Transferrable property relationships between magnetic exchange coupling and molecular conductance

Calculated conductance through Au-n-S-Bridge-S-Au-n (Bridge = organic s/p-system) constructs are compared to experimentally-determined magnetic exchange coupling parameters in a series of Tp(Cum,Me)ZnSQ-Bridge-NN complexes, where Tp(Cum,Me) = hydro-tris(3-cumenyl-1-methylpyrazolyl) borate ancillary ligand, Zn = diamagnetic zinc(II), SQ = semiquinone (S = 1/2), and NN = nitronylnitroxide radical (S = 1/2). We find that there is a nonlinear functional relationship between the biradical magnetic exchange coupling, J(D -> A), and the computed conductance, gmb. Although different bridge types (monomer vs. dimer) do not lie on the same J(D -> A) vs. g(mb), curve, there is a scale invariance between the monomeric and dimeric bridges which shows that the two data sets are related by a proportionate scaling of J(D -> A). For exchange and conductance mediated by a given bridge fragment, we find that the ratio of distance dependent decay constants for conductance (beta(g)) and magnetic exchange coupling (beta(J)) does not equal unity, indicating that inherent differences in the tunneling energy gaps, Delta epsilon, and the bridge-bridge electronic coupling, H-BB, are not directly transferrable properties as they relate to exchange and conductance. The results of these observations are described in valence bond terms, with resonance structure contributions to the ground state bridge wavefunction being different for SQ-Bridge-NN and Au-n-S-Bridge-S-Au-n systems.