Study of the Electronic Structure of Molecules. XVII. Analysis of the Formation of the Acetylene, Ethylene, and Ethane Molecules in the Hartree-Fock Model

Abstract

The electronic density and energy of the C2H2, C2H4, and C2H6 molecules are computed in the Hartree-Fock approximation and the results compared. Each molecule is computed at three different carbon-carbon internuclear distances, namely, those experimentally known for the equilibrium geometry in C2H2, C2H4, and C2H6. The comparison is extended by reporting computations on the lowest singlet state of the C2 molecule. The analysis is performed by making use of Mulliken's electron population analysis and our technique for partitioning the energy (bond energy analysis). For C2H4 we have also considered the twisted configuration (where one CH2 group is perpendicular to the other) and for C2H6 we have considered both staggered and eclipsed configurations (and therefore, we are in a position to add a few comments on the barrier to internal rotation). The basis set is sufficiently large and extended so as to be near to the Hartree-Fock limit for all the computations reported. The binding energy computed in the Hartree-Fock approximation has been corrected for the correlation error making use of Wigner's formula relating the electronic density to the correlation energy. It is shown that the one-center energies, the molecular orbital valence state (MOVS) energies, are regular functions of the 2s and 2p population at the C atom, complementing previous work where it was shown that the MOVS energies are functions of the gross atomic charges. Also, it has been shown that the two-center energy terms are proportional to bond strengths traditionally used in the chemical literature. The difficulty of analyzing small energy differences in the barrier to the internal rotation of C2H6 has been removed by analyzing the barrier at smaller R(C–C) distances where the barrier is considerably larger. It has been proposed that the observed (or computed) small barrier is the result of internal charge transfer and conjugation between the pseudo-2p orbitals on H3 and the 2p orbitals on C.