Pnicogen bonds: a theoretical study based on the Laplacian of electron density

Although, most of the authors classify the pnicogen bonds as σ-hole bonding, there are some evidence that show they do not require any positive electrostatic potential around interacting molecules. In this work, the Laplacian of electron density is used to study pnicogen bonds in different dimer and trimer complexes. It is shown that the noncovalent P···P, P···N, and N···N bonds can be categorized as lump-hole interactions; a region of charge depletion and excess kinetics energy (hole) in the valence shell charge concentration (VSCC) of pnicogen atom combines with a region of charge concentration and excess potential energy (lump) in the VSCC of another molecule and form a pnicogen bond. In fact, since the full quantum potential (according to the local statement of virial theorem) has been used in the definition of the Laplacian, the lump-hole concept is more useful than the σ-hole in which the electrostatic part of potential is only considered. It is shown that the existence of hole in the VSCC of pnicogen atom is responsible for formation and (in the absence of other interactions) geometry of pnicogen bonded complexes. Because there is (at least) one hole in their VSCC, the pnicogen atoms in PH3, PH2F, H2C═PH, H2C═PF, and NH2F can engage in direct pnicogen-pnicogen interactions. However, the VSCC of nitrogen atom in the NH3 is devoid of hole and hence cannot act as an electron acceptor in pnicogen-bonded complexes.