This paper provides a qualitative analysis of the physical content of the low-energy states of a spin-transition compound presenting a light-induced excited spin state trapping (LIESST) phenomenon, namely, [Fe(dipyrazolpyridine)2](BF4)2, which has been studied using the wave function-based CASPT2 method. Both the nature of the low-energy states and the relative position of their potential energy wells as a function of the geometry are rationalized from the analysis of the different wave functions. It is shown that the light-induced spin transition occurring in such systems could follow several pathways involving different excited spin states. In an ideal octahedral geometry, the interconversion from the excited singlet state to the triplet of lower energy, which is usually seen as an intermediate state in the LIESST mechanism, is quite unlikely since there is no crossing between the potential energy curves of these two states. On the contrary, in lower-symmetry complexes, the geometrical distortion of the coordination sphere due to ligand constraints is responsible for the occurrence of a crossing between these two states in the Franck-Condon region, leading to a possible participation of this triplet state in the LIESST mechanism. In the reverse LIESST process, a crossing between the potential energy curves of another triplet state and the excited quintet state occurs in the Franck-Condon region as well.

The variational energies of broken-symmetry single determinants are frequently used (especially in the Kohn-Sham density functional theory) to determine the magnetic coupling between open-shell metal ions in molecular complexes or periodic lattices. Most applications extract the information from the solutions of m(s)(max) and m(s)(min) eigenvalues of S(z) magnetic spin momentum, assuming that a mapping of these energies on the energies of an Ising Hamiltonian is grounded. This approach is unable to predict the possible importance of deviations from the simplest form of the Heisenberg Hamiltonians. For systems involving s=1 magnetic centers, it cannot provide an estimate of neither the biquadratic exchange integral nor the three-body operator interaction that has recently been proven to be of the same order of magnitude [Phys. Rev. B 70, 132412 (2007)]. The present work shows that one may use other broken-symmetry solutions of intermediate values of m(s) to evaluate the amplitude of these additional terms. The here-derived equations rely on the assumption that an extended Hubbard-type Hamiltonian rules the interactions between the magnetic electrons. Numerical illustrations on a model problem of two O(2) molecules and a fragment of the La(2)NiO(4) lattice are reported. The results obtained using a variable percentage of Fock exchange in the BLYP functional are compared to those provided by elaborate wave function calculations. The relevant percentage of Fock exchange is system dependent but a mean value of 30% leads to acceptable amplitudes of the effective exchange interaction.