Unraveling pnicogen bonding cooperativity: Insights from molecular electrostatic potential analysis

A theoretical investigation on the cooperativity of a series of binary, ternary, and quaternary complexes interconnected by pnicogen bonds has been conducted using calculations at the M06-2X/aug-cc-pVTZ level of density functional theory. By measuring changes in the molecular electrostatic potential (MESP) at the nucleus of interacting atoms in all of the complexes, it is possible to quantify the substantial reorganization of the electron density triggered by the formation of pnicogen bonds. The positive change in MESP, indicating a loss of electron density from the donor molecule in a dimer, facilitates the acceptance of electron density from a third molecule, resulting in the formation of a ternary complex with a stronger pnicogen bond compared to the one present in the binary complex. Similarly, the acceptor molecule in a dimer with a negative change in MESP showed an enhanced tendency to donate electron density to an electron-deficient third molecule. The MESP analysis provided valuable insights into the donor/acceptor characteristics of pnicogen bonds within the quaternary complexes. The proposed MESP hypotheses are consistent with the positive cooperativity observed in the pnicogen-bonded clusters. To quantify the changes in MESP, both at the donor atom (ΔV_donor ) and the acceptor atom (ΔV_acceptor ), for all pnicogen bonds in the cluster, the total change in MESP (ΔΔV_n ) was measured as ΔΔV_n  = ∑(ΔV_donor )-∑(ΔV_acceptor ). Remarkably, ΔΔV_n exhibited a strong linear relationship with the sum of the bond energies of the pnicogen bonds in the cluster. This establishes the MESP analysis as a robust approach for understanding the strength and cooperative behavior of pnicogen-bonded clusters. Additionally, the MESP features provided clear evidence of pnicogen bond formation, further supporting the reliability of this approach.