3504
J. Phys. Chem. 1996, 100, 3504-3506
Heat of Formation of Dodecahedrane Raymond L. Disch and Jerome M. Schulman* Department of Chemistry, The City UniVersity of New York, Queens College, Flushing, New York 11367 ReceiVed: September 6, 1995; In Final Form: NoVember 13, 1995X
The heat of formation of dodecahedrane is estimated from the difference of ab initio RMP2(FC)/6-31G*// 6-31G* energies of dodecahedrane and pagodane, as well as from two homodesmic reactions. The results, 18.9, 17.5, and 16.7 kcal/mol, are in reasonable agreement with the value estimated by Beckhaus et al., 22.4 ( 1 kcal/mol. A discussion is given of the geometry and strain energy of two dicarboxymethyl esters of pagodane and their utility in estimating the ∆Hf° of dodecahedrane.
The uniquely symmetrical hydrocarbon dodecahedrane 1 remains a source of fascination to chemists. The two landmark syntheses of it, by Paquette et al.1 and by Prinzbach et al.,2 were of great interest. Owing to its unusual structure, dodecahedrane has also provided theorists with a severe test case for the calculation of heats of formation, as evidenced by the disparate values obtained.3,4
A recent thermochemical study by Beckhaus et al.5 obtained experimental heats of formation of the isomer pagodane 2 and of the dicarboxymethyl esters of pagodane and dodecahedrane, 2a and 1a. While these authors were unable to obtain an experimental ∆Hf° of 1, their results provide indirect aids to its computation, which are utilized in this study. Method Three new approaches to a theoretical estimate of ∆Hf° of 1 are presented here. The first is the energy change of the reaction
1f2
(1)
computed at the RMP2(FC)/6-31G* frozen-core level for molecular geometries optimized at the HF/6-31G* level.6 This energy difference, with the experimental ∆Hf° of 2, leads to that of 1. It is expected that inclusion of electron correlation will largely overcome inadequacies in the differencing of the HF energies of 1 and 2, whose interconversion is not homodesmic owing to the different substructures: (CH)20 vs (CH)12(CH2)4C4. The second approach uses ∆H of the homodesmic reaction
5 adamantane f 1 + 5 cyclohexane
(2)
also computed at the RMP2(FC)/6-31G*//6-31G* level, with corrections for zero-point energies and differences in H°298 X
Abstract published in AdVance ACS Abstracts, January 15, 1996.
0022-3654/96/20100-3504$12.00/0
H°0. This result and the known ∆Hf° of adamantane and cyclohexane lead to ∆Hf° of 1. The third approach utilizes a homodesmic reaction involving cubane, 3, and the diester 1,4-bis(methoxycarbonyl)cubane, 3a:
1a + 3 f 1 + 3a
(3)
The ∆H of this reaction, computed at the HF/6-31G* level, together with the experimental ∆Hf° of 3, 3a, and 1a, give ∆Hf° of dodecahedrane.
The RMP2 calculations were performed using vectorized programs written by us for IBM 3090 Models. The SCF calculations on the diesters were performed using GAUSSIAN 927 on SGI indigo R4000 workstations. Additional modeling was done with PCMODEL,8 HyperChem (Release 2), and Yuh and Allinger’s MM2(82). Heats of Formation Table 1 contains the HF/6-31G* energies of 1, 2, 3, and the diesters 1a, 2a, and 3a at the optimized geometries. RMP2/631G*//6-31G* values are given for 1 and 2. The ab initio HF and RMP2 energies of 2 exceed those of 1 by 43.6 and 29.0 kcal/mol, respectively. Combining these values with the experimental heat of formation of pagodane, 47.9 kcal/mol,5 leads to ∆Hf° values for dodecahedrane of 4.3 and 18.9 kcal/ mol. The energy difference for the homodesmic reaction (2) at the RMP2(FC)/6-31G* level is 41.2 kcal/mol. The energies of adamantane and cyclohexane at this level are -389.333 659 and -234.991 62 au,4b respectively, and their experimental ∆Hf° are -32.53e and -29.5 kcal/mol.10 The correction for differential zero-point energies and thermal enthalpies amounts to -8.7 kcal/mol,3e so ∆H of reaction 2 is predicted to be 32.5 kcal/mol. This leads to ∆Hf° ) 17.5 kcal/mol for 1. The corresponding value at the SCF level is 4.6 kcal/mol,4b indicating again the importance of correlation energies in this problem. © 1996 American Chemical Society
Heat of Formation of Dodecahedrane
J. Phys. Chem., Vol. 100, No. 9, 1996 3505
TABLE 1: Calculated Total and Relative Energiesa and Experimental ∆Hf°
a
molecule
HF/6-31G*
RMP2/6-31G*//6-31G*
dodecahedrane, 1, Ih pagodane, 2, D2h dodecahedrane diester, 1a, Cs pagodane diester, 2a, C2 pagodane diester, 2b, C2 cubane, 3, Oh cubane diester, 3a, C2h
-769.047 34 (0.0) -768.977 84 (43.6) -1222.335 14 (0.0) -1222.257 07 (49.0) -1222.263 99 (44.6) -307.393 91 -760.688 23
-771.644 44 (0.0) -771.598 27 (29.0)
∆Hf°b 47.9 -151.8 (0.0) -107.3 (44.5)
Relative energies in kcal/mol are in parentheses. b Reference 5.
TABLE 2: Framework Geometrical Parameters of Pagodane 2 and the Diester 2a parametera C1-C2 C1-C5 C1-C11 C3-C4 C3-C7 C6-C7 C16-C17 C4‚‚‚C19 H4e‚‚‚H19e
pagodane diesterb
pagodane c
1.556 (1.573) 1.532 (1.536) 1.541 (1.549) 1.539 (1.544) 1.553 (1.559) 1.583 (1.589) 1.583 (1.589) 3.528 (3.530) 2.352e
1.554 (1.589)d 1.534-1.536 (1.536) 1.547 (1.547) 1.538-1.544 (1.558) 1.549-1.551 (1.544) 1.588 (1.625) 1.585 (1.625) 3.604 (3.611)
a Bond lengths in angstroms, calculated at the HF/6-31G* level. b For pagodane diester we give a range of bond lengths; for example, the table entry for C1C5 also encompasses values for C1C20, C2C3, C2C18, C8C12, C12C13, C10C11, and C11C15. c Experimental values in parentheses are from ref 2e. d Experimental values in parentheses are from ref 2b. e These are the proximal methylene hydrogens on carbons 4 and 19.
The HF/6-31G* energies of cubane, 3, and diester 3a are given in Table 1. Their difference, 453.294 32 au, is larger than that of 1 and 1a, 453.287 80 au, by 4.09 kcal/mol. The ∆H of reaction 3, -4.09, combined with the ∆Hf° of 1a (-151.8), cubane (148.7),11 and the diester 3a (-23.9),12 gives ∆Hf° ) 16.7 kcal/mol for dodecahedrane. The three values of ∆Hf° of dodecahedrane, 18.9, 17.5, and 16.7 kcal/mol, are somewhat smaller than the value 22.4 ( 1 kcal/mol obtained by Beckhaus et al. using empirical group increments to convert the measured ∆Hf° of 1a to that of 1. Geometries The HF/6-31G* CC and CH bond lengths of dodecahedrane are 1.548 and 1.084 Å, respectively, the former being slightly larger than the range of bond lengths, 1.535-1.541 Å, reported for the X-ray structure.1d The geometric parameters of pagodane at the HF/6-31G* level were previously reported13 and are given in Table 2 with values for the pagodane diester. The geometries chosen for 1a and 2a are of Cs and C2 symmetry, respectively; the latter symmetry is found in the X-ray structure of the pagodane diester.2b The HF/6-31G* framework CC bond lengths of dodecahedrane diester range from 1.546 to 1.560 Å, the larger value corresponding to the six bonds to the ester-containing carbons. Thus, ester substitution produces only a small geometric perturbation of the dodecahedrane framework. Similarly, the framework geometry of pagodane diester 2a (Figure 1) is close to that of pagodane (Table 2). The largest difference is in the nonbonded distance C4‚‚‚C19, which increases from 3.528 Å in 2 to 3.604 Å in 2a. There is significant disagreement with the X-ray values2b of certain bond lengths: C1C2, 1.554 vs 1.589 Å; C6C7 and C16C17, 1.588 and 1.585 Å vs 1.625 Å. The reason for these discrepancies is not clear, especially since the nonbonded distances, C4‚‚‚C19, are in good agreement with the X-ray values. Discussion The internal agreement among our three theoretical estimates of the ∆Hf° of dodecahedrane and their similarity to the estimate
Figure 1. Perspective drawings of the pagodane diesters 2a (top) and 2b (bottom). The oxygen atoms are not explicitly labeled.
of Beckhaus et al.5 are encouraging. This is especially so given that the calculation of ∆Hf° by ab initio methods requires both an accurate total energy and an accurate method for conversion of this large number into the much smaller heat of formation. It should be noted that the second-order correlation energies of 1 and 2 exceed 1600 kcal/mol, but their difference, 14.6, is less than 1% of this. Despite the success of the present calculations, there remains a curious unresolved point regarding the use of the ester exchange reaction
1a + 2 f 1 + 2a
(4)
to estimate the ∆Hf° of 1. Consider the identity
∆H°f,1 ) [∆H°f,1 - ∆H°f,1a + ∆H°f,2a - ∆H°f,2] + ∆H°f,1a - ∆H°f,2a + ∆H°f,2 (5) where the quantity in square brackets, ∆H of the exchange reaction (4), is evaluated by theoretical methods and the last three terms by experiment. Substitution of the ∆Hf° of 1a, 2, and 2a, -151.8, 107.3, and 47.9 kcal/mol,5 leads to
∆H°f,1 ) [∆H°f,1 - ∆H°f,1a + ∆H°f,2a - ∆H°f,2] + 3.4 kcal/mol Beckhaus et al. have argued, on the basis of MM2 strain energies, that due to “cavity strain,” 2a had 15-16 kcal/mol of strain energy in excess of that of pagodane, whereas the strain energies of dodecahedrane and its diester are similar.5 Since the quantity in brackets is a measure of the difference between ∆H of the reaction 1 f 2 and that of the reaction 1a f 2a, this implies that it is approximately 15 kcal/mol, giving ∆H°f,1 ) 18-19 kcal/mol. However, as seen from Table 3 and our strain
3506 J. Phys. Chem., Vol. 100, No. 9, 1996
Disch and Schulman
TABLE 3: Calculated Valuesa of the Terms in Brackets in Eq 5 method
[∆H°f,1 - ∆H°f,1a + ∆H°f,2a - ∆H°f,2]
MM2 MMX AM1c HF/6-31G*
1.5b -0.6 -1.2 5.4
a In kcal/mol. b Calculated with MM2(82). c The individual AM1 heats of formation, ref 3f, are very different from experiment, but the errors largely cancel.
energies,14 values of this quantity obtained by MMX, MM2, AM1, and ab initio calculation are fairly small. An alternate assessment of the strain in the pagodane diester was obtained by considering the isomeric C2 form of the diester, 2b, in which the methoxycarbonyl groups are outside the cavity (Figure 1). This diexo diester should have a cavity strain similar to that of pagodane itself. The HF/6-31G* energy of 2a, Table 1, is less than 5 kcal/mol higher than that of 2b, implying that the strain energy of 2a exceeds that of 2 by a similar amount. A small contribution to the quantity in brackets arises from the fact that the methoxycarbonyl groups replace methylene hydrogens in 2 vs methine hydrogens in 1. A reaction that models this effect involves the esters EtCH(CH3)CO2Et, 4, and (CH3)3CCO2Et, 5:
4 + isobutane f 5 + butane
(6)
From the measured ∆Hf°, -123.35 and -125.62,15 and those of butane and isobutane, -30.02 and -32.07,10 the exchange reaction (6) is nearly thermally neutral (-0.2 kcal/mol).16 The largest value of the quantity in brackets in eq 5 (Table 3), obtained at the HF/6-31G* level, is 49.0 - 43.6 ) 5.4 kcal/ mol. This leads to ∆H°f,1 ) 8.8 kcal/mol. We conclude that present theoretical methods based upon reaction 4 give a smaller value of ∆H°f,1. It is possible that this result would change substantially were the quantity in brackets evaluated with inclusion of second-order correlation energies. It is worth noting that ∆H°f,1 ) 12.8 kcal/mol4c using ab initio group equivalents, a method which applied to pagodane gives ∆Hf° ) 47.1 kcal/mol, in good agreement with the experimental value, 47.88 kcal/mol.10 A conservative statement is that the ∆Hf° of dodecahedrane is 13-19 kcal/mol. Finally, the problem of obtaining an accurate heat of formation of 1 using molecular mechanics lies in the torsional part of the force field, since torsion is the predominant form of strain in dodecahedrane. It is interesting that a molecular mechanics method recently developed by Dillen,3h who has revised the torsional force-field contribution, produces ∆Hf° ) 8.5 kcal/mol, an increase of 17 kcal/mol over the value obtained in his earlier treatment, -8.4.3g Note Added in Proof. The authors of ref 5 have recently revised their estimate of the dodecahedrane heat of formation to 18.2 ( 1 kcal/mol (J. Am. Chem. Soc. 1995, 117, 8885). Acknowledgment. This work was supported in part by grants 669274, 664059, and 666313 of the PSC-CUNY Research
Award Program of the City University of New York. A grant of computing time from the City University Committee on Research Computing is gratefully acknowledged. We are pleased to acknowledge the assistance of Mr. Prashant Joshi of the Queens College Computer Science Department and to acknowledge the generous support of that department. We thank Mr. Albert Rivera and staff of City University Computing and Information Services for a great deal of valuable assistance. References and Notes (1) (a) Ternansky, R. J.; Balogh, D. W.; Paquette, L. A. J. Am. Chem. Soc. 1982, 104, 4503. (b) Ternansky, R. J.; Balogh, D. W.; Paquette, L. A.; Kentgen, G. J. Am. Chem. Soc. 1983, 105, 5446. (c) Paquette, L. A. Chem. ReV. 1989, 89, 1051. (d) Gallucci, J. C.; Doeke, C. W.; Paquette, L. A. J. Am. Chem. Soc. 1986, 108, 1343. (2) (a) Fessner, W.-D.; Prinzbach, H.; Rihs, G. Tetrahedron Lett. 1983, 24, 5857. (b) Fessner, W.-D.; Sedelmeier, G.; Spurr, P. R.; Rihs, G.; Prinzbach, H. J. Am. Chem. Soc. 1987, 109, 4626. (c) Prinzbach, H.; Weber, K. Angew. Chem., Int. Ed. Engl. 1994, 33, 2239. (d) Fessner, W.-D.; Prinzbach, H. In Cage Hydrocarbons; Olah, G. A., Ed.; John Wiley and Sons: New York, 1990. (e) Prakash, G. K. S.; Krishnamurthy, V. V.; Herges, R.; Bau, R.; Yuan, H.; Olah, G. A.; Fessner, W.-D.; Prinzbach, H. J. Am. Chem. Soc. 1988, 110, 7764. (f) Fessner, W.-D.; Murty, B. A. R. C.; Worth, J.; Hunkler, D.; Fritz, H.; Prinzbach, H.; Roth, W. D.; Schleyer, P. v. R.; McEwen, A. B.; Maier, W. F. Angew. Chem., Int. Ed. Engl. 1987, 26, 452. (3) Molecular mechanics and semiempirical estimates of ∆Hf° of dodecahedrane (in kcal/mol) include the following. (a) EAS, -0.22: Engler, E. M.; Andose, J. D.; Schleyer, P. v. R. J. Am. Chem. Soc. 1973, 95, 8005. (b) MM2, 22.2; MM1, 45.3: Clark, T.; Knox, T. Mc O.; McKervey, M. A.; Mackle, H.; Rooney, J. J. J. Am. Chem. Soc. 1979, 101, 2404. (c) MM3, 39.4: ref 5. (d) MINDO/3, 62.3: Schulman, J. M.; Disch, R. L. J. Am. Chem. Soc. 1978, 100, 5677. (e) MNDO, -46.9: Schulman, J. M.; Disch, R. L. J. Am. Chem. Soc. 1984, 106, 1202. (f) AM1, -33.7: this work. (g) EFF ’90, -8.4: Dillen, J. L. M. J. Comput. Chem. 1990, 11, 1125. (h) EFF, 8.5: Dillen, J. L. M. J. Comput. Chem. 1995, 16, 595. (4) Previous ab initio estimates of ∆Hf° of dodecahedrane (in kcal/ mol) include the following. (a) STO-3G, -8.1; 4-31G, -3.5: ref 3d. (b) 6-31G* (homodesmic reaction), 4.6: Schulman, J. M.; Disch, R. L. J. Am. Chem. Soc. 1985, 107, 1904. (c) 6-31G* (group equivalents), 12.8: Disch, R. L.; Schulman, J. M. J. Am. Chem. Soc. 1988, 110, 1202. (5) Beckhaus, H.-D.; Ru¨chardt, C.; Lagerwall, D. R.; Paquette, L. A.; Wahl, F.; Prinzbach, H. J. Am. Chem. Soc. 1994, 116, 11775. (6) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; John Wiley and Sons: New York, 1986. (7) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. GAUSSIAN 92, Revision D.3; Gaussian, Inc.: Pittsburgh, PA, 1992. (8) The PCMODEL/MMX empirical force-field program is distributed by Serena Software, Box 3076, Bloomington, IN 47402-3076. (9) The MP2 value for adamantane in ref 4b was estimated. (10) Cox, J. D.; Pilcher, D. Thermochemistry of Organic and Organometallic Compounds; Academic Press: New York, 1970. (11) Kybett, B. D.; Carroll, S.; Natalis, P.; Bonnell, D. W.; Margrave, J. L.; Franklin, J. L. J. Am. Chem. Soc. 1966, 88, 626. (12) Kirklin, D. R.; Churney, K. L.; Domalsky, E. S. J. Chem. Thermodyn. 1989, 21, 1105. This study furnished an experimental ∆Hf° ) -52.33 for solid 3a and an estimated heat of sublimation of 28.42 kcal/ mol. (13) Schulman, J. M.; Disch, R. L. J. Mol. Struct. (THEOCHEM) 1995, 358, 51. (14) Using MM2(82) we obtain strain energies (kcal/mol) of 113.0 and 115.1 for 2 and 2a and 68.9 and 69.1 for 1 and 1a. (15) Verevkin, S.; Dogan, B.; Beckhaus, H.-D.; Ru¨chardt, C. Angew. Chem., Int. Ed. Engl. 1990, 29, 674. (16) An identical ∆H is obtained from HF/6-31G* calculations on the methylester analogue of reaction 6.
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