Quantitative Analysis of Metal-Centered π-Holes in {TM(cyclen)}²⁺ Complexes

Metal-centered π-holes are regions of electronic depletion located above pseudoplanar coordination environments that can promote weak axial interactions. However, their characterization remains limited. In this context, this work establishes quantitative descriptors for identifying and comparing π-holes in transition-metal coordination environments. Here, a high-throughput computational analysis of 1296 {TM(cyclen)}²⁺ (TM = Co(II), Ni(II), Cu(II), and Zn(II) and cyclen = 1,4,7,10-tetraazacyclododecane) complexes is presented, considering four macrocyclic conformations and all combinations of methyl/ethyl nitrogen substitutions in cyclen. Electrostatic potentials were evaluated on electron density isosurfaces and analyzed using an algorithm that identifies π-hole candidates. Local maxima along the axis perpendicular to the nitrogen coordination plane are also validated by comparison with surrounding sectors. Validated π-holes, typically located 1.8-2.4 Å above the metal center, were detected in 84.6% of the complexes. Analysis of them shows that the maximum electrostatic potential alone does not reliably describe axial electron depletion in charged complexes. Instead, relative electrostatic descriptors provide consistent measurements of π-hole depth and anisotropy. Across the series examined, the π-hole intensity follows the order Zn(II) > Co(II) > Cu(II) > Ni(II), in good agreement with experimental findings. Conformational distortions and nitrogen substitution further modulate the magnitude and spatial distribution of the electrostatic potential.