Magnetic coupling constants in three electrons three centres problems from effective Hamiltonian theory and validation of broken symmetry based approaches

In the most general case of three electrons in three symmetry unrelated centres with localized magnetic moments, the low energy spectrum consists of one quartet ( ) and two doublet ( , ) pure spin states. The energy splitting between these spin states can be described with the well-known Heisenberg-Dirac-Van Vleck (HDVV) model spin Hamiltonian, and their corresponding energy expressions are expressed in terms of the three different two-body magnetic coupling constants , and . However, the values of all three magnetic coupling constants cannot be extracted using the calculated energy of the three spin adapted states, since only two linearly independent energy differences between pure spin states exist. This problem has been recently investigated (JCTC 2015, 11, 3650), resulting in an alternative proposal to the original Noodleman's broken symmetry mapping approach. In the present work, this proposal is validated by means of ab initio effective Hamiltonian theory, which allows a direct extraction of all three values from the one-to-one correspondence between the matrix elements of both effective and HDVV Hamiltonian. The effective Hamiltonian matrix representation has been constructed from configuration interaction wave functions for the three spin states obtained for two model systems showing a different degree of delocalization of the unpaired electrons. These encompass a trinuclear Cu(II) complex and a -conjugated purely organic triradica