SPIN-FREE QUANTUM CHEMISTRY .6. SPIN CONSERVATION

Many chemical systems are well described by the Breit-Pauli Hamiltonian with the spin-free term and spin terms treated as zero-order and perturbation Hamiltonians, respectively. If the zero-order levels are widely separated and the spin effects are small, a system admits, to a good approximation, a spin-free formulation. Since the spin-free Hamiltonian commutes with the group of permutations on spatial electron coordinates, the partitions [λ] which label the irreducible representations of this group are good quantum numbers and label the spin-free states. In this regime [λ] is conserved in collisions, chemical reactions, and electric dipole radiative processes. The Pauli principle restricts the physically significant permutation states and establishes a one-to-one correspondence with spin states. It follows that in the spin-free regime spin is a good quantum number and is conserved. Rules are derived for the conservation of permutational quantum numbers between separated and composite systems. The conventional spin analogs of these rules are the Wigner spin conservation rules. We discuss two types of breakdown of the spin-free permutational symmetry: (i) the breakdown of local permutational symmetry while preserving total spin-free permutational symmetry (an example is the enhancement of singlet-triplet transitions by collision with paramagnetic molecules); (ii) the breakdown of total spin-free permutational symmetry. The breakdown is practically complete in those cases for which the zero-order states are degenerate or near degenerate. A number of photochemical processes are discussed with particular reference to methylene and benzene.