13394
J. Phys. Chem. 1993,97, 13394-13402
Thermochemistry of Strained Cycloalkenes: Experimental and Computational Studied Alan D. Sbickland and Richard A. Caldwell' Department of Chemistry, The University of Texas at Dallas, Richardson, Texas 75083 Received: August 19, 1993; I n Final Form: October 4, 1993'
Pulsed time-resolved photoacoustic calorimetry in combination with quantum yield determinations afforded the relaxed triplet energy of 1-phenylcyclooctene and the energy of geometric isomerization of cis- 1-phenylcyclooctene. These values are combined with previous values of the energies of isomerization of cis- 1-phenylcycloheptene, cis-1-phenylcyclohexene, and cyclooctene to evaluate several computational approaches for modeling strained cycloalkenes.
Introduction The study of the degree of strain of olefinic bonds has been approached experimentally by attempts to measured enthalpies of various series of compounds. Schleyer suggested measuring the 'olefinic strain" by calculating the difference in the strain energy of the olefin and the strain energy of the alkane obtained by hydrogenating the olefin.' Such studies have usually been performed by measuring the enthalpy of hydrogenation of the olefin.2 Measuring the heats of formation of both compounds is a potentially less accurate approach since the desired value is the difference of two much larger numbers. Neither experimental approach has been successful for the study of molecules with large degrees of strain since such molecules are quite unstable and therefore unsuitable for isolation and chara~terization.~.~ Computational chemistry programs allow calculation of energies for molecules which cannot be isolated, but the accuracy of the results depends on the computational protocol. Forcefield techniques assume a model based on potential energy formulas similar tovibrational formulas. Separate Taylor series expansions are made for bond stretching, angle bending, bond torsion, and various interactions of these basic proper tie^.^-^ Only the third (and occasionally the fourth) terms of the series are considered since the formulas are describing potential energy minima for the properties and since terms beyond the fourth terms are quite small.5 A set of molecules with accurately determined experimental values for heat of formation and structural features is then used to develop the parameters for these equations. Ab initio calculations, while being free of adjustable parameters, are the most time-consuming and, thus, difficult to apply to molecules of substantial size without formidable hardware requirements. No ab initio program can completely manage electron correlation. Semi-empirical programs use quantum mechanics but take parameters derived from experimental data to provide the results of many of the integrals, decreasing required computational time enormously from that required for ab initio programs. Since the parameters derived from experimental data are based on data for individual atoms and pairs of atoms, they are potentially more general than the parameters used in force field calculations.Semiempirical calculations may lead to more accurate results than ab initio calculations since the parameters determined from experiment automatically will take into account the most important factor neglected in the ab initio programs, electron correlation. In general, which computational technique is to be preferred when answers of good accuracy are required depends strongly on the system of interest. Calculating the energies of an alkene and its hydrogenation product simulates measurement of the 'olefinic strain" of the f This article is dedicated to the memory of Gerhard L. Closs, a friend and colleague who is sorely missed. Abstract published in Advance ACS Abstracts, November 15, 1993.
0022-3654/93/2097- 13394$04.00/0
alkene. Different isomers of an alkene can be compared by computational programs. Although this technique allows investigation of molecules that are difficult or impossibleto isolate, the results must be evaluated by comparison with experimental results on molecules that can be observed adequately as shortlived species. Small and medium ring size trans-cycloalkenes provide a model for examination of olefinic strain. Investigation of the energy of isomerization from the cis-cycloalkene to the trans-cycloalkene for rings with 5-10 carbons can provide experimental data to evaluate computational studies.6~~Experimentally, trans-cycloocteneis the smallest isolable trans-cycloalkene,though transcycloheptene has been tentatively identified as surviving for a few hours in NMR experimentsat -80 0C.3+gHowever, it appears that olefinic strain is already low in the eight-membered ring, so a study of smaller rings is needed. This laboratory is examining the photoisomerization of cis- 1-phenylcycloalkenes. Since these moleculeshave the styrene chromophoreas part of their structure, they are easily photosensitized with many triplet sensitizers. The choice of sensitizer can include many with intersystem crossing yields of unity.9-12 Accurate determination of the energies of the photoisomerizationsthat follow the formation of the triplets can then be accomplished with time-resolved photoacoustic calorimetry (PAC)13 since all that is required in addition to the PAC experiment is the cis to trans quantum yield. Thus, this series of compounds is ideal for evaluation of the accuracy of the available computational approaches. This report covers an experimental study of 1-phenylcyclooctene and computational results on the six-, seven-, and eight-membered rings.
Experimental Section Preparation of 1-Phenylcyclooctene. Cyclooctanone and phenylmagnesium bromide, each obtained from Aldrich and used without further purification, were refluxed overnight in freshly distilled, dry ether under nitrogen. Hydrolysis (iced 25% aqueous NH4Cl), extraction (ether), repeated water rinses, drying (anhydrous MgS04), and evaporation of ether resulted in an 88% yield of 1-phenylcyclooctan-1-01as a pale yellow oil. Repeated crystallization from methanol at -14 OC yielded white needles (33%). mp 57 OC. Infrared spectrum: broad peak with maxima at 3417 and 3366,2900, 1475, 1433, 1030 cm-1. 1H NMR: 5 H (complex) between 7.26 and 7.54 ppm; 1 H (singlet) at 3.49 ppm; 14 H (complex) between 1.50 and 2.17 ppm. 13C NMR: 128, 126, 125, 96, 38, 27.4, 26.9, 21.9 ppm.14Js Dehydration under nitrogen with freshly distilledphosphorylchloride in freshly distilled pyridine, quenching with water, extraction (ether), washing with saturated saline, drying (anhydrous MgSOd), and evaporation of ether under reduced pressure resulted in cis-1phenylcyclooctene in 82%yield with an overall yield of 27% from cyc1ooctanone.l6 No contaminants were detected by gas chro0 1993 American Chemical Society
Thermochemistry of Strained Cycloalkenes matographyon a Restek Rtx20 (80%methyl and 20%phenylsilane substitution) megabore capillary column of 30 m with helium carrier gas and a temperature program from 140 to 250 OC over 20 min. These conditions allowed the detection of a 0.2% by area contaminant in one batch of cis-I-phenylcyclooctenedehydrated with polyphosphoric acid. Infrared and nuclear magnetic resonance spectra, obtained on a JEOL 200 MHz spectrometer, were consistent with the molecule (IR: 3022,2922,2851,2683, 1449,758, and 696 cm-l. IH NMR: 5 H (complex) between 7.23 and 7.38 ppm; 1 H (triplet) at 6.01 ppm with J = 7.93 Hz; 2 H (complex) at 2.63 ppm; 2 H (complex) at 2.28 ppm; 8 H (complex) between 1.26 and 1.55 ppm. 13C NMR: 143, 140, 128.2, 127.5, 126.4, 125.7,29.8,29.3,28.3,27.2, 26.7, and 25.9 ppm).15 Spectral and chromatographic properties of the cis-lphenylcyclooctene were independent of whether the sample was vacuum distilled. Laser flash photolysis of 1-phenylcyclooctene was performed as previously generally described," with a Continuum Model YG671C-10 nano/pico Nd:YAG laser using the Q switch mode with a wavelength of 355 nm, repetition rate of 10 Hz, energies between 1.O and 7.3 mJ/pulse measured after two Schott glass filters, and fwhm of 5 ns after the doubling crystal. An Oriel 66005 flash lamp and CVI Digikrom 240 photomultiplier provided detection. Thioxanthone, Michler's ketone, and p-methoxyacetophenone were purchased from Aldrich. After repeated recrystallization of thioxanthone and Michler's ketone from ethanol and ofp-methoxyacetophenone from benzene and toluene, they were used as sensitizers. Spectroscopic grade cyclohexane and heptane from Aldrich were used as solvents without further purification. Continuous sparging with nitrogen degassed the samples during studies. Data were collected using a Tektronix DSA 602 digitizing signal analyzer and transferred to an AST Premium 386 personal computer for analysis. Laser and flash lamp control and kinetic analyses were performed with the PC RAD and KS-01 software packages from Kinetic Instruments (P.O. BOX49434, Austin, TX 78765). Ten repetitions at each quencher concentration were averaged, background was subtracted, and both one component and two component expontential decay fits were considered. Excited-state spectra were also obtained using this software. Bulk sensitized photolysis experiments were performed on cis1-phenylcyclooctenein either toluene or cyclohexane. Sensitizers investigated included fluorenone,chrysene, 9-~yanophenanthrene, Michler's ketone, thioxanthone, and benzophenone. Irradiation was performed with a Hanovia medium-pressure mercury vapor lamp with a Corning 3320 uranyl glass filter sleeve. For each irradiation, 180 mL of solution was placed in a well surrounding the lamp and degassed with nitrogen sparging for 20 min before irradiation began and throughout theirradiation. Photostationary stpes were reached in 30-90 min at ice bath temperatures. The same products were obtained in the same ratio from irradiation with Michler's ketone without the ice bath, but irradiation times of 8-12 h were required. The products of photolysis were examined by gas chromatography, liquid chromatography, and proton NMR. Quantumyields were measured using ferrioxalate actinometry with a carousel to provide uniform irradiation of the actinometers and the experimental solutions as previously described in the literature.18Jg A Bausch and Lomb 33-86-01 monochromator with a 1.50-mm slit and an SP-200mercury light source provided light. A solution with p-methoxyacetophenone (0.035 M), cis1-phenylcyclooctene (0.052 M), and an internal standard of octadecane (0.022 M) in cyclohexane was prepared in the dark. Four 13-mm 0.d. Pyrex irradiation tubes were prepared in the dark by syringing 3.00 mL of the solution into each tube and performing four freeze-pumpthaw cycles. Irradiation was at 3 13 nm with a mercury vapor lamp in a monochromator. A solution of thioxanthone (0.002 M), cis-1-phenylcyclooctene
The Journal of Physical Chemistry, Vol. 97, No. 50, 1993 13395 (0,0128 M), and octadecane (0.0036 M) in cyclohexane was processed identically and irradiated with 366-nm light from the monochromator. Irradiations were performed for different lengths of time for the four tubes. Upon completion of irradiation, each tube was opened for analysis of the solution in triplicate by gas chromatography. Correction for back-reaction of the trans isomer was made as described in the literature.20 Proton NMR confirmed the presence of the trans isomer. pulsed, timeresolved photoacoustic calorimetry was performed as described in prior publications with a front face photoacoustic cell anda l-I'$Hz transducer.13~2' The PC RAD softwareprogram managed data acquisition and initial processing. The Nd:YAG laser at 355 nm with a 355-nm, 90' dielectric mirror in the PAC cell was used for the studies with thioxanthone as the sensitizer. Since p-methoxyacetophenone has a very low absorption coefficient at 355 nm, a Lumonix TE 860 nitrogen laser was used at 337 nm with a 337-nm dielectric mirror in the PAC cell for the studies with this sensitizer. Deconvolution was performed as previously described.13 Computational searches for conformational minima initially used PCMODEL 4.0 (Serena Software, Bloomington, IN 47402) to determine optimized structures for the cis and trans forms of cyclohexene, cycloheptene, cyclooctene, 1-phenylcyclohexene, 1-phenylcycloheptene, and 1-phenylcyclooctene. Attempts to construct in PCMODEL 4.0 all the conformations noted in the literature were made.22.23Local minima were submitted to MM2 (87), obtained from QCPE, and to all Hamiltonians supplied with AMPAC 4.0 (copyright 1992,Semichem, 12715 West 66th Terrace, Shawnee, KS 66216).Zkz9 The 12 structures with the lowest energy for the cis and trans isomers of each cycloalkene and phenycycloalkene were then submitted as input for MM3 calculation. GAMESS (Department of Chemistry,North Dakota State University and Ames Laboratory-U.S. Department of Energy, Iowa State University) was used for ab initio calculations of the optimum structure for the cis and trans forms of cyclohexene, cycloheptene, and cyclooctene using the lowest energy minima in PCMODEL as input structures. Optimizationswere performed with the 3-21G basis set at the SCF level. Energies were then calculated on these optimized structures using the 6-3 1G basis set, The 3-21G structures were then submitted for energy calculation at the 6-31G SCF level.
Results The cis-trans isomerization of 1-phenylcycloalkenes is an example of the interconversion of 1,2-disubstituted ethenes such as styrene or stilbene. The model of these interconversions by triplet sensitizers has been extensively studied.llJ2 A Jablonski diagram for this process, modified to include indications of lifetimes ( 7 ) and fractional energy releases (ax= [Eltart - Ermrl]/ Ehv) for each process in keeping with customary PAC nomenclature," is in Figure 1. In this model, the sensitizer is excited to an excited triplet state and decays to its relaxed triplet state with a time constant of 71 and an energy decrease of a,. The transfer of excitation from the relaxed triplet state of the sensitizer to ground-state alkene produces triplet alkene with constants 72 and +Z and recovery of the ground-state sensitizer. The triplet alkene relaxes rapidly to its perpendicular preferred geometry.12 The decay of the triplet alkene to a mixture of cis and trans ground-state isomers with constants 7 3 and +3 occurs without any conversion to other compounds or reaction with solvent or sensitizer in the caseof styrenederivatives.llJ2 When this process is carried out with pulsed excitation, study of the individual time and rate constants is possible. When continuous irradiation is given in a bulk photolysis experiment, a stable photostationary state will develop.12 Laser flash photolysis studies afforded the rate constants for quenchingof each sensitizerby 1-phenylcycloocteneandthe triplet lifetime of 1-phenylcyclooctene. Transient spectra obtained from
Strickland and Caldwell
13396 The Journal of Physical Chemistry, Vol. 97,No. 50, 1993
-
Snsltizer +
2
z
I
4.1
0
50
I
I
I
100
160
200
Time, nanoseconds
A
Figure3. Kinetic fit for 0.69 M 1-phenylcycloocteneinheptane, sensitized with thioxanthone and observed at 326 nm.
Sensitizer +
U C e H 5
Figure 1. Modified Jablonski diagram.
0.1
-
0-
I
310
I
310
3dO
do
Wavelength, nm
Figure 2. Transient spectrum of 1-phenylcyclooctene. Times: 4 (B), 15 (O), 50 (A),and 180 (*) ns after pulse.
thioxanthone, p-methoxyacetophenone, and Michler's ketones matched those in the literature.30J1 With 1-phenylcyclooctene above 0.25 M, the absorptions from the sensitizers are quenched so rapidly that they are no longer seen. At these high concentrationsof I-phenylcyclooctenewith thioxanthone,a new transient for the excited state of the quencher is observed at 326 nm with a transient lifetime of 32.2 f 0.7 ns. Due to absorption by the ground state of thioxanthone, the transient spectrum could not beobservedbetween 336 and 390 nm. No transientswere observed above 390 nm at high 1-phenylcyclooctene concentrations. Similar observations of the 326-nm transient with the other two sensitizers were not possible due to interference of ground-state absorption, but quenching of the triplet could be observed for all sensitizersand no new transients were found above 400 nm. Figure 2 shows the transient spectrum for 0.69 M cis- 1-phenylcyclooctene and 0.001 M thioxanthone. the first-order decay of this transient is shown in Figure 3. Both the lifetime and the absorption maximum are unexceptional for a styrene triplet, and we assign the transient accordingly. The absence of transients other than sensitizer and l-phenylcyclooctene triplets is particularly important, as such transients might have been ketyl-likeradicals derived from hydrogen transfer to triplet sensitizer, which would have greatly complicated or vitiated the PAC analysis if present. Demonstration of their absence was thus critical. Kinetic analysis was performed with each of the three triplet sensitizers. Figure 4 plots the pseudo-first-order decay rate constant for the thioxanthone triplet against increasing concen-
[cis-1-Phenyicyclooctene], M
Figure 4. Quenching curve for cis- 1-phenylcyclooctenesensitized by thioxanthone in cyclohexane.
trations of cis- 1-phenylcyclooctene. The quenching rate constant is the slope of this line. All data for decay of the excited sensitizers fit single-component,first-order exponential curves. The quenching rate constants for cis- 1-phenylcyclooctenein cyclohexaneare 5.36 X lo9 f 0.015 X 109 for thioxanthone, 4.84 X 109 f 0.046 X lo9for p-methoxyacetophenone, and 3.90 X 109 f 0.18 X lo9 for Michler's ketone. Michler's ketone has the slowest rate since it has the lowest energy triplet (61 kcal/mol as opposed to 65.5 kcal/mol for thioxanthone and 7 1.8 kcal/mol for p-methoxyacetophenone). These are similar to the high-energy rate constant limit for styrene and stilbene compounds.ll.*l Bulk sensitized photolysis experiments in general afforded stationary-state mixtures of cis- and trans- 1-phenylcyclooctene. Analysis by gas chromatography on a Restek Rtx2O 30-m megabore column revealed the production of one and only one new peak during photolysis. This peak followed that for cis-1phenylcyclooctene and could not be completely resolved from it. The best resolution obtained for the two peaks was R = 0.51,32 which allows excellentquantitation by the instrumentalintegration for solutions with more than about 10% trans isomer. Gas chromatography with a Restek Stabilwax column gave comparable resolution but with reversal of the order of the peaks. Proton NMR spectroscopy was used to corroborate the conversions detected by the gas chromatographic experiments. The olefinic proton of cis-1-phenylcyclooctene is a triplet at 6.01 ppm with J = 7.93 Hz, in excellent agreement with other observations.lS*33J4 The olefinic proton of trans- 1-phenylcyclooctene is a doublet of doublets at 5.76 ppm with Jvalues of 12.42 f 0.13 Hz and 3.67 f 0.09 Hz. The chemical shift agrees acceptably with prediction
Thermochemistry of Strained Cycloalkenes from group shift constants,34and the coupling constants agree with literature values for trans-l-acetylcyclotene.s."6 The ratio of the integration of the two regions of olefinic protons matched the ratio of the areas of the peaks on gas chromatography examinations of solutions with over 10% trans isomer. Photostationary-stateratios of trans to total phenylcyclooctene were examined for sensitizersof different triplet energies, although it was only possible to begin from the cis isomer. No loss of 1-phenylcycloocteneoccurred in the experimentsexcept as noted. Fluorenone (triplet energy 53 kcal/mol) and chrysene (triplet energy 57.3 kcal/mol) formed no trans isomer as measured by both gas chromatography and NMR. A photostationary state with 32% trans was found with 9-cyanophenanthrene (ET= 58 kcal/mol) and Michler's ketone (ET = 62.5 kcal/mol). Thioxanthone (ET = 65.5 kcal/mol) gave a 42% trans ratio at the photostationary state. Sensitization with benzophenone (ET= 68.6 kcal/mol) resulted in loss of all the I-phenylcyclooctene and formation of a white precipitate (presumably benzopinacol) which had no olefinic protons in its NMR spectrum. These results fit well with other 1,2-disubstituted ethenes and styrenes.12 Attempts at isolation of trans-1-phenylcyclooctene failed. Liquid chromatography using a variable-wavelength ultraviolet detector with both normal and reversed phase columns and a variety of solvents and solvent gradients failed to resolve the isomers. Thin layer chromatography with silica plates and a cyclohexanemobile phase did not separate the isomers. Attempts at separation with silver nitrate modified silica columns or plates were met with inconsistent results. Isolation was alsocomplicated by the stability of trans-1-phenylcyclooctene. When passed through a silica column with a cyclohexane mobile phase, a mixtureof cis and trans isomers of phenylcycloocteneis recovered as only the cis isomer. If the silica column is first washed with base, both isomers are recovered. Evaporating the cyclohexane solvent to redissolve a crude solution from a bulk photolysis with Michler's ketone and redissolving it in deuterochloroformfor an NMR experiment caused no change in the percentages of the isomers asjudged by gas chromatography. However, evaporating the cyclohexane,redissolving in carbon tetrachloride, evaporating this solvent, and then dissolving in deuterochloroform caused total loss of the trans isomer. A cyclohexane solution of the photostationary-state mixture from a thioxanthone-sensitized photolysis experiment had 4 1% trans- 1-phenylcyclooctene. Only 8.8% trans isomer remained of the mixture after being left at room temperature in the dark for 12 h. If the photostationarystate solution was passed through a base-prepared silica column to remove thioxanthone, the resulting solution of 40% trans and 60% cis isomers was stable at room temperature in the dark for 1 week. No analyses for times longer than 1 week were attempted. Similarprolonged stability for trans-1-acetylcyclooctenehas been noted with reversion to the cis isomer when in contact with water, acid, or alcohol. We suggest that trans-1-phenylcyclooctene is stable but undergoes rapid reversion to the cis isomer due to the presence of adventitiousacid in those experimentsin which backisomerization occurs. Quantumyields were determined with ferrioxalate actinometry as described above. Because the analysesof the smaller percentage conversions to trans isomer that are necessary for quantum yield experiments required more careful modeling of the gas chromatograph peaks, the irradiated solutions were analysed by gas chromatography with least-squares fitting to two Gaussiancurves. Since chromatography peaks are theoretically Gaussian.32 leastsquares fitting of the sum of two Gaussian curves to the digitial data from the chromatograph was done with a Quattro Pro spreadsheet. Following optimizationof retention times, standard deviations, and amplitudes to minimize the squares of the residuals, the areas of the Gaussian curves of the two peaks reflect the ratio of the two species present after irradiation. The fitting routine
The Journal of Physical Chemistry, Vol. 97, No. 50, 1993 13397
Time, seconds Figure 5. Gaussian fitting of one gas chromatogram of cis-l-pbenylcyclooctene sensitized by pmethoxyacetophenoneduring quantum yield experiments. trans-I-Phenylcyclooctene= 4.32%.
correctly handled a calibration series. An example of the results is given in Figure 5 . The moles of trans isomer produced were calculated for each tube and then corrected for the amount of back-conversion by literature techniques.20 The incident light was measured directly for each tube by actinometers that were irradiated concurrently with the experimental solutions. The quantum yields were determined to be 0.359 f 0.033 for thioxanthone and 0.432 f 0.039 for p-methoxyacetophenone. Accordingly, the quantum yields compare acceptably with each other. For high-energy sensitizers (ones with ET greater than the ET for either phenylalkene isomer), the photostationary state should be determined solely by the decay fraction of trans to total phenylalkene.20 The quantum yields compare acceptably with the photostationarystate trans conversion of 0.42 f 0.05 for thioxanthone in the bulk photolysis experiments. Pulsed,time-resolvedphotoacousticcalorimetry was performed on cyclohexane solutions of cis- 1-phenylcyclooctene with either thioxanthone, p-methoxyacetophenone,or Michler's ketone as the sensitizer. Deconvolution used the three-component, sequential decay model discussed above. Since no other chemical processes are occurring, deconvolution with a three-component model, as depicted in Figure 1, is appropriate. We take 71 as an arbitrary constant of 0.1 ns whose value has negligible effect on the fit, @ I is calculated from the sensitizer triplet energy, and 7 2 is calculated from the appropriate quenching rate constant reported above and the concentration of 1-phenylcyclooctene. These values are kept constant while the program fits @2, @3, and 73. The @3 created by the deconvolution program represents a weighted average between the fractional energy returned when the triplet quencher returns to ground-state cis conformationand that returned when the transition is to the ground-state trans isomer. The weighting factor is the fraction of trans isomer being formed. All relevant PAC data are given in Table I. The deconvolution program gave good fits for the studies with thioxanthone andp-methoxyacetophenone. A representativePAC deconvolution is given in Figure 6. The deconvolution of data from trials with Michler's ketone has large residuals indicating poor fitting to thecurves. The 7 3 calculatedby the fitting program represents the lifetime of the phenylcyclooctene triplet and is reported in Table I. The excellent agreement of 73 (30.1 1 i 0.35 ns) with the lifetime of the phenylcyclooctene triplet measured by kinetic experimentssupports the contention that both the kinetic and photoacousticexperimentsare studying the same processes: the formation of the triplet phenylcyclooctene and its decay into
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13398 The Journal of Physical Chemistry. Vol. 97, No. 50, 1993
TABLE I: Photoacoustic Calorimetrv Results sensitizer(n). @IC 02 03 73, ns 01+ 0 2 + 0 3 Eap, kcal/mou Em, kcal/molg 6.06 f 0.43# 0.156 0.227 f 0.071d 0.542 f 0.074d 32.92 f 1.4P 0.925 f 0.015d 49.70 f 2.1P thio~anthone(24)~ 5.05 & 0.12' pmetho~yacetophenone(12)~ 0.154 0.207 f 0.0216 0.580 f 0.021d 29.88 & 0.40. 0.941 f 0.004d 54.22 0.64' 55.67 f 1.50. 6.82 & 1.34e 0.224 0.078 f 0.0496 0.613 f 0.072d 30.14 & 1.33' 0.915 & 0.046" Michler's ket0ne(24)~ a n is the number of independent determinations. bp-Methoxyacetophenoneat 337 nm, others at 355 nm. e Determined by PAC in the absence of quencher. d Standard deviation. 90% confidence limit of the mean. 1 Energy of 1-phenylcyclooctenetriplet calculated as I&,( 1-01-02) Residual energy calculated as ,!?hv( 141-0243). ~~
*
1
0.5
0
-0.5
1
Time, nanoseconds
Figure6. Photoacoustic calorimetry waves for a representativeexperiment with cis-1-phenylcyclooctenesensitizedwith thioxanthonein cyclohexane. Parameters of fit: 01 = 0.1563, TI = 0.1 ns, 0 2 = 0.2216, 7 2 = 1.71 ns, 03 = 0.6155, 73 = 30.83 ns.
either the original cis isomer or the trans isomer. The triplet energy of the phenylcyclooctene and the residual energy not released during the experiment are calculated from these values and are also reported in Table I. Since there is some storage of the energy of the incident light, the trans isomer must be higher in energy than the cis isomer. The energy of isomerization can be calculated using the data from the quantum yield experiment and these values for residual energy. Calculation of the energy of isomerization involves dividing the residual energy E c ( l-@I-@&) from the photoacoustic calorimetry experiments by the quantum yield for the same sensitizer. Errors in e2 and e3 tend to compensate, in order to fit the total E-wave amplitude. The residual energies are accordingly available to good precision even though they are differences between unity and a sum close to unity. Values of Eh,,, are 12.16 kcal/mol (with variance 5.80) for p-methoxyacetophenone and 17.90 kcal/mol (with variance 22.65) for thioxanthone. The variances for each sensitizer were determined from the sums of variances for the quantum yields and the residual energies. Averaging these values using their variances as weighting factors, as described by Young for averaging values ~ithdifferentvariances,3~gives 13.3 2.9 (90%confidencelimit) kcal/mol for the energy of isomerization of cis- l-phenylcyclooctene to the trans isomer. Computationalstudies of cis and trans isomers of cycloalkenes and 1-phenylcycloalkeneswith ring sizes of six, seven, and eight carbons (c-C6, t-C6, c-C7, t-C7, c-C8, t-C8, c-PC6, t-PC6, c-PC7, t-PC7, c-PC8, and t-PC8) were performed; initial efforts to identify optimized structures for local minima used PCMODEL 4.0 to construct known conformations.22.23 Two conformations of c-C6 are known-a half-chair and a half-boat. PCMODEL4.0allowedcreationoftwoformsoftranscyclohexene by removal of two hydrogens from either the chair form of cyclohexane or the boat form of cyclohexane. Saunders has reported already that there are two forms.36 Each led to a different minimum in subsequent computations. Similar conformations were found for the PC6 isomers. Literature reports
*
four conformations for cycloheptane-chair, boat, twist-chair, and twist-boat. Cyclooctane has three families of conformations: the boat family with a boat-boat form and a twist-boat form, the crown family with a crown form, a chair-chair form, and a twist-chair-chair form, and the boat-chair family with a boat-chair form and a twist-boat-chair form. Conformational analysis of cyclooctene is not well developed in the literature. Attempts to develop each of the conformations for cyclooctane and then remove adjacent hydrogens to create all conformations of cyclooctene on PCMODEL 4.0 were made, and resultant structures that were accepted as local minima by the program were evaluated. Although it is impossible to know that all local minima were located, 59 conformations of local minima were found with some duplication of structures that had the same gross conformation but slightly different values for heats of formation from PCMODEL. Each of these structures was entered into MM2 (87) for routinecalculation. MM2 found 30structures that werestable minima, with the other structures altering conformationsslightly to merge with one of the 30 conformations. Each of the 59 structures was also entered into AMPAC 4.0 for analysis with each of the Hamiltonians provided by the program and documented in the l i t e r a t ~ r e .Some ~ ~ ~ ~of the Hamiltonians in AMPAC found only 24 of the conformations found by MM2. AMPAC found no new structures. The 12 structures with the lowest energies were submitted for calculation by MM3. MM3 made no significant changes in the structures. The six lowest energy structures for the unsubstituted cycloalkenes were used for input into optimization by GAMESS. Each structure was optimized with the 3-21G basis set and SCF level. Energies of these optimized conformations with the 6-3 1G basis set were found. These optimized structures were then submitted for optimization with the 6-31G basis set at the SCF level. The energies of isomerizationcalculated by all these techniques are given in Table I1 in kcal/mol. For simplicity,only the lowest energy configurations for the cis and trans isomers are subtracted to give the energies of isomerization. Figure 7 depicts the configurations of the trans isomers of 1-phenylcyclohexene, 1-phenylcycloheptene, and 1-phenylcyclooctene. Data for the angles and energies of each configuration from selected programs from each technique are given in Table 111.
Discussion Use of flash photolysis and time-resolved photoacoustic calorimetry allows accurate measurement of the energy of isomerization of the phenylcycloalkenes and the measurement of properties of the molecules and their triplets. Previous studies find the energy of isomerizationof c-PC6 to be 44.7 5 kcal/mol or 47.0 f 3.0 kcal/mol and that of c-PC7 to be 29 3 kcal/ Here, we find the energy of isomerization of c-PC8 to be 13.3 2.9 kcal/mol. An updated value for the energy of isomerization of c-C8, reported by Allinger, is 11.37 0.46 kcal/ mol.41 No experimental values for c-C6 or c-C7 are reported. Olefinic strain in these cyclic alkenes increases as the size of the rings decreases. The experimental values for c-C8 and c-PC8 suggest that the substitution of a phenyl substituent for one of theolefinic hydrogensdoes not greatly affect the thermochemistry of the molecule as Allinger suggested for trans-l-phenylcyclo-
*
*
*
The Journal of Physical Chemistry, Vol. 97,No. 50, 1993 13399
Thermochemistry of Strained Cycloalkenes
TABLE II: Energies of Isomerization from Modeling Programs molecule source
C6
c7
exptl PCMODEL 4.0 MM2 MM3 MNDO MIND0/3 AM 1 PM3 SAM 1 HF/3-21G HF/6-3 1G//HF/3-21G
59.88 33.33 35.03 60.51 56.61 59.36 56.94 60.69 64.19 73.64
33.19 20.24 22.16 34.97 36.95 30.90 30.17 31.69 44.60 47.09
tRn)l-PhenylCyclohXeM
lnn-a-l-Ph.ny~doheptm
tran8-l-Phenylcycl~teM
Figure 7. AMPAC 4.0 (PM3) optimized structures for t-PC6, t-PC7, and t-PC8.
h e ~ e n e . ~That the energy of cis to trans isomerization of 1-phenylcyclooctenewould be about 2 kcal/mol larger than that for cyclooctene appears reasonable, as the phenyl appears more crowded in the trans. A range of values for this energy, 4to +3 kcal/mol, is found by molecular mechanics techniques, and 1 4 kcal/mol is found by the various AMPAC Hamiltonians as shown in Table 11. The reported lifetimesof these molecules also support increasing strain with decreasing ring size. The reported lifetime of t-PC6 is 5-9 ps at 300 K while t-PC7 reportedly has a lifetime of 250 5.394’3942 trans-1-Phenylcycloocteneappears to be stable for at least 1 week and possibly indefinitely. trans-Cycloocteneis also stable indefinitely at room temperature>J5 Assuming the preexponential factor of 1014for trans- 1-phenylcyclohexene isomeri z a t i ~ nholds ~ ~ , for ~ ~ all the 1-phenylcycloalkenes and that the activation energy for the isomerization of the phenylcycloalkene is equal to the difference between the ET and the energy of the trans isomer (Le. assuming the triplet surface minimum energy, which is known, and the desired singlet surface energy maximum are nearly isoenergetic21) results in lifetimes calculated from the Arrhenius equation of 4 ps for t-PC6, 50 min for t-PC7, and 7 X 108 years for t-PC8 at room temperature. The relaxed triplet energy (ET) of 1-phenylcyclohexene is reported as 56.4 f 0.8 kcal/mol,39 and the ET of l-phenylcycloheptaneis 52.8 f 1.2 kcal/mol.a Combining the present data from the three sensitizers, the ET of 1-phenylcyclooctene is 53.2 f 0.9 kcal/mol. This value is well within our expectations.21 The 1-phenylcyclooctene triplet affords somewhat less trans isomer than expected. The decay fractions of 0.50 for acyclic ~ t y r e n e s ,0.42 ~ ~ .for ~ ~PC7, and 0.36 for PC6 would have suggested a value of 0.45 or higher.21.39.a This lower trans decay ratio could rationally be explained (albeit post hoc) if the preferred conformationof the PC8 triplet is nonperpendicular,but biased toward the ‘cis-like” geometry as a result of conformational factors within the eight-membered ring. Although displacement of the relaxed triplet from perpendicularity would be expected to increase the energy, decreasesin ring strain in a ‘cis-like” geometry could offset this. Table I1 compares the experimental energies of isomerization with the results from the various computational techniques. Also
C8 11.37 12.01 7.47 9.32 14.34 18.34 9.85 10.55 11.20 12.51 14.49
PhC6 41 39.98 26.77 26.57 60.10 56.36 57.60 54.42 58.72
PhC7 29 20.88 20.3 1 20.63 36.07 36.68 31.06 30.29 32.32
PhC8 13.3 7.80 10.90 10.43 18.47 19.76 13.16 14.18 14.56
Fd
0.3033 0.3768 0.3426 0.3435 0.4893 0.1570 0.1098 0.1674
tabulated is Fd, which we define as the standard deviation of (Eexp- E a d / E e x p for C8, PC6, PC7, and PC8 for each calculational technique,Le. a measure of the fractional accuracy. Comparison of these values shows that the AMPAC 4.0 PM3 Hamiltonian gives the best overall results. The force field programs are all too low in their estimates for the phenylcycloalkenes. Only the PCMODEL program is close to the value for cyclooctene. The value of 9.32 kcal/mol for cyclooctene by MM3 differs from the 10.82 kcal/mol for this differencereported by A l l i ~ ~ g eThe r . ~ trans-cyclooctene reported here matches all the parameters reported in Allinger’s article. The difference in isomerization values between our calculations is presumably due to differences in the cis isomers found, but no details of the cis isomer are given in Allinger’s paper. The isomerization enthalpies for MM3 calculated here match those Allinger reports for cyclohexene and cycloheptene. Calculations of OSE for pyramidalized olefinic bonds using MM2 have also found values that are below experimental v a l ~ e s . ~ , ~ . ~ ~ Three of the semiempirical Hamiltonians compute isomerization enthalpies that come closer to the experimental values than the force field calculations. In another study of pyramidalized olefins, the semiempirical techniques were also more accurate than the force field calculation~.~sThe parameters of the force field programs are not based on any molecules as highly strained as these trans-cycloalkenes. However, the semiempirical technique depends on parameterizationof atomic and interatomic integrals and makes no assumptions analogous to (e.g.) the torsional potential functions in a molecular mechanics calculation. While a force field technique is likely to be preferable when interpolating within the range of its validation, the more fundamental quantum mechanical computation of the semiempirical techniques seems to us the preferable technique for extrapolation. The data from the ab initio calculations show only the cycloalkenes, since the phenylcycloalkenes would have required too much computer time to converge. A more extensive ab initio study of cis- and trans-cyclohexenewas done by Verbeek et a1.6 Our ab initio values for the isomerization energy of cis-cyclohexene are much higher than thevalueof 56.0 kcal/mol Verbeek reports. The configurations of the cis and trans isomers of cyclohexene in Verbeek’s article closely match those of our calculationsdespite a greater degree of accuracy in his electronic wave functions. Verbeek’s results are close to those achieved by the semiempirical Hamiltonians but clearly required far more computationaleffort. Table I11 gives the energies and angles predicted by each of the modeling techniques. Certain of the dihedral angles between the phenyl ring and the olefinic bond are included. The dihedral angles made by theolefinic bond with the planeof the substituents on each end of the olefinic bond are given. We define these as the dihedral angle formed by a line connectingthe exocyclic atom (either the attached carbon of the phenyl group or the hydrogen attached to the olefinic carbon) to the endocycliccarbon attached to the same olefiniccarbon and the double bond along the direction of the bond connecting the endocyclic carbon with the olefinic
13400 The Journal of Physical Chemistry, Vol. 97, No. 50, 1993
Strickland and Caldwell
TABLE 111: Summary of Computa~onalResults A. Force Field Calculations dihedral angles heat of formation PCMODEL MM2 MM3 C-C6 half C-C6 half twist t-C6 twist t-C6 chair c-c7 twist c-c7 twist c-c7 boat c-c7 chair t-C7 twist c-C8 boat c-C8 boat c-C8 twist t-C8 chair t-C8 c - P C ~ half c - P C ~ half t-PC6 half t-PC6 half c-PC7 chair c-PC7 twist c-PC7 twist c-PC7 boat t-PC7 twist t-PC7 chair c-PC8 twist c-PC8 chair c-PC8 boat t-PC8 perpend t-PC8 twist t-PC8 parallel
chair boat chair boat boat chair ch. ch. boat chair chair chair boat chair boat boat chair boat ch. ch. chair boat tw. ch. chair chair
-6.21 4.67 42.66 43.41 -6.79 -5.78 -4.12 -2.81 16.35 -6.93 -5.56 -3.52 4.44 6.15 17.64 21.78 57.62 60.50 16.05 18.15 18.87 19.48 36.93 37.26 14.41 17.93 18.81 22.21 23.17 28.08
-1.76 4.31 30.78 -2.43 -1.73 4.04 1.81 17.69 -3.27 -1.77 0.61 4.19 10.90 20.36 20.32 47.13 48.29 19.10 20.84 50.54 22.49 39.41 39.67 17.41 21.16 21.30 28.31 29.08 34.35
phenyl-vinyl angle PCMODEL MM2 MM3
PCMODEL phenyl Hend
phenyl
Hend
phenyl
Hend
-1.64
179.37
179.04
179.04
178.73
178.73
33.39
-126.29
-126.29
-2.85
147.87 147.91 145.24 145.27 179.76 -179.76
122.77 122.76 179.89 -179.87
19.31 -4.02
157.25 156.72 178.83 -179.79
139.97 137.82 140.71 178.55 -179.69 -178.49
138.31 179.67
166.09
166.09
156.22
156.19
155.27
155.27
179.36
179.94
178.96
179.62 -178.93
153.62 -176.23 147.81 -170.29 178.40 -178.59
-108.96 111.53 177.36
160.74
5.30 20.78 46.78 17.81
38.44 16.32 26.75
-36.50 -38.53 -34.81 -25.58 44.67 44.93 45.25 42.14 -3 1.49 -40.33 40.26 -55.83 -43.24 40.55 -47.66 36.02
-33.38 -3 1.88 24.98 17.41 42.43 42.70 -5.41 38.54 -32.15 -41.05 34.73 -52.74 -41.58 41.44 -49.14 41.06
179.37
39.90 -179.65 -33.20
159.19 159.07 -179.40
-48.10
MM2
MM3
179.42 -179.42
115.79
179.29 -178.35
165.06
157.02
160.41
128.12
159.57
133.34
-43.70 -45.60
179.07
179.38
179.19
179.40 -177.19
179.26
-40.80
-173.12
-166.61
-169.05
-154.01
170.96
154.76
B. Semiempirical Calculations dihedral anglcs heat of formation c-C6 C-C6 t-C6 t-C6 c-c7 c-c7 c-c7 c-c7 t-C7 c-C8 c-C8 c-C8 t-C8 t-C8 c-PC6 c-PC~ t-PC6 t-PC6 c-PC7 c-PC7 c-PC7 c-PC7 t-PC7 t-PC7 c-PC8 c-PC8 c-PC8 t-PC8 t-PC8 t-PC8
half half twist twist chair twist twist boat chair twist boat boat twist chair half half half half chair twist twist boat twist chair twist chair boat perpend twist parallel
chair boat chair boat boat chair ch. ch. boat chair chair chair boat chair boat boat chair boat ch. ch. chair boat tw. ch. chair chair
MNDO
AM1
PM3
-9.91 -9.91 50.51 50.60 -1 1.68 -10.13 -9.30 -9.30 23.29 -10.20 -9.25 -9.81 4.53 5.26 15.56 15.56 75.66 75.66 14.83 16.64 17.37 17.37 50.90 51.20 15.27 18.69 17.63 33.74 34.37 34.37
-10.06 -10.06 49.30 49.31 -14.14 -12.98 -11.67 -10.48 16.76 -15.10 -16.09 -15.75 -5.90 -4.04 15.55 15.55 73.15 73.64 11.78 13.10 14.42 14.42 42.84 43.14 8.50 10.81 12.00 21.66 23.16 23.16
4.88 -1.57 51.52 52.06 -7.14 -5.22 -5.22 -2.84 23.04 -7.73 -8.09 -7.06 2.83 4.83 19.80 22.78 74.22 74.69 17.36 19.71 20.45 19.64 47.72 47.65 13.91 17.41 16.38 28.09 29.66 29.66
phenyl-vinyl angle MNDO
-90.19 -90.47 -54.20 54.16 -90.88 -88.91 90.43 90.43 71.61 58.81 -92.42 -90.00 92.67 -74.00 74.91 -74.54
AM1
37.30 37.18 -30.50 28.01 -44.62 -43.08 44.83 45.05 40.59 34.80 -38.18 43.77 52.73 -40.46 47.00 -47.04
MNDO
AM 1
PM3
phenyl
Hend
53.81 44.98 -23.37 28.22 -53.86 -54.83 54.28 -62.48 55.01 34.1 1 -45.46 78.02 65.23 -51.85 66.56 -67.07
-179.24 -179.21 146.69 -146.98 -178.89 179.03 -179.94 178.35 -157.63 -179.69 179.87 -178.37 -165.67 -166.11 -179.05 -179.07 158.16 -158.16 -178.62 178.65 178.30 -178.31 -168.07 -168.68 -178.33 179.63 178.76 175.23 -175.70 175.72
-179.25 -179.22 146.68 -146.98 178.89 179.04 -178.36 179.93 -156.97 178.85 178.92 -179.89 -1 65 -68 -1 66.10 -179.17 -179.17 146.16 -146.15 178.97 178.78 -179.59 179.63 -156.67 -156.32 178.84 -178.99 -178.21 165.46 -165.46 165.44
phenyl -179.18
Hend -179.18
142.61 -143.43 -179.34
142.61 -143.43 179.37
-155.70 179.22
-153.95 179.32
-164.73
-164.72
-179.18
-179.36
151.18 -1 54.14 -179.33
141.23 -141.33 -1 80.00
-163.28 -162.55 -177.87
-152.65 -153.81 179.09
171.88
163.52
PM3 phenyl 179.18 -179.43 141.80 -142.71 -179.63 179.47 -179.47 179.38 -155.22 179.86 179.13 -178.89 -163.68 -164.25 -179.50 -178.66 149.57 -150.89 -179.93 179.37 179.57 -179.27 -159.65 -161.35 179.97 -179.54 -179.06 169.06 -169.58 169.58
C. Ab Initio Calculations energy, kcal/mol C-C6 t-C6 c-c7 t-C7 c-C8 t-C8
half chair twist chair chair chair twist ch. ch. twist chair
3-21G 0.00 64.19 0.00 44.60 0.00 12.51
6-31G 0.00 73.64 0.00 47.09 0.00 14.49
dihedral angle (3-21G) phenyl H end -179.36 179.67 133.54 133.57 -1 78.62 -178.65 148.23 148.31 -178.25 177.75 161.55 159.64
Hend -179.18 178.94 141.78 -142.70 179.65 179.49 -179.48 -179.61 -153.23 -179.95 179.00 -178.62 -163.68 -164.25 -179.12 179.29 141.38 -141.97 179.98 179.38 179.77 -179.30 -154.46 -152.80 179.74 179.43 -179.17 163.17 -163.31 163.30
Thermochemistry of Strained Cycloalkenes
e
n
Exocyclic H or Ph Figure 8. Dihedral angle used to determine pyramidalization of olefinic carbon. carbon. This apparently complicated definition is actually the most convenient in the sense that PCMODEL permits its evaluation easily. Figure 8 depicts this angle. For an sp2center, this angle would be 180O. For a symmetrical tetrahedron, this angle would be 120". Thus, an estimate of the degree of pyramidalization of one end of the olefinic bond can be obtained by comparison to these values (Dg,, = [180 - angle]/[l80 1201); Dg,, = 0 for a pure sp2 carbon and 1 for an sp3. All of the models show distortionof the dihedral angles across the olefinic bond and extensive pyramidalization. Calculating the Dg, from the angles from the PM3 calculations gives 0.64 for t-C6,0.45 for t-C7, and 0.27 for t-C8. Our calculations agree with those of Verbeek that the distortion of the double bond of t-C6 actually places the olefinic hydrogens on the same side of the plane of the 7r bond as the carbons of the ring. In the phenylcycloalkenes, the end of the olefinic bond with the phenyl substituent is less pyramidalized (0.51,0.34,and 0.18,respectively,for t-PC6, t-PC7, and t-PC8), but the unsubstituted end is quite close to the values for thecycloalkene(0.64,0.43, and0.28, respectively). Thephenyl substituents in these molecules in their lowest energy conformations form phenyl-vinyl dihedral angles of 23O in t-PC6,34O in t-PC7, and 67O in t-PC8. Calculations for styrene with the phenyl ring twisted at various angles from the plane of the 'A bond with AMPAC 4.0 using the AM1 Hamiltonian showed that the dihedral angle made by the phenyl ring with the olefinic bond is of minor consequence to the stability of the styrene chromophore, consistent with a computed length of the bond between the phenyl group and the vinyl carbon that only varies from 1.452 A for t-PC6 with a phenyl-vinyl dihedral angle of 28' to 1.469 A for t-PC8 with a phenyl-vinyl dihedral angle of 67O. Since phenylvinyl conjugation is expected to be even lower in the tramcycloalkenes than in styrene because the pyramidalization of the vinyl carbon will decrease overlap, the difference in the degree of pyramidalization of the ends of the olefinic bonds of the phenylcycloalkenes appears to result from steric factors. Altering the torsional parameters of the C=C double bond in the MM2 (87) program improves the simulation of these strained cycloalkenes. Simultaneously,we chose tovalidate the parameters we changed through this effort on cyclooctatetraene,cis-Zbutene, trans-2-butene, and 2,3-dimethyl-l,3-butadiene.In MM2 (87), hydrogen is atom type 5 , sp3 carbon is atom type 1, and sp2carbon is atom type 2. Since the second-order torsional constant is the primary constant affecting rotation around an olefinic bond, the V2 parameters for 1-2=2-1, 1-2=2-2, 1-2=2-5, 2-2=2-5, 2-232-2, and 5-2=2-5 were increased to simulate increased strain as the bond was distorted. The default values for these V2 parametersinMM2(87)are 10,10,12.5,9,8,and 15,respectively. Although increasing just the first four of these V2 parameters by 10modeled the cycloalkenesand 1-phenylcycloalkeneswell, these parameters were inappropriate for cyclooctatetetraene and 2,3dimethyl-l,3-butadiene. Cyclooctatetraene is known to have a heat of formation of 71.13 f 0.33 kcal/mol, a C=C-C bond angle of 126.8 f 1.9O, a C=C-C=C torsion angle of 55.7 f 3.9O, a C-C bond length of 1.456 f 0.012 A, and a C = C bond
The Journal of Physical Chemistry, Vol. 97,No. 50, 1993 13401 length of 1.330 f 0.006 The heat of formation of 2,3-dimethyl-1,3-butadieneis known to be 10.78 f 0.30 kcal/ mol.48 It is known to bea nonplanar molecule, though thedihedral angle is not well known. The best combination of V2 values found to model 12428,t-C8, c-PC6, t-PC6, c-PC7, t-PC7, c-PC8, t-PC8, cyclooctatetraene, and 2,3-dimethyl-1,3-butadieneis 16, 15, 19, 10, 14, and 25 in the same order as that given above. The Fd value for MM2 with these altered V2 parameters is 0.1838, as in Table 11. This agreement with experimentalvalues is much better than that of MM2 or MM3. The Fd can be further lowered to 0.1560 by increasing the V2 for 1-2=2-5 from 19 to 25, but this results in 2,3-dimethyl- 1,3-butadiene being planar. Allinger suggestedthat MM3 did not perform adequately on t-PC6 because the phenyl group had some unexpected effect on the m0lecule.4~ It appears to us that simply using higher V2 values in the MM2 program models the strained tram-cycloalkenes and 1-phenylcycloalkenes well. Cyclooctatetraene is calculated, with the altered V2 values, to have a heat of formation of 78.79 kcal/mol withaC4-Cangleof 127.01°,aC=C-C=Cdihedralangle of 55.53O, and carbonxarbon bond lengths of 1.346 and 1.474 A. Dimethylbutadiene is found to have an s-trans form with a heat of formation of 12.72 and a dihedral angle of 179.17O and an s-cis form with a heat of formation of 12.30 kcal/mol and a dihedral angle of 2.84O. Although these heats of formation are too high, they are identical to the ones calculated by MM2 with the usual V2 parameters. AMPAC 4.0 (AM 1) calculation of the heat of formation of 2,3-dimethyl-1,3-butadiene with dihedral angles from 0 to 180° showed only a 0.7 kcal/mol variation, making it difficult to evaluate any V2 parameter-based dihedral angles in this molecule. The effect of increasing the V2 values would, of course, be negligible for any alkene with an approximately planar double bond. In accord with this prediction, values for cis- and trans-2-butene calculated with the new parameters match exactly their values in MM2 (87). We do not assert that our values are optimum values for the V2 parameters, since a larger range of validation would be needed. It is nonetheless apparent that values much larger than those included in MM2 (87) perform better for the highly strained trans-cycloalkenes of small and medium ring size, without compromising the ability of MM2 to provide accurate results for unconjugated acyclic alkenes and with only modest changes in its success with conjugated polyenes (cf. cyclooctatetraene) with substantial dihedral angles around the central, essential single bond. However, thevalues chosen here would clearly make large differences in any calculation of an energy for a transition state in alkene geometric isomerization. Conclusions
The increasing body of experimentalthermochemistryof highly strained compounds, which we here exemplify by a series of tram1-phenylcycloalkenes, allows validation of the various computational techniques by which such properties might be estimated for unknown molecules. For the present series, semiempirical calculations give the best results. Among these the PM3 Hamiltonian is in closest agreement with experiment. Molecular mechanics calculations for this series require modification of the V2 torsional parameters before accuracy comparable to that for the semiempirical calculations can be achieved. This work suggests alternate parameters, but experimentalwork with a wider range of alkenes should be performed to validate them. Acknowledgment. This work was supported by the National Science Foundation (Grant CHE-9 121313) and the Robert A. Welch Foundation (Grant AT-0532). We wish to thank Andrew Podosenin, Ph.D., of New York University for running the input supplied through the MM3 program, Anna Helms and Jeffery Elbert for valuable discussions, and Professor John Wiorkowski for advice on the statistical treatment.
13402 The Journal of Physical Chemistry, Vol. 97, No. 50, 1993
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