Charge distributions and chemical effects. XXI. A new energy formula for molecules

The energy of atomization of molecules in their hypothetical vibrationless state at K, ΔEa*, is conveniently partitioned into nonbonded and bonded contributions and the latter are further partitioned into individual bond terms εij, i.e., ΔEa* (bond) =Σεij. A straightforward application of Politzer’s formula for molecular energies yields εij=εij0+aijΔqi+aij Δqj, where the Δq’s are the increments in net atomic charges on atoms i and j relative to those of a reference ij bond whose εij value is ε0ij. The aij’s are given by aij= (∂Ei/∂Ni)0 −(3/7) Zj<rij−1≳, where Ei is the valence shell electronic energy of atom i, Ni its electron population, and Zj is the effective nuclear charge of the j atom bonded to i. The derivative is evaluated for Ni=N0i, i.e., the population on i in the reference bond, and 〈rij−1〉 is the average inverse distance between nucleus j and the Ni electrons of atom i. The calculated ΔE*a’s of saturated hydrocarbons agree with their experimental counterparts, within ±0.157 kcal/mol (average deviation).