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

(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.