A σ-hole bond is a noncovalent interaction between a covalently-bonded atom of Groups IV–VII and a negative site, e.g. a lone pair of a Lewis base or an anion. It involves a region of positive electrostatic potential, labeled a σ-hole, on the extension of one of the covalent bonds to the atom. The σ-hole is due to the anisotropy of the atom's charge distribution. Halogen bonding is a subset of σ-hole interactions. Their features and properties can be fully explained in terms of electrostatics and polarization plus dispersion. The strengths of the interactions generally correlate well with the magnitudes of the positive and negative electrostatic potentials of the σ-hole and the negative site. In certain instances, however, polarizabilities must be taken into account explicitly, as the polarization of the negative site reaches a level that can be viewed as a degree of dative sharing (coordinate covalence). In the gas phase, σ-hole interactions with neutral bases are often thermodynamically unfavorable due to the relatively large entropy loss upon complex formation.

A covalently-bonded atom typically has a region of lower electronic density, a “σ-hole,” on the side of the atom opposite to the bond, approximately along its extension. There is often a positive electrostatic potential (strongest shown in red) associated with a σ-hole, although it may deviate from the extension of the bond.

Recent work by others has shown that the densities of C,H,N,O molecular crystals are, in many instances, given quite well by the formula M/V_m, in which M is the molecular mass and V_m is the volume of the isolated gas phase molecule that is enclosed by the 0.001 au contour of its electronic density. About 41% of the predictions were in error by less than 0.030 g/cm³, and 63% by less than 0.050 g/cm³. However, this leaves more than one-third of the compounds with errors greater than 0.050 g/cm³, or in some instances, 0.100 g/cm³. This may indicate that intermolecular interactions within the crystal are not being adequately taken into account in these cases. Accordingly, the effectiveness of including a second term that reflects the strengths, variabilities and degree of balance of the positive and negative electrostatic potentials computed on the surfaces of the isolated molecules, has been included. The database was selected such that half of the densities predicted by M/V_m had errors larger than 0.050 g/cm³. The introduction of the electrostatic interaction correction produced a marked improvement. Overall, 78% of the predictions are within 0.050 g/cm³ of experiment, with 50% within 0.030 g/cm³. Among those that originally all had errors larger than 0.050 g/cm³, 67% are now less. The reasons for the better performance of the dual-variable formula are analysed.