The Group Equivalent Reaction An Improved Method for Determining Ring Strain Energy Steven M. Bachrach Northern Illinois University, DeKalb, IL 601 15 Many physical organic concepts are defined by comparisons t o arbitrary reference systems. Ring strain energy (RSE), an example of such aconcept, isdefinedas the energy needed to distort bonds and hond angles to close a ring structure ( I ) . A reference system must contain unstrained components of the test molecule in the absence of the ring. In this note, we wish to provide an algorithm for choosing adequate reference systems for ring strain energy by making a modification t o t h e standard homodesmic reaction scheme. Tradnlonal Methods Conventional RSE is obtained as the heat of formation of the strained ring molecule less the heat of formation obu ~eauivalents. tained bv summina onlv the auuronriate a- r o . . following ~ e n s o n ' h ( 2&thodoiog).. ) The reference system is a hvuothetical "unstrained" analorue of the strained ring. However, if the necessary groupequivalents or the heat of formation of the compound of interest are unknown, another approach is required. A balanced chemical reaction can he created for which the reactant and product differ by the presence of a ring. For such a reaction, the reaction energy is the RSE. Two such methods have been devised: isodesmic (3)and homodesmic (4) reactions. Isodesmic reactions retain the same number of bonds of every given formal type allowing for a change in their relationship t o each other. Reference systems are composed of molecules containine two h e a w atoms (nonhvdroaens) . .. . and thus are based on preserving only nearest-neighbor interactions. The eeneral forms of the isodesmic reaction for determining RSE for cycloparaffins, cyclo-mono-olefins, and cyclooxaparaffins are given in the table. The homodesmic reaction maintains the same number of each type of hond and maintains the same numher of C, N, 0 , etc., atoms with zero, one, two or three attached hydrogens. This reaction preserves the type of atom and therefore preserves some next nearest-neighbor interactions. The reference molecules have three heavy atoms. The general forms of the homodesmic reaction for determining RSE for cycloparaffins, cyclo-mono-olefins, and cyclo-oxaparaffins are given in the table. George, Trachtman, Bock, and Brett (4) determined the RSE for a series of cycloparaffins and other strained molecules, comparing the results obtained using the isodesmic and homodesmic methods. For small rings, the discrepancies between the isodesmic and homodesmic RSE's were small hut increased dramatically with increasing ring size, as shown in Figure 1. Isodesmic reactions allow for too many other chemical changes between the reactants and products to isolate just the effects of the ring. One must conserve more than just hond types. Close examination of the homodesmic reaction reveals that next nearest neighbors are not always conserved, and this has energetic consequences. For example, let us analyze the homodesmic reaction for ohtaining the RSE of cyclooxaparaffins, eq 1.The left-hand side has two carhon atoms bound to one C, one 0 , and two H atoms (in Benson's notation this is C-(C)(O)(H)Z).There are no such carbon atoms
in the products. Rather, this C must correspond with the methylene C in propane (C-(C)Z(H)Z).These groups are not energetically equivalent; the Benson group equivalents for C-(C)(O)(H)Z and C-(C)Z(H)Z are -8.1 and -4.93 kcal mol-', respectively. The homodesmic reaction energy includes a portion due to the differences in the number and type of equivalent groups nn each side of the equation and is thus not providing n direct measure of RSE.
Improved Method. The Group Equlvalent Reactlon We will now describe an algorithm for ohtaining a halanced chemical equation that is homodesmic and conserves chemical groups as defined by Benson. This reaction, termed the group equiualent reaction, conserves next-nearest neighbors. The method is a direct extension of the disproportionation reaction of Benson and Buss (5)and the group separation reaction of Dill, Greenberg, and Liehman (6). The procedure for generating the group equivalent reaction is straightforward and will he presented for oxetane. Every equivalent group in the ring (reactant) must he paired with an equivalent group in a short acyclic molecule in the products. Since next-nearest neighhors are conserved, the possible product molecules must have at least three nonhydrogen atoms. Oxetane contains the following groups: 0(C)2, C-(C)Z(H)Z, and two C-(C)(O)(H)Z. We choose the smallest acyclic molecules containing these groups to serve as the products. For this case, thev are dimethvl ether. nropane, and two molecules of ethanol, respectir.&. ~ h b ' l n s t step is to balance the equation b\.addinr molecules containing two nonhydrogen atoms to t h e reactants. These molecules are selected to balance the equivalent groups in the
ring size Figure 1. Ring strain energy In kcal mol-' for cycloparaffins determined using isadesmlc (open triangles) and homodesmic (apen squares) reactions.
Number 11 November 1990
General Equations for Delermlning RSE
Group Equivalent Reactions
+ n - lCH,CH, + CH,=CH, 2CH,CH=CH, + n - 2CH,CH,CH, (CH,),,--O + nCH,CH3-CH,OCH, + n - lCH,CH,CH,
(CH,), + nCH,CH, nCH,CH,CH, + n - 3CHSCH, + CH,==CH, +2CH,CH,CH=EH2 + n - 4C%CH,& + n - ZCH,CH, + PCH,OH -CH,OCH, + n - SCH&H,CH, + ZCH,CH,OH +
products. Thus, two molecules of methanol and two molecules of ethane will balance the reaction and conserve the equivalent groups, giving eq 2.
+ 2CH,OH CH,OCH, + CH,CH,CH3 + 2CH,CH20H
The general forms of the group equivalent reaction for determining RSE for cycloparaffins, cyclo-mono-olefins, and cvclo-oxaoaraffins are &en in the table. Comoarison of -~~~~~ the RSE derermined usin(: the homodesmic and group equivalent reactions for cyclo-oxaparaffins are shown in Figure 2. The algorithm presented above yields the groqp equivalent reaction requiring the smallest possible molecules. This reaction is not unique however. Equations 3-6 are proper group equivalent reactions for determining the RSE of tetrahydrofuran. The values of the RSE's obtained from these reactions are nearly identical: eq 3, RSE = 5.25; eq 4, RSE = 5.18; eq 5, RSE = 6.12; eq 6; RSE = 6.50. The group equivalent reactions are nearly internally consistent. This is not surprising since the reaction is based on group equivalents which Benson (2)has shown to be quite self-consistent. ~
ring size F gwe 2. R ng straln energy m kcal mol-' tor cyclo-oxaparaff ns delermmw us,ng homoaeomfc(open squares) and grobp equivalenl 1111ea clrc es, reac-
calculation of RSE, but it can he generally applied to other problems, such as resonance energy. Acknowledgment I thank Carmen Nitsche for many helpful discussions and suggestions. Literature Cited Conclusion The modified homodesmic reaction that conserves group equivalents, presented here as the group equivalent reaction, provides a balanced chemical reaction that can he used to quantify the energy associated with various structural features while minimizing the effects of all other chemical contributions. This reaction has been applied here to the
Journal of Chemical Education
1. Greenblg,A.;Liehmsn,J. F.SfminadRingMolrrule$;Academic:New York, 1978:snd references cited there.? 2. (a) Benson, S. W.: Cruikshnk, F. R.: Golden, D. M.; Hargen, G. R.; O'Nesl. H. E.; Rodgers,A.S.; Shaw,R.: Ws1sh.R. Chem.Reu. 1969.69.279. lb) Eigenmann, H. K.; Benson, S. W.: Golden, 0. M. J . Phys, Chem 1973, 77, 1687. Icl Benron, S. W. Thermoch~micolKinerira, 2nd ed.; Wiley: New York, 1976. 3. Hehre, W. J.:Drtchfield,R.: Radom,L.;Poplo,J. A. J . Am. Chem.Soc. 1970.92.4796. 4. (s)Geowe,P.:Traehtman,M.:Back.C. W.;Brctt,A.M. Tetrahedron 1916.32.317. Ihi Georgc,P.:Traehtman,M.:Brett,A. M.;Back,C. W. J. Chem.Soc.,PmkinsZ 1977,