heat of formation of the radical anion when kept within D4h bond-angle-alternation symmetry constraints was 55.78 kcaVmo1. The bond-angle-alternated D4h structure was shown to be a transition state on the potential energy surface, since one negative vibrational frequency was calculated. Its energy is 3.3 kcaVmol above that of the bond-length-alternated D4h structure, in excellent agreement with recent ab initio data (6-3 lG* basis set, including 0-and n-configuration interaction), where this difference amounts to 3.8 kcal/mol.I8 The calculated heats of formation of COT and COT- lead to a calculated EA of 66.66-52.20 = 14.46 kcaumol. This compares very well with the experimental value of 13.3 f 1.0 kcaVm01.I~ The dianion of COT was calculated to be a planar, regular octagon-as was to be expected for an aromatic l0n-electron system-with AHf = 140.07 kcaVmo1. For the disproportionation reaction of eq 3, this yields an enthalpy of +lo2 kcaV mol. This large positive value is due to the electron-electron repulsion energy in the dianion and implies the nonexistence of COT dianion in the gas-phase if COT is present, in agreement with experimentalz0 and earlier theoretical (MIND0/2) findings.2'
Results and Discussion Geometries and Energetics of the Ions. To obtain calculated values of AEA, accurate structures of both the neutral and ionic species are required. COT is calculated to have DU symmetry, with alternating C-C bond lengths of 1.335 and 1.458 A and C-C-C angles of 125.2'. The molecule is tubshaped, with the tube angle being 60.3', and AHf = 66.66 kcaV mol, all in good agreement with experimental data.17 The radical anion is obtained by addition of an electron to a nonbonding orbital (calculated orbital energy: 1.O kcaumol). As a result the tub-shaped COT flattens. The degree to which this is calculationally reproduced depends on the quantum mechanical method used. A fully planar geometry is obtained when the structure of the radical anion of COT is calculated by using the unrestricted Hartree-Fock (UHF) formalism. In agreement with the results of ab initio calculationsI8 it has a D4h rather than a D8h symmetry, due to Jahn-Teller distortions. Unlike the ab initio results the bond-angle-alternated optimized geometry (Figure 1) is lower in energy (AHf = 49.63 kcal/mol) than the bondlength-alternated optimized one with D4h symmetry, which is no stationary point on the potential energy surface. The geometry (see Table 1) with the lowest calculated energy was shown to be a minimum since it has only positive frequency numbers for the vibrations. Nonplanar starting geometries-e.g., that of neutral COT-invariably optimize to a planar structure, although very tight gradient criteria had sometimes to be used to achieve this. By use of the default BFGS optimizer in MOPAC a nonplanar geometry was obtained when the optimization started from the nonplanar RHF structure (vide infra), even if the calculation was made more accurate by the use of the keyword PRECISE. Vibrational frequency calculations on this species, however, showed negative vibrational frequencies, showing that this geometry was not that of a stationary point. With ROHF theory the radical anion potential energy surface shows two minima. One of these corresponds to a planar bondlength-alternated structure with D4h symmetry (AHf = 52.49 kcal/mol; see Table 1). Slightly lower in energy, however, a geometry was obtained which was distinctly nonplanar (&d
+
2 COT'-
*L,
COT
+ COT2-
(3)
The results obtained can be confronted with the long-standing discussion about the planarity or nonplanarity of COT radical anion. Using NMR, Katz22measured in 1960 that the electron exchange between COT and COT radical anion was much slower than the corresponding exchange between COT radical anion and COT dianion. This difference in activation barrier could most readily be explained by assuming very different geometries for the first two species and very similar ones for the latter two. Since COT dianion has a well-established planar structure, he concluded a planar structure of COT radical anion. This hypothesis was reinvestigated with ESR by Strauss, Katz, and F r a e ~ k e l .They ~ ~ concluded that a conformation more stable than a planar one by a small amount, with bond angles substantially smaller than the 135' expected for a regular octagon, would be consistent with all their data, while a completely planar conformation radical anion would not. Using a variety of electrochemical techniques Allendoerfer and Rieger24 came to the conclusion that the transition state for electron transfer to COT to obtain the radical anion comes close to being planar. However, they state that their data give no reason for assuming that the transition state, which is shown to be close to the radical anion geometry, is entirely planar. On the planarity of COT radical anion was cast substantial doubt by detailed electrochemical studies of Anderson et al.,25 who compared the electrochemical reduction of COT with that of 2-methoxyazocines. They concluded that conformational change is rate-determining neither for the one-electron reduction of COT nor for that of COT radical anion, which points to an intermediate conformation for the radical anion, neither strongly puckered (as COT) nor completely planar (as COT dianion). In our opinion the presently available experimental data suggest that COT radical anion is slightly puckered and that this geometry has an energy slightly less than that of a planar conformation. The ROHF data obtained (difference of 0.3 kcal/ mol between a planar and puckered structure, with the puckered structure the more stable one) are in good agreement with these
J. Phys. Chem., Vol. 99, No. 20, 1995 8035
Isotope Effects on Cyclooctatetraene Reductions
COT dadon
COT m d h l mbn
COT
Figure 2. Stepwise reduction of COT to COT dianion. TABLE 2: Zero-Point Energies of Cyclooctatetraene, Its Puckered (Du)and Planar (De)Radical Anions, and Its Dianion, As Obtained from PM3-RHFBOHF Calculations (in kcaymol) isotopomer
neutral compd
puckered rad anion
planar rad anion
dianion
CaHs CDs 13C*H8 I3C8D8
82.328 67.134 81.187 65.957
79.829 65.045 78.799 63.916
79.594 64.812 78.504 63.686
78.082 63.512 77.019 62.418
TABLE 3: Calculated" and Experimental Isotope Effects with Respect to CsH8 on the One-Electron.Reductionsof Cyclooctatetraene (Eq 1) and CyclooctatetraeneRadical Anion (Eq 2) (in caymol) isotopomer CsDs I3C8Hs I3CsD8
puckered
eq 1 planar
exptl
puckered
eq 2 planar
-347 -48 -395
-412 -51 -463
50 -12 64
-277 -30 -312
-212 -27 -244
exptl -86
a Using the zero-point energy differences obtained from PM3-RHF/ ROHF calculations for the planar and puckered structure of COT radical anion.
experimental results. The reduction of COT to its dianion via the radical anion can therefore be depicted as in Figure 2 , in which the calculated structures for these species are shown. The ROHF calculations also reproduce the experimentally observed indistinguishability of the carbon atoms in the radical anion.23326This is not the case for the PM3-UHF method, which produces erroneous results with respect to both the planarity of the radical anion (it predicts it to be planar) and the geometry, which is calculated to be of bond-angle-altematedD 4 k symmetry with two types of distinguishable carbon atoms. The effects of isotopic substitution on the electron affinities of COT and COT radical anion will therefore be based on the ROHF data. The UHF formalism gives-for a planar geometry-similar values.27 Electron Transfer Isotope Effects. Using the optimized structures described above, force constant calculations were performed, to obtain the IEs on the electron-transfer processes in eqs 1 and 2. The EA of a compound at 0 K can be described as the difference between the sums of electronic and zero-point energies of the neutral molecule and its negatively charged counterpart. The effect of isotopic substitution on the EA is then given by the difference between the calculated EA'S of the different isotopomers.8 The zero-point energy data from which the IEs are calculated are given in Table 2. The resulting calculated isotope effects of eqs 1 and 2 are given in Table 3, for all the COT isotopomers for which experimental data have been reported.I3 Negative numbers in Table 3 imply that the lighter isotopomer is more easily reduced than its heavier analogues. Addition of the First Electron. Table 3 shows that only negative numbers are calculated for the enthalpies of eq 1 for the various isotopomers of COT under study. This means that, in contrast with experiment, the calculated IE on the transfer of an electron is in the same direction as that observed and calculated for aromatic compounds. Stevenson et al. have put forward the argument that addition of an electron to an 1-538
orbital with net antibonding character in a neutral compound results in an overall reduction in bond strengths and therefore in shallower potential energy curves. This results in expected preference of reduction of the lighter isotopomers for aromatic compounds.' For nonaromatic 8 n-electron systems such as COT, addition of an electron is suggested to make the molecule approach aroniatic character, and thus the heavier isotopomer is predicted to be preferentially reduced.'3b It should be noted, however, that the measure of aromaticity proposed by Zhou, Parr, and Garst,2s in which aromaticity is related to the HOMOLUMO gap, does not predict an increase of aromatic character. The gap between the highest doubly occupied orbital and the orbital directly above it in the radical anion (3.6 eV) is reduced by several eV, with respect to the gap both in the neutral species (9.0 eV) and in the dianion (8.1 eV), as is expected for a species with a singly occupied molecular orbital (SOMO). Thus this calculated measure of aromaticity of the radical anion suggests no aromatic character at all. Anyhow, the data in Table 2 show that the one-electron reduction of COT leads to shallower potential energy curves and not to tighter ones as suggested if aromaticity would increase in this process. This makes the hyp~thesis'~ used to rationalize the experimental data for COT, which show an IE (see Table 3, data for eq 1) opposite to those observed for reductions which decrease aromaticity, as is the case for, e.g., benzene or pyrene,'~~ somewhat disputable. The discrepancy between the calculated and observed EA values may well be caused by factors which are not computationally accounted for. We will consider two of them, namely, medium effects and the effect of deviations of the vibrational partition function from one. Environmental effects are important, since COT radical anion and sodium cation will not be completely present as free ions in ammonia at low temperatures. (Under these conditions the dielectric constant c of ammonia is estimated to be ca. 25.29) Strong evidence for the presence of ion pairs of COT radical anion with alkali cations in ammonia was obtained by using ESR.30 Studies of the line widths of the individual hyperfine splittings, of the activation energies of the line-broadening processes, and of the spin concentration all pointed to the presence of ion pairs. Furthermore, it was noted that the solutions in ammonia yield large variations in the equilibrium constants for the disproportionation reaction of eq 4, depending 2COT'- M+ F.JH, COT
+ M+COT2- M+
(4)
on the counter ion: with M+ = Li+ or Na+ as gegenion the reaction lies far more to the left than for M+ = K+ (equilibrium constants for eq 4 differ more than 4 orders of magnitude). This difference can be explained by the hypothesis that the smaller cations fit better in the tub-shaped COT radical anion than the larger potassium cation and therefore complex much more strongly. Supposedly this better complexation overcomes the undoubtedly better solvation of Li+ or Na+ compared with that of K+. The weaker complexation of K+ with COT radical anion is also in line with another observation. In the presence of potassium counterions, two radical anionic species of COT are observed, while with M+ = Li+ or Na+ only one radical anion is observed.30 This suggests that the weaker complexationleads, besides to the formation of contact ion pairs as with Li+ and Na+, to the formation of solvent-separated or free ion pairs, in which COT radical anion has a distinct electron distribution, leading to distinguisable ESR features. The NMR data of Katz,22who measured the rate of electron exchange between the radical anion and the dianion of COT, also indicate that the radical data forms ion pairs with the cation. In the presence of
8036 J. Phys. Chem., Vol. 99, No. 20, 1995 lithium and potassium gegenions this rate was about lo4 lower with Li+ than with Kf. This can be explained by the fact that with lithium gegenions the reorganization energy for electron transfer is much larger due to the complexation of the radical anion with the cation, thereby slowing down the rate of electron tran~fer.~' If COT radical anion exists in a puckered conformation, the small sodium ion will be associated efficiently with the "tub"shaped radical anion. A rigid structure for the Na+/COT'- ion pair in a matrix was also proposed on the basis of vibrational fine structure in the absorption and emission spectra.32 The rigid ion-pairing will restrict, among others, ring breathing and outof-plane bending vibrations, which contribute significantly to the overall isotope effect.8 As a result the potential energy curves of some nuclear coordinates become steeper than those in a free radical anion, resulting in an overall steeper potential energy surface in the sodium cation solvated radical anion. This effect might then contribute to the reversal in IE in comparison with the planar systems studied up to now. A second effect not accounted for computationally is the thermal population of higher vibrational levels of energetically low-lying vibrations. In contrast with the case of the aromatic species studied quantum chemically up to now,8 several very low-lying vibrations (< 175 cm-I) are present in the reduced species of COT (both the radical anion and the dianion), which are not present in the neutral precursor. In spite of the fact that the experiments are carried out at low temperatures (205 K),I3 contributions from populations of higher vibrational levels can thus not be neglected a priori. Therefore the isotope effect on the equilibrium of eq 1 is better calculated by using eq 5 than on the basis of zero-point energies only. In eq 5 q is the
molecular partition function and AAE the difference in energy between the lowest energy levels of CsH8'- and CsDs and those of CsD8'- and CsHs. Since the total partition function is the product of the electronic, vibrational, rotational, and translational partition function, the ratio (between parentheses) of partition functions in eq 5 can be split in four ratios, signifying the isotope effects of each contribution. Since all calculations are performed by using the Born-Oppenheimer approximation, the equality of the electronic partition functions for isotopomers is assumed from the start. It is not to be expected that the ratios for rotational and translational partition functions differ significantly for the two i ~ o t o p o m e r s . Therefore ~~ AAE is given by the difference of zero-point energy differences as presented in Table 3, and q can be replaced by qv,the vibrational partition function. For a polyatomic molecule with n normal modes with wavenumber P,, this is given by eq 6.33 qv = n [ l - exp(-hcV,/kr)]-' n
The vibrational partition function will be higher for deuterated than for protonated compounds and the more so the shallower the potential energy surface around the equilibrium geometry. When calculated for the species in eq 1, the term in parentheses in eq 5 becomes (5.9009 x 4.0016)/(9.0932 x 2.7691) = 0.938. As a result of this the calculated values of K would be smaller (closer to one) by about 6% when this effect would be taken into account. This explains part of the discrepancy between theory and experiment. The effect is a minor one though, and the approximation of using only zero-point energy differencess is a good one.
Zuilhof and Lodder From these considerations it can be concluded that the formation of ion pairs between COT radical ion and alkali ions might contribute significantly to the magnitude of AEA. The effect of population of higher vibrational levels is relatively small. Addition of the Second Electron. The experimental reaction enthalpy for the addition of the second electron is such that further reduction of the perhydrogen COT radical anion is favored with respect to that of the perdeuterated radical anion. This effect is reproduced computationally (Table 3, data for eq 2 ) and points to a further decrease in bonding in the dianion. This is expected for a molecule with very high electron-electron repulsion contributions to the total energy, as is reflected in the HOMO energy of the dianion: 79.9 kcal/m01.~~The dianion therefore has substantially shallower potential energy curves, leading to negative values for the reaction enthalpy of reaction 2. The experimental data for the isotope effects on one- and two-electron reductions have different signs.'3b We do not find theoretical support for this difference in the direction of the E. Although it is well-established that the dianion is a fully planar and aromatic species, this does not imply stronger overall bonding or specifically stronger C-H bonding than in the "less aromatic" radical anion or nonaromatic neutral COT. On the contrary, bonding becomes increasingly weaker. Therefore, theory and experiment agree that there are one-electron reductions in which a more aromatic system is obtained (e.g., from COT radical anion) and others in which a less aromatic system is obtained (e.g., from benzene or pyrene), where in both preferentially the perhydrogen rather than the perdeutero compound is reduced. In other words, we find no evidence for a general relation between aromaticity and increased (C-H) bond strength. The fact that the experimental value points to a more shallow potential energy surface for the dianion than for the radical anion is easily explained by the complexation argument. The dianion will be symmetrically solvated by two sodium atoms on either side. In contrast with the situation for the radical anion, slight puckering of the ring to one side will result in diminished solvation from one sodium atom, but this will be compensated by the effect bending has on the complexation with the other sodium atom. Therefore it is expected that bending will be looser in the dianion than in the radical anion. This argument points in the same direction as the argument based on increased electron-electron repulsion interactions: both effects contribute to a negative value for the reaction enthalpy of eq 2, as is indeed observed experimentally. Conclusions The direction of the isotope effects on the one- and twoelectron reductions of COT is calculated to respectively disagree and agree with the experimentally observed data. The disagreement is explained in terms of ion-pairing effects, which are not accounted for computationally and for which strong experimental evidence is present. The outcome of the calculations presented in this paper support the notion that strong environmental effects can exist on the size and even direction of electron-transfer equilibrium isotope effects. l 2 Combined experimental and theoretical efforts are needed to further clarify the (relative) importance of intrinsic and solvatiodcomplexation effects. Acknowledgment. We thank Prof. N. H. Velthorst (Free University, Amsterdam) for helpful discussions.
J. Phys. Chem., Vol. 99, No. 20, 1995 8037
Isotope Effects on Cyclooctatetraene Reductions
References and Notes (1) Stevenson, G. R.; Reidy, K.; Peters, S. J.; Reiter, R. C. J. Am. Chem. SOC.1989, 111, 6578-6581 and references therein. (2) Stevenson, G. R.; Reiter, R. C.; Espe, M. E. J. Am. Chem. SOC. 1986, 108, 532-533. (3) Stevenson, G. R.; Reiter, R. C.; Espe, M. E.; Bartmess, J. E. J . Am. Chem. SOC.1987, 109, 3847-3849. (4) Stevenson, G. R.; Sturgeon, B. E. J. Org. Chem. 1990, 55, 40904093. (5) Goodnow, T. T.; Kaifer, A. E. J. Phys. Chem. 1990, 94, 76827683. (6) (a) Coolidge, M. B.; Marlin, J. E.; Stewart, J. J. P. J. Comput. Chem. 1991,12,948-952. (b) Healy, E. F.; Holder, A. J. Mol. Struct. (Theochem) 1993, 281, 141-156. (7) Saunders. M.: Laidig. K. E.: Wolfsberz. M. J. Am. Chem. SOC.1989. 1I1 ,'8989-8994. (8) Zuilhof. H.: Lodder. G. J . Phys. Chem. 1992. 96, 6957-6962. (9) (a) Stevenson, G. R.; Reiter, R. C.; Au-Yeuno, W.; Pescatore, J., Jr.; Stevenson, R. D. J. Org. Chem. 1987, 52, 5063-5064. (10) Marx, D.; Kleinhesselink, D.; Wolfsberg, M. J . Am. Chem. SOC. 1989, 111, 1493-1494. (11) Willi, A. V. Isotopeneffekte bei chemischen Reaktionen; George Thieme Verlag: Stuttgart, 1983. (12) Stevenson, G. R.; Wehrmann. G. C., Jr.; Reiter, R. C. J. Phys. Chem. 1991, 95, 6936-6939. (13) (a) Stevenson, G. R.: Peters, S. J.; Reidy, K. Tetrahedron Lett. 1990, 31, 6151-6154. (b) Stevenson, G. R.; Peters; S. J.; Reidy, K.; Reiter, R. C. J. O m . Chem. 1992, 57, 1877-1882. (14) la) Stewart, J. J. P. J. Comput. Chem. 1989, 10, 209-220. (b) Stewart, J. J. P. J. Comput. Chem. 1989, 10, 221-265. (15) (a) Hurley, A. C. Introduction to the Electron Theory of Small Molecules; Academic Press: New York, 1976; pp 242-253. (b) Dewar, M. J. S. The Molecular Orbital Theory of Organic Chemistry; McGrawHill: New York, 1969, pp 250-277. (16) Zemer, M. C. Analytic Derivative Methods and Geometry Optimization. In Szabo, A,, Ostlund, N. S. Modern Quantum Chemistry; McGraw-Hill: New York, 1989; pp 437-458. (17) Experimental values: (a) C=C, 1.340 A; C-C, 1.476 A; C-C-C angle, 126.1" (Traetteberg, M. Acta Chem. Scand. 1966, 20, 1724-1726). Y
_
I
-
(b) AHf = 69.5 kcal/mol, calculated from the heat of combustion (Springall, H. D.; White, T. R.; Cass, R. C. Trans. Faraday SOC.1954, 50, 815-819) and the heat of vaporization (Scott, D. W.; Gross, M. E.; Oliver, G . D.; Huffmann, H. M. J . Am. Chem. SOC.1949, 71, 1634-1636). (18) Hammons, J. H.; Hrovat, D. A.; Borden, W. T. J . Am. Chem. SOC. 1991, 113, 4500-4505. (19) Wentworth, W. E.; Ristau, W. J. Phys. Chem. 1969, 73, 21262133. (20) Stevenson, G. R. In Molecular Structure and Energetics; Liebman, J. F.. Greenberg. " A,. Eds.. VCH Publishers: Deerfield Beach, FL,1986; Chapter 2. (21) Dewar, M. J. S.; Harget, A,; Haselbach, E. J. Am. Chem. SOC.1969, 91, 7521-7523. (22) Katz, T. J. J. Am. Chem. SOC. 1960,82, 3785-3786. (23) Strauss, H. L.; Katz, T. J.; Fraenkel, G. K. J. Am. Chem. SOC.1963, 85, 2360-2364. (24) Allendoerfer. R. D.: Rieger, P. H. J. Am. Chem. SOC.1965, 87, 2336-2344. (251 Anderson. L. B.: Hansen. J. F.; Kakihana, T.; Paauette, L. A. J. Am. Chem. SOC.1971, 93, 161-167. (26) Katz, T. J.: Strauss. H. L. J, Chem. Phys. 1960, 32, 1873-1875. (27) E.g., using UHF an isotope effect of -437 cal/mol is calculated for the reduction of COT-ha versus that of COT-ds, where the ROHF data yield -412 cal/mol. (28) (a) Zhou, Z.; Parr, R. G.; Garst, J. F. Tetrahedron Lett. 1988,48434846. (b) Zhou, Z.; Parr, R. G. J.Am. Chem. SOC.1989,111,7371-7379. (29) Handbook of Chemistry and Physics, 64th ed.; Weast, R. C., Ed.; 1983; p E-50. (30) Smentowski, F. J.; Stevenson, G. R. J . Phys. Chem. 1969,73,340345. (31) Eberson, L. Electron Transfer Reactions in Organic Chemistry; Springer Verlag: Berlin, 1987; pp 20-54. (32) Dvorak, V.; Michl, J. J . Am. Chem. SOC.1976, 98, 1080-1086. (33) Atkins, P. W. Physical Chemistry, 4th ed.; Oxford University Press: Oxford, 1990; pp 594-601. (34) Cf. the energy of this orbital in COT (in which it is the LUMO) and the radical anion (in which it is the SOMO): 1.0 and 29.9 k c a h o l , respectively. Y
JP9423209
