The Concept of Protobranching and Its Many Paradigm Shifting Implications for Energy Evaluations

Abstract

Branched alkanes like isobutane and neopentane are more stable than their straight chain isomers, n-butane and n-pentane (by 2 and 5 kcal mol(-1), respectively). Electron correlation is largely responsible. Branched alkanes have a greater number of net attractive 1,3-alkyl-alkyl group interactions, there are three such stabilizing 1,3 "protobranching" dispositions in isobutane, but only two in n-butane. Neopentane has six protobranches but n-pentane only three. Propane has one protobranch and is stabilized appreciably, by 2.8 kcal mol(-1), relative to methane and ethane. This value per protobranch also applies to the n-alkanes and cyclohexane. Consequently, energy evaluations employing alkane reference standards, for example, of small ring strain and stabilizations due to conjugation, hyperconjugation, and aromaticity, should be corrected for protobranching, for example, by employing Pople's isodesmic bond separation reaction method. This reduces the ring strain of cyclopropane to 19.2 from the conventional 27.7 kcal mol(-1), while the stabilization energies of alkenes and alkynes due to hyperconjugation (5.5 and 7.7 kcal mol(-1) for propene and propyne) and conjugation (14.8 and 27.1 kcal mol(-1) for butadiene and butadiyne) are considerably larger than the traditional estimates. Widely diverging literature evaluations of benzene resonance energy all give approximately 65 kcal mol(-1) after adjusting for conjugation, hyperconjugation, and protobranching "contaminations." The BLW (block localized wavefunction) method, which localizes pi bonds and precludes their interactions, largely confirms these stabilization estimates for hyperconjugation, conjugation, and aromaticity. Protobranching is seriously underestimated by theoretical computations at the HF and most DFT levels, which do not account for electron correlation satisfactorily. Such levels give bond separation energies, which can differ greatly from experimental values.

On the Harmonic Oscillator Model of Electron Delocalization (HOMED) Index and its Application to Heteroatomic π-Electron Systems

“…For strongly conjugated aromatic systems, the HOMED indices are close to unity. This order of the HOMED indices is in good agreement with the BLW-based data order for energy evaluation of σ -π hyperconjugation (6.3 kcal mol −1 for propene), π -π conjugation (12.7 kcal mol −1 for butadiene) and aromaticity (ASE 25.7 and RE 65.4 kcal mol −1 for benzene) [39,40,63].…”

“…hyperconjugation, conjugation, aromaticity, tautomerism, proton-transfer, and/or hydrogen bonding, may take place [10,11,[36][37][38][39][40]. We analyzed π-electron delocalization for simple σ-π hyperconjugated, n-π conjugated, π -π conjugated, and aromatic compounds including those displaying prototropic tautomerism.…”

“…The C=C double bond in ethene, the C=N double bond in methylimine, and the C=O bond in formaldehyde were proposed for the reference R d bonds [20][21][22][23]. For all reference molecules, weak electron delocalization (e.g., hyperconjugation in ethane, methylamine and methanol [40,[42][43][44][45]) takes place, and thus, the reference CC and CX bonds could be treated as almost pure single and pure double bonds. The oHOMA values estimated for simple heteroaromatic compounds are close to unity [22,23].…”

“…Many substitution, addition, and condensation reactions can be understood and explained taking the σ-π hyperconjugation effect into account [48,51]. Recently, it has been also suggested that hyperconjugation is responsible for the structure of σ -bonded organic compounds such as alkanes, alcohols, and amines [40,[42][43][44][45]. The conformational preferences seem to be favored by this special type of resonance, not by steric repulsion.…”

Communication: Practical intramolecular symmetry adapted perturbation theory via Hartree-Fock embedding

“…Several alternative choices of link bond assignment are not appropriate in this case: if the link bonds are shared or wholly assigned to A or B, the overlap between the two linking σ bonds causes enormous charge penetration contributions to the electrostatics and induction terms. Thus, although IS-APT reasonably reflects the dependence of the energy components on the geometry, the absolute value of the 1,3-methylmethyl interaction (central to the protobranching debate [15][16][17][18][19] remains to be accurately determined once these artifacts are eliminated.…”