The Unrestricted Hartree-Fock Theory of Chemical Reactions. III: Instability Conditions for Paramagnetic and Spin Density Wave States and Application to Internal Rotation of Ethylene

Abstract

Instability conditions applicable to paramagnetic and spin density wave electronic configurations with a time reversal invariant set of spacial orbitals are derived. It is shown that there are four types of instability, the spin-unflip and spin-flip instabilities preserving or breaking time reversal invariance. The instability conditions are applied to internal rotation of ethylene. It is shown that the spin density wave state becomes spin-flip unstable in the region where it becomes of higher energy than the triplet paramegnetic state and the latter state which is initially spin-flip unstable becomes stable in the region. All solutions of the UHF equation for homopolar two-center two-electron system, including those with orbitals of torsional spin arrangement and of broken time reversal symmetry, are listed up and their properties are discussed. The stability-instability correlation between the paramagnetic and spin density wave solutions and the adiabatic potentials of the UHF solutions are discussed in relation to internal reaction of ethylene.