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Odd-electron bonds have unique electronic structures and are often encountered as transiently stable, homonuclear species. In this study, a pair of copper complexes supported by Group 13 metalloligands, M[N(( o -C 6 H 4 )NCH 2 P i Pr 2 ) 3 ] (M = Al or Ga), featuring two-center/one-electron (2c/1e) σ-bonds were synthesized by one-electron reduction of the corresponding Cu( i ) ⇢ M(III) counterparts. The copper bimetallic complexes were investigated by X-ray diffraction, cyclic voltammetry, electron paramagnetic spectroscopy, and density functional theory calculations. The combined experimental and theoretical data corroborate that the unpaired spin is delocalized across Cu, M, and ancillary atoms, and the singly occupied molecular orbital (SOMO) corresponds to a σ-(Cu–M) bond involving the Cu 4p z and M n s/ n p z atomic orbitals. Collectively, the data suggest the covalent nature of these interactions, which represent the first examples of odd-electron σ-bonds for the heavier Group 13 elements Al and Ga.

Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn–Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin–orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in themore »nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.« less