Properties of atoms and bonds in carbocations

Abstract

The quantum theory of atoms in molecules defines structures for and determines the properties of the atoms and bonds in the series of carbocations [(CH3)nCH3−n]+ with n = 0–3, and their parent hydrocarbons. In this theory, an atom in a molecule and its properties are defined by quantum mechanics. The quantum condition defining the atom is given in terms of a property derived from the charge density, as are the other concepts of the molecular structure hypothesis. In terms of the amount of electronic charge density accumulated between the carbon nuclei and its spatial distribution, a C—C bond of the carbocations exhibits an order greater than one. There is a transfer of charge from the hydrogens of methyl to the central carbon that destroys the axial symmetry of these C—C bonds and concentrates the charge in a plane perpendicular to the plane of substitution, in a manner consistent with the hyperconjugative mechanism of electron transfer. The positive charge of a carbocation is thus delocalized over all the atoms in the molecule, and the extent of this delocalization increases with increased methyl substitution. The electron population of each atom in a carbocation increases with this increase in the delocalization of positive charge and its energy is correspondingly decreased (the atom becomes more stable). These effects are most pronounced for the carbon atom bearing the methyl groups and they account for the observed increase in the relative stabilities of the carbocations with increasing methyl substitution. The electron populations and energies of the atoms in saturated hydrocarbons are also determined. The group additivity scheme for the energy in the homologous series of normal alkanes is predicted and explained in terms of the properties of the quantum atoms. It is the possibility of such transferability of the quantum atoms and their properties between systems that identifies them with the atoms of chemistry.