On the Physical Nature of Halogen Bonds: A QTAIM Study - The

Article pubs.acs.org/JPCA

On the Physical Nature of Halogen Bonds: A QTAIM Study Olga A. Syzgantseva, Vincent Tognetti,* and Laurent Joubert Normandy Université, COBRA UMR 6014 and FR 3038, Université de Rouen, INSA Rouen, CNRS, 1 rue Tesniére, 76821 Mont Saint Aignan, Cedex, France S Supporting Information *

ABSTRACT: In this article, we report a detailed study on halogen bonds in complexes of CHCBr, CHCCl, CH2CHBr, FBr, FCl, and ClBr with a set of Lewis bases (NH3, OH2, SH2, OCH2, OH−, Br−). To obtain insight into the physical nature of these bonds, we extensively used Bader’s Quantum Theory of Atoms-in-Molecules (QTAIM). With this aim, in addition to the examination of the bond critical points properties, we apply Pendás’ Interacting Quantum Atoms (IQA) scheme, which enables rigorous and physical study of each interaction at work in the formation of the halogen-bonded complexes. In particular, the influence of primary and secondary interactions on the stability of the complexes is analyzed, and the roles of electrostatics and exchange are notably discussed and compared. Finally, relationships between QTAIM descriptors and binding energies are inspected. concept of their approach is the so-called “σ-hole”:50−55 this is a region of positive electrostatic potential on the outer side of the halogen atom, concentrated along the X···Y axis. Its presence is conditioned by the electronegativity of the halogen atom, by the degree of sp hybridization of its valence orbitals, and by the withdrawing force of the group to which the halogen atom is bound. In addition to this electrostatic viewpoint, the σ-hole can also be visualized through density Laplacian maps, appearing as a domain of charge depletion (∇2ρ > 0) at the outer part of halogen atoms.56−59 The formation of the halogen bond is then simply explained by the electrostatic interaction between the region of this positive electrostatic potential (whose size controls the bond strength) and the negative one (facing the halogen) that is generated by the Y lone pairs, the high directionality being linked with the anisotropy of the electron density induced by the R−X bond, which limits the angular extension of the σ-hole. The nature of halogen bonds was investigated as well from a molecular orbital perspective, especially using the NBO formalism, as done by Grabowski and others.60−64 Complementarily, the interaction was characterized using Bader’s Atoms-in-Molecules theory (QTAIM),65,66 principally looking at the main properties (density, Laplacian and energy density values) at the X···Y bond critical points, which were shown to be highly correlated to the computed interaction energies.67−71 Another way of describing such bonds has been provided by Michalak72,73 and co-workers using the ETS-NOCV approach that allows visualizing the formation of the σ-hole and decomposing the interaction energy into various energetic

1. INTRODUCTION Halogen bonds1−5 are ubiquitous in chemistry and play an important role in biological systems6−11 for ligand binding, molecular folding, and recognition and are important in a tremendous variety of applications12 ranging from, among others, drug design,13 supramolecular chemistry and crystal engineering,14−21 liquid crystals,22 and polymers.23,24 They have been experimentally characterized by UV−vis,25 rotational,26−28 NMR29,30 and Raman spectroscopies,31 molecular beam scattering,32 and X-ray crystallography.33 All these data led to the identification of several common features for all observed halogen bonds. Actually, according to the IUPAC provisional recommendation, “a halogen bond R−X···Y−Z occurs when there is evidence of a net attractive interaction between an electrophilic region on a halogen atom X belonging to a molecule or a molecular fragment R−X (where R can be another atom, including X, or a group of atoms) and a nucleophilic region of a molecule, or molecular fragment Y−Z”34 and is usually described as a highly directional noncovalent interaction.35 It is worth mentioning that such a definition could be extended to include rare gases as nucleophilic moieties,36 and that unconventional or novel types of halogen bonds are still regularly revealed.37−39 Finally, the proximity of halogen bonds to other noncovalent bonds such as those of chalcogens and pnicogens deserves to be mentioned,40−43 for which the σ-hole concept also fruitfully applies. Thus, owing to the ubiquity and chemical importance of these bonds, many theoretical studies have been published in order to quantify their energy44,45 and to explore their nature. Noteworthy are Politzer and co-workers who have recently reviewed the main theoretical findings accounting for the formation and the stability of such bonds.46−49 The key © XXXX American Chemical Society

Received: June 17, 2013 Revised: July 28, 2013

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dx.doi.org/10.1021/jp4059774 | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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contributions. As an alternative, Allen and co-workers performed an IMPT analysis,74 whereas other groups60,75−79 advocated the use of the SAPT, Morokuma’s, or NEDA schemes. Otherwise, Romaniello and Lelj performed a Ziegler− Rauk decomposition within their relativistic calculations.80 A similar approach was implemented by Pinter et al.,81 who promisingly used conceptual DFT to gain further insight into the bond formation. Obviously, all of these approaches can and were already used in conjunction, as they are not excluding one from another, each of them bringing a useful piece of information that contributes to reveal the physical ingredients that account for the formation and the stability of halogen bonds. Nevertheless, from our viewpoint and despite these substantial advances, some issues are still to be clarified, in particular the role of the local environment and the physical nature of the interaction without referring to (possibly) arbitrary references. We think that the interacting quantum atoms (IQA) framework, developed by Pendás and coworkers,82−85 constitutes an appropriate tool to answer these questions. Indeed, it notably allows decomposing the total energy of the system into intra-atomic and inter-atomic contributions, from which the pure nonbiased inter-fragment interaction energy can be calculated. Moreover, within the same approach one can discriminate classical Coulombic electrostatic and exchange-correlation contributions. Such an approach was fruitfully applied to discuss the nature of intermolecular hydrogen bonds86 and intramolecular interactions between electronegative atoms,87 and thus, we expect it to be relevant for casting some light on the nature of halogen bonds. We now discuss the choice of the studied systems. It should be noted that halogen bonds in particular are theoretically extensively studied on small model complexes, which allow the use of post Hartree−Fock methods (with extended basis sets), such as MP2 or CCSD(T).88−96 As IQA calculations are computationally expensive (since they involve the numerical evaluation of six-dimensional [6D] integrals), we will only focus on small molecules of the RX···D type (where R = CHC−, CH2CH−, F, Cl ; X = Cl, Br ; D = NH3, OH2, OCH2, SH2, OH−, Br−), forming a set of 30 representative complexes. As they feature various types of halogenated species (dihalogen and hydrocarbon) and a wide range of Lewis bases, they may be convenient to elucidate the nature of the interactions and the role of the local environment. We note also that, for most of these systems, quantum mechanical and topological characterizations were previously reported.56,57,66,88,90,91,93,95,97 We also intentionally excluded fluorine and iodine complexes. Indeed, it was formerly believed that no halogen bond can be created with fluorine. However, evidence was recently found that, when fluorine is connected to a very strong but very particular electron acceptor, a σ-hole may appear.98,99 As for iodine, the treatment is constrained by the core−electron description with a pseudopotential, so that the comparison on equal footing with all-electron basis sets is not possible. Finally, it must be emphasized that less “conventional” halogen bonds exist where the role of the Lewis base is played by π-electrons (for instance of acetylene) or by hydrides.100 However, such bonds are outside the scope of this paper.

(including empirical correction for dispersion of the Grimme’s type102) and Dunning aug-cc-pVTZ augmented triple-ζ basis set. Geometry optimizations and frequency calculations were carried out with the Gaussian 09 program,103 all minima being characterized by the absence of imaginary frequencies. Binding energy is considered with respect to unrelaxed fragments F1 and F2 in the geometry of the F1···F2 complex: bind ESCF = E(F1 ... F2) − E(F1) − E(F2)

(1)

Basis set superposition errors were evaluated using Boys and Bernardi’s counterpoise scheme.104 The highest obtained values for the molecular set do not exceed 0.4 kcal/mol and are less than 6% of the binding energy, so that they were not included in Ebind SCF. To benchmark ωB97XD binding energies, full MP2 calculations (including MP2 geometry optimizations) were carried out. Note that it is clearly outside the scope of this paper to assess in more detail this computational protocol. We refer the interested reader to the recent papers by Kozuch and Martin105 who showed that ωB97XD is among the most suitable functionals for the study of halogen bonds, and by Bankiewicz and Palusiak106 for extensive studies on this point. We also underline that only gas-phase SCF energies will be used, without zero-point energy corrections. We refer the reader to the stimulating paper by Murray and Politzer about the role of temperature and entropy to account for the experimental stability of halogen-bonded complexes.107 In addition, the role of solvent (modeled by a polarizable continuum) was recently theoretically investigated by Lu et al.108 and Forni et al.109 All QTAIM calculations were performed using the AIMAll Professional package for topological analysis.110 The “Proaim” basin integration method using “superfine” interatomic surface mesh and “superhigh Lebedev” outer angular quadrature was applied, and the accuracy of basin integrations was monitored by checking the atomic (integrated) Laplacian values. In the IQA framework, the energy is decomposed into intraatomic contributions (EAIQA) and pair interactions (EAB IQA). This can be rigorously done because Bader’s atomic basins do not overlap and fully partition real space. EAB IQA can be expressed as AB the sum of electron−nuclear (EAB en ), nuclear−nuclear (Enn ), and AB electron−electron (Eee ) interaction energies: AB AB AB E IQA = Enn + EenAB + Ene + EeeAB

(2)

AB Eee

can further be exactly decomposed into classical electrostatic interaction (EAB ee,cl) and into quantum exchange AB and correlation contributions (EAB ee,x,Eee,c): AB AB AB EeeAB = Eee,cl + Eee, x + Eee,c

(3)

The total “classical” electrostatic interaction energy is then defined by: AB AB AB EclAB = Enn + EenAB + Ene + Eee, cl

(4)

Using IQA energy decomposition, we can estimate the interaction energy between fragments F1 and F2 inside the F1···F2 complex, once it is formed: inter E IQA =

∑ ∑ A ∈ F1 B ∈ F2

2. COMPUTATIONAL DETAILS All complexes were studied within density functional theory, using the range-separated hybrid functional ωB97XD101

AB E IQA

(5)

This quantity is a pure measure of interaction between F1 and F2 as it excludes the use of any reference. B



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Table 1. Binding (bind) and Interaction (inter) Energies (in kcal/mol) for All 30 Studied Systems (see main text for definition)

a

cmpd

Ebind DFT

Ebind MP2

Ebind IQA

Einter IQA

Einter disp

% dispa

ΔEatoms IQA

ΔEinteractions IQA

CHCBr···NH3 CHCBr···OH2 CHCBr···SH2 CHCBr···OH− CHCBr···OCH2 CHCCl···NH3 CHCCl···OH2 CHCCl···SH2 CHCCl···OH− CHCCl···OCH2 CH2CHBr···NH3 CH2CHBr···OH2 CH2CHBr···SH2 CH2CHBr···OH− CH2CHBr···OCH2 FBr···NH3 FBr···OH2 FBr···SH2 FBr···OH− FBr···Br− FCl···NH3 FCl···OH2 FCl···SH2 FCl···OH− FCl···Br− ClBr···NH3 ClBr···OH2 ClBr···SH2 ClBr···OH− ClBr···Br−

−3.9 −2.5 −1.7 −30.3 −2.5 −2.2 −1.4 −0.9 −15.9 −1.5 −1.6 −1.2 −1.0 −14.3 −1.4 −16.2 −7.6 −8.2 −83.2 −42.2 −12.3 −5.2 −5.5 −85.9 −41.2 −9.3 −4.4 −4.2 −89.6 −41.4

−4.6 −3.4 −2.8 −30.2 −3.9 −2.7 −2.2 −1.8 −16.0 −2.6 −2.2 −1.7 −2.0 −14.9 −2.7 −18.3 −8.5 −10.3 −82.1 −46.9 −13.6 −5.7 −6.7 −81.4 −46.8 −11.0 −5.4 −6.0 −83.4 −45.4

−2.5 −2.2 −2.3 −25.7 −2.1 −1.9 −1.2 −2.2 −11.0 −2.6 −1.6 −0.8 −3.5 −10.4 −2.4 −9.8 −4.3 −2.6 −85.4 −33.6 −2.5 −1.9 −0.2 −86.0 −29.3 −3.5 −1.9 −1.7 −93.5 −33.9

−21.8 −16.4 −13.8 −99.5 −17.4 −14.8 −10.2 −8.6 −60.6 −12.4 −15.6 −10.2 −11.1 −73.0 −13.0 −77.3 −41.4 −52.0 −161.0 −87.3 −69.9 −33.4 −42.1 −156.2 −90.1 −52.3 −27.0 −31.2 −173.2 −91.5

−0.6 −0.4 −0.4 −0.2 −0.5 −0.4 −0.3 −0.3 −0.2 −0.5 −0.5 −0.5 −0.5 −0.2 −0.6 −0.5 −0.4 −0.4 −0.1 −0.1 −0.4 −0.3 −0.4 −0.1 −0.1 −0.6 −0.4 −0.4 −0.1 −0.2

14 16 24 1 22 20 22 34 1 33 33 42 50 2 44 3 5 5 0 0 3 6 7 0 0 6 9 10 0 0

27.5 22.9 10.4 62.6 17.7 16.6 13.2 5.6 52.3 9.8 18.9 12.5 6.9 82.6 10.7 63.4 43.6 28.7 54.0 30.4 56.2 34.8 26.0 30.7 33.3 49.7 31.4 20.4 59.2 39.1

−8.2 −8.7 1.1 11.3 −2.4 −3.7 −4.2 0.8 −2.7 0.0 −4.9 −3.1 0.7 −20.0 −0.1 4.1 −6.5 20.7 21.6 23.4 11.2 −3.3 15.8 39.6 27.4 −0.9 −6.3 9.2 20.5 18.5

bind % disp = 100Einter disp /EDFT.

the interaction energy between the two atoms linked by the bond path between the two interacting fragments. We stress that, up to now, all formulas are fully exact, no approximation having been made. However, in practice, we use an approximate electron density and an approximate wave bind function (so that Ebind IQA might slightly differ from ESCF). We refer the reader to ref 87 for a detailed discussion on the specific use of IQA in a DFT context. On the top of that, dispersion effects are mainly described by Grimme’s pair potential correction that depends only on the nuclei position and not on the electron density (this contribution is thus not taken into account by AIMAll). We can thereby estimate the dispersion weight into interaction energy according to:

Finally, one can evaluate the energy associated with the formation of the complex. This energy can be decomposed into three main contributions. When the complex is formed, the energy of each fragment is changed for two reasons: the energy of each atom within the fragment is modified, and the interaction energies between each atom pairs inside the fragment also vary. For instance, for fragment F1, these two terms can be calculated following: atomsF1 ΔE IQA =

A [E IQA (A in F1···F2)

∑ A ∈ F1

A − E IQA (A in isolated F1)] interactionsF1 ΔE IQA =

(6)

1 AA ′ (A , A′ in F1···F2) ∑ ∑ [EIQA 2 A ∈ F1 {A ′∈ F1} ≠ A AA ′ (A , A′ in isolated F1)] − E IQA

inter Edisp =

(7)

∑ ∑ A ∈ F1 B ∈ F2

In addition to the variation of the energy of the two fragments, one has to add the interaction between them when the complex is formed, so that the total energy change when F1···F2 is created reads:

AB Edisp

(9)

We expect Einter disp to be slightly lower (in absolute value) than the exact dispersion energy as exchange functionals can include spurious attraction.111 In the following, we refer to the halogen atom X and the electronegative atom of the Lewis base as “main atoms”. The secondary atoms are all other atoms of the complex. Consequently, the primary interaction is the interaction between main atoms, the secondary interactions correspond to any other.

Note that we do not use the phrase “halogen bond energy” (favoring “binding”) as it contains some ambiguity: in the strictest sense “halogen bond” should be preferred to refer to C



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(Ebind DFT) for CHCCl···OCH2, and up to 50% for CH2CHBr··· SH2. Qualitatively, the stronger the binding, the lower the dispersion contribution. Quantitatively, a linear fit gives the following predictive model (R2 = 0.94):

3. RESULTS AND DISCUSSION 3.1. Geometries. Geometrical features of halogen-bonded systems have been extensively discussed in detail by many research groups, and thus, we mention here only our observed general trends (see Figure S1 in the Supporting Information [SI]). The measured bond lengths lie in the 2.3−3.0 Å range, although those in FX···OH− and ClBr···OH− are much shorter: ∼1.8−1.9 Å. The bond angles are close to 180°, corroborating the high directionality of the bond, with the exception of complexes formed by OCH2, for which it belongs to the 160− 170° range. 3.2. Global Energetic Properties. The values for Ebind SCF are typically about 1−10 kcal/mol for neutral systems (see Table 1), while they are around 14−30 kcal/mol for anionic cases involving alkyls substituents and 40−90 kcal/mol in anionic cases involving FX species. These results definitively prove that halogen bonds are not necessarily weak bonds. For the CHCBr, CHCCl, CH2CHBr, and ClBr groups, one has the following ranking (in increasing absolute binding energies): SH2 < OCH2 ≈ OH2 < NH3 ≪ OH−. For the FBr and FCl families, we note a slight inversion, SH2 giving a stronger interaction than OH2, but the differences are very small. Given all these results, the following common trend, regarding the role of the Lewis base, is: SH 2 ≈ OCH 2 ≈ OH 2 < NH3 <
OH2 > OCH2. In dihalogen complexes, the tendency is similar: OH− > Br− > NH3 > SH2 > OH2, while |ΔqCT| attains 0.5e value for anionic ones. As expected,

Figure 4. Values of the η (red curve) and λ (blue curve) ratios (see text for definition) for all complexes.

ratio. Importantly, it is always higher than 0.29, proving that exchange can never be neglected in order to evaluate the strength of the primary interaction. In eight cases (representing 27% of the cases), η > 1, so that exchange becomes the major contribution. Note that the exchange interaction between these atoms is closely related to the delocalization index between them (see Graph S1 in SI, R2 = 0.98): Exprimary (kcal/mol) = 4.3 − 128.0DIprimary

(14)

(13)

It can be seen that this result can be theoretically justified.87,120 One can now determine if Eprimary is correlated with Ebind IQA IQA . A linear fit proves that it is not true (R2 = 0.76). This paradox can be solved by invoking the role of secondary interactions. More precisely, it appears that, in most cases, the total secondary interactions (which are mainly of electrostatic nature, see Table S1 in SI) are repulsive (with a mean value equal to 18.2 kcal/mol and a maximal one equal to 71.7 kcal/mol) and thus decrease the total interaction energy. The only exceptions are all complexes involving SH2 as Lewis base (in this case, the G



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the softer the Lewis base, the easier the charge transfer toward the electron acceptor halogenated moiety. As for the accepting species, CT is stronger toward CHCBr than CHCCl or CH2CHBr, which both share main characteristics. For dihalogen electron acceptors, CT characteristics are similar, being slightly lower in ClBr neutral complexes. One can wonder whether this charge transfer is correlated to the binding energy. It appears that it is absolutely not the case (R2 < 0.1). For instance, for CHCBr···NH3 and FBr···NH3, the values for Ebind IQA are similar (−2.5 kcal/mol), but the charge transfers between the two fragments are considerably different (respectively 0.03 and 0.16e). 3.6. Bond Critical Points Properties for the Primary Interaction. Investigating the main properties of the bond critical point (BCP) between the two fragments is the most widespread QTAIM approach for the study of halogen bonds. To this aim, the following BCP descriptors were considered: the electron density value, ρc; BCP density Laplacian value, ∇2ρc; and the BCP energy density, Hc. The corresponding data are presented in Table S2 in SI. Their tendencies throughout the series are in good agreement with previously published results.56,57,67,91,93,95 According to the relatively low values of BCP electron densities and the positive sign of density Laplacians, halogen bonds for all neutral complexes can be classified as “closedshell” bonds. For the strongest bonds (FX···NH3, FX···Br−, FX···SH2, FX···OH−, ClBr···NH3, ClBr···OH−, CH2CHBr··· OH−) the energy density (Hc) is negative, reflecting the increase in covalent character.122 The value of the BCP electron density can be decomposed into atomic contributions to characterize the role of each atom, thanks to the Source Function SΩ,123 which allows evaluation of the contribution of each atom to the given BCP density value, according to eq 15:

Figure 5. Relative contributions of main % Smain (filled blue diamonds) and secondary % Ssecondary (open red squares) atoms as a function of the BCP electron density ρc. 2 2 inter that Ebind DFT and EIQA are correlated with ρc (R = 0.96 and R = 0.99, respectively) according to:

inter E IQA (kcal/mol) = −1324.4ρc (au) − 2.2

(16)

Then, we assess to what extent this model is accurate to predict energies that are outside the range used to build it; as shown in Figure 6, it allows a nice prediction of Einter IQA for the

When a basin has a negative contribution, it is called a sink and tends to withdraw electrons at the BCP position. Conversely, if it is positive, it is called a source. In practice,124,125 percentages are more commonly used since they are easier to compare. As can be inferred from Figure S3 in SI, in hydrocarbon complexes (with the exception of CHCBr··· OH2) all electronegative Lewis base atoms (N, O, S) act as sinks. Meanwhile, this withdrawing effect is largely compensated by positive contributions of hydrogen (NH3, H2O) or carbon atoms (OCH2) of the Lewis base. Halogen atoms are another significant source for electron density. In contrast to it, in dihalogen complexes, major contributions are given both by the halogen atom and the electronegative atom of the Lewis base. For neutral complexes, the highest source percentage comes from X. In all anionic complexes the major part of ρc is brought by X and D atoms, which align with the more covalent character of the X−D bond. In contrast, for weak densities, the contribution of the main atoms becomes negligible or even negative. As it clearly appears in Figure 5, the source percentages of the main atoms increase with ρc, while the contributions of the secondary atoms decrease with it. We now check to see if these local descriptors can give insight into the global energetics of these halogen-bonded systems. We first only consider neutral complexes. It turns out

Figure 6. Correlation between the IQA interaction energy Einter IQA and BCP electron density ρc; 21 points (neutral complexes) are used to construct the regression line. Points for anionic complexes are shown in red.

anionic systems (see Figure 6). This definitely proves the robustness of such a model. On the contrary, no correlation is observed between ∇2ρc or 2 inter Hc, and Ebind DFT or EIQA (R < 0.90, as shown in Graphs S2 and S3 in SI). 3.7. A Peculiar Topology. CH2CHBr···OCH2 displays a particular molecular graph (Figure 7): an additional bond path appears between the halogen atom and one of the hydrogens (Br6−H8). As a consequence of the Poincaré−Hopf theorem, a ring critical point also appears, defining the BrOCH fourmembered ring. This can be justified using the exchange channel concept,126 in the spirit of our recent work on intramolecular bonds between electronegative atoms.87 Indeed, the exchange energy between Br and this hydrogen atom is equal to −2.5 kcal/mol. In order to determine whether a BCP is present between them, one has to determine if the closest secondary exchange channels are competitive. These H



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Figure 7. Energy decomposition for CH2CHBr···OCH2 complex (classical electrostatic counterpart in blue italics, exchange counterpart in plain green).

channels are the ones between Br and C7, and between H8 and C4. The corresponding exchange interaction energies are respectively equal to −1.1 kcal/mol and −0.04 kcal/mol. As these values are lower in absolute value than the ones for the Br···H interaction, this last one thus features a BCP. Note that this also justifies the fact that a BCP between Br and O is located: the corresponding exchange energy is equal to −5.3 kcal/mol, considerably stronger than the secondary Br···C7 one. As alluded to in ref 87, such an analysis can be equivalently performed on the basis of delocalization indexes: the one between Br and C7 (0.01) is inferior to the ones between both Br and H8 (0.03) and Br and O (0.06). In addition, it must be emphasized that the inspection of total IQA interaction energies competition, instead of the sole exchange counterpart, would lead to an erroneous topology. Indeed, the interaction between Br and C7 is much more stabilizing (−7.2 kcal/mol) than the one between Br and H8 (−2.8 kcal/mol), because the classical electrostatic interaction is almost zero for the latter one (−0.3 kcal/mol), whereas it amounts to −6.1 kcal/mol for the first one. This can be rationalized by noting that bromine is slightly negatively charged (−0.07 e), while C7 is considerably more positive (1.07 e) than H8 (0.03 e). Such an observation is another example that exchange is the key energetic component to account for the observed topologies. These observations are quite important for the understanding of halogen bonding in biological systems, as formaldehyde-like fragments exist in proteins. Indeed, they suggest that the attraction between the >CO fragment and the Br atom is the result of an ensemble of stabilizing interactions, implicating not only the main atoms (Br and O). At short-range, the exchange interaction is important with subsequent electron sharing, while at long-range secondary electrostatic interactions contribute to the stabilization of this complex.

between them can occur, so that the total interaction energies can consequently vary from one system to another. In addition, in all cases the main atoms are destabilized, and this effect tends to dominate the variation of the interatomic energies inside the fragments when the complex is formed. Furthermore, dispersion is all the more important as the other interactions are weak, and it may be the main stability factor in the case of small binding energies. More generally, all these factors mean that IQA binding and interaction energies are not correlated; these two concepts must actually be considered as distinct and complementary. Finally, the analysis of the competition between exchange channels enables the recovery of the full topology. From our point of view, all of these findings constitute arguments to strengthen the incentive to foster the use of Bader’s theory to study halogen bonds.

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ASSOCIATED CONTENT

S Supporting Information *

Additional tables and graphs, figures with the views of all optimized complexes. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The CRIHAN (Centre de Ressources Informatiques de HauteNormandie) computational center is gratefully acknowledged for providing HPC resources. We also thank the Centre National de la Recherche Scientifique (CNRS) for a “Chaire d’Excellence” at the University of Rouen.

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4. CONCLUSIONS In this contribution, halogen bonding was investigated using QTAIM local indexes and the IQA energy decomposition scheme. The primary interaction was shown always to be stabilizing and, in general but not systematically, electrostatically attractive. Importantly, the quantum exchange counterpart in the interaction between the main atoms can never be neglected and may constitute the dominant contribution at the equilibrium geometry (while electrostatics dominates when the reactants are remote enough). However, the overall energy of this primary interaction cannot be used to predict the total interaction energy between the two fragments because of the possible considerable secondary interactions. These last ones were essentially proved to be of classical electrostatic nature and are, in general, destabilizing. However, compensations

REFERENCES

(1) Metrangolo, P., Resnati, G., Eds. Halogen Bonding: Fundamentals and Applications, Structure and Bonding; Structure and Bonding, No. 126; Springer: Berlin, 2008. (2) Metrangolo, P.; Pilati, R.; Resnati, G. Halogen Bonding and Other Noncovalent Interactions Involving Halogens: A Terminology Issue. CrystEngComm 2006, 8, 946−947. (3) Metrangolo, P.; Resnati, G. Halogen Bonding: Where We Are and Where We Are Going. Cryst. Growth Des. 2012, 12, 5835−5838. (4) Legon, A. C. The Halogen Bond: An Interim Perspective. Phys. Chem. Chem. Phys. 2010, 12, 7736−7747. (5) Fourmigué, M. Halogen Bonding: Recent Advances. Curr. Opin. Solid State Mater. Sci 2009, 13, 36−45. (6) Parisini, E.; Metrangolo, P.; Pilati, T.; Resnati, G.; Terraneo, G. Halogen Bonding in Halocarbon-Protein Complexes: A Structural Survey. Chem. Soc. Rev. 2011, 40, 2267−2278. I



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Broadband Rotational Spectroscopy. Phys. Chem. Chem. Phys. 2011, 13, 20736−20744. (28) Stephens, S. L.; Mizukami, W.; Tew, D. P.; Walker, N. R.; Legon, A. C. The Halogen Bond Between Ethene and a Simple Perfluoroiodoalkane: C2H4···ICF3 Identified by Broadband Rotational Spectroscopy. J. Mol. Spectrosc. 2012, 280, 47−53. (29) Weingarth, M.; Raouafi, N.; Jouvelet, B.; Duma, L.; Bodenhausen, G.; Boujlel, K.; Scöllhorn, B.; Tekley, P. Revealing Molecular Self-Assembly and Geometry of Non-Covalent Halogen Bonding by Solid-State NMR Spectroscopy. Chem. Commun. 2008, 45, 5981−5983. (30) Chudzinski, M. G.; McClary, C. A.; Taylor, M. S. Anion Receptors Composed of Hydrogen- and Halogen-Bond Donor Groups: Modulating Selectivity with Combinations of Distinct Noncovalent Interactions. J. Am. Chem. Soc. 2011, 133, 10559−10567. (31) Hauchecorne, D.; Szostak, R.; Herrebout, W. A.; van der Vekken, B. J. CX···O Halogen Bonding: Interactions of Trifluoromethyl Halides with Dimethyl Ether. ChemPhysChem 2009, 10, 2105− 2115. (32) Cappelletti, D.; Candori, P.; Pirano, F.; Belpassi, L.; Tarantelli, F. Nature and Stability of Weak Halogen Bonds in the Gas Phase: Molecular Beam Scattering Experiments and ab Initio Charge Displacement Calculations. Cryst. Growth Des. 2011, 11, 4279−4283. (33) Hassel, O.; Hvoslef, J. The Structure of Bromine 1,4-Dioxanate. Acta Chem. Scand. 1954, 8, 873. (34) Desiraju, G. R.; Ho, P. S.; Kloo, L.; Legon, A. C.; Marquardt, R.; Metrangolo, P.; Politzer, P.; Resnati, G.; Rissanen, K. Definition of the Halogen Bond. Chem. Int. 2012, 34, http://media.iupac.org/reports/ provisional/abstract12/metrangolo_prs.pdf. (35) Politzer, P.; Murray, J. S.; Clark, T. Halogen Bonding: An Electrostatically-Driven Highly Directional Noncovalent Interaction. Phys. Chem. Chem. Phys. 2010, 12, 7748−7757. (36) Carter, M.; Shing, Ho, P. Assaying the Energies of Biological Halogen Bonds. Cryst. Growth Des. 2011, 11, 5087−5095. (37) Hauchecome, D.; van der Veken, B. J.; Herrebout, W. A.; Hansen, P. E. A 19F NMR Study of C−I···π Halogen Bonding. Chem. Phys. 2011, 381, 5−10. (38) Gushchin, P. V.; Kuznetsov, M. L.; Haukka, M.; Kukushkin, V. Y. Recognition of a Novel Type X = N−Hal···Hal (X = C, S, P; Hal = F, Cl, Br, I) Halogen Bonding. J. Phys. Chem. A 2013, 117, 2827−2834. (39) Johansson, M. P.; Swart, M. Intramolecular Halogen-Halogen Bonds. Phys. Chem. Chem. Phys. 2013, 15, 11543−11553. (40) Wang, W.; Ji, B.; Zhang, Y. Chalcogen Bond: A Sister Noncovalent Bond to Halogen Bond. J. Phys. Chem. A 2009, 113, 8132−8135. (41) Scheiner, S. The Pnicogen Bond: its Relation to Hydrogen, Halogen, and Other Noncovalent Bonds. Acc. Chem. Res. 2013, 46, 280−288. (42) Bauzá, B.; Quiñonero, D.; Deyá, P. M.; Fontrera, A. Halogen Bonding versus Chalcogen and Pnicogen Bonding: A Combined Cambridge Structural Database and Theoretical Study. CrystEngComm 2013, 15, 3137−3144. (43) Scheiner, S. Sensitivity of Noncovalent Bonds to Intermolecular Separation: Hydrogen, Halogen, Chalcogen, and Pnicogen Bonds. CrystEngComm 2013, 15, 3119−3124. (44) McAllister, L. J.; Bruce, D. W.; Karadakov, P. B. Quantum Chemical Investigation of Attractive Non-Covalent Interactions Between Halomethanes and Rare Gases. J. Phys. Chem. A 2012, 116, 10621−10628. (45) Riley, K. E.; Hobza, P. Strength and Character of Halogen Bonds in Protein−Ligand Complexes. Cryst. Growth Des. 2011, 11, 4272−4278. (46) Politzer, P.; Lane, P.; Concha, M. C.; Ma, Y.; Murray, J. S. An Overview of Halogen Bonding. J. Mol. Model. 2007, 13, 305−311. (47) Politzer, P.; Riley, K. E.; Bulat, F. A.; Murray, J. S. Perspectives on Halogen Bonding and Other σ-Hole Interactions: lex parsimoniae (Occam’s Razor). Comput. Theor. Chem. 2012, 998, 2−8. (48) Politzer, P.; Murray, J. S. Halogen Bonding: An Interim Discussion. ChemPhysChem 2013, 14, 278−294.

(7) Lu, Y.; Wang, Y.; Zhu, W. Nonbonding Interactions of Organic Halogens in Biological Systems: Implications for Drug Discovery and Biomolecular Design. Phys. Chem. Chem. Phys. 2010, 12, 4543−4551. (8) Auffinger, P.; Hays, F. A.; Westhof, E.; Ho, S. Halogen Bonds in Biological Molecules. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 16789− 167945. (9) Hardegger, L.-A.; Kuhn, B.; Spinnler, B.; Anselm, L.; Ecabert, R.; Stihle, M.; Gsell, B.; Thoma, R.; Diez, J.; Benz, J.; Plancher, J.-M.; Hartmann, G.; Banner, D. W.; Haap, W.; Diederich, F. Systematic Investigation of Halogen Bonding in Protein-Ligand Interactions. Angew. Chem., Int. Ed. 2011, 50, 314−318. (10) Jentzsch, A. V.; Matile, S. Transmembrane Halogen-Bonding Cascades. J. Am. Chem. Soc. 2013, 135, 5302−5303. (11) Wilcken, R.; Zimmermann, M. O.; Lange, A.; Joerger, A. C.; Boeckler, F. M. Principles and Applications of Halogen Bonding in Medicinal Chemistry and Chemical Biology. J. Med. Chem. 2013, 56, 1363−1388. (12) Meyer, F.; Dubois, P. Halogen Bonding at Work: Recent Applications in Synthetic Chemistry and Materials Science. CrystEngComm 2013, 15, 3058−3071. (13) Lu, Y.; Shi, T.; Wang, Y.; Yang, H.; Yan, X.; Luo, X.; Jiang, H.; Zhu, W. Halogen BondingA Novel Interaction for Rational Drug Design? J. Med. Chem. 2009, 52, 2854−2862. (14) Metrangolo, P.; Resnati, G.; Pilati, T.; Biella, S. Halogen Bonding in Crystal Engineering. Struct. Bonding (Berlin) 2008, 126, 105−136. (15) Metrangolo, P.; Meyer, F.; Pilati, T.; Resnati, G.; Terraneo, G. Halogen Bonding in Supramolecular Chemistry. Angew. Chem., Int. Ed. 2008, 47, 6114−6127. (16) Metrangolo, P.; Resnati, G. Halogen Bonding: A Paradigm in Supramolecular Chemistry. Chem.Eur. J. 2001, 7, 2511−2519. (17) Voth, A. R.; Hays, F. A.; Ho, P. S. Directing Macromolecular Conformation through Halogen Bonds. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 6188−6193. (18) Vidal, F.; Dávila, M. A.; Torcuato, A. S.; Gómez-Sal, P.; Mosquera, M. E. Functionalized Imido-Bridged Ti(IV) Complexes As New Building Blocks for Supramolecular Arrangements: Generation of a 1D Structure through a Mg-Cl···I-C Halogen Bonding Interaction. Dalton Trans. 2013, 42, 7074−7084. (19) Metrangolo, P. ; Resnati, G. ; Pilati, T. ; Biella, S. In Halogen Bonding: Fundamentals and Applications: Metrangolo, P., Resnati, G., Eds.; Springer: Berlin, 2008; pp 105−136. (20) Abate, A.; Biella, S.; Cavallo, G.; Meyer, F.; Neukirch, H.; Metrangolo, P.; Pilati, T.; Resnati, G.; Terraneo, G. Halide Anions Driven Self-Assembly of Haloperfluoroarenes: Formation of OneDimensional Non-Covalent Copolymers. J. Fluorine Chem. 2009, 130, 1171−1177. (21) Minguez Espallargas, G.; Zordan, F.; Arroyo Marin, L.; Adams, H.; Shankland, K.; van de Streek, J.; Brammer, L. Rational Modification of the Hierarchy of Intermolecular Interactions in Molecular Crystal Structures by Using Tunable Halogen Bonds. Chem.−Eur. J. 2009, 15, 7554−7568. (22) Nguyen, H. L.; Horton, P. N.; Hursthouse, M. B.; Legon, A. C.; Bruce, D. W. Halogen Bonding: A New Interaction for Liquid Crystal Formation. J. Am. Chem. Soc. 2004, 126, 16−17. (23) Lauher, J. W.; Fowler, F. W.; Goroff, N. S. Single-Crystal-toSingle-Crystal Topochemical Polymerizations by Design. Acc. Chem. Res. 2008, 41, 1215−1229. (24) Goroff, N. S.; Luo, L.; Wilhelm, C.; Sun, A.; Webb, J. A. Halogen-Bond-Driven Assembly of Polyynes for Topochemical Polymerization. Abstracts of Papers; 238th ACS National Meeting, Washington, DC, United States, August 16−20, 2009. (25) Benesi, H. A.; Hildebrand, J. H. Ultraviolet Absorption Bands of Iodine in Aromatic Hydrocarbons. J. Am. Chem. Soc. 1948, 70, 2832− 2833. (26) Novick, S. E.; Janda, K. C.; Klemperer, W. HFClF: Structure and Bonding. J. Chem. Phys. 1976, 65, 5115−5121. (27) Stephens, S. L.; Walker, N. R; Legon, A. C. Internal Rotation and Halogen Bonds in CF3I···NH3 and CF3I···N(CH3)3 Probed by J



Article

(49) Politzer, P.; Murray, J. S. Halogen Bonding and Beyond: Factors Influencing the Nature of CN-R and SiN-R Complexes with F-Cl and Cl2. Theor. Chem. Acc. 2012, 131, 1114. (50) Clark, T.; Hennemann, M.; Murray, J. S.; Politzer, P. Halogen Bonding: The Sigma-Hole. J. Mol. Model. 2007, 13, 291−296. (51) Brinck, T.; Murray, J. S.; Politzer, P. Surface Electrostatic Potentials of Halogenated Methanes As Indicators of Directional Intermolecular Interactions. Int. J. Quantum Chem. 1992, 44, 57−64. (52) Murray, J. S.; Lane, P.; Politzer, P. Expansion of the Sigma-Hole Concept. J. Mol. Model. 2009, 15, 723−729. (53) Murray, J. S.; Lane, P.; Clark, T.; Politzer, P. σ-Hole Bonding: Molecules Containing Group VI atoms. J. Mol. Model. 2007, 13, 1033−1038. (54) Hennemann, M.; Murray, J. S; Riley, K. E.; Politzer, P.; Clark, T. Polarization-Induced σ-Holes and Hydrogen Bonding. J. Mol. Model. 2012, 18, 2461−2469. (55) Clark, T. σ-Holes. WIRES Comp. Mol. Sci. 2013, 3, 13−20. (56) Amezaga, N. J. M.; Pamies, S. C.; Peruchena, N. M.; Sosa, G. L. Halogen Bonding: A Study Based on the Electronic Charge Density. J. Phys. Chem. A 2010, 114, 552−562. (57) Zhang, X.; Zeng, Y.; Li, X.; Meng, L.; Zheng, S. A Computational Study on the Nature of the Halogen Bond between Sulfides and Dihalogen Molecules. Struct. Chem. 2011, 22, 567−576. (58) Duarte, D. J. R.; Angelina, E. L.; Peruchena, N. M. On the Strength of the Halogen Bonds: Mutual Penetration, Atomic Quadrupole Moment and Laplacian Distribution of the Charge Density Analyses. Comput. Theor. Chem 2012, 998, 164−172. (59) Eskanderi, K.; Zariny, H. Halogen Bonding: A Lump-Hole Interaction. Chem. Phys. Lett. 2010, 492, 9−13. (60) Grabowski, S. J. Halogen Bond and Its Counterparts: Bent’s Rule Explains the Formation of Nonbonding Interactions. J. Phys Chem. A 2011, 115, 12340−12347. (61) Grabowski, S. J. Hydrogen and Halogen Bonds Are Ruled by the Same Mechanisms. Phys. Chem. Chem. Phys. 2013, 15, 7249−7259. (62) Grabowski, S. J. Non-Covalent InteractionsQTAIM and NBO Analysis. J. Mol. Model. 2012, DOI: 10.1007/s00894-012-1463-7. (63) Wang, W.; Hobza, P. Origin of the X-Hal (Hal = Cl, Br) BondLength Change in the Halogen-Bonded Complexes. J. Phys. Chem. A 2008, 112, 4114−4119. (64) Wang, W.; Zhang, Y.; Ji, B. On the Difference of the Properties between the Blue-Shifting Halogen Bond and the Blue-Shifting Hydrogen Bond. J. Phys. Chem. A 2010, 114, 7257−7260. (65) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; The International Series of Monographs on Chemistry: No. 22; Oxford University Press: New York, 1990. (66) Popelier, P. L. Atoms in Molecules: An Introduction; Pearson Education: Harlow, U.K., 2000. (67) Alkorta, I.; Rozas, I.; Elguero, J. Charge-Transfer Complexes between Dihalogen Compounds and Electron Donor. J. Phys. Chem. A 1998, 102, 9278−9285. (68) Lu, Y.-X.; Zou, J.-W.; Wang, Y.-H.; Jiang, Y.-J.; Yu, Q.-S. Ab Initio Investigation of the Complexes between Bromobenzene and Several Electron Donors: Some Insights into the Magnitude and Nature of Halogen Bonding Interactions. J. Phys. Chem. A 2007, 111, 10781−10788. (69) Grabowski, S. J. QTAIM Characteristics of Halogen Bond and Related Interactions. J. Phys. Chem. A 2012, 116, 1838−1845. (70) Forni, A. Experimental and Theoretical Study of the Br···N Halogen Bond in Complexes of 1,4-Dibromotetrafluorobenzene with Dipyridyl Derivatives. J. Phys. Chem. A 2009, 113, 3403−3412. (71) Wang, W. Halogen Bond Involving Hypervalent Halogen: CSD Search and Theoretical Study. J. Phys. Chem. A 2011, 115, 9294−9299. (72) Mitoraj, M. P.; Michalak, A. Theoretical Description of Halogen BondingAn Insight Based on the Natural Orbitals for Chemical Valence Combined with the Extended-Transition-State Method (ETSNOCV). J. Mol. Model. DOI: 10.1007/s00894-012-1474-4. Open Access. 2012. (73) Dyduch, K.; Mitoraj, M. P.; Michalak, A. ETS-NOCV Description of σ-Hole Binding. J. Mol. Model. 2013, 19, 2747−2758.

(74) Lommerse, J. P. M.; Stone, A. J.; Taylor, R.; Allen, F. H. The Nature and Geometry of Intermolecular Interactions between Halogens and Oxygen or Nitrogen. J. Am. Chem. Soc. 1996, 118, 3108−3116. (75) Domagała, M.; Matczak, P.; Palusiak, M. Halogen Bond, Hydrogen Bond and N···C InteractionOn Interrelation among These Three Noncovalent Interactions. Comput. Theor. Chem. 2012, 998, 26−33. (76) Palusiak, M. On the Nature of Halogen BondThe Kohn− Sham Molecular Orbital Approach. J. Mol. Struct. (THEOCHEM) 2010, 945, 89−92. (77) Xu, L.; Lv, J.; Sang, P.; Zou, J.-W.; Yu, Q.-S.; Xu, M.-B. Comparative Insight into the Halogen Bonding of 4-Chloropyridine and its Metal [CuI, ZnII] Coordinations with Halide Ions: A Theoretical Study on M−C−X···X′. Chem. Phys. 2011, 379, 66−72. (78) Riley, K. E.; Hobza, P. Investigations into the Nature of Halogen Bonding Including Symmetry Adapted Perturbation Theory Analyses. J. Chem. Theory Comput. 2008, 4, 232−242. (79) Wang, Z.; Liu, Z.; Ding, X.; Yu, X.; Hou, B.; Yi, P. Comparisons of the Halogen-Bonded and Hydrogen-Bonded Complexes of Furan, Thiophene and Pyridine with Lewis Acids (ClF, HCl). Comput. Theor. Chem. 2012, 981, 1−6. (80) Romaniello, P.; Lelj, F. Halogen Bond in (CH3)nX (X = N, P, n = 3; X = S, n = 2) and (CH3)nXO (X = N, P, n = 3; X = S, n = 2) Adducts with CF3I. Structural and Energy Analysis Including Relativistic Zero-Order Regular Approximation Approach in a Density Functional Theory Framework. J. Phys. Chem. A 2002, 106, 9114− 9119. (81) Pinter, B.; Nagels, N.; Herrebout, W. A.; De Proft, F. Halogen Bonding from a Hard and Soft Acids and Bases Perspective: Investigation by Using Density Functional Theory Reactivity Indices. Chem.Eur. J. 2013, 19, 519−530. (82) Pendás, A. M.; Blanco, M. A.; Francisco, E. Two-Electron Integrations in the Quantum Theory of Atoms in Molecules. J. Chem. Phys. 2004, 120, 4581. (83) Blanco, M. A.; Pendás, A. M.; Francisco, E. Interacting Quantum Atoms: A Correlated Energy Decomposition Scheme Based on the Quantum Theory of Atoms in Molecules. J. Chem. Theory Comput. 2005, 1, 1096−1109. (84) Pendás, A. M.; Blanco, M. A.; Francisco, E. A Molecular Energy Decomposition Scheme for Atoms in Molecules. J. Chem. Theory Comput. 2006, 2, 90−102. (85) Tiana, D.; Francisco, E.; Blanco, M. A.; Macchi, P.; Sironi, A.; Pendás, A. M. Bonding in Classical and Nonclassical Transition Metal Carbonyls: The Interacting Quantum Atoms Perspective. J. Chem. Theory Comput. 2010, 6, 1064−1074. (86) Pendás, A. M.; Blanco, M. A.; Francisco, E. The Nature of the Hydrogen Bond: A Synthesis from the Interacting Quantum Atoms Picture. J. Chem. Phys. 2006, 125, 184112. (87) Tognetti, V.; Joubert, L. On the Physical Role of Exchange in the Formation of an Intramolecular Bond Path between two Electronegative Atoms. J. Chem. Phys. 2013, 138, 024102. (88) Karpfen, A. The Intermolecular Interaction in the ChargeTranfer Complexes between Amines and Halogens: A Theoretical Characterization of the Trends in Halogen Bonding. Theor. Chem. Acc. 2003, 110, 1−9. (89) Karpfen, A.; Kryachko, E. S. On Blue Shifts of C−H Stretching Modes of Dimethyl Ether in Hydrogen- and Halogen-Bonded Complexes. Chem. Phys. Lett. 2006, 431, 428−433. (90) Zou, J.-W.; Jiang, Y.-J.; Guo, M.; Hu, G.-X.; Zhang, B.; Liu, H. C.; Yu, G.-X. Ab Initio Study of the Complexes of Halogen-Containing Molecules RX (X = Cl, Br, and I) and NH3: Towards Understanding the Nature of Halogen Bonding and the Electron-Accepting Propensities of Covalently Bonded Halogen Atoms. Chem.Eur. J. 2005, 11, 740−751. (91) Lu, Y.-X.; Zou, J.-W.; Wang, Y.-H.; Yu, Q.-S. Ab Initio and Atoms in Molecules: Analyses of Halogen Bonding with a Continuum of Strength. J. Mol. Struct. (THEOCHEM) 2006, 776, 83−87. K



Article

(92) Wang, Y.-H.; Zou, J.-W.; Lu, Y.-X.; Yu, Q.-S.; Xu, H.-Y. SingleElectron Halogen Bond: Ab Initio Study. Int. J. Quantum Chem. 2007, 107, 501−506. (93) Lu, Y.-X.; Zou, J.-W.; Fan, J.-C.; Zhao, W.-N.; Jiang, Y.-J.; Yu, Q.-S. Ab Initio Calculations on Halogen-Bonded Complexes and Comparison with Density Functional Methods. J. Comput. Chem. 2009, 30, 725−732. (94) Li, Q.-Z.; Dong, X.; Jing, B.; Li, W.-Z.; Cheng, J.-B.; Gong, B.-A.; Yu, Z.-W. A New Unconventional Halogen Bond C−X···H−M between HCCX (X = Cl and Br) and HMH (M = Be and Mg): An Ab Initio Study. J. Comput. Chem. 2010, 31, 1662−1669. (95) Ramasami, P.; Ford, T. A. Ab Initio Studies of the Properties of Some Halogen-Bonded Complexes of Ammonia, Water, Phosphine and Hydrogen Sulphide. Comput. Theor. Chem. 2012, 990, 227−235. (96) Tsuzuki, S.; Uchimaru, T.; Wakisaka, A.; Ono, T.; Sonoda, T. CCSD(T) Level Interaction Energy for Halogen Bond between Pyridine and Substituted Iodobenzenes: Origin and Additivity of Substituent Effects. Phys. Chem. Chem. Phys. 2013, 15, 6088−6096. (97) Karpfen, A. Theoretical Characterization of the Trends in Halogen Bonding. Struct. Bonding (Berlin) 2008, 126, 1−15. (98) Politzer, P.; Murray, J. S.; Concha, M. C. Halogen Bonding and the Design of New Materials: Organic Bromides, Chlorides and Perhaps even Fluorides as Donors. J. Mol. Model. 2007, 13, 643−650. (99) Metrangolo, P.; Murray, J. S.; Pilati, T.; Politzer, P.; Resnati, G.; Terraneo, G. The Fluorine Atom as a Halogen Bond Donor, viz. a Positive Site. CrystEngComm 2011, 13, 6593−6596. (100) Lipkowski, P.; Grabowski, S. J.; Leszszynski, J. Properties of the Halogen−Hydride Interaction: An ab Initio and “Atoms in Molecules” Analysis. J. Phys. Chem. A 2006, 110, 10296−10302. (101) Chai, J.-D.; Head-Gordon, M. Long-Range Corrected Hybrid Density Functionals with Damped Atom-Atom Dispersion Corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615−6620. (102) Grimme, S. Semiempirical GGA-type Density Functional Constructed with a Long-Range Dispersion Correction. J. Comput. Chem. 2006, 27, 1787−1799. (103) Frisch, M. J. et al. Gaussian 09, Revision B.01; Gaussian, Inc.: Wallingford, CT, 2009. (104) Boys, S. F.; Bernardi, F. The Calculation of Small Molecular Interactions by the Differences of Separate Total Energies. Some Procedures with Reduced Errors. Mol. Phys. 1970, 19, 553−566. (105) Kozuch, S.; Martin, J. M. L. Halogen Bonds: Benchmarks and Theoretical Analysis. J. Chem. Theor. Comput. 2013, 9, 1918−1931. (106) Bankiewicz, B.; Palusiak, M. The Shape of the Halogen AtomAnisotropy of Electron Distribution and its Dependence on Basis Set and Method Used. Struct. Bonding (Berlin) 2013, 24, 1297− 1306. (107) Politzer, P.; Murray, J. S. Enthalpy and Entropy Factors in Gas Phase Halogen Bonding: Compensation and Competition. CrystEngComm 2013, 15, 3145−3150. (108) Lu, Y.; Li, H.; Zhu, X.; Liu, H.; Zhu, W. Effects of Solvent on Weak Halogen Bonds: Density Functional Theory Calculations. Int. J. Quantum Chem. 2012, 112, 1421−1430. (109) Forni, A.; Rendine, S.; Pieraccini, S.; Sironi, M. Solvent Effect on Halogen Bonding: The Case of the I···O Interaction. J. Mol. Graphics 2012, 38, 31−39. (110) Keith, T. A. AIMAll, Version 12.09.23; TK Gristmill Software: Overland Park, KS, U.S.A., 2012 (aim.tkgristmill.com). (111) Cooper, V. R. Van der Waals Density Functional: An Appropriate Exchange Functional. Phys. Rev. B 2010, 81, 161104. (112) Grimme, S.; Schreiner, P. R. Steric Crowding can Stabilize a Labile Molecule: Solving the Hexaphenylethane Riddle. Angew. Chem., Int. Ed. 2011, 50, 12639−12642. (113) Fradera, X.; Austen, M. A.; Bader, R. F. W. The Lewis Model and Beyond. J. Phys. Chem. A 1999, 103, 304−314. (114) Fradera, X.; Poater, J.; Simon, S.; Duran, M.; Solá, M. ElectronPairing Analysis from Localization and Delocalization Indices in the Framework of the Atoms-in-Molecules Theory. Theor. Chem. Acc. 2002, 108, 214−224.

(115) Matito, E.; Solá, M.; Salvador, P.; Duran, M. Electron Sharing Indexes at the Correlated Level. Application to Aromaticity Calculations. Faraday Discuss. 2007, 135, 325−345. (116) Firme, C. L.; Antunes, O. A. C.; Esteves, P. M. Electronic Nature of Planar Cyclobutenyl Dication Derivatives. J. Phys. Chem. A 2007, 111, 11904−11907. (117) Ponder, J. W.; Case, D. A. Force Fields for Protein Simulations. Adv. Protein Chem. 2003, 66, 27−85. (118) Popelier, P. L. A. Quantum Chemical Topology: Knowledgeable Atoms in Peptides. AIP Conf. Proc. 2012, 1456, 261−268. (119) Jahromi, H. J.; Eskanderi, K. Halogen Bonding: A Theoretical Study Based on Atomic Multipoles Derived from Auantum Theory of Atoms in Molecules. Struct. Chem. 2013, 24, 1281−1287. (120) Rafat, M.; Popelier, P. L. A. Topological Atom−Atom Partitioning of Molecular Exchange Energy and Its Multipolar Convergence. In The Quantum Theory of Atoms in Molecules: From Solid State to DNA and Drug Design; Matta, C. F., Russel, J., Eds.; Wiley-VCH Verlag GmbH & Co: Weinheim, Germany, 2007. (121) Popelier, P. L. A.; Joubert, L. The Elusive Atomic Rationale for DNA Base Pair Stability. J. Am. Chem. Soc. 2002, 124, 8725−8729. (122) Cremer, D.; Kraka, E. Chemical Bonds without Bonding Electron DensityDoes the Difference Electron-Density Analysis Suffice for a Description of the Chemical Bond? Angew. Chem., Int. Ed. 1984, 23, 627−628. (123) Bader, R. F. W.; Gatti, C. A Green’s Function for the Density. Chem. Phys. Lett. 1998, 287, 233−238. (124) Gatti, C.; Cargnoni, F.; Bertini, L. Chemical Information from the Source Function. J. Comput. Chem. 2003, 24, 422−436. (125) Gatti, C.; Lasi, D. Source Function Description of Metal− Metal Bonding in d-Block Organometallic Compounds. Faraday Discuss. 2007, 135, 55−78. (126) Pendás, A. M.; Francisco, E.; Blanco, M. A.; Gatti, C. Bond Paths as Privileged Exchange Channels. Chem.Eur. J. 2007, 13, 9362−9371.

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