Total energies of alkanes in terms of through-space and through-bond interactions. Analysis of the one-electron density matrix

Abstract

The total energy of alkanes has been expressed in terms of two principal matrices G( 1) , and G( 2) introduced previously [V. Gineityte, J. Mol. Struct. (Theochem), 343 (1995)183] and describing the direct (through-space) and indirect (through-bond) interactions of bond orbitals (BOs). As a result, the stabilization energy of an alkane versus the respective set of isolated bonds has been related to sum of squares of the through-space interactions over the whole molecule. The common one-electron density matrix (DM) of alkanes containing the same matrices G( 1) and G( 2) has been transformed into the basis of sp 3-hybrid AOs of carbon atoms and ls HAOs of hydrogen atoms. Analysis of this new representation of the DM allowed the stabilization energy to be alternatively expressed as spur of the so-called rebonding matrix. This matrix is among the building blocks of the transformed DM and describes redistribution of bond orders when making up an alkane molecule. In this connection, stabilization of alkanes has been concluded to be due to the rebonding effect. The extent of additivity of the stabilization energy with respect to contributions of separate bonds also has been studied.