Physical Origin for the Unusual g-Values Observed for a Pb(I) Radical Complex: Quenching the Spin Angular Momentum...

Heavy main-group radical complexes likely exhibit unusual magnetic properties thanks to the intrinsically strong spin-orbit coupling (SOC) of the heavy elements. Herein, we elucidate the physical origin for the distinct magnetic anisotropy observed for group 14 Ge^I, Sn^I, and Pb^I radical anions 1-E (E = Ge, Sn, Pb) whose doublet ground states feature an (ns)²(np_z)¹ electron configuration. Complexes 1-Ge and 1-Sn display moderate magnetic anisotropy manifested by g_x,y,z = 1.976, 1.976, 1.999 and g_x,y,z = 1.879, 1.906, 1.982, respectively, (Angew. Chem., Int. Ed. 2022, 61, e202201248), with all g-factors close to the spin-only value, g_e. In contrast, 1-Pb is distinguished by a highly anisotropic g-tensor with g_x,y,z = 1.335, 1.410, and 1.693, in particular, having an exceptionally low g_z-factor. Effective Hamiltonian analyses based on wave function-based ab initio calculations reveal that 1-Ge and 1-Sn possess orbitally nondegenerate ground states, wherein the weak SOC between the ground state and the two low-lying excited states with dominant electron configurations of (ns)²(np_y)¹ and (ns)²(np_x)₁ partially restores the orbital angular momentum in the x- and y-directions, resulting in g_x ≈ g_y < g_z ≈ g_e. However, the ground level of 1-Pb features a triple orbital near-degeneracy, and the ensuing strong SOC with the same excited states not only introduces the considerable orbital angular momentum in the x- and y-directions but also, more critically, substantially quenches the spin angular momentum in the z-direction due to the conservation of the total angular momentum. As a consequence, all three g-components of 1-Pb are significantly lower than g_e, exhibiting a pattern of g_x ≈ g_y < g_z < g_e. This work, therefore, provides a general framework for correlating g-matrices measured experimentally with electronic structures of S = 1/2 main-group and transition-metal complexes.