Sigma and Pi Electronic Reorganization in Acetylene

Abstract

Accurate SCF—LCAO—MO wavefunctions have been computed for acetylene neutral ground state, singly excited π→π* states, and for the acetylene anion and cation. A limited basis set of Slater orbitals was used, the carbon 2s, 2pπ, and 2pσ orbital exponents were independently optimized for each state, and hydrogen 1s for the ground state. All integrals were computed accurately. For the ground state the C2p±1 optimized orbital (ξ=1.59) is very different from the C2pσ optimized orbital (ξ=2.03) with the result that the Π cloud does not penetrate the Σ cloud as greatly as would be predicted by Slater or best-atom AO. However, the penetration remains sizeable (Fig. 2). The ground-state energy − 76.678 a.u. (1 a.u.=27.2098 eV) is improved by 0.134 a.u. over McLean's best-atom calculations, but is 0.176 a.u. poorer than McLean's Hartree—Fock calculations. Reorganizations of the sigma and pi electronic shells with change in state of the pi system are computed to be large. A gain or loss of a pi electron is accompanied by a sigma energy change of 0.2 a.u. partially due to deformation of the C2s AO and partially due to sigma polarization away from the H atoms in the cation and vice versa in the anion. The large reorganization in the pi distribution is illustrated by the 2pπ exponents: cation 1.68, anion 1.45, ground state 1.59. The total reorganization energy in acetylene (−0.033 a.u. G state→cation; −0.069 a.u. G state→anion) is only 6% of the largest reorganization term: the change in sigma—pi interaction (0.586 and 1.262 a.u., respectively). The success of conventional pi-electron theory then basically depends on cancellation of the sigma and pi reorganization energy terms with the change in the sigma—pi interaction. The Hijcore parameters are found to be nearly independent of pi density providing justification for pi-electron approaches which adjust the pi atomic orbitals according to pi density.