The
majority of experimental data in electron spin resonance and
molecular magnetism are interpreted in terms of the spin-Hamiltonian
(SH) formalism. However, this is an approximate theory that requires
a proper testing. In the older variant, the multielectron terms are
used as a basis in which the D-tensor components
are evaluated by employing the second-order perturbation theory (PT)
for nondegenerate states; here, the spin–orbit interaction
expressed via the spin–orbit splitting parameter
λ serves for the perturbation. The model space is restricted
only to the fictitious spin functions |S, M⟩. In the case of the orbital
(quasi) degeneracy of
the ground term, the PT tends to diverge and the subtracted D, E, and
g
parameters are false. In the second variant working in the “complete
active space” (CAS), the spin–orbit coupling operator
is involved by the variation method resulting in the spin–orbit
multiplets (energies and eigenvectors) The multiplets can be evaluated
either by applying ab initio CASSCF + NEVPT2 + SOC
calculations or by using semiempirical generalized crystal-field theory
(with the one-electron SOC operator depending upon ξ). The resulting
states can be projected onto the subspace of the spin-only kets in
the way that the eigenvalues stay invariant. Such an effective Hamiltonian
matrix can be reconstructed using six independent components of the
symmetric D-tensor from which the D and E values are obtained by solving linear equations.
The eigenvectors of the spin–orbit multiplets in the CAS allow
determining the dominating composition of the spin projectioncumulative
weights of |±M⟩.
These are conceptually different from those generated by the SH
alone. It is shown that in some cases, the SH theory works satisfactorily
for a series of transition-metal complexes; however, sometimes it
fails. The ab initio calculations on the SH parameters
are compared with the approximate generalized crystal-field theory
conducted at the experimental geometry of the chromophore. In total,
12 metal complexes have been analyzed. One of the criteria that assesses
the validity of SH is the projection norm N for spin
multiplets (this has not to be far from 1). Another criterion is the
gap in the spectrum of the spin–orbit multiplets that separates
the hypothetical (fictitious) spin-only manifold from the rest of
the states.