being greater as they are closer to the region in question [140]. In other words, ESP maps do not necessarily correlate with overall electron density.
Disclaimer aside, ESP maps are still highly informative. They have helped justify the amphoteric behavior of halogens observed in the solid state, where electrophiles approach the halogen “side‐on” orthogonal to the CX bond and nucleophiles “head‐on” in line with the CX bond [4]. In particular, ESP studies by Politzer and Murray [5,141] led to the establishment of the σ‐hole concept, which has proven to be a widely valuable tool for conceptualizing the halogen bond and has contributed to the renaissance of other σ‐hole‐type interactions like chalcogen and pnictogen bonding [142]. Additionally, the ease of constructing ESP maps has led to their use in predicting relative halogen bond strength. For example, Politzer showed that the iodine VS,max values of iodobenzene derivatives largely positively correlate with their interaction energies with acetone [139] (Figure 1.14; Table 1.2). This relationship has been demonstrated a number of times theoretically [130,143] and has led to the use of VS,max values as predictors of solid‐state structures [72,75,144] and performance in solution [145]. Widespread application of VS,max and ESP maps has likely contributed to the halogen bond being mistakenly viewed as a purely electrostatic interaction; however other components are frequently important to fully describe the interaction [146]. For example, there are a number of cases where a more positive VS,max does not correlate with a stronger halogen bond [147].
Figure 1.14 Computed ESP maps on 0.001 au molecular surfaces of (a) iodobenzene, (b) meta‐difluoroiodobenzene, (c) ortho‐difluoroiodobenzene, and (d) pentafluoroiodobenzene. Color ranges, in kcal/mol, are red, greater than 20; yellow, between 20 and 10; green, between 10 and 0; and blue, negative. Black hemispheres denote the positions of the iodine VS,max.
Source: From Riley et al. [139]. © 2011 Springer Nature.
Table 1.2 Table of iodine VS,max values and interaction energies (ΔE) of iodobenzene derivatives with acetone.
Source: Adapted from Riley et al. [139]. Copyright 2011 John Wiley & Sons.
| Interaction angle | |||
| At (X⋯O<span class="dbondb"</span>C) = 180° | At optimum X⋯O<span class="dbondb"</span>C angle | ||
| System | VS,max (kcal/mol) | ΔE (kcal/mol) | ΔE (kcal/mol) |
| Iodobenzene | 17.3 | −2.44 | −3.22 |
| meta‐Difluoroiodobenzene | 26.1 | −3.38 | −4.13 |
| ortho‐Difluoroiodobenzene | 25.5 | −3.64 | −4.71 |
| para‐Fluoroiodobenzene | 35.9 | −4.88 | −5.97 |
1.4.3 Limitations on Electrostatic Potential
While ESP is an effective tool for predicting and conceptualizing interactions, there are limitations. Obviously, contacts that are not primarily electrostatic in nature cannot be accurately predicted, such as those reliant on polarization or charge transfer. Furthermore, ESP maps are only for isolated molecules and therefore do not account for other nuances when two molecules come together. For example, ESP maps do not calculate changes in electron distribution resulting from polarization due to incoming molecules. Therefore, to more accurately predict the strength of a halogen bond, more involved computational techniques that factor additional variables should be considered.
1.4.4 Atomic Orbital Theory and the σ‐Hole
Formation of the σ‐hole and the halogen bond interaction can also be described using atomic orbital theory. To paraphrase Clark, Murray, and Politzer, the electron‐deficient σ‐hole is caused by depleted occupancy in the outer lobe of a p‐orbital of a covalent bond [8]. The halogen “X” has an s2px2py2pz1 electronic configuration where the RX bond is on the z‐axis. In this electron configuration, two p‐orbitals are filled, and one is half filled, thus highlighting the depleted electron density in the pz orbital. This picture becomes more relevant with larger halogens and is more exaggerated when the halogen is covalently bound to an electron‐withdrawing system. For example, this orbital character does not appear for fluorine. As fluorine is very electronegative, it shares more of the sigma bonding electrons, creating a higher degree of sp hybridization than larger halogens. Moving additional electron density into the pz orbital affectively reduces the σ‐hole. For example, in a CF bond, 71.4% of electrons reside on F, whereas for less electronegative, larger halogens, like I, only ∼50% of the electron density resides on the halogen [8]. Meanwhile, the σ‐hole does not form for neutral, symmetric halogen containing molecules with equal electron distribution (e.g. carbon tetrahalides, hexahalobenzenes). This does not necessarily mean that symmetric or F‐based systems do not form halogen bonds; rather other attractive components become the dominate force.
1.4.5 Charge Transfer
Charge transfer has long been associated with halogen bonding, and Mulliken's investigations of I2 and organics containing O, S, or N heteroatoms are prime examples [42]. More recently, Palusiak utilized the Kohn–Sham molecular orbital (MO) theory to describe the interaction [148]. Halogen bonds and hydrogen bonds can have significant covalent character due to charge transfer from a guest to the antibonding σ* orbital (LUMO) of the R–X or R–H species [149] (Figure 1.15). The lower‐energy σ* orbital and higher‐energy σ orbital in this halogen bonding example allow for increased orbital mixing (σ orbital mixing shown for R–X donor in Figure 1.15b). These charge‐transfer adducts often result in lengthening of the RX or RH bond, which was highlighted in an early theoretical study of halogen bonding complexes between dihalogens (including interhalogens) and Lewis bases [150]. Here, elongation of the halogen–halogen bond is largest in the strongest complexes, up to 0.065 Å in the FBr⋯NH3 complexes. The study also demonstrated that the most polarizable halogens, and the interhalogens (FBr, FCl, etc.) with the biggest dipole, resulted in the largest interaction energies. Other studies have revealed that charge transfer can be a significant factor in organic halogen bond systems as well. One example evaluated complexes of bromocarbons (e.g. CBr3F, CBr3NO2, CBr3COCBr3, CBr3CONH2, Br3CCN) with anions (Br–, N3–, NCO–,