Abstract
Recent advances in the computational techniques available to characterize spin-forbidden processes with the Breit-Pauli approximation are reviewed and the use of these techniques is illustrated. These computational advances include: (i) The use of symbolic matrix element techniques to evaluate matrix elements of the full microscopic spin-orbit Hamiltonian (both the spin-orbit and spin-other-orbit terms) and the dipolar spin-spin Hamiltonian. This approach permits the Breit-Pauli interaction to be characterized in terms of large configurations state functions (CSF) spaces ≥ 106 terms. (ii) The relativistic wavefunctions are determined, directly in the CSF basis, using quasi-degenerate perturbation theory. This approach avoids the computational bottleneck which occurs if the perturbed wavefunction is determined in the eigenstate basis of H0 the non-relativistic Born-Oppenheimer Hamiltonian. (iii) The use of a Lagrange-Newton, analytic gradient-Mcscf/CI wavefunction based, algorithm for determining the minimum energy point on the surface of intersection of two potential energy surfaces of different spin multiplicity. This algorithm facilitates determination of the energetically accessible portion of the crossing hypersurface without having to characterize the entire crossing surface.

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