σ-Hole Interactions: Perspectives and Misconceptions

Abstract

After a brief discussion of the σ-hole concept and the significance of molecular electrostatic potentials in noncovalent interactions, we draw attention to some common misconceptions that are encountered in that context: (1) Since the electrostatic potential reflects the contributions of both the nuclei and the electrons, it cannot be assumed that negative potentials correspond to "electron-rich" regions and positive potentials to "electron-poor" ones; (2) The electrostatic potential in a given region is determined not only by the electrons and nuclei in that region, but also by those in other portions of the molecule, especially neighboring ones; (3) A σ-hole is a region of lower electronic density on the extension of a covalent bond, not an electrostatic potential; (4) Noncovalent interactions are between positive and negative regions, which are not necessarily associated with specific atoms, so that "close contacts" between atoms do not always indicate the actual interactions.Keywords: σ-holes; noncovalent interactions; electrostatic potential; close contacts A Brief History of the σ-HoleThe σ-hole concept was introduced by Clark in the context of halogen bonding, at a conference in 2005 [1], although it did not appear in the chemical literature until 2007 [2]. Halogen bonding involves a favorable noncovalent interaction between a covalently-bonded halogen and a negative site, such as a lone pair. Such interactions were already known to experimentalists in the 19th century [3,4], and were studied extensively in the 20th [5][6][7][8][9][10], with crystallography playing a major role [10][11][12][13]. Nevertheless the basis for halogen bonding was not really understood. It was frequently rationalized as "charge transfer" from an electron "donor" (e.g., the lone pair) to an "acceptor" (the halogen), invoking the valence bond formalism of Mulliken [14] (which was later put in molecular orbital terms by Flurry [15,16]).However, the halogen is the most electronegative atom in each row of the periodic table, and a singly-bonded halogen atom is generally viewed as being negative in character. So why should it interact attractively with a donor of electronic charge? It was in fact pointed out long ago [7,17] that Mulliken's charge-transfer formalism was not intended to be an elucidation of the bonding in a ground-state noncovalent complex; it was purely a mathematical modeling of the transition of the ground-state complex to a low-lying excited state. The existence of halogen bonding was thus viewed by many as an enigma.The key to resolving the enigma was the molecular electrostatic potential. This is the potential V(r) that is created at any point r in the space of a molecule by its nuclei and electrons, given rigorously by Equation (1):Z A is the charge on nucleus A, located at R A , and ρ(r) is the molecule's electronic density. Regions in which V(r) is positive, indicating the dominance of the nuclear contribution, are attractive to

Can Combined Electrostatic and Polarization Effects Alone Explain the F···F Negative-Negative Bonding in Simple Fluoro-Substituted Benzene Derivatives? A First-Principles Perspective

“…In the solid state a "non-bonded bond" is often referred to as a "close contact" that indicates an attractive non-covalent interaction. A geometry-based criterion widely used to identify a non-covalent bond is that the distance between the interacting atoms should be less than (or approximately equal to) the sum of their van der Waals radii [73]. As such, the distance between the F atoms in the F···F directional interaction in (C 6 H 4 F 2 ) 2 , at 3.049 Å, is shorter than the non-directional F···F interaction, 3.105 Å.…”

“…A failure of this feature has been noted previously. Dance [75], Alvarez [81], and others [38,73] have pointed out that using the sum of van der Waals radii as a criterion is likely to overlook many non-covalent interactions, which may be several tenths of an Å greater than that sum. There are several other examples documented in the literature that recognize the van der Waals radii feature as a poorly defined criterion for assigning weak interactions, as in [82].…”

“…isodensity envelope mapped potential on the electrostatic surfaces of molecules is generally labeled as V S (r). This envelope has often been suggested to be appropriate for encompassing 96% of molecular electronic densities [12][13][14][15]37,[72][73][74][75], although Bader et al [76] have suggested the use of either 0.0010 or 0.0020 a.u. isodensity envelopes since the choice of the isodensity envelope is dependent on the nature of the atomic domains constituting the molecule.…”

“…isodensity envelopes since the choice of the isodensity envelope is dependent on the nature of the atomic domains constituting the molecule. Moreover, while some have shown that the 6-31G* and 6-31G** minimal basis sets give reliable predictions of electrostatic potentials [12,13,[72][73][74], others have argued that both the magnitude and sign of electrostatic potential are basis set dependent [35,77]. Thus, an appropriate basis set must be used to avoid an incorrect interpretation of the nature of surface reactivity inferred from the sign of the maxima and minima (V s,min and V s,max , respectively) of electrostatic potential, especially when its magnitude is close to zero.…”

A Simple Model for Halogen Bond Interaction Energies

“…The above points clearly indicate that electrostatics are important in such systems. However, the "makeup" of halogen bonds has attracted considerable debate [37][38][39][40][41][42][43][44][45][46][47]. It has been comprehensively shown that electrostatics alone are not sufficient to fully describe these interactions [9,48].…”