17148
J. Phys. Chem. 1996, 100, 17148-17151
Ab Initio Calculations of Enthalpies of Hydrogenation and Isomerization of Cyclic C4 Hydrocarbons Donald W. Rogers,* Frank J. McLafferty, and Andrew V. Podosenin Chemistry Department, The Brooklyn Center, Long Island UniVersity, Brooklyn, New York 11201 ReceiVed: April 17, 1996; In Final Form: July 17, 1996X
We have calculated enthalpies of hydrogenation (∆hydH) and enthalpies of isomerization (∆isomH) at 0 K and 298 K for 20 reactions involving C4 hydrocarbons using the G2 and G2(MP2) ab initio methods. The mean unsigned difference between G2 and G2(MP2) values of ∆hydH298 is 0.13 kcal mol-1, and the largest difference is 0.3 kcal mol-1. The mean unsigned differences between G2 and G2(MP2) calculations and the five experimental results that are known for these reactions are 0.9 and 0.8 kcal mol-1, respectively. Combination of ∆hydH298 or ∆isomH298 with a known enthalpy of formation ∆fH298 in the set leads to the ∆fH298 of any other molecule in the set. We have obtained values of ∆fH298 ) 126.6, 100.5, and 94.0 kcal mol-1 for tetrahedrane, cyclobuta-1,3-diene, and methylenecyclopropene, respectively, and a computed ∆isomH of cyclobutane to methylcyclopropane of only -0.4 kcal mol-1. Our results encourage use of the simpler G2(MP2) procedure for calculating ∆fH298.
Molar enthalpies of hydrogenation at 0 K (∆hydH0) follow from ab initio calculation of the total energy (Eo) for the constituents in the reaction
alkene + H2 ) alkane ∆hydH0 ) ∆Eo ) Eo(product) - Eo(reactant) - Eo(H2)
(1)
A comparable reaction and equation can be written for alkynes, cycloalkenes, polyenes, cyclopolyenes, and some strained alkanes. Molar enthalpies of isomerization at 0 K (∆isomH0) are even more simply obtained because there is no hydrogen to consider. There are about 500 molar enthalpies of hydrogenation, measured at or near 298 K (∆hydH298), in the literature.1 Most ∆hydH298 values are very accurate, some having an experimental uncertainty as small as 0.1 kcal mol-1. If ∆hydH298 is known, an experimental molar enthalpy of formation (∆fH298) of either the product or the reactant leads to ∆fH298 of the other, which may not be known. Knowing ∆hydH298 for different isomers that are hydrogenated to the same product, one can obtain their molar enthalpy of isomerization (∆isomH298). Like isodesmic reactions2 hydrogenations involve similar species as reactant and product, the only change upon reaction being saturation of one or more double bonds. Individual ab initio calculations of Eo for reactant, hydrogen, and product may be in error, but, because of the structural and electronic similarity between reactant and product, errors may largely cancel in the computed ∆Eo.3 Unlike isodesmic reactions, however, hydrogenations involve a change in carbon orbital hybridization which may interfere with error cancellation. Unlike isodesmic reactions, which may have large stoichimometric coefficients, almost all hydrogenation reactions in the literature have a stoichiometric coefficient of 1 for the reactant and product, and 1, 2, or 3 for hydrogen. Isomerizations are even simpler, having 1:1 stoichiometric coefficients. This can be an advantage because, whatever the error may be in a thermochemical measurement, it is multiplied by the stoichiometric coefficient of the components of the reaction. A “worst X
Abstract published in AdVance ACS Abstracts, September 15, 1996.
S0022-3654(96)01122-7 CCC: $12.00
case” illustration is calculation of ∆hydH298 of cubane from the isodesmic reaction
5 cyclobutane + 8 methylpropane + 8 ethane f cubane + 20 propane in which any error in the experimental value ∆hydH298 of propane, for example, enters into the result 20-fold because of its coefficient in the reaction. Thus, the advantage of small stoichiometric coefficients in hydrogenations and isomerizations may counterbalance the disadvantage of change in hybridization, making computed ∆hydH298 of general utility in obtaining ∆fH298 Via computational thermochemistry. The G2 method4 is within thermochemical accuracy in computing ∆fH298 for small molecules such as ethylene and ethane;5 hence, one anticipates reliable results in calculating ∆hydH298. The G2 method has the drawback that the calculations make significant demands in CPU time and system memory; hence, it has only been applied to relatively small molecules. To alleviate this limitation, Curtiss, Raghavachari, and Pople have developed the simpler G2(MP2) modification of the original method.6 In this paper, we investigate G2 and G2(MP2) calculations of molar enthalpies of hydrogenation (∆hydH) and molar enthalpies of isomerization (∆isomH) for 3- and 4-carbon atom cyclic and acyclic hydrocarbons. We have determined the molar enthalpy of formation of tetrahedrane, cyclobuta-1,3-diene, methylenecyclopropene, and bicyclo[1.1]butane by combining computed ∆hydH298 and ∆isomH298 with experimental ∆fH298 values where they exist. Our results for cyclobutadiene and tetrahedrane agree with a recent estimate by Glukhovtsev, Laiter, and Pross7 obtained using G2 calculations and isodesmic and homodesmotic7,8 reactions. Computational Methods G2. G2 ab initio calculations4 have been very successful in calculating Eo for small hydrocarbons. The method has been described in detail.4b Briefly, calculations are carried out at four levels of basis set complexity and three levels of correlation interaction. Not all 12 combinations of basis set and electron correlation are feasible because of computer limitations. © 1996 American Chemical Society
Enthalpies of Cyclic C4 Hydrocarbons
J. Phys. Chem., Vol. 100, No. 43, 1996 17149
Eight calculations are carried out with the intention of reaching the QCISD(T)/6-311+G(3df,2p) level by a series of linear extrapolations on the premise that this is close enough to the true solution of the Schroedinger equation to give thermochemical accuracy. There is good evidence that the procedure comes very close to the QCISD(T)/6-311+G(3df,2p) level of computation6 and that thermochemical accuracy is attained for simple hydrocarbons.5 After the extrapolation to Eo[QCISD(T)/6-311+G(3d,2p)], the zero point energy is added. Zero point energies are calculated from the harmonic frequencies and scaled by the factor 0.8929.4a Following this, a “high-level correction” (HLC) is added to correct for remaining deficiencies in the basis set. This is essentially an empirical term4b which, in neutral molecules, is -2.50 mhartrees, added to Eo for each paired valence electron. Absolute differences between G2 calculated energies of atomization and experiment for 55 selected compounds is 1.2 kcal mol-1.4b G2(MP2). G2(MP2) works on the same principle as G2, except that calculations are not carried out at the MP4 level; hence, the extrapolation described above is simpler but slightly less accurate. G2(MP2) calculations have been shown to produce energies with a mean difference from experimental values of 1.6 kcal mol-1 for a set of 125 test cases. The advantage of the G2(MP2) method is that it produces ∆fH (and other molecular properties) at a significant reduction in computer time and storage relative to the complete G2 procedure; hence, it is an appropriate method to use if one wishes to extend G2 calculations to molecules with 3, 4, or 5 heavy atoms. The total G2(MP2) energy Eo is
Eo ) E[QCISD(T)/6-311G(d,p)] + ∆MP2 + HLC + ZPE (2) where E[QCISD(T)/6-311G(d,p)] is the total energy calculated at the 6-311G(d,p) basis set level and the quadratic configuration interaction level and
∆MP2 ) [MP2/6-311+G(3fd,2p) - MP2/6-311G(d,p)] HLC and ZPE are the high-level correction and zero point energy as they appear in the G2 method. Conversion of ∆hydH0 to ∆hydH298. Conversion of ∆hydH0 resulting from the G2 and G2(MP2) calculations to ∆hydH298 is by multiplication of the temperature interval into the molar ∆Cp for reaction 1
∆Cp ) Cp(alkane) - Cp(alkene) - Cp(H2) followed by calculating ∆∆hydH = ∆Cp∆T. Ethene,9 for example, has
∆∆hydH ) (12.58 - 10.41 - 6.98)(298) ) -1.41 kcal mol-1 between 0 and 298 K, where all heat capacities are experimentally measured. In general, ∆∆hydH is somewhat larger than it is for ethene. In simple hydrogenations, Cp(alkane) is not very different from Cp(alkene) and is larger; hence, the correction from 0 to 298 K has, as its approximate upper limit,
∆∆hydH = Cp(H2)∆T = -2.0 kcal mol-1 where Cp(H2) ) 6.9 cal K-1 mol-1. If isomerization is concomitant with hydrogenation, the difference in Cp may be reversed (Cp(alkane) < Cp(alkene)), but only by a few tenths
SCHEME 1: Calculated G2 ∆hydH0 and ∆hydH298 for Stepwise Hydrogenation of Acetylene4,6
TABLE 1: Stepwise Enthalpies of Hydrogenation of Acetylene G2(0 K) G2(298 K) G2(MP2)(0 K) G2(MP2)(298 K) A B
-40.1 -30.5
-41.9 -32.3
-40.1 -30.3
-42.0 -32.1
expt (298 K) -42.1 ( 0.2 -32.6 ( 0.1
of a calorie per kelvin mole. The similarity between Cp(alkene) and Cp(alkane) means that ∆∆hydH from 0 to 298 K remains about -2.0 kcal mol-1 of hydrogen added for different hydrogenations (see Results) even though the Cp values themselves may vary widely. In G2 and G2(MP2) calculations, the final result is converted to any temperature (default ) 298 K).9 The vibrational contribution to the temperature conversion is calculated at the harmonic approximation. This calculation yields G2(298) and G2(MP2, 298 K) (Tables S1-S3 in the Supporting Information). Considering isomerization reactions only, one does not need the heat capacity correction for hydrogen. Thus, ∆Eo by G2 calculations give ∆isomH0 and ∆isomH298 that are nearly the same. For example, for the reaction CH3CH
CH2
the G2(0 K) isomerization enthalpy10 is -8.7 kcal mol-1 and the G2(298 K) value is -8.3 kcal mol-1. The experimental value11a is ∆Hisom298 ) -8.0 ( 0.2 kcal mol-1. Results In contrast to most isodesmic reactions, isomerizations and hydrogenations can actually be carried out by classical thermochemical experiments so that the results can be compared with theoretical predictions. A simple example is calculation of ∆hydH0 and ∆hydH298 for stepwise hydrogenation of acetylene (Scheme 1)
CHCH f CH2CH2 f CH3CH3 and comparison with the classical thermochemical results.1,11a,b Computed values and a comparison with experimental results are shown in Table 1. Scheme 2 shows hydrogenations and nearest-neighbor isomerizations of cyclic and acyclic C3 hydrocarbons. Computed values and a comparison with experimental results are shown in Table 2. Several thermochemical cycles are evident; for
17150 J. Phys. Chem., Vol. 100, No. 43, 1996
Rogers et al.
SCHEME 2: Enthalpies of Hydrogenation and Isomerization of Cyclic and Acyclic C3 Hydrocarbons by G2 and G2(MP2) ab Initio Calculations
TABLE 3: Enthalpies of Hydrogenation and Isomerization of C4 Hydrocarbons G2(0 K) G2(298 K) G2(MP2)(0 K) G2(MP2)(298 K)
TABLE 2: Enthalpies (kcal mol-1) of Hydrogenation and Isomerization of C3 Hydrocarbons G2(0 K) G2(298 K) G2(MP2)(0 K) G2(MP2)(298 K) A B C D E F G H I J K
-22.9 -0.8 -52.4 -29.5 -61.1 -38.2 -37.4 -8.7 -66.0 -65.2 -27.8
-22.6 -0.8 -54.4 -31.8 -62.7 -40.0 -39.3 -8.3 -69.7 -68.9 -29.6
-23.0 -0.7 -52.3 -29.4 -61.0 -38.0 -37.3 -8.6 -65.7 -65.0 -27.7
-22.7 -0.6 -54.4 -31.7 -62.5 -39.8 -39.2 -8.1 -69.3 -68.7 -29.5
expt (298 K) -20.7 ( 0.7 -1.3 ( 0.3 -53.5 ( 0.6 -32.8 ( 0.3 -61.4 ( 0.6 -40.8 ( 0.3 -39.4 ( 0.3 -8.0 ( 0.2 -70.6 ( 0.3 -69.2 ( 0.2 -29.8 ( 0.2
-26.0 -10.1 -72.6 -46.6 -61.3 -40.3 -30.2 -44.2 -33.3 14.7 -21.0 -14.0 10.9 -45.0 -30.3 -51.4 -52.1 -38.1 -49.0 -0.7
A B C D E F G H I J K L M N O P Q R S T
-26.0 -10.0 -74.7 -48.7 -63.3 -41.8 -31.9 -46.1 -34.8 14.6 -21.5 -14.2 11.2 -46.8 -32.2 -53.7 -54.1 -39.9 -51.1 -0.4
-25.8 -9.9 -72.3 -46.5 -61.0 -40.0 -30.1 -44.2 -33.2 14.5 -21.0 -14.1 11.0 -44.8 -30.3 -51.3 -52.0 -37.9 -48.8 -0.7
-25.8 -9.9 -74.4 -48.6 -63.0 -41.5 -31.8 -46.1 -34.8 14.4 -21.5 -14.3 11.3 -46.6 -32.1 -53.7 -54.0 -39.7 -51.1 -0.4
expt (298 K)
14.4 ( 0.4 10.3 ( 0.5 -45.1 ( 0.2 -30.7 ( 0.4
-0.5 ( 0.2
TABLE 4: G2 Enthalpies (kcal mol-1) of Formation at 298 K of C4 Hydrocarbonsa
SCHEME 3: Enthalpies of Hydrogenation and Isomerization of Cyclic C4 Hydrocarbons by G2 and G2(MP2) ab Initio Calculations
a
compound
reaction
∆fH298
hydrogen methylenecyclopropene 3-methylcyclopropene methylenecyclopropane 1-methylcyclopropene methylcyclopropane cyclobutadiene cyclobutene bicyclo[1.1.0]butane cyclobutane tetrahedrane
H L b b R E b b b A
0 94.0 62.1 47.9 ( 0.4 58.2 ( 0.3 8.0 101.1 37.5 ( 0.4 51.9 ( 0.2 6.8 ( 0.1 126.6
Entries with error limits are experimental.
b
References 11 and 13.
Discussion
example, G2(0 K) values for reactions G, K, and -J sum to zero (-37.4 + (-27.8) - (-65.2) ) 0). Scheme 3 shows hydrogenations and nearest-neighbor isomerizations of cyclic and acyclic C4 hydrocarbons. Computed values and a comparison with experimental results are shown in Table 3. Several thermochemical cycles are evident. ∆fH298. Knowing ∆fH298 for five of the compounds in Scheme 3 from combustion thermochemistry,11a,c13 we have calculated ∆fH298 for the five that are not known. All ∆hydH298 are listed in Table 4 along with the letters of the reactions in Scheme 3 used to obtain them. In each case, the G2 calculation of the nearest neighbor was used to obtain ∆hydH298; that is, the minimum number of computed ∆hydH298 or ∆isomH298 values were used.
G2 calculated ∆hydH298 for stepwise hydrogenation of acetylene in Scheme 1 and Table 1 are 0.2 and 0.3 kcal mol-1 less exothermic than the experimental values. G2(MP2) ∆hydH298 are 0.1 and 0.5 kcal mol-1 less exothermic than experimental values. Experimental values have been taken from a standard source11a and have been cross-checked with the original experimental ∆hydH355 measured by Kistiakowskty et al.11b The experimental values in Table 2 differ slightly from the original results,11b mainly through the temperature correction from 355 to 298 K. Kistiakowsky and Nickle12 carried out a very precise study of ∆hydH298 for ethylene and propene which confirms the values given in Tables 1 and 2: ∆hydH298 ) -32.60 ( 0.05 and -29.85 ( 0.05 kcal mol-1, respectively. Present G2 results in Scheme 2 and Table 2 are 0.6 kcal mol-1 (arithmetic mean) less exothermic than those previously reported.10 That there should be any difference at all is owed to differences in locating minima on the potential energy surface, machine differences, and a difference in the heat capacity correction. The present statistical calculation of the enthalpy difference between 0 and 298 K takes into account statistical thermodynamic “thawing” of vibrational motion, whereas the previous calculation did not. The mean absolute difference between G2 and G2(MP2) results in Scheme 2 is 0.10 kcal mol-1; hence we are encouraged to use the G2(MP2) method in future studies on larger molecules. In Scheme 2, all three reactions of cyclopropene, A, C, and E, are calculated to be more exothermic than the
Enthalpies of Cyclic C4 Hydrocarbons experimental value (arithmetic mean difference 1.4 kcal mol-1) and all three hydrogenations of allene are calculated to be about 0.8 kcal mol-1 less exothermic than the measured value. The difference between ∆hydH0 and ∆hydH298, which we have previously estimated to be about -2.0 kcal mol-1 (see above), has an arithmetic mean of -1.9 kcal mol-1 of hydrogen added. In Scheme 3, the arithmetic mean unsigned difference between G2 and G2(MP2) computed ∆hydH298 and ∆isomH298 values is 0.13 kcal mol-1, and their mean unsigned differences from measured values are 0.9 and 0.8 kcal mol-1, respectively. Isomerization of methylenecyclopropane to 1-methylcyclopropene is calculated to be 0.9 kcal mol-1 more endothermic than the measured value, and both hydrogenations having cyclobutane as the product have calculated ∆hydH298 that are more exothermic than the measured value by about 1.5 kcal mol-1. The difference between ∆hydH0 and ∆hydH298 has an arithmetic mean of -1.9 kcal mol-1. Of special interest is the calculated ∆hydH298 ) -74.7 kcal mol-1 for hydrogenation of tetrahedrane to bicyclo[1.1.0]butane, for which we have a reliable ∆fH298 ) 51.9 ( 0.2 kcal mol-1.11a,c The resulting calculated ∆fH298(tetrahedrane) ) 126.6 kcal mol-1 compares with 127.9 ( 1.0 kcal mol-1 obtained by Glukhovtsev, Laiter and Pross using isodesmic reactions.7a By the same reasoning, the G2 and G2(MP2) calculation of ∆fH298 for cyclobutadiene yields 100.5 kcal mol-1 as compared to 101.8 kcal mol-1 by Glukhovtsev, Laiter, and Pross. We estimate the uncertainty of our calculations to be about 1.0 kcal mol-1. The small ∆isomH298 ) -0.4 kcal mol-1 of cyclobutane to methylcyclopropane is noteworthy. We do not have a gas phase ∆fH298(methylcyclopropane), but the isomerization enthalpy can be estimated to be 0.5 ( 0.2 kcal mol-1 from the liquid phase ∆fH298 measured by Karsemacher and Coops.11a,13a and by Good.11a,13b Enthalpies of vaporization of C4H8 hydrocarbons vary within a range of 4.9-5.9 kcal mol-1. On the reasonable assumption that ∆vapH298(cyclobutane) is not very different from ∆vapH298(methylcyclopropane), the calculated ∆isomH298 (cyclobutane to methylcyclopropane) agrees with experimental work. On the same assumption, one arrives at ∆fH298 (methylcyclopropane, g) ) 6.4 ( 0.3 kcal mol-1 where the experimental uncertainty has been doubled in recognition of the uncertainty in the estimated ∆vapH298. It is surprising that conversion of a four-membered ring to a three-membered ring is enthalpically null. Evidently, the energetic advantage gained by releasing one carbon atom from the ring is sufficient to compensate for increased strain in the smaller ring.
J. Phys. Chem., Vol. 100, No. 43, 1996 17151 Acknowledgment. We wish to thank the trustees and release time committee of Long Island University for a grant of release time for this research. We acknowledge a grant of computer time from the National Science Foundation and the Pittsburgh Supercomputing Center. Supporting Information Available: Total G2 and G2(MP2) energies (2 pages). Ordering information is given on any current masthead page. References and Notes (1) See, for example: (a) Jensen, J. L. Prog. Phys. Org. Chem. 1976, 12, 189. (b) Turner, R. B.; Mallon, B. J.; Tichy, M.; Doering, W. von E.; Roth, W. R.; Schroeder, G. J. Am. Chem. Soc. 1973, 95, 8605. (c) Roth, W. R.; Adamczak, O.; Breuckman, R.; Lennartz, H.-W.; Boese, R. Chem. Ber. 1991, 124, 2499. (d) Fang, W.; Rogers, D. W. J. Org. Chem. 1992, 57, 2294. (2) See: Schulman, J. M.; Disch, R. L. J. Am. Chem. Soc. 1984, 106, 1202, and subsequent papers. (3) Hehre, W. J. Practical Strategies for Electronic Structure Calculations; Wavefunction: Irvine, CA, 1995. (4) (a) Pople, J. A.; Head-Gordon, M.; Fox, D. J.; Raghavachari, K.; Curtiss, L. A. J. Chem. Phys. 1989, 90, 5622. (b) Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J. Chem. Phys. 1991, 94, 7221. (c) Curtiss, L. A.; Carpenter, J. E.; Raghavachari, K.; Pople, J. A. J. Chem. Phys. 1992, 96, 9030. (5) Nicolaides, A.; Radom, L. J. Phys. Chem. 1994, 98, 3092. (6) Curtiss, L. A.; Raghavachari, K.; Pople, J. A. J. Chem. Phys. 1993, 98, 1293. (7) (a) Glukhovtsev, M. N.; Laiter, S.; Pross, A. J. Phys. Chem. 1995, 99, 6828. (b) Glukhovtsev, M. N.; Laiter, S. Theor. Chim. Acta 1995, 92, 327. (8) George, P.; Trachtman, M.; Bock, C. W.; Brett, A. M. Theor. Chim. Acta 1975, 38, 121. (9) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; HeadGordon, M.; Gonzalez, C.; Pople, J. A.; GAUSSIAN 94, Revision C.2; Gaussian, Inc: Pittsburgh PA, 1995. (10) Rogers, D. W.; McLafferty, F. J. J. Phys. Chem. 1995, 99, 1375. (11) (a) Pedley, J. B.; Naylor, R. D.; Kirby, S. P. Thermochemical Data of Organic Compounds, 2nd ed.; Chapman, and Hall: London, 1986. (b) Kistiakowsky, G. B.; Romeyn, J. R., Jr.; Smith, H. A.; Vaughan, W. E. J. Am. Chem. Soc. 1935, 57, 65. (c) Wiberg, K. B.; Fenoglio, R. A. J. Am. Chem. Soc. 1968, 90, 3395. (12) Kistiakowsky, G. B.; Nickle, A. G. Discuss. Faraday Soc. 1951, 10, 175. (13) (a) Kaarsemaker, S.; Coops, J. Recl. TraV. Chim. Pays-Bas 1952, 71, 261. (b) Good, W. D. J. Chem. Thermodyn. 1972, 4, 709.
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