Pnicogen Bonds: A Theoretical Study Based on the Laplacian of Electron Density

Abstract

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.

“Pnicogen bonds” or “chalcogen bonds”: exploiting the effect of substitution on the formation of P⋯Se noncovalent bonds

“…24 Another study on pnicogen bonding categorized it as lump-hole interactions. 41 The study on pnicogen bonded complexes involving anions showed the presence of some covalent character in these interactions. 42 The strength of pnicogen bonds involving N, P, and As was also investigated and it was observed to be highly stabilizing.…”

Electron density Laplacian and halogen bonds

“…This space region is thus prone to interact with the lone electron pair(s) carried by the partner. Recently, a similar analysis (also valid for homologous noncovalent bonds) has been proposed using, as the primary physical observable, the electron density Laplacian ∇ 2 ρ(� r) [25][26][27][28] instead of MEP, leading to the so-called lump-hole interaction paradigm [29]: the electron-deficient region at the periphery of the halogen atom is then viewed as a "hole" that can be filled by the electron-rich Lewis base's lump. Indeed, it is very well known that charge depletion areas are easily characterized by positive ∇ 2 ρ(� r) values, while charge concentration occurs when ∇ 2 ρ(� r) is negative.…”

Noble Gas Bonding Interactions Involving Xenon Oxides and Fluorides

“…These interactions can be divided into σ–hole [ 21 , 22 , 23 , 24 ] and π–hole interactions [ 25 , 26 , 27 , 28 , 29 ] and are nowadays entered into the toolkit supramolecular chemists. Actually, tetrel (Tt) [ 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 ], pnictogen (Pn) [ 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 ], and chalcogen (Ch) [ 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 ] bonding interactions (see Figure 1 ) have been studied by many theoretical works and are progressively used experimentally in relevant fields such as supramolecular catalysis, polymers, transmembrane ion transport and, especially, crystal engineering [ 15 , …”