12236
J. Phys. Chem. 1994, 98, 12236-12241
Theoretical and Experimental Study of the Structure, Vibrational Frequencies, and Strain Energy of Tricycle[3.1.0.0276]hexane Steven R. Davis* and Puei L. Tan Department of Chemistry, University of Mississippi, University, Mississippi 38677 Received: June 27, 1994; In Final Form: September 12, I994@
The equilibrium geometry and vibrational frequencies of tricycl0[3.1 .0.02,6]hexanehave been determined at the MP216-311G(d,p) level by using ab initio calculations. An appropriate homodesmic reaction was used to determine the strain enthalpy and heat of formation, giving values of 71.3 and 57.3 kcal/mol, respectively. The strain energy and heat of formation are compared to those of structurally related molecules. The IR spectrum has been obtained in the gas phase and in an argon matrix, while the Raman spectrum was collected of the liquid sample. The vibrational fundamentals are assigned to specific normal modes by comparison of the calculated and experimental spectra.
Introduction Benzene is the most stable valence isomer of a series of structures which partially include benzene, Dewar benzene, benzvalene, prismane, and 3,3'-bicyclophenyl. The less stable isomers all contain considerable amounts of strain energy ranging from 63.6 kcaYmol for Dewar benzene to 148.9 kcaY mol for prismane as determined by ab initio calculations at the MP2 level.' One such isomer, benzvalene, has been found to have a strain energy of 81.3 kcdmol and a heat of formation of 90.2 kcdmol from ab initio calculations.' Turro et al.*have studied the isomerization of benzvalene to benzene and found the reaction to proceed via first-order kinetics in the temperature range 40-57 "C with an activation energy of 26.7 kcdmol. If the unsaturation point of benzvalene is removed, the resulting structure, tricyclo[3. 1.0.02*6]hexane(dihydrobenzvalene,DHB), is much more thermally stable, decomposing at 400 "C, producing exclusively 1,3-~yclohexadiene.~At a thermolysis temperature of 300 "C, only 10% of the DHB was found to decompo~e.~ This molecule was first reported in the literature by Lema1 and Shim4 in 1964 as a photolysis product of A2-cyclopentyldiazomethane in ether. It was later produced in large yield via a purely synthetic route by Christ1 and Briintrup3 by the reduction of benzvalene with diimine. However, to date, the published information regarding the chemistry and properties of DHB has been rather limited. Adam et at.5 reported the 185nm photolysis of DHB in which four products were detected including methylenecyclopentane,1,3-~yclohexadiene,and both the cis- and truns-1,3,5-hexatriene. The treatment of DHB with aluminum chloride, in dioxane, was shown to produce the more thermally stable bicycl0[3.1.0]hex-2-ene.~~~ The formation of DHB from the reaction of cyclopentylcarbene has been studied theoretically, by noting the energy difference between the two structures, which was reported as being -65.1 kcaYmol at the MP216-31G(d)1 I SCFl3-2 1G level.* Although the NMR spectra3 of DHB have been discussed, the vibrational spectrum and thermodynamic properties are missing, as is the optimized geometry at a correlated level of theory. In particular, we were interested in the amount of strain energy contained in the structure as well as its heat of formation. These values can be determined from a knowledge of the vibrational frequencies and relative energies. Therefore, this @
Abstract published in Advance ACS Abstracts, November 1, 1994.
0022-365419412098-12236$04.5010
paper reports the results of ab initio calculations of the DHB molecule to determine the equilibrium geometry, strain energy, and heat of formation, along with the experimental infrared and Raman spectra and a vibrational analysis.
Experimental Section The DHB sample was obtained from Professor Bob Moriarty at the University of Illinois at Chicago with NMR and GC analysis revealing benzene as the only i m p ~ r i t y .The ~ sample was used without further purification for both the IR and Raman experiments. The infrared spectrum of DHB was obtained in the both the gas phase and isolated in a solid argon matrix at 10 K, while the Raman spectrum was recorded of the neat liquid. The IR spectrometer and accompanying vacuum chamber has been described in detail elsewhere.IO For the gas-phase IR spectrum, the sample was attached directly to the vacuum chamber and allowed to evaporate such that the bands in the spectrum were of reasonable intensity. For the matrix spectrum, a gas-phase aliquot of DHB was diluted in argon to a mole ratio of Ar/DHB = 50011. The sample was deposited on the matrix support at a rate of 4 mmol/h for a total of 8 mmol and then the spectrum recorded. Since the sample contained some benzene, both the gas-phase and the matrix spectrum of benzene were obtained in an analogous manner. The benzene spectrum was subtracted from the spectrum of the DHB sample resulting in the spectrum of dihydrobenzvalene. All infrared spectra were recorded by using a Nicolet 740 FTIR spectrometer at 1-cm-' resolution. The Raman spectrum was obtained by placing the liquid sample in a Pyrex tube and collecting the 90" scattered light by using a Bruker RFSlOO FT-Raman spectrometer. The laser power used was 500 mW and the resolution 1 cm-'. As was done in the IR experiments, the Raman spectrum of liquid benzene was collected and subtracted from the spectrum of the mixture. The ab initio calculations were performed by using the Gaussian 9211 suite of programs. Initially the standard 6-31G(d,p) basis was used at the Hartree-Fock level to determine the minima. All SCF calculations were done by using the restricted methodology for closed shells. The equilibrium geometries were obtained by analytic gradient techniques using the Bemy algorithm.12 The stationary points were characterized as a minimum by determination of harmonic vibrational frequencies using analytic second derivatives. l 3 Electron correlation effects were included by using MollerPlesset perturbation theory through second and fourth order,14 0 1994 American Chemical Society
. I Phys. . Chem., Vol. 98, No. 47, 1994
Experimental Study of Tricyclo[3.1 .0.02s6]hexane
12237
0.95 0.90
-
0.80 0.85
0.75-
0.707 0.85-
0.55 0.60
1
0.50
0.457 0.40
-
0.35 -
-
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0.250.20
,1.
-
0.150.10-
4
I
3200
3000
2800
2600
2400
2200
2000 1800 WaVenMkKll (an-1)
1600
1400
1200
J 1000
800
J!
1 600
Figure 1. FTIR difference spectrum of a matrices formed by deposition of ArDHB = 500/1 and Arbenzene = 500/1 samples at 10 K.
including all single, double, triple, and quadruple excitations (MP4SDTQ). Geometries were optimized at the MP2 level by using analytic gradientst5with only the valence electrons active. The basis set used in the MP2 and MP4 calculations was the standard 6-3 11G(d,p).16 Vibrational frequencies were also determined at the MP2 level of theory, with only the valence orbitals active, by calculation of analytic second derivatives. Perturbation theory through fourth order, MP4SDTQ, was used at the MP216-3 1lG(d,p) optimized geometries to calculate relative energies. The strain energies and heats of formation have been evaluated by using appropriate homodesmic reactions.l7 In this way, the structural groups of a strained molecule are compared with those of closely related unstrained analogues. The strain energy is then the heat of reaction. The reaction energy, AE, was converted to an enthalpy change at 0 K by including the zero-point energies. The vibrational frequencies used were those obtained at the MP216-311G(d,p) level scaled by 0.93. Although we have the experimental frequencies for DHB, the calculated ones were used for consistency with the other moieties in the homodesmic reaction. The enthalpy of formation of DHB was determined as well from the above reaction by using the calculated reaction enthalpy and the experimental enthalpies of formation. The reaction enthalpy at 0 K was converted to enthalpy at 298 K by use of the method given by Hehre et aL1*
Results and Discussion I. Vibrational Spectrum. The point group of the DHB molecule is Czv and a vibrational analysis gives the representa-
+
+
+
tion r = 12A1 7A2 8B1 9B2 for a total of 36 fundamental frequencies. All are Raman active, while those belonging to irreps AI, B1, and B2 are infrared active. Both the matrix infrared and liquid Raman spectra of DHB were recorded and are shown in Figures 1 and 2, while spectral peak positions are given in Table 1. Figure 3 gives a pictorial view of the molecule and atom numbering used in the text. The matrix spectrum of DHB exhibits very sharp vibrational bands resulting from the cryogenic conditions and is very useful in assigning the fundamental frequencies. The vacuum chamber and optics are designed to maximize the IR signal coming from the matrix, therefore the sensitivity of the gas-phase spectrum is less than that of the matrix spectrum. Most bands exhibit a small gas-to-matrix shift such that the matrix peak positions are within an average of 3 cm-' of the gas-phase values. The experimental spectra were compared to that calculated at the MP216-31 lG(d,p) level and assignments made on this basis. Several of the normal modes contain displacements which are essentially isolated on various parts of the molecule, especially so in the CH stretching region. From symmetry, there are only three symmetry nonequivalent carbon and hydrogen atoms in DHB, and fundamental frequencies are present which are essentially isolated on symmetry equivalent atoms. In the C-H stretching region the highest frequency band is due to the symmetric C1, C2 CH stretch. This band was not observed in the IR, but in the Raman an intense band at 3132 cm-' is observed and assigned to this fundamental. The absence of the IR band follows the calculated intensity which is quite low, while the calculated Raman activity is relatively high. The C1, C2 antisymmetric CH stretch is observed weakly in the matrix
Davis and Tan
12238 J. Phys. Chem., Vol. 98, No. 47, 1994 0.38 0.36
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0.32 -
0.34
0.30
-
0.26 -
0.28
0.24
'
-
!
0.22-
I
0.20
-
I
I
0.18-
Jll
3200
! 3000
2800
2600
2400
22MI
2000
1800 1600 Wavenumben (an.1)
1400
1200
lo00
800
800
400
Figure 2. Raman difference spectrum of DHB and benzene in the liquid phase.
Figure 3. Optimized geometry of DHB calculated at the MP216-311G(d,p)lIMF'216-31 lG(d,p) level.
IR spectrum at 31 15 cm-I and as a shoulder at 31 17 cm-l on the red side of the intense 3132-cm-I band in the Raman spectrum. The C3, C4 CH symmetric stretch is observed at 3047 cm-I with medium intensity in the IR and with a strong intensity band at 3046 cm-I in the Raman. The analogous antisymmetric stretch is weakly present at 3039 cm-' in the IR but is not resolved in the liquid Raman spectrum. The C5, C6 CH2 stretches are spanned by four normal modes, one repre-
sented by each of the four irreps of the C2" point group. The two symmetric CH2 stretches are in-phase and out-of-phase with respect to each other and belong to the al and b2 irreps, respectively, both being IR and Raman active. The two antisymmetric stretches are bl (in-phase) and a2 (out-of-phase) with the a2 vibration being inactive in the IR. The next four observed absorptions belong to these normal modes with the bl band present at 2962 cm-I, being the most prominent in this region of the IR spectrum, while the Raman observed mode is also strongly present but is shifted 1 1 cm-l to 2951 cm-I in the liquid phase. The a2 out-of-phase symmetric stretch is observed at 2938 cm-I in the Raman spectrum as a shoulder on the intense 2951 cm-I band. The a1 in-phase symmetric CH2 stretch is observed at 2923 cm-I in the IR and 2912 cm-I in the Raman, of moderately strong intensity, while the analogous b2 out-of-phase symmetric vibration is observed as a very strong band located at 2885 cm-I in the IR and as a strong band at 2872 cm-I in the Raman. Normal modes in the bending and C-C stretching regions are not as clearly localized as in the C-H stretches. The only other localized modes occur in the C5, C6 CH2 bending modes for which the in-phase symmetric CH2 scissor is observed at 1491 cm-' in the IR and 1468 cm-I in the Raman, while the out-of-phase symmetric scissor is represented by weak bands at 1217 cm-' in the IR and 1216 cm-' in the Raman spectrum. A C-C stretching mode in the form of a ring breathing motion occurs in the IR at 1398 cm-I and a strong band at 1393 cm-l in the liquid Raman spectrum. The remaining fundamentals are combinations of bending and stretching modes and are delocalized over much of the molecule. The seven IR inactive
Experimental Study of Tricyclo[3.1 .0.02~6]hexane
J. Phys. Chem., Vol. 98, No. 47, 1994 12239
TABLE 1: Calculated and Observed Vibrational Frequencies, Intensities, and Assignments for DHB' frequency Raman frequency calcdb IR intensity activity IR (gas) IR (matrix) Raman (soln) hep 3122 3109 303 1 303 1 2976 2986 2917 2908 1491 1467 1417 1307 1293 1247 1226 1226 1189 1154 1105 1103 1060 1017 994 953 930 910 880 854 849 795 760 738 717 521 445 228
0.007 0.259 3.46 27.2 46.6 0 53.3 33.2 1.14 0.424 7.41 2.55 3 1.52 0.102
0 4.39 0.706
0 12.4 0 0.399 0.404 0.183 1.34 0.265 0 5.6 0.0434 0 70.3 0.183 0.0662 11.2 2.16 0
140.7 85.81 179.7 32.19 96.81 64.87 165.2 47.19 7.3 13.85 10.33 0.953 0.472 4.213 3.059 10.46 0.996 24 0.41 1 19.21 0.887 8.172 10.4 0.547 6.41 1 16.3 15.69 0.849 0.006 2.673 3.507 10.28 2.462 2.711 0.069 0.056
Frequency in cm-', IR intensity in "01, b Scaling factors given in text.
n.0. 3107 305 1 3044 2962
na 2923 2885 1491 1457 1398 1307 1277 1248 1217 na 1181 1159 na 1096 na n.0. 962
n.0. 914 n.0. na 849 n.0. na 756 749 677 570 452
na
n.0. 3115 3047 3039 296 1 na 2918 2819 1484 1451 1398 1302 1277 1247 1216 na 1179 1160 na 1094 na 989 964 n.0. 913 887 na 846 n.0. na 756 744 675 573 456 na
3132 3117 sh 3046 nr 295 1 2938 2912 2872 1468 1449 1393 1301 n.0. 1243 1216 1206 sh
nr 1155 1118 1095
n.0. n.0. 969 944 912 886 869 n.0. n.0. 777 754 sh 746 65 1 564
n.0. 260
assignment
C1, C2 sym CH str C1, CZasym CH str C3, C4 sym C-H str C3, C4 asym C-H str C5, c.5in-phase asym C-H str C5, Cg out-of-phase asym C-H str CS,c6 in-phase sym C-H str C5, c6 out-of-phase sym C-H str CI, CZin-phase CH2 scis CI, CZout-of-phase CHz scis
ring breath ring def ring def C5, c6 out-of-phase CHI wag CHz wag, CH bend CS,Cg CH2 twist CH bend ring breath CH bend CHz twist, CH bend CHZrock, CH bend CH bend ring breath, CH2 rock, CH bend CH rock, CH bend ring pucker CH bend CH rock, ring def CHz twist ring def, CHz rock, CH bend ring def, CH2 def, CH bend CH bend CH bend ring def
ring pucker ring def, asym CHZdef, CH bend ring def, CH2 twist
Raman activity in A4/amu. n.0. = not observed; nr = not resolved; na = not active; sh = shoulder.
modes are only weakly observed in the Raman spectrum and the one calculated to be 1038 cm-' is not observed. The calculated values for the vibrational frequencies closely match the experimental vibrational frequencies after scaling to account for anharmonicity and calculation defenciencies. A very simple scaling method was used in which the C-H stretches, C-C stretches, C-C-H bends, and C-C-C bending modes were each treated separately. A scaling factor was determined for each mode in its particular normal mode set and then an average calculated. The average for all the C-C-H and C-C-C bending modes was the same at 0.9769 while that for the C-H stretches was calculated to be 0.9432. 11. Ab Initio Calculations. The equilibrium geometry for DHB has been determined at the MP216-311G(d,p)lIMP21631 lG(d,p) level. The structure is shown pictorially in Figure 3, while the geometric parameters are given in Table 2. The molecule is found to posess C2, symmetry with the atoms C3, C4, C5, and C6 occupying a plane and C1 and C2 being above and below the plane, respectively. There are four distinct C-C bond distances and three distinct C-H bond lengths, the others being related due to symmetry. The molecule has considerable strain energy, as witnessed by the deviation of bond angles from 109.5'. The DHB molecule is compared through a homodesmotic reaction in which the CH2 groups are likened to that in propane, while the CH groups are likened to that of isobutane. Therefore it is also instructive to compare the geometric parameters in DHB to those of their unstrained analogues. Compared to the straight-chainedhydrocarbon propane, the C5C6 bond length in DHB is greater by 0.0323 A with a value at
TABLE 2: Optimized Geometrical Parameters for DHB Calculated at the MPU6-311G(d,p) Levela geometric param value R(C1-C2) R(C1-C3) R(C3-C5) R(C5-C6) R(C1-H1) R(C3-H3) R(C5-H5) L(C 1-c2-c3) L(C 1-c3-c2) L(Cl-C3-C5) L(C3-C 1-C4) L(C3-C5-C6) L(H1-C 1-C2) L(H1-C 1-C3) L(H3-C3 -C 1) L(H3-C3-C5) L(H5-C5-C6) L(H5 -C5 -C3) L(H5 -C5 -H6) L(C3-C5-C6-C4) L(C1-C2-C3/C1-C2-C4) L(C3-C5-C6-C4/Cl -C3-C4)
1.4941 1.5064 1.5272 1.5609 1.0782 1.0869 1.0948 60.27 59.46 109.83 91.64 101.32 130.85 134.01 119.7 122.22 111.03 112.36 108.63 0 111.82 134.63
Distance in angstroms; angle in degrees. 1.5609 A, signifying a slightly weaker bond. The C3-C5 bond has average character with a length only 0.0014 8, shorter than the C-C single bond in propane. The remaining two bond lengths, however, are substantially shorter than the C-C bond in isobutane. The bond length for C3-C5 is 0.023 shorter,
12240 J. Phys. Chem., Vol. 98, No. 47, 1994 TABLE 3: Homodesmic Reactions Used To Determine Strain Energies and Heats of Formation
+ + + +
- -
+
DHB 8CzH6 2CH3CHzCH3 4(CH3)3CH BV Cz& 7C2H6 2CH3CHCH2 4(CH3)3CH BCB f 5CzH6 2(CH3)3CH 2CH3CHzCH3 CPP 3Cz& -... 3CH3CHzCH3
+
+
while Cl-C2 is 0.0353 A shorter, resulting from the bond angle strain among these carbon atoms. The geometry of the four carbons C1, C2, C3, and C4 comprise a bicyclo[l.O.O]butane (BCB) derivative, which can also be thought of as two cyclopropane rings fused with a common side. Comparing the two bond lengths C1-C3 and C1 -C2 with that in cyclopropane (1SO92 A) shows that those in DHB are shorter by 0.0028 and 0.0151 A, respectively. The Cl-C2 bond length is 0.0178 A shorter than the BCB counterpart while the Cl-C3 length is 0.0074 A longer than the BCB counterpart. The angle between the two planes made by the two three-membered rings in DHB is 10.52' less than in BCB, resulting from the presence of the ethyl moiety to carbons C3 and C4. Another difference in the bond angles is that the angle situated in the bridgehead carbons of DHB is slightly greater than 60', while that at the terminal carbons is slightly less than 60'; this trend is reversed in BCB. The C-H bond lengths also exhibit deviations from their unstrained counterparts. The C3-H3 bond is 0.0115 8, shorter than the C-H bond of isobutane while the C1-H1 bond is 0.0202 8, shorter. Even compared to the C-H bond length in cyclopropane, the C3-H3 and C1-H1 bond lengths are slightly less. The C1-H1 bond is the shortest due to the greater distortion in the bond angles on C1 and C2, giving the C-H bond more s-type character. Comparison to BCB shows that the 1.0782 A C1-H1 bond length in DHB is almost identical to that of the BCB counterpart at 1.007 88 A. The corresponding C3-H3 bond length in DHB is very close to that of its BCB counterpart as well, with only a 0.0028-A difference, while the greatest differences in H-C-C bond angles occurs in the H3-C3-C1 angle, which is 119.70' in DHB and 117.72' in BCB . Each carbon atom in DHB is tetravalent and the normal bond angles should be close to that in a tetrahedron. Significant discrepancies are present as a result of bond strain in the ring structure. The bond angle at C3 is in the normal range, while angles located at the other carbon atoms (LC-C-C) are strained to various degrees with an angle less than normal. At C5, the angle is approximately 8' less than tetrahedral, while those located at C1 are 91.64' for LC3-Cl-C4 and 60.27' for LC3-Cl-C2. The smallest angle is LCl-C3-C2, which is 59.46'. As a result of the strain in the carbon bonds, those containing hydrogens are greater than tetrahedral, with the only exception being the H5-C5-H6 type bond angles. The H5C5-C3 angle is only slightly increased to 112.36', while that for H3-C3-C5 is 122.22'. The largest increase is present in the bonds containing the H1 and H2 atoms, with the H1-C1C2 angle being 130.85' and LHl-Cl-C3 equal to 134.01'. The strain energies of DHB and closely related rings were calculated by using the homodesmic reactions given in Table 3 and the values are given in Table 4. Where experimental values are available, they compare very favorably to those calculated. As a general trend, the zero-point energy corrections for the homodesmic reactions are fairly large; for example, the strain energy for DHB is 7.9 kcal/mol higher without the ZPE correction. Also, the inclusion of electron correlation raises the calculated strain energy over the SCF results in each case and is most marked for the DHB molecule, which is 9.3 kcal/mol higher at the MP2/6-31 lG(d,p) level. Calculating the strain energy by using fourth-order Moller-Plesset theory (MP4SDTQ)
Davis and Tan
TABLE 4: Strain Energies and Heats of Formation (kcaVmo1) AEstrain
molecule
SCF"
MP2b
mstrain(298K) MP4'
~
DHB BV BCB CPP
69.9 83.3 67.9 28.1
MP2b ~
79.2 88.6 73.2 30.7
72.6 82.9 68.0 28.3
AHr(298K)
exu
MP2b
exp
57.3 93.0 55.5 14.2
51.9' 12.7'
~
71.3
80.3 67.1 27.9
63.9"' 26.5'
'SCF(6-3lG(d,p)j/SCF/6-3lG(d,p). MP4SDTQ16-311 G(d,p)1 /Mp2/6311G(d,p). cMP2(6-311G(d,p)(IMP2(6-311G(d,p). dReference20. e Reference 2 1. at the MP2 geometries increased the values only slightly. In order for the calculated values to match closely with experiment, electron correlation much be included at least at the MP2 level, along with correction for ZPE. A fortuitous cancellation of errors occurs for strain energies calculated at the SCF level without ZPE correction, which gives values close to that calculated at the MP2 level including ZPE corrections. However, the closest match to experimental values comes at the MP2 level including ZPE correction. There is no experimental value reported for either the strain energy or heat of formation of DHB, therefore we compared closely related structures for which experimental values do exist. The strain energy of BCB has been calculated by Nagase and Kudor,19 at the SCF level not including ZPE correction, to be 68.9 kcal/mol. Our calculation at the MP2 level including ZPE correction supplied a value of 67.1 kcal/mol, which compares well with the experimental value20 of 63.9 kcal/mol. Our value for the strain energy of CPP is 27.9 kcavmol, which is very close to the experimental value21 of 26.5 kcaYmol and that calculated previously.22 A comparison of the strain energy of DHB on a structural basis with BCB and CPP shows interesting trends. The DHB structure contains a substituted BCB moiety and contains almost all of the strained bond angles. Therefore, the strain energies should be similar for these two structures. From the values in Table 4, the strain energy in BCB is only 4.2 kcaYmol less than that in DHB. The additional strain energy could be due to the two angles represented by C3-C5-C6, which are slightly less than tetrahedral at 101.3'. Comparison with CPP shows that the strain energy of DHB and BCB is significantly more than that of two CPP moieties due to the two three-membered rings sharing a common side in DHB. In a recent study of the valence isomers of benzene, Schulman and Disch' noted that the strain energy of Dewar benzene is very close to twice that of cyclobutene, suggesting that the strain energy due to ring fusion is small. However, the strain energy calculated for bicyclobutane is 2.4 times that of cyclopropane, suggesting that ring fusion in this case does increase the strain energy substantially. The strain energy calculated for BV is only slightly higher than that for DHB (5.2 kcal/mol) due to the additional strain in the sp2 bonds on C1 and C2. The heats of formation have been determined by use of the calculated enthalpy of the homodesmic reactions and the experimental heats of formation for the other species, with the values given in Table 4. The AHf(298 K) of DHB is found to be 57.3 kcal/mol calculated at the MP2/6-31 lG(d,p) level. The heat of formation of the closely related molecule, BCB, is almost identical, with a value of 55.5 kcal/mol.
Summary and Conclusions The infrared and Raman spectra of tricyclo[3.1 .0.02,6]hexane have been obtained and the equilibrium geometry and harmonic vibrational frequencies calculated at the MP216-3 1lG(d,p) level. Each of the fundamental frequencies has been assigned to a
Experimental Study of Tricyclo[3.1.0.02~6]hexane normal mode in the molecule by comparing the experimental and theoretical spectra. The C-H stretches are each isolated on symmetrically equivalent parts of the molecule, while the C-C stretches and bending modes are much more delocalized. Using an appropriate homodesmic reaction, the bond strain energy has been determine to be 71.3 kcal/mol. This value compares very closely to that of the related molecule bicyclo[l.O.O]butane for which the strain energy is calculated to be 67.1 kcUmo1. The heat of formation of DHB is proposed to be 57.3 kcaymol, again very close to the calculated value of 55.5 kcal/mol for BCB. The strain energy and heat of formation for DHB are somewhat less than those calculated for BV, corresponding to the much greater thermal stability of DHB, which has been reported in previous studies. The strain energy of DHB is 2.4 times that for CPP, showing that the fusion of the two three-membered rings adds substantially to the total. The C-C and C-H bond lengths in the strained part of the molecule are markedly shorter than normal, owing to the bent bonds present in the strained end of the molecule.
Acknowledgment. The financial support of the Office of Naval Research under Grant N00014-93-1-0019 and computer time from the Mississippi Center for Supercomputer Research are gratefully acknowledged. References and Notes (1) Schulman, J. M.; Disch, R. L. J. Am. Chem. SOC. 1985,107,5059. (2) Turro, N. J.; Renner, C. A.; Katz, T. J. Tetrahedron Lett. 1976, 46, 4133.
J. Phys. Chem., Vol. 98, No. 47, 1994 12241 (3) Christl, M.; Briintrup, G. Chem. Ber. 1974, 107, 3908. (4) Lemal, D. M.; Shim, K. S. Tetrahedron Lett. 1964.44, 3231. ( 5 ) Adam, W.; Alt, C.; Braun, M.; Denninger, U.;Zang, G. J. Am. Chem. SOC.1991, 113, 4563. (6) Christl, M.; Heinemann, U.; Kristof, W. J. Am. Chem. SOC. 1975, 97, 2299. (7) Ellis, R. J.; Frey, H. M. J. Chem. SOC. A 1966, 553. (8) Evanseck, J. D.; Mareda, J.; Houk, K. N. J. Am. Chem. SOC. 1990, 112, 73. (9) Professor Bob Moriorty, personal communication. (10) Liu, L.; Davis, S. R. J. Phys. Chem. 1992, 96, 9712. (11) Frisch, M. I.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A.; Head-Gordon, M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.;Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92/DFT, Revision F.3. Gaussian, Inc.; Pittsburgh, PA, 1993. (12) Schlegel, H. B. J. Comp. Chem. 1982, 3, 214. (13) Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Int. J. Quantum. Chem. 3 1979, S13, 325. (14) Krishnan, R.; Pople, J. A. Int. J. Quantum Chem. 1978, 14, 91. (15) Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Int. J. Quantum Chem. 1979, S13, 325. (16) Franc], M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S . ; Defrees, D. J.; Pople, J. A. J. Chem. Phys. 1982, 77, 3654. (17) George, P.; Trachtman, M.; Brett, A. M.; Bock, C. W. J. Chem. SOC., Perkin Trans. II 1977, 1036. (18) Hehre, W. J.; Ditchfield, R.; Radom, L.; Pople, J. A. J. Am. Chem. SOC. 1970, 92, 4796. (19) Nagase, S.; Kudo, T. J. Chem. SOC., Chem. Commun. 1988, 54. (20) Wiberg, K. B. Angew. Chem., Int. Ed. Engl. 1986, 25, 312. (21) Cox, R. D.; Pilcher, G. Thermochemistry of Organic and Organometallic Compounds; Academic Press: New York; p 170. (22) Boatz, J. A.; Gordon, M. S . ; Hilderbrandt, R. L. J. Am. Chem. SOC. 1988, 110, 352.
