# A Simple Model for Halogen Bond Interaction Energies

^{*}

## Abstract

**:**

## 1. Introduction

^{−}⋯B

^{+}[54], suggesting an extreme form of polarization. It is also true that dispersion, which is the purely quantum mechanical interaction due to the instantaneous fluctuations of electrons, can be formally derived from polarizabilities. Exchange-repulsion is somewhat distinct but necessarily contaminates all other terms. This does not mean that such decompositions are meaningless, but rather that they should be treated with caution. It is sensible to distinguish “local” polarization and charge transfer, as this allows for a simple descriptor of when certain systems may behave substantially differently and uses an idea that is well-established within both the experimental and theoretical communities. The local distinction in this context simply refers to distortions and anisotropies in the electron density of a molecule constrained primarily to said molecule, as opposed to distortions effected by the surrounding environment resulting in substantial transfer of density away from the original molecule. Several examples of such unusually strong interactions have been reported [45,46,55,56,57,58], and there has been experimental evidence for charge transfer, from both rotational [12,59] and X-ray absorption [60] spectroscopy.

_{2}O⋯HCl. Tests of this model showed remarkably small deviations from experiment of less than 0.5 kcal mol${}^{-1}$ in many cases, although unsurprisingly these errors increased upon extrapolation to new systems. More recent work has attempted to extend this approach to other types of non-covalent interaction, including halogen bonds [68,69]. Such a model would be ideal for halogen-bonded systems as it requires minimal effort. High-accuracy calculations or experiments would only be needed for a small number of “standard” systems before the parameters so determined could be used to quickly predict interaction strengths in new complexes.

## 2. Results and Discussion

_{2}O, CH

_{2}O, H

_{2}S, CH

_{2}S, HCN, and H

_{3}N, covering the most commonly found acceptor atoms (O, N, and S) in different environments.

_{2}, Cl

_{2}, and CF

_{3}X where X = Cl, Br, or I; crucially, the latter three are no longer diatomics. Similarly, the acceptors were larger, comprising methanol, ethene, oxirane, thiirane, and phosphine. Of particular note is the inclusion of a $\pi $-to-halogen bond, and a different acceptor atom in phosphorous. Complete basis set (CBS) limit CCSD(T)-F12b counterpoise-corrected interaction energies and geometries for all systems can be found in the Supplementary Materials (SM). In agreement with previous investigations [12,75], the interaction energies are found to be sensitive to small changes in geometries, and to the size of the basis set. In particular, correctly identifying the extent to which the AX bond length increases on complex formation is vital in accurately determining the interaction strength. Notably the geometries agree well with spectroscopic data where available, and the predictive rules of Legon [76].

#### 2.1. Model Fitting

#### 2.2. Principal Component Analysis

_{2}the value of ${X}_{i}$ becomes very small, which is consistent with F

_{2}forming weakly bound complexes with Lewis bases that arguably do not meet the established criteria for a halogen bond [35,49]. The ${B}_{j}$ parameters associated with the Lewis bases do not display any obvious trends; while harder bases (such as H

_{2}O) tend to have ${B}_{j}$ values that are smaller in magnitude than softer bases (such as H

_{2}S), there is no correlation between ${B}_{j}$ and the absolute hardness of Pearson [78,79] when the full set of Lewis bases considered is examined. It is perhaps unsurprising that we have been unable to find a correlation between the model parameters (${X}_{i}$ and ${B}_{j}$) and properties of the isolated monomers—the model has been fit to interacting complexes where a degree of polarization/perturbation of the charge distribution of a given monomer by its halogen bonding counterpart has taken place.

#### 2.3. Validation and Comparison with Other Methods

_{3}.

_{6}F

_{5}X with X = Cl, Br, and I. The interacting atom on the acceptors were the nitrogen in sulphoximine and the carbonyl oxygen on the amino acids; geometries can be found in the Supplementary Materials. The parameters for the model were determined with respect to the reference molecules at the same level of theory. Table 3 shows the results of these tests. Despite being extrapolated to calculations with different systems, not involving any of the original fitting data, the mean-absolute deviation is 0.49 kcal mol${}^{-1}$. The mean-absolute deviation of the $P4$ model from the M06-2X results across the fitting and validation sets is 0.48 kcal mol${}^{-1}$, suggesting that similar error levels have been maintained despite the significant increase in molecule size. The $P4$ model therefore represents a rapid and accurate approach to predicting the interaction energies of halogen-bonded systems.

#### 2.4. The Nature of the Halogen Bond

## 3. Materials and Methods

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The predicted versus true interaction energies for the linear (

**left**, Equation (2)) and $P0$ (

**right**, Equation (3)) models. In the former, a non-linear trend is seen, suggesting non-normality of errors. The gradient and adjusted ${\mathrm{R}}^{2}$ value of the line in the right-hand figure are 1.0 and 0.995, respectively. A perfect model would have unit gradient and zero intercept.

**Figure 3.**Violin plots of the error distributions of the $P4$ model, M06-2X/aVTZ, and $\omega $B97X-D/aVTZ, compared to CCSD(T)-F12b/CBS results. The model is split into data from the fitting (Fit.) and validation (Val.) sets. The shape of the violin shows where the density of errors is concentrated—i.e., the frequency with which errors are found in a small interval—such that an ideal distribution would be a very short, wide density centered on the origin. Please note that the density is plotted symmetrically about the vertical axis, and the horizontal scale is relative (so it is the same for all the violins); the total area of a violin integrates to the number of points, the width representing a proportion of the total number. The individual data points have also been plotted, with a small amount of jitter added in the horizontal direction to aid visibility.

**Figure 4.**The error [relative to the CCSD(T)-F12b/CBS values] as a percentage of the overall interaction energy for the $P4$ model (

**a**) compared with the ratio of the dispersion (

**b**) and induction (

**c**) contributions to the electrostatic component of the symmetry-adapted perturbation theory of the energy.

**Figure 5.**Comparison of induction energy with the energy due to the second component in the principal component analysis, each as a percentage of the total interaction energy, averaged over all systems containing the given molecule in the fitting set. Most systems fall in the middle, but those with larger dispersion (bottom right) or induction (top left) show a marked increase in the importance of the second component to the predicted energy. Please note that the values for ClI overlap those of BrI, so we only show the latter for clarity.

**Table 1.**Summary statistics for the linear, $P0$, $k{R}_{\mathrm{e},ij}^{-6}$, and $P4$ models over the fitting set of 60 complexes. These include the root-mean-square, maximum, mean-signed, and mean-absolute errors in kcal mol${}^{-1}$.

Model | RMSE | Max. | MSE | MAE |
---|---|---|---|---|

Linear | 1.13 | 3.13 | 0.00 | 0.75 |

$P0$ | 0.30 | 0.68 | −0.01 | 0.24 |

$k{R}_{\mathrm{e}}^{-6}$ | 2.99 | 7.11 | 0.50 | 2.32 |

$P4$ | 0.14 | 0.41 | 0.00 | 0.11 |

**Table 2.**Selected parameters for halogen-bond donors and Lewis bases as fitted to the $P4$ model. The optimized value of c for this model is 3327.9474 kcal mol${}^{-1}$ Å${}^{4}$, all other parameters are dimensionless. A table of all parameters can be found in the Supplementary Materials.

Halogen-Bond Donor | ${\mathit{X}}_{\mathit{i}}$ | Lewis Base | ${\mathit{B}}_{\mathit{j}}$ |
---|---|---|---|

F_{2} | 0.0621 | H_{2}S | $-0.4643$ |

FCl | 0.2215 | CH_{2}O | $-0.3056$ |

FBr | 0.3306 | H_{3}N | $-0.4416$ |

FI | 0.4600 | H_{2}O | $-0.2947$ |

**Table 3.**The energies for each pair of new halogen-bond acceptor and donor at the M06-2X/aVTZ level, along with the energies predicted by the model, in kcal/mol.

Lewis Base | C_{6}F_{5}Cl | C_{6}F_{5}Br | C_{6}F_{5}I | |||
---|---|---|---|---|---|---|

M06 | Pred. | M06 | Pred. | M06 | Pred. | |

Sulphox. | $-3.32$ | $-4.06$ | $-4.61$ | $-4.95$ | $-5.96$ | $-6.48$ |

Glycine | $-2.49$ | $-3.14$ | $-3.66$ | $-3.83$ | $-5.18$ | $-5.01$ |

Valine | $-3.75$ | $-3.68$ | $-4.58$ | $-4.49$ | $-6.22$ | $-5.87$ |

Leucine | $-5.12$ | $-4.04$ | $-4.97$ | $-4.94$ | $-6.45$ | $-6.46$ |

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Shaw, R.A.; Hill, J.G.
A Simple Model for Halogen Bond Interaction Energies. *Inorganics* **2019**, *7*, 19.
https://doi.org/10.3390/inorganics7020019

**AMA Style**

Shaw RA, Hill JG.
A Simple Model for Halogen Bond Interaction Energies. *Inorganics*. 2019; 7(2):19.
https://doi.org/10.3390/inorganics7020019

**Chicago/Turabian Style**

Shaw, Robert A., and J. Grant Hill.
2019. "A Simple Model for Halogen Bond Interaction Energies" *Inorganics* 7, no. 2: 19.
https://doi.org/10.3390/inorganics7020019