A hierarchy of homodesmotic reactions for thermochemistry

Chemical equations that balance bond types and atom hybridization to different degrees are often used in computational thermochemistry, for example, to increase accuracy when lower levels of theory are employed. We expose the widespread confusion over such classes of equations and demonstrate that the two most widely used definitions of "homodesmotic" reactions are not equivalent. New definitions are introduced, and a consistent hierarchy of reaction classes (RC1-RC5) for hydrocarbons is constructed: isogyric (RC1) superset of isodesmic (RC2) superset of hypohomodesmotic (RC3) superset of homodesmotic (RC4) superset of hyperhomodesmotic (RC5). Each of these successively conserves larger molecular fragments. The concept of isodesmic bond separation reactions is generalized to all classes in this hierarchy, providing a unique sectioning of a given molecule for each reaction type. Several ab initio and density functional methods are applied to the bond separation reactions of 38 hydrocarbons containing five or six carbon atoms. RC4 and RC5 reactions provide bond separation enthalpies with errors consistently less than 0.4 kcal mol(-1) across a wide range of theoretical levels, performing significantly better than the other reaction types and far superior to atomization routes. Our recommended bond separation reactions are demonstrated by determining the enthalpies of formation (at 298 K) of 1,3,5-hexatriyne (163.7 +/- 0.4 kcal mol(-1)), 1,3,5,7-octatetrayne (217.5 +/- 0.6 kcal mol(-1)), the larger polyynes C(10)H(2) through C(26)H(2), and an infinite acetylenic carbon chain.