Metal-Centered π-Holes in {TM(cyclen)}2+ Complexes: Quantitative Electrostatic Descriptors and Axial Binding Trends

Metal-centered π-holes provide directional electrophilic regions above pseudoplanar coordination environments, influencing weak coordination and supramolecular recognition. Here, a high-throughput computational study of 1296 {TM(cyclen)}²⁺ complexes (TM = Co, Ni, Cu, Zn) was performed by combining cyclen conformations with methyl/ethyl N-substitution patterns, followed by GFN2-xTB preoptimization, DFT refinement, and electrostatic potential analysis. Using the author-developed VHoleMapper sector-validation algorithm, axial π-hole candidates were quantified through relative descriptors of depletion depth and anisotropy. The results show that V_s,max alone is insufficient to characterize metal-centered electron depletion, while sector-based descriptors provide a more chemically meaningful measure. π-hole intensity and axial binding energies with NH₃ and Cl^⁻ follow the trend Zn(II) > Co(II) > Cu(II) > Ni(II), supporting VHM descriptors as predictive tools for directional binding.