σ-Hole Bond vs π-Hole Bond: A Comparison Based on Halogen Bond

Review pubs.acs.org/CR

σ‑Hole Bond vs π‑Hole Bond: A Comparison Based on Halogen Bond Hui Wang,† Weizhou Wang,‡ and Wei Jun Jin*,† †

College of Chemistry, Beijing Normal University, Beijing 100875, People’s Republic of China College of Chemistry and Chemical Engineering, Luoyang Normal University, Luoyang 471022, People’s Republic of China

‡

ABSTRACT: The σ-hole and π-hole are the regions with positive surface electrostatic potential on the molecule entity; the former specifically refers to the positive region of a molecular entity along extension of the Y−Ge/P/Se/X covalent σ-bond (Y = electronrich group; Ge/P/Se/X = Groups IV−VII), while the latter refers to the positive region in the direction perpendicular to the σ-framework of the molecular entity. The directional noncovalent interactions between the σ-hole or π-hole and the negative or electron-rich sites are named σ-hole bond or π-hole bond, respectively. The contributions from electrostatic, charge transfer, and other terms or Coulombic interaction to the σ-hole bond and π-hole bond were reviewed first followed by a brief discussion on the interplay between the σ-hole bond and the π-hole bond as well as application of the two types of noncovalent interactions in the field of anion recognition. It is expected that this review could stimulate further development of the σ-hole bond and π-hole bond in theoretical exploration and practical application in the future.

CONTENTS 1. Introduction 2. Concept and Nature of the σ-Hole Bond and πHole Bond 2.1. Concept 2.2. Nature 2.2.1. Surface Electrostatic Potential Analysis 2.2.2. Energy Decomposition Analysis 2.2.3. Coulombic Interaction 3. Directionality and Strength of the σ-Hole Bond and π-Hole Bond 3.1. Directionality 3.2. Strength 4. Types of σ-Hole Bond and π-Hole Bond Acceptors 4.1. n-Type Bond Acceptors 4.2. π-Type Bond Acceptors 4.3. Free-Radical-Type Bond Acceptors 4.4. Anion-Type Bond Acceptors 5. Interplay between the σ-Hole Bond and π-Hole Bond 6. Application of the σ-Hole Bond and π-Hole Bond in Anion Recognition 6.1. Recognized by the Simple Bond Donors 6.2. Recognized by the Macrocyclic Bond Donors 6.3. Anion Transport 6.4. Organocatalysis 7. Conclusions and Perspective Appendix I: Brief Introduction of Some Energy Decomposition Analysis Methods Author Information Corresponding Author Notes Biographies

© 2016 American Chemical Society

Acknowledgments Appendix II: Abbreviations References

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1. INTRODUCTION The study of the halogen bond (XB) goes back 200 years with the first reported phenomenon dating to the I2···NH3 adduct by Colin in 18141 2 years after iodine was accidentally discovered2 and isolated in 1812.3 In the same year, Colin and Claubry discovered the blue-black amylose−iodine/polyiodide complex.4 Many other significant studies have been performed over the past 2 centuries.5,6 Interest in the halogen bond rose again at the turn of the century7 and has since become a popular topic in many fields with the first international symposium on the halogen bond (ISXB-1) successfully organized at Lecce, Italy, in 2014.3 The halogen bond refers to a net attractive interaction between an electrophilic region associated with a halogen atom in a molecular entity and a nucleophilic region in another or the same molecular entity.8 According to the molecular surface electrostatic potential, Politzer et al.9−15 named the halogen bond the σ-hole bond (σhB). Anion−π or lone electron pair (lp)−π interactions are another new set of supramolecular interactions.16−28 When hydrogen is the only substituent in a benzene ring, the electron cloud of a delocalized/conjugated large π-bond is distributed evenly above and below the ring plane and the quadrupole moment is negative (Qzz(C6H6) = −8.48 B). However, the quadrupole moment can flip from negative to positive by attaching electron-withdrawing

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Special Issue: Noncovalent Interactions Received: September 9, 2015 Published: February 17, 2016 5072

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Figure 1. Surface electrostatic potentials of ICF2CF2I, SeFCl, PH2Cl, and GeH3Br recalculated at the M06-2X/aug-cc-pVTZ(-pp) level of theory according to ref 38: (blue) positive region, (red) negative region, and (green) transition region. The magnitude of the iodine σ-hole along the extension of the C−I bond in the ICF2CF2I molecule is 125.9 kJ·mol−1. The magnitudes of two selenium σ-holes along the extension of F−Se and Cl−Se bonds in SeFCl molecule are 173.9 and 153.9 kJ·mol−1. The magnitudes of phosphorus σ-holes along the extension of Cl−P and H−P bonds in the PH2Cl molecule are 134.9 and 63.0 kJ·mol−1. The magnitudes of germanium σ-holes along the extension of Br−Ge and H−Ge bonds in the GeH3Br molecule are 157.8 and 86.0 kJ·mol−1. The tetrels represent Group IV elements, i.e., silicon, germanium, etc.

substituents to the ring (Qzz(C6F6) = +9.50 B).29 In other words, the quadrupole moment can be adjusted by substituents on the aromatic ring. This special π system has various names such as “πelectron-deficient cavity”,30 “π-acid”,31 “π-acidic rings”,16 and “πelectron-poor”32 arenes. In this case, the attractive interaction between the special π system and the electron-rich element (anion or lone electron pair) can occur. In 1986, Kebarle et al.33 confirmed via calculation that a strong complex would form between C6F6 and Cl− with ΔH = −70.3 kJ·mol−1. Yamabe et al.34 further showed that C6F6 and X− (X = Cl, Br, and I) could form stable complexes in the gas phase with the X− positioned above the arene centroid. Inspired by these works, theoretical calculations further confirmed these stable structures between 1,3,5-triazine, trifluoro-1,3,5-triazine, and F−, Cl−, and N3− using the MP2 method16 as well as between several perfluoro-aromatic compounds and anions (F−, Cl−, Br−, and CN−)17 in 2002. Deyà et al.18 first called this interaction the “anion−π interaction”. In 2004, two reports provided the first experimental evidence of an attractive interaction between the anion and the electrondeficient aromatic ring.35,36 Later, Gamez et al.37 discovered that inorganic nitrates interacted with the centers of triazine rings in cocrystals with bond lengths of 3.006−3.202 Å from the ring− centroid to an O atom. In fact, the so-called halogen-bond and anion/lone electron pair−π interactions have some key features in common: First, a positive surface electrostatic potential region on a molecular entity participates in the bond. Second, they are directional noncovalent interactions. As a result, according to the σ-hole bond model, the anion/lone electron pair−π interaction could more reasonably be called the π-hole bond (πhB).15,38,39 This nomenclature is helpful for systematization of the discipline as well as clarification of the intrinsic or extrinsic relationships between the concepts. In addition, it is conducive to increasing the understanding of various types of weak interactions with high directionality. Therefore, it is necessary to treat the σ-hole bond and π-hole bond similarly.

of a molecule. It is a fundamentally important physical characteristic that is very useful for understanding and predicting noncovalent interactions. A closed or semiclosed region on a molecule entity with a positive surface electrostatic potential is called surface electrostatic potential holes, which can be classified as the σ-hole and πhole. Theoretical calculations indicate that the halogen atoms that form a halogen bond have a region of positive surface electrostatic potential on the outermost section centered on the Y−X axis and named the σ-hole.9−15 This concept was first proposed by Clark at a conference in Prague in 20059 and can be traced back to 1992 when a theoretical calculation indicated that Cl and Br with very positive surface electrostatic potentials in CCl4 and CBr4 can interact directionally with electron-rich sites.41 More broadly, the σ-hole refers to the positive surface electrostatic potential region of a molecular entity along extension of Y−Ge/P/Se/X covalent σ-bond (Y represents an electron-rich group or element atom with higher electronegativity; Ge/P/Se/X represent Group IV, V, VI, and VII elements, tetrel, pnicogen, chalcogen, and halogen, respectively).9−15,38,42−45 Among them, Group IV−VI interactions have long been known experimentally, although not recognized as involving σ-holes until the papers by Murray et al.11,12,38,46,47 For a series of Y1−4−L (L = Group IV−VII) molecules, the positive surface electrostatic potentials are all present on the surfaces of L (Ge, P, Se, and I) atoms along the extensions of the Y−L covalent bonds and ascribed to the anisotropic charge distributions of the covalently bonded L atom,9−15,38,42−44,48 whereas the induction effect of the electron-withdrawing group adjacent to L makes the σ-hole larger and more positive (Figure 1). Moreover, the number of σ-holes is consistent with the number of covalent bonds in these molecules.38 To understand the σ-hole characteristics more easily, Hobza et al.49 introduced a simplified description, i.e., the size and magnitude of a σ-hole referring to the spatial range and most positive surface electrostatic potential (Vs,max) of the σ-hole, respectively. Similarly, Politzer et al.15,38,39 proposed a π-hole concept corresponding to the unoccupied or depleted p orbital on the central atom, e.g., SO2, SeO2, BX3 (X = F, Cl, Br, and I), silenes, H3C−C(O)F, H3C−C(O)NH2, FNO2, F2CO, and Cl2CO. As an expansion of this concept, the region with a positive surface electrostatic potential in the direction perpendicular to the σframework of the molecular entity can be reasonably called the πhole.50 It is due to the induction effect of the electronwithdrawing group or more electronegative atom bound to the π system.39 Therefore, the π-hole exists in π-nonconjugated or πconjugated (the aromatic or nonaromatic) organic molecules and nonconjugated inorganic molecules with and without covalent π bonds. These usually involve the π-molecular orbital

2. CONCEPT AND NATURE OF THE σ-HOLE BOND AND π-HOLE BOND 2.1. Concept

The electrostatic potential V(r) that the nuclei and electrons of a molecule produce at any point r is given by eq 19,40 V (r ) =

∑ A

ZA − |RA − r |

∫

ρ(r′)dr′ |r ′ − r |

(1)

in which ZA is the charge on nucleus A located at RA and ρ(r) is the electronic density. When V(r) is calculated on a molecular surface it is designated as VS(r), the surface electrostatic potential 5073

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Figure 2. Common types of molecules that include one or more π-holes.

Figure 3. Surface electrostatic potential of F2CO (Vs,max = 185.3 kJ·mol−1) and 1,4-DITFB recalculated at the M06-2X/aug-cc-pVTZ(-pp) level of theory by the authors’ group: (blue) positive region; (red) negative region; (green) transition region. Magnitudes of the surface electrostatic potential of 1,4-DITFB are 63.4 kJ·mol−1 for the C1/C3/C4/C6 atoms, 37.2 kJ·mol−1 for C2/C5 atoms, 54.4 kJ·mol−1 for the center−O3, 135.2 kJ·mol−1 for the I11/I12 atoms, −42.7 kJ·mol−1 for the F7/F8/F9/F10 atoms, and −15.5 kJ·mol−1 for the I belt perpendicular to the C−I covalent bond axis.

subsets and special cases of the σ-hole bond.38 As shown in Figure 1, the regions with positive surface electrostatic potential values in Y2−4−L (L = Groups IV−VI) molecules are all σ-holes. They can also interact with the electron-rich site to form weak and directional noncovalent interactions resembling the halogen bond. These are called tetrel, pnicogen, and chalcogen bonds.11,12,38,44,46,53−57 It is more significant that the σ-hole bond model has been used to describe hydrogen-bond systems.58 However, this review will not discuss further the hydrogen bond and the σ-hole bond of any other forms except the halogen bond due to limit of the length of this review. The π-hole bond is an alternative description of the anion/ lone electron pair−π interaction. The former is more extensive than the latter, that is, the π-hole includes not only organic π-hole systems involving π-bond or conjugated π-bond but also inorganic π-hole systems involving a π-bond and non-πbond.15,38,39 In addition to the anion and lone electron pair, its bond acceptor also includes the π-system (the so-called πhole···π bond, which is described later). Anion−π interaction gives the impression of a negative−negative interaction. However, the intrinsic characteristic of the “π” is clear here, i.e., the π-hole refers to a region of positive surface electrostatic potential in a molecular entity, and the π-hole bond is also distinct, as described above. Therefore, the π-hole bond nomenclature is more intuitive and easier to understand. It contains more information than the anion/lone electron pair−π interactions. Briefly, the name halogen bond originates from the element name of the bond donor, and the term anion−π interaction is derived from the interacting chemical species. However, the σhole bond and π-hole bond are described using the same physical framework: the surface electrostatic potential of the bond-donor molecules. They possess specific scientific significance and broader application prospects.

or p orbital of one central atom. Organic and inorganic π-holes completely cover the π-hole concept system. Common types of organic π-hole systems are illustrated in Figure 2. As with the σ-hole, the π-hole characteristics can be described in terms of size and magnitude. The magnitude of the π-hole in a specific molecule is consistent with the order of the Hammett substituent constants (σm) of its substituents. Here, σmx = σmF (0.34) < σmCN (0.56) < σmNO2 (0.71),51 and the subscript/ superscript m and x in σmx refer to the meta position and electron-withdrawing substituents, respectively. For example, the magnitude of the π-hole calculated at the M06-2X/aug-cc-pvtz level is 241.8 and 268.4 kJ·mol−1 for inorganic BF3 and B(CN)3 and 9.6, 108.6, and 132.5 kJ·mol−1 for aromatic C6H3F3, C6H3(CN)3, and C6H3(NO2)3, respectively. In other words, the surface electrostatic potential of the π-hole becomes more positive as the Hammett substituent constants increase. In addition, the relative π-hole bond ability can be predicted using Hammett constants either fully or at least to a certain degree. Similar to the definition of a halogen bond,8 the noncovalent attraction interaction between a surface electrostatic potential hole (σ-hole or π-hole) in a molecular entity named bond donor and a negative site (B) in a molecular entity named bond acceptor is called a σ-hole bond or a π-hole bond. These can be expressed as the σ-hole···B bond or the π-hole···B bond. Figure 3 shows the surface electrostatic potentials of F2CO and 1,4diiodoperfluorobenzene (1,4-DITFB). F2CO possesses a positive region on the central C atom, and 1,4-DITFB possesses both a σ-hole (on the I atom) and a π-hole (all involving six C atoms on the π-system). This means that the latter can act as both a σ-hole bond and a π-hole bond donor. Simultaneously, because of the high electron density on the F atoms as well as the negative belt around the central portion of I atoms, 1,4-DITFB can also act as a σ-hole bond and π-hole bond acceptor. Thus, the σ-hole bond is much more general than the halogen bond. The halogen bond and other intermolecular interactions involving Group IV−VI, even Group 18,52 elements are only 5074

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Figure 4. Plots of interaction energies of σ-hole bond complexes vs the σ-hole Vs,max with NH3 and HCN (a) and with DTCA and DABCO (b) as well as vs the Vs,min of anions for the CF3Cl···anion complexes described by the authors’ group (c). (a) Adapted with permission from ref 38. Copyright 2013 PCCP Owner Societies. (b) Adapted with permission from ref 59. Copyright 2014 PCCP Owner Societies.

Table 1. Interaction Energies ΔE and σ-Hole Vs,max for the Gas-Phase Complexes with NH3 and HCN Computed by Politzer et al. and Those for DTCA and DABCO Computed by Hobza et al.a σhB complexes

Vs,max

ΔE

σhB complexes

Vs,max

ΔE

FF···NH3 F3CCl···NH3 F3CBr···NH3 BrCCBr···NH3 H2FP···NH3 H2FAs···NH3 FCl···NH3 HFS···NH3 ClF3Si···NH3 HFSe···NH3 σhB complexes

46.0 83.7 104.6 125.5 163.2 184.1 188.3 192.5 200.8 213.4 Vs,max

−6.3 −10.5 −15.5 −17.6 −30.1 −36.4 −43.1 −35.1 −43.9 −47.3 ΔE

F3CCl···NCH Br2CCBr2···NCH BrCCBr···NCH H3FSi···NCH Cl2Se···NCH H2FP···NCH F2S···NCH H3FGe···NCH H2FAs···NCH FBr···NCH σhB complexes

83.7 100.4 125.5 146.4 150.6 163.2 167.4 179.9 184.1 221.8 Vs,min

−6.7 −8.8 −11.3 −17.6 −16.7 −19.7 −18.8 −20.5 −23.8 −29.7 ΔE

DTCA···I2 DTCA···IF DTCA···Br2 DTCA···Cl2 DTCA···N2 DTCA···ICH3 DABCO···I2 DABCO···IF DABCO···Br2 DABCO···Cl2 DABCO···N2 DABCO···ICH3

124.4 235.2 116.3 102.1 −36.8 56.2 124.4 235.2 116.3 102.1 −36.8 56.2

−25.0 −87.1 −22.7 −5.7 40.0 43.6 −101.2 −133.8 −61.4 −23.8 58.2 −12.6

CF3Cl···F− CF3Cl···Cl− CF3Cl···NC− CF3Cl···CN− CF3Cl···Br− CF3Cl···NCS− CF3Cl···I−

−714.7 −585.3 −581.6 −569.7 −552.6 −520.6 −515.1

−90.0 −46.7 −44.0 −43.5 −39.7 −33.8 −33.1

a

NH3 and HCN: Adapted with permission from ref 38. Copyright 2013 PCCP Owner Societies. DTCA and DABCO: Adapted with permission from ref 59. Copyright 2014 PCCP Owner Societies. The ΔE and anion Vs,min for the gas-phase complexes with CF3Cl were prepared by the authors’ group. Computational levels: Vs,max (in kJ·mol−1): M06-2X/6-311G(d), ΔE (in kJ·mol−1): M06-2X/aug-cc-pVTZ for the complexes with NH3 and HCN; Vs,max (in kJ·mol−1): B97-D3/def2-QZVP, ΔE (in kJ·mol−1): DFT-SAPT/aug-cc-pVDZ level for complexes with DTCA and DABCO; and Vs,max and ΔE (in kJ·mol−1): M06-2X/aug-cc-pVTZ(-pp) level for the CF3Cl···anion complexes.

and R2 = 0.977 for HCN as shown in Figure 4a (Table 1). Moreover, Hobza et al.59 also noted through analyzing the interactions of X2 (X = Cl, Br, and I) and heterosystems (IF, ICH3, and N2) with the sulfur/nitrogen atom from 1,3-dithiole2-thione-4-carboxyclic acid (DTCA)/1,4-diaza[2.2.2]bicyclooctane (DABCO) that the total interaction energies of the σ-hole bond complexes correlated with the Vs,max for a given negative site (R2DTCA = 0.873, R2DABCO = 0.910) as shown in Figure 4b. Figure 4c, completed by the authors’ group, shows further that the interaction energies of the complexes with the same σ-hole bond donor CF3Cl correlate well with the most negative surface electrostatic potentials (Vs,min) of various anions (Table 1). The

2.2. Nature

2.2.1. Surface Electrostatic Potential Analysis. In general, stronger σ-hole bond and π-hole bond complexes are more likely to be formed as the σ-hole and π-hole surface electrostatic potentials become more positive, and there is a good relationship between the molecular surface electrostatic potential of a σ-hole and the noncovalent interaction ability/strength. Politzer et al.38 showed that the interaction energies (ΔE) of the noncovalent complexes of molecules containing Group IV−VII elements with the nitrogen lone pairs from neutral NH3 and HCN correlated well with the σ-hole magnitude for a given negative site. The correlation coefficient was R2 = 0.950 for NH3 5075

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Additional studies performed by the authors’ group have shown good correlation between the Vs,max of the different π-hole bond donors (1,3,5-substituent triazines) and the same anion I− as well as Vs,min of different anions and the same π-hole bond donor (1,3,5-trifluorotriazine; cf. Figure 6 and Table 2).

data provide a better understanding of the correlation between the interaction energy of the σ-hole bond and the Vs,max of the σhole or Vs,min of the negative site. Similar to the σ-hole bond, the interaction energy of the π-hole bond also correlates well with the magnitude of the positive and negative surface electrostatic potentials of the π-hole and anions. Politzer et al.38,39 indicated that the interaction energies became generally more negative as the magnitude of the π-hole increased. For example, the π-hole Vs,max values for Cl2CO, F2CO, H2SiO, and F2SiO are 95.4, 171.1, 181.6, and 279.1 kJ·mol−1, respectively. These were calculated at the B3PW91/6-31G(d,p) level by Politzer and co-workers. The corresponding interaction energies with neutral bond acceptor NCH are −12.5, −17.1, −54.4, and −103.3 kJ·mol−1, respectively.39 Wheeler et al.60 showed that strong electron-withdrawing groups (−CN and −NO2) on the ring markedly increase the positive surface electrostatic potential of the π-hole. The predicted interaction energies of C6H6−nRn···Cl− complexes (n = 0−4, 6; R = substituents) correlated well with the surface electrostatic potentials above the ring centroid (cf. Figure 5). On the basis of these results, Wheeler et al. suggested that the calculated surface electrostatic potential should provide a faithful predictor of anion-binding energies.

Table 2. Vs,max of Triazine−πh and Interaction Energies ΔE for the Gas-Phase Complexes with I− as well as the Vs,min of Anions and ΔE for the Gas-Phase Complexes with C3F3N3a triazine−πhB complexes −

Vs,max

ΔE

C3H3N3···I C3I3N3···I− C3Br3N3···I− C3Cl3N3···I− C3F3N3···I− C3(CN)3N3···I−

61.2 108.5 122.3 126.5 151.9 217.1

−5.5 −12.4 −12.5 −12.4 −13.6 −23.8

C3(NO2)3N3··· I−

254.6

−27.8

triazine−πhB complexes −

C3F3N3···F C3F3N3···Cl− C3F3N3···NC− C3F3N3···CN− C3F3N3···Br− C3F3N3··· NCS− C3F3N3···I−

Vs,min

ΔE

−714.7 −585.3 −581.6 −569.7 −552.6 −520.6

−122.3 −75.4 −74.1 −70.5 −66.1 −61.0

−515.1

−56.6

The computational levels are Vs,max, Vs,min, and ΔE (all in kJ·mol−1): M06-2X/aug-cc-pVTZ(-pp) (by the authors’ group). a

2.2.2. Energy Decomposition Analysis. Although the nature of the σ-hole bond and π-hole bond was analyzed from the perspective of the surface electrostatic potential, the analyses cannot comprehensively and quantitatively determine their origin. Moreover, experiments can only provide a few possible explanations for the nature of both bonds. In general, the stability of intermolecular complexes can be analyzed by decomposing the interaction energy into contributions from electrostatics, charge transfer, dispersion, and others. Depending on the degree of contribution of each energy component, the strengths of the σhole bond and π-hole bond vary over a wide range. Understanding their contributions also enables insight into the physical nature of both bonds. Some methods for energy decomposition analysis are briefly introduced to understand the properties of interaction energy as appendix material (cf. Appendix I). Contribution of the Electrostatic Term. Politzer et al.61,62 used density functional symmetry-adapted perturbation theory (DFT-SAPT) to show that the attractive nature of the halogen bond between substituted chloro/bromo-benzenes and acetone comes primarily from electrostatic and dispersion terms. The other interaction energies play minor roles in stabilizing these halogen-bond complexes. Moreover, the relative contribution of electrostatic and dispersion forces depends substantially on the

Figure 5. Plot of M06-2X/6-31+G(d) and estimated CCSD(T)/AVTZ interaction energies for C6H6−nRn···Cl− complexes above the ring centroid vs the surface electrostatic potential (Vs,max) of C6H6−nRn molecules. Reprinted with permission from ref 60. Copyright 2010 American Chemical Society.

Figure 6. Plots of interaction energies for gas-phase complexes vs Vs,max of different π-hole (1,3,5-substituent triazines) with I− (a) and Vs,min of different anions with C3F3N3 (b). All data are calculated by the authors’ group and listed in Table 2. 5076

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σ-hole magnitude at the halogen atom or the substituent attached to the ring (Table 3). In other words, electrostatic interaction

1:2 (O2NX/NH3) complexes (cf. Figure 7, configurations III− V) have been analyzed by the many-body interaction energy. However, Hobza et al.64−67 noted that the dispersion energy was dominant in many complexes. Thus, it is not sufficient to explain the electrostatic term-dominant factor to the halogen bond in all cases. They analyzed the contribution of different energy components to the total interaction energy of the X···π (between X2 and C6H6, X = F, Cl, and Br) and C−X···O (between H2CO and halogenated molecules) halogen-bond complexes using the DFT-SAPT method.65 It is clear from the energy decomposition data that the dispersion energy is the largest contributor to the attraction in all three X···π halogen bonds. In all formaldehyde-containing complexes, the dispersion energy is comparable to the electrostatic energy, and the two contributions are almost completely responsible for total attraction (Table 5). Through the analysis of hundreds of halogen-bond complexes in aromatic and aliphatic systems, Hobza et al.68 concluded that when the absolute value of interaction energy E > 29.3 kJ·mol−1, the contributions of the individual energy components were electrostatic > induction > dispersion, whereas when the absolute value of interaction energy E < 29.3 kJ·mol−1 they decreased in the order dispersion > electrostatic > induction. In other words, the electrostatic interaction is dominant in the strong interaction regime, and the dispersion interaction is dominant for weak interactions. Contribution of Charge Transfer and Other Terms. The electron density may flow from the σ-hole (or π-hole) bond acceptor to the σ-hole (or π-hole) bond donor during the formation of a complex, and both the σ-hole bond and π-hole bond are reinforced through this factor. The contribution of charge transfer to a σ-hole bond or a π-hole bond can be considerable. Therefore, charge transfer and molecular orbital theories are also acceptable for dealing with both types of bond complexes and can predict where the charge comes from and goes to during the formation of a complex. The degree of charge transfer, q, can be estimated roughly, from 0.05 to unity (100%, cf. Figure 8), corresponding to partial charge to an electron completely transfering from bond acceptor to donor.69 Fourmigué et al.70 showed that in strong halogen-bond interactions the degree of charge transfer from halogen-bond acceptors to donors in a cocrystal was selectively modified upon cooling without a structural transition. This might lead to the formation of ionic salts. For instance, in the charge transfer complexes derived from iodinated tetrathiafulvalene (EDTTTFI2) and tetracyanoquinodimethane derivatives (TCNQFn, n = 0, 1, 2), EDT-TTFI2 interacted with TCNQ and TCNQF2 to form a neutral complex [(EDT-TTFI2)2·TCNQ] and an ionic salt [(EDT-TTFI2)2+·(TCNQF2)−], respectively. When a neutral−ionic conversion was observed, the charge on TCNQF strongly decreased (cf. Figure 9) upon cooling in the

Table 3. Selected DFT-SAPT results from Politzer et al.a complexes

Vs,max

Eelst

Edisp

Eint

chlorobenzene 3,5-difluorochlorobenzene chloropentafluorobenzene bromobenzene 3,5-difluorobromobenzene bromopentafluorobenzene

22.2 49.8 79.1 51.0 77.0 113.8

−4.5 −7.5 −13.3 −10.7 −14.8 −23.7

−9.7 −10.4 −12.5 −13.0 −13.4 −15.9

−5.0 −7.1 −10.9 −8.7 −11.0 −16.3

Vs,max: in kJ·mol−1. Eelst and Edisp (in kJ·mol−1): the estimated electrostatic and dispersion energies. Eint (in kJ·mol−1): the interaction energies. Adapted with permission from ref 62. Copyright 2013 Springer. a

becomes the main driving force as the magnitude of the σ-hole increases. Conversely, dispersion interaction dominates the bond as the magnitude of the σ-hole decreases. The calculations showed that there are two configurations for 1:1 complexes in the interaction of the σ-hole and inorganic πhole of O2NX (X = F, Cl, Br, and I) with NH3.63 One was the σhole bond complex where NH3 points toward the σ-hole of the X atom, and the other was the π-hole bond complex where NH3 points toward the π-hole of the N atom of the O2NX molecule. In addition, the calculation predicted that the σ-hole bond was stronger than the π-hole bond except in the O2NCl complexes. The DFT-SAPT method was used to explore the source of the interaction energy, and the energy decomposition data listed in Table 4 indicate that electrostatics is the most important Table 4. DFT-SAPT Energy Decomposition (in kJ·mol−1) for All of the 1:1 Complexes Calculated at the MP2/aug-ccpVTZ/LANL2DZ Levela complexes

Eelst

Eexch

Eind

Edisp

Eint

O2NCl···NH3 (conf. I) O2NBr···NH3 (conf. I) O2NI···NH3 (conf. I) H3N···O2NF (conf. II) H3N···O2NCl (conf. II) H3N···O2NBr (conf. II) H3N···O2NI (conf. II)

−36.8 −70.4 −100.7 −30.8 −28.0 −27.1 −25.0

53.1 99.0 155.7 31.6 31.5 31.9 32.1

−6.2 −17.2 −59.5 −2.7 −2.7 −2.7 −3.3

−15.2 −22.5 −22.7 −13.6 −14.5 −14.8 −14.2

−15.1 −27.8 −39.5 −16.6 −14.7 −13.7 −11.5

a

Adapted with permission from ref 63. Copyright 2012 American Chemical Society.

contribution. The other interaction energy terms contribute less to the total interaction energy. All of these terms are very sensitive to the halogen atom in the σ-hole bond complexes, but they remain almost invariant in the π-hole bond complexes. In addition, the cooperative and diminutive energetic effects for the

Figure 7. Two configurations (I and II) considered for the 1:1 complexes and the three configurations (III, IV, and V) considered for the 1:2 complexes (O2NX/NH3). Adapted with permission from ref 63. Copyright 2012 American Chemical Society. 5077

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Table 5. Selected DFT-SAPT/aug-cc-pVTZ Interaction Energies (in kJ·mol−1) for the Individual Termsa

a

complexes

XB

Eelst

Eexch

Eind

Edisp

Eint

F2···C6H6 Cl2···C6H6 Br2···C6H6 chloroform···H2CO halothane···H2CO halothane···H2CO enfurane···H2CO isofurane···H2CO

F···π Cl···π Br···π C−Cl···O C−Br···O C−Cl···O C−Cl···O C−Cl···O

−4.0 −13.3 −21.0 −10.3 −19.7 −11.9 −11.9 −9.7

8.7 27.3 41.1 12.0 21.9 13.4 13.0 11.8

−2.0 −7.2 −12.0 −1.9 −4.0 −2.2 −2.0 −1.8

−7.4 −19.0 −24.5 −11.2 −14.6 −12.1 −14.1 −11.8

−5.1 −13.1 −17.7 −11.4 −16.4 −12.8 −15.1 −11.5

Adapted with permission from ref 65. Copyright 2013 PCCP Owner Societies.

Rosokha et al.71−73 showed that charge transfer occurred between bond donor bromocarbons (R−Br) and neutral or anionic bond acceptors (B) based on studies of their spectral, structural, and thermodynamic characteristics. Intense absorption bands in the 200−400 nm range characterized the R−Br···B halogen-bond complexes. The absorption band energies of R− Br···B complexes correlated well with the lowest unoccupied molecular orbital (LUMO) energies of the R−Br molecules (cf. Figure 10) in agreement with the Mulliken theory of charge transfer. In addition, the bond energies of R−Br···B correlated well with the combination of charge transfer (orbital) and electrostatic energies but correlated poorly with the magnitude of the Br σ-hole. This indicates that in addition to the electrostatic interactions governing the geometries of supramolecular assemblies, charge transfer (orbital) interactions play a vital role in R−Br···B halogen-bond complexes. On the basis of molecular orbital theory, energy decomposition analysis, and Voronoi deformation density analyses of the charge distribution, Bickelhaupt et al.74 showed that the DX···X− (D, X = F, Cl, Br, and I) halogen bonds originated not only from electrostatic attraction but also from the favorable highest occupied molecular orbital (HOMO)−LUMO orbital interaction between the np orbital of the halide X− and the empty σ* orbital in the DX molecule. Taking FX···Cl− (X = F, Cl, Br, and I) complexes as an example, the energy decomposition data listed in Table 6 show that a stronger orbital interaction (Eoi) contributes to the bond energy in most cases. This results from the low orbital energy of the empty dihalogen σ* orbital (ε(σ*)). The electrostatic term is less favorable but also important in the halogen bond. Charge transfer interactions are frequently accompanied by a red shift in the νC−X in the FT−IR or Raman spectra of σ-hole

Figure 8. X-ray structures of some charge transfer complexes. Reprinted with permission from ref 69. Copyright 2008 American Chemical Society.

complex [(EDT-TTFI2)2·TCNQF], reflecting the reinforcement of halogen-bond interactions.

Figure 9. Changes in the I···N bond length in the (EDT-TTFI2)2· TCNQF cocrystal and charges (ρ) on the TCNQFn. Adapted with permission from ref 70. Copyright 2013 Wiley-VCH Verlag GmbH & Co. KGaA.

Figure 10. (Left) Plot of absorption band energies of complexes vs LUMO energies of the R−Br molecules: (1) CBr3NO2, (2) CBr3COCBr3, (3) CBr4, (4) CBr3CN, (5) CBr3F, (6) CBr3COOH, (7) CBr3CONH2, (8) CHBr3, (9) C3Br2F6, (10) tetracyanoethylene, (11) tetrachloro-o-benzoquinone, (12) tetrachloro-p-benzoquinone, (13) tetracyanopyrazine, (14) 1,2,4,5-tetracyanobenzene, and (15) 1,3,5-trinitrobenzene. Absorption band energies of complexes 10−15 are from ref 75. (Right) Correlation between the bond energies (ΔE) and the linear combination of the electrostatic and orbital components (αVmax + ECT). Reprinted with permission from ref 71. Copyright 2013 Wiley-VCH Verlag GmbH & Co. KGaA. 5078

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Table 6. Analysis of the Halogen-Bond Mechanism in FX···Cl− Complexesa complexes −

FF···Cl FCl···Cl− FBr···Cl− FI···Cl− a

Eint

Eelst

Eexch

Eoi

ΔEσoi

ΔEπoi

ε(σ*)

−324.3 −238.9 −241.8 −232.6

−219.2 −257.7 −275.7 −289.1

451.0 361.5 330.9 308.8

−556.0 −342.7 −297.1 −252.3

−538.5 −320.1 −274.5 −225.9

−17.6 −22.6 −23.0 −26.4

−6.2 −4.9 −5.0 −4.9

The interaction energies (in kJ·mol−1) were computed at the ZORA-BP86/TZ2P level. ε(σ*): orbital energy of halogen-bond donors (in eV).74

Figure 11. Relationship between the interaction energies (in kJ·mol−1) and Vs,max (in kJ·mol−1) of the halogen atom σ-hole (a) as well as the quantity of charge transfer qCT (in au) of B···ClY and B···BrY complexes (b). Adapted with permission from ref 78. Copyright 2011 Springer.

bond. For example, the Raman shift bands of the νC−I stretching vibrations for 1,4/1,2-DITFB (1,2-diiodoperfluorobenzene) are 157 and 234 cm−1. These bands both shift to lower wavenumbers, 156 and 232 cm−1, respectively, in magnetic cocrystals composed of 1,4/1,2-DITFB and nitroxide radicals.76 In addition, the Raman band at 779.8 cm−1 from the νC−I stretching vibration in tetraiodoethylene (TIE) shifts to lower wavenumbers by 7−25 cm−1 to 772.7 cm−1 in the TIE/Cl− cocrystal, 772.7 in the TIE/Br− cocrystal, and 756.2 cm−1 in the TIE/I− cocrystal.77 Natural bond orbital analysis is also an efficient method for understanding intermolecular complexes. It stresses the role of intermolecular orbital interactions in the complex, especially charge transfer. Zhang et al.78 showed the interaction energies of halogen-bond complexes B···XY (B = H2S, H2CS, and (CH2)2S; XY = ClF, Cl2, BrF, BrCl, and Br2) correlate well with the magnitude of the halogen atom σ-hole and with the quantity of charge transfer (qCT), respectively (Figure 11). These results imply that the charge transfer contribution is an important factor in the halogen bond formed by dihalogen molecules along with the electrostatic terms. For the π-hole bond there have also been several efforts to determine its physical nature, that is, the π-hole bond is driven mainly by the electrostatic and polarization terms. For example, Alkorta et al.17 used the GMIPp method to analyze the contributions of the electrostatic and polarization terms to the total interaction energy of complexes of several π-hole systems (electron-deficient π systems including perfluoro derivatives of benzene, naphthalene, pyridine, thiophene, and furan) with several different anions (F−, Cl−, Br−, H−, CN−, CNO−, and CH3−) (cf. Appendix I for the theory of GMIPp). The data listed in Table 7 show that the polarization energy ranged from onehalf to equal of the electrostatic energy indicating that the electrostatic energy with a possible polarization term plays a significant role in the stabilization of these π-hole bond complexes. Deyà et al.18 first described the π-hole···anion bond interactions between C6F6 and anions (the so-called “anion−π” interactions). This work shed light on the physical properties of

Table 7. Electrostatic, Polarization, and Dispersion− Repulsion Contributions (in kJ·mol−1) to the Total Interaction Energy Calculated Using the GMIPp Method at the RHF/6-31+G** Levela complexes

Eelst

Epol

EVW

Eint

C6F6···Cl− C4F4O···Cl− C4F4S···Cl− C5F5N···Cl− C10F8···Cl−

−49.4 −36.0 −25.5 −58.1 −59.8

−27.6 −24.3 −26.3 −29.3 −41.0

21.8 31.0 21.3 33.5 39.3

−55.2 −29.3 −30.5 −54.0 −61.5

a

Adapted with permission from ref 17. Copyright 2002 American Chemical Society.

π-hole bond using the MIPp method to determine if polarization is important (cf. Appendix I for the theory of MIPp). Taking C6F6···F− as an example, the variation in the individual energy components with the length of F−O (the center of the aromatic ring) shows that the induction term is similar to the electrostatic term in the distance range of 2.0−3.0 Å (cf. Table 8). Later, the physical nature of a series of π-hole bond complexes was explored using MIPp methods by Deyà et al.,29,79−82 where the main contributions to the total interaction energy were the electrostatic and polarization terms (cf. Table 9). Figure 12 Table 8. Electrostatic, Polarization, and Dispersion− Repulsion Contributions (in kJ·mol−1) to the Total Interaction Energy Calculated Using the MIPp Method at the HF/6-311+G** Level for the C6F6···F− Complex at Several Bond Distances (Angstroms)a distance

Eelst

Epol

EVW

Eint

1.5 2.0 2.5 3.0 3.5

−153.1 −93.9 −68.6 −53.0 −41.4

−183.4 −104.1 −58.3 −32.5 −19.8

4384.1 498.1 56.2 −2.1 −3.5

4047.5 300.1 −70.7 −87.6 −64.8

a

Adapted with permission from ref 18. Copyright 2002 Wiley-VCH Verlag GmbH & Co. KGaA.

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Table 9. Electrostatic, Polarization, and Dispersion−Repulsion Contributions (in kJ·mol−1) to the Total Interaction Energy Calculated Using the Developed MIPp Method at the HF/6-311+G** Level for the Compounds Interacting with Cl−a compounds

Eelst

Epol

EVW

Eint

Qzz

α∥

trifluoro-s-triazine hexazine 1,4-dichloroperfluorobenzene 1,3,5-trichloroperfluorobenzene s-triazine 1,3,5-trifluorobenzene

−54.0 −51.5 −33.9 −30.1 −9.2 −4.6

−18.8 −16.7 −25.9 −28.0 −17.2 −20.1

3.8 4.6 −2.5 −2.9 −1.2 −4.2

−69.0 −63.6 −62.3 −61.1 −27.6 −28.9

8.23 7.57 4.76 3.32 0.90 0.57

30.26 25.94 49.48 56.13 30.34 38.79

a Qzz: quadrupole moment (in B). α∥: molecular polarizabilities (au). Adapted with permission from ref 29. Copyright 2003 Wiley-VCH Verlag GmbH & Co. KGaA.

Figure 12. Correlation between the quadrupole moments (Qzz) and the electrostatic contribution (Eelst) to the total interaction energy and between the molecular polarizabilities (α∥) as well as the polarization contribution to the total interaction energy. Adapted with permission from ref 29. Copyright 2003 Wiley-VCH Verlag GmbH & Co. KGaA.

electrostatic term, whereas the dispersion, induction, and charge transfer terms contributed less. In addition, Frontera et al.84 analyzed the interactions between several six-membered inorganic rings with anions. The energy decomposition data using the DF-DFT-SAPT method indicated that the electrostatic interaction was dominant in all the π-hole bond complexes except for the borazine complexes (e.g., B3N3H3···Cl− complex, cf. Table 11). The electrostatic, induction and dispersion terms contributed equally.

indicates that the contributions of the electrostatic term and ioninduced polarization to the total interaction energies can be correlated with the quadrupole moment (Qzz) and the molecular polarizability (α∥) of the aromatic units containing the π-holes, respectively. The data listed in Table 9 suggests that the π-hole bond is dominated by the electrostatic interaction between the πhole and the anion as the Qzz of the π-hole increases (e.g., trifluoro-s-triazine, Qzz = +8.23 B). In contrast, it will be dominated by the polarization interaction as the Qzz of the π-hole decreases (e.g., 1,3,5-trifluorobenzene, Qzz = +0.57 B). In contrast to the above conclusions about the dominant role of the electrostatic and induction terms using the GMIPp and MIPp methods, researchers using the Morokuma or SAPT methods have indicated that the π-hole bond is primarily dominated by the electrostatic or electrostatic and induction terms. For instance, Tehrani et al.83 quantitatively decomposed the energy of the π-hole bond complexes of coinage metal anions (Au−, Ag−, and Cu−) with substituted benzene derivatives (cf. Table 10) via the Morokuma method and concluded that the largest contribution to the π-hole bond came from the

Table 11. SAPT Interaction Energy and Their Energy Components (in kJ·mol−1) for π-Hole···Cl− Complexes at the RI-DFT/aug-cc-pVDZ Level of Theory Using the DFT-SAPT Methoda

a

−1

Table 10. Interaction Energy Components (in kJ·mol ) for π-Hole···M− Complexes Calculated at the MP2/6-311+ +G**∪aug-cc-pVDZ-PP Level of Theory Using the Morokuma Methoda

a

complexes

Eelst

Eexch

Eoi

Edisp

Eint

C6F6···Cu− C6F6···Ag− C6F6···Au−

−198.3 −185.3 −202.1

212.5 198.7 221.3

−53.1 −51.8 −79.9

−23.4 −28.4 −47.3

−62.3 −66.9 −107.9

complexes

Eelst

Eexch

Eind

Edisp

Eint

N6···Cl− B3O3H3···Cl− B3N3H3···Cl− B3N3···Cl− B3S3H3···Cl−

−93.7 −82.8 −21.8 −125.9 −74.9

87.4 94.1 46.4 125.1 101.2

−23.0 −33.5 −21.7 −36.8 −41.0

−22.6 −25.5 −18.8 −29.3 −30.5

−51.9 −47.7 −15.9 −66.9 −45.2

Adapted with permission from ref 84. Copyright 2012 Elsevier Ltd.

Also, in the π-hole···anion bond complexes of halide (F−, Br−, and I−), linear (CN−, NC−), and planar anions (NO3− and CO32−) with the π-hole systems (tetrafluoroethene, hexafluorobenzene, and 1,3,5-triazine),19 the largest contributions to the total interaction energy are the electrostatic and induction energies. In the other complexes, the dispersion energy is comparable to the electrostatic and induction energies taking the C3N3H3···anion complexes as an example as listed in Table 12. Kim et al.85 employed the DFT-SAPT method and reported that the electrostatic energy is substantially larger than other energy

Adapted with permission from ref 83. Copyright 2013 Springer. 5080

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quadrupole interactions are simply electrostatic interactions in the π-hole bond case.26,29,79,80,92 According to the the Hellmann−Feynman theorem, energy decomposition does not make sense. There are several problems with energy decomposition procedures: one is that some of the energy components are real (i.e., physically measurable) while others are simply constructs derived from a mathematical model. Another difficulty is that many of these components are not independent of each other, so that different decomposition schemes can increase the role of one at the cost of another. Also, a major conceptual problem with decomposition analyses is their failure to distinguish between what has a physical basis and what results from one or more of the mathematical models used in the calculations.88 Charge transfer is simply a mathematical formulation of the polarization that is an intrinsic part of any Coulombic interaction. Thus, to argue polarization, charge transfer or dispersion which is dominant in the σ-hole bond and π-hole bond is not valuable according to the Coulombic interaction model.88,91 However, anyway, it is also noted that the popular charge transfer theory and energy decomposition methods can be still accepted by many researchers, and they can still provide very important and useful references for revealing the nature of the noncovalent interaction to a certain degree. In addition, as described above, the formation of a σ-hole bond is accompanied by the red shift of νC−I in the FT−IR or Raman spectra. All of these red shifts can be understood and predicted using the frameworks of electrostatic, induction, and dispersion interactions. They do not need to invoke the orbitals according to Politzer et al.14,40,90 However, as described above, molecular orbital theory including natural bond orbital analysis is still useful in the explanation or analysis of the red-shift phenomenon. It is very clear from molecular orbital theory or charge transfer interactions that the shift is the result of n → σ* or π → σ* (or HOMO to LUMO) transitions71,93,94 or spin density delocalization in C−X of the σ-hole bond complexes.95,96 Moreover, the electrostatic nature of the σ-hole bond and πhole bond seems not to encompass everything. The covalency of weak interactions should also be notable. For example, Beer et al.97 revealed by K-edge X-ray spectroscopy significant charge transfer from halide to the iodotriazole halogen-bond donors and further revealed the degree of covalency in the halogen bond, which is comparable to that observed in transition metal complexes. Also, the results are supported by density functional theory calculation. Theoretical calculation reveals that 1,2,4,5tetracyanobenzene as the π-hole bond donor can form a strongly covalent σ complex with F− while forming the weakly covalent σ complex with Cl− and Br−.20,98 Furthermore, through employing the quantum theory of atoms in molecules method, Marek et al.99 revealed that compared to the closely related covalent anion−σ complexes, the π-hole bond systems benefit from an extensive degree of electron sharing between the anions and all atoms of the π-rings. The number of all shared electrons (0.16−0.35 au) is significantly larger that for the conventional noncovalent interaction, with a typical electron sharing of ∼0.10 au, suggesting that the π-hole bond complexes benefit from a multicenter covalency. Also, the interacting quantum atomsenergy decomposition analysis validated the above results. Sometimes the noncovalent interactions are too strong or too weak. The strong noncovalent interaction may have a certain degree of covalency, implying that there is no strict boundary between noncovalent and covalent interactions in some cases. In fact, it is not novel because the compton scattering experiment

Table 12. SAPT Interaction Energy Components (in kJ· mol−1) for the C3N3O3H3···Anions Complexes and C3N3H3··· Anions Complexes Calculated at the MP2/aug-cc-pVDZ Levela πhB complexes

Eelst

Eexch

Eind

Edisp

Eint

C3N3O3H3···Cl− C3N3O3H3···NO3− (πs) C3N3O3H3···NO3− (πe) C3N3O3H3···ClO4− (πs) C3N3H3···F− C3N3H3···Cl− C3N3H3···Br− C3N3H3···CN− C3N3H3···NC− C3N3H3···NO3− C3N3H3···CO32−

−118.5 −71.5 −92.0 −81.5 −78.4 −51.0 −48.1 −54.8 −47.6 −38.8 −141.3

96.5 65.8 79.0 92.2 154.7 129.3 137.4 121.8 92.7 96.7 329.4

−33.8 −24.7 −30.7 −25.9 −90.4 −75.9 −79.9 −69.6 −50.2 −38.3 −182.2

−29.2 −35.8 −31.9 −41.7 −24.9 −25.1 −30.2 −27.4 −26.2 −39.9 −74.9

−72.8 −57.9 −65.3 −49.2 −38.9 −22.6 −20.8 −29.9 −31.3 −20.2 −68.9

a

Adapted with permission from refs 85 and 19. Copyright 2008 and 2004 American Chemical Society, respectively.

components in these π-hole bond complexes formed by the πhole systems (cyanuric acids, C3N3O3H3, and cyameluric acids, C6N7O3H3) with Cl−, planar anion NO3−, and tetrahedral ClO4− (cf. Table 12, taking C3N3O3H3···anion complexes as an example), that is, the electrostatic interaction is predominant in these π-hole bonds, but other energy components, i.e., induction and dispersion terms, are important and cannot be neglected. Unfortunately, relevant references for exploring the nature of both the σ-hole bond and the π-hole bond by ALMO are not currently available (cf. Appendix I for ALMO theory). In summary, for the σ-hole and π-hole bond complexes, the electrostatic attraction is dominant in most cases (the proportion of Eelst is 51−68%). In some cases, the electrostatic and induction (the proportions of Eelst and Eind are 49−67% and 31−51%, respectively; cf. Tables 7 and 8) or induction (the proportions of Eelst and Eind are 33−40% and 33−50%, respectively; cf. the C3N3H3···anion complexes in Table 12) terms dominate. In a few cases, the charge transfer or orbital terms (the proportion of Eoi is 47−72%; cf. Table 6) are dominant. However, for weakly bound complexes, dispersion, induction, or dispersion and induction are dominant.64−66 It is also noted that energy decomposition is a kind of mathematic treatment of the physical nature of the noncovalent interaction. It is still controversial whether the decomposed terms can correctly/accurately reflect the nature of interactions or the different contributions can be separated clearly or accurately. Moreover, the different methods may give different results.38,64,86 2.2.3. Coulombic Interaction. On the nature of both the σhole bond and the π-hole bond, it is worthy of appreciation that Politzer and Clark’s group38,40,62,87−90 proposed that polarization (induction) and dispersion are an intrinsic part of any Coulombic interaction according to the Hellmann−Feynman theorem, that is, the σ-hole bond and π-hole bond are purely Coulombic in nature. They stress the physical reality of noncovalent interactions, the electrostatic interaction leaded by the polarization of the atom’s electronic charge toward the covalent bond should be the nature of various weak interactions, and anything that enhances this polarization will increase the magnitude of the σ-hole: increased polarizability of the atom itself or the electron-withdrawing nature of other atoms/groups within the molecule as described in ref 91. Moreover, the 5081

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such that the actual bond angle may deviate somewhat from 180°. For the π-hole bond, Politzer et al.39 indicated by calculation that the bond angle of complexes formed between inorganic πhole molecules and NH3/HCN can deviate from 90° (up to 100°) due to the effects of secondary interactions. In general, the bond angles may span a wide range in the gas phase, i.e., from 77° to 108°. Concurrently, Mooibroek et al.112 systematically analyzed noncovalent interactions between organic π-hole molecules (−C6H5/−C6F5) and solvent molecules or anions through the retrieval of CSD. They observed that both the πhole···anion and the π-hole···lp interactions had directional character. In the solid state, the bond angles also span from 75° to 90°.21,113 In addition, from the cocrystal structure of 1,3,5triazine and inorganic nitrates, Gamze et al.37 observed that the π-hole bond angles are 65.9−76.1°. Thus, it can be concluded that the π-hole bond is limited to the π-hole boundary between the π-hole plane and the bond acceptor. In addition, the equilibrium position of the anion with respect to the aromatic ring in the π-hole···anion bond complexes may vary with specific circumstances.114 For inorganic small molecules without π-bond or conjugated π systems, the directionality is similar to that of the σ-hole bond.39 Both the σ-hole bond and the π-hole bond have high directionality, but the π-hole bond is less directional than the σhole bond as shown in Figure 14, where θ refers to the bond angle

unambiguously demonstrated that the hydrogen bond also is partly covalent besides its main electrostatic attraction in an O− H···O bond.100,101

3. DIRECTIONALITY AND STRENGTH OF THE σ-HOLE BOND AND π-HOLE BOND 3.1. Directionality

Directionality is one of the most important characteristics of intermolecular interactions. The directionality of the σ-hole bond refers to the angle between the Y−X covalent bond and the vector direction from the center of the σ-hole to the bond acceptor. Similarly, the directionality of the π-hole bond refers to the angle formed between the σ-framework plane and the vector direction from the center of the π-hole (or interacting atom/s) to the bond acceptorit resembles a mortise−tenon joint structure,102 as shown in Figure 13. The directionality of the σhole bond and π-hole bond can be described as follows.

Figure 13. Photo of a Chinese wooden building using tenon−mortise structures (The protruding part of the wooden member is called the tenon, and the concave part is called the mortise. The connection between the mortise and the tenon along the designated directions forms the basic structure of wooden buildings with defined geometries).

For the σ-hole bond with a halogen bond as an example, Murray-Rust et al.103−105 analyzed the Cambridge Structural Database (CSD) and found that the bond angles span from 160° to 180°. Theoretical calculations confirmed that the bond angles also range from 160° to 180° in the gas phase,15,106,107 whereas in solution they are close to 180°.107,108 Previously, the directionality of the halogen bond was thought to arise from n → σ* or π → σ* charge transfer interactions.109−111 However, the directionality can be well understood based on the σ-hole model. The directionality of halogen bond is determined mainly from the anisotropic charge distributions of the covalently bound halogen atoms. Halogen atoms have an s2px2py2pz1 electron configuration, and when halogen atoms interact with other atoms such as carbon to form a covalent bond, the single electron in the pz1 orbital will move to the center of the C−X axis. This results in the formation of a σhole, a positive potential on the outermost portion of the X surface centered around the C−X bond, and a belt of negative electrostatic potential perpendicular to the C−X axis caused by the other three pairs of unshared electrons.9 On the anisotropic charge distributions of the covalently bound halogen atoms and origination of the σ-hole, an alternative description is that when the atom forms a covalent bond, some of its electronic charge is polarized toward the bond region, leading to the atom’s electronic density being diminished in its outer region (along the extension of the bond) but increased on its equatorial sides.38 When there is a suitable bond acceptor or donor, they will interact along the direction of the σ-hole or perpendicular to the C−X axis. The type of orbitals and steric hindrance of the bond acceptor can also influence the bond angle of the halogen bond

Figure 14. Comparison of the directionalities and bond angles of the σhole bond (top) and π-hole bond (bottom). θ refers to the bond angle (approaching 180° and 90° in the σ-hole bond and π-hole bond, respectively). ϕ refers to the angle between the Y−X axis and the π plane in the case of the σ-hole···π bond (approximately 90°), and α refers to the dihedral angle between the bond donor and acceptor planes in the case of the π-hole···π bond. Lp refers to lone electron pair or lone single electron.

and α refers to the dihedral angle between the bond donor and the acceptor planes in the case of a π-hole···π bond. The anion or lone electron pair can interact with the center of the π-hole and the center of a CC or a carbon atom. 3.2. Strength

As described above, in general, the strength of the halogen bond, as a representative of the σ-hole bond, correlates well with the magnitudes of the positive surface electrostatic potential in the σ5082

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Figure 15. Surface electrostatic potential of XF compounds shows the potential abilities of different halogen atoms in XF to form a halogen bond. The magnitudes of the σ-hole in XF (X = F, Cl, Br, and I) are 56.5, 169.3, 205.9, and 258.3 kJ·mol−1, respectively. Results were calculated at the M06-2X/augcc-pVTZ(-pp) level of theory by the authors’ group.

Figure 16. Increasing σ-hole Vs,max of Br atoms in bromobenzene molecules with different groups. Results were recalculated at the M06-2X/aug-ccpVTZ level of theory according to ref 61. Adapted with permission from ref 61. Copyright 2009 American Chemical Society.

(56.5 kJ·mol−1) < Cl (169.3 kJ·mol−1) < Br (205.9 kJ·mol−1) < I (258.3 kJ·mol−1) (cf. Figure 15). Karadakov et al.123 reported that the interaction energies of F−X···CNCH3 are −49.5, −66.1, and −81.4 kJ·mol−1 for FCl, FBr, and FI, respectively. These results indicate that for a given halogen-bond acceptor, the more positive the σ-hole of the halogen-bond donor is the stronger the halogen-bond interaction becomes. (2) The effect of the hybrid state of the carbon atoms covalently bound to the halogen atom: the halogen-bond complexes formed by halocarbons usually follow the order Hal−C(sp) > Hal−C(sp2) > Hal−C(sp3).7,124 In general, halogenated alkynes are good halogen-bond donors. (3) The effect of an electron-withdrawing substituent that is directly or indirectly bound to a halogen. For example, CF3Cl, CF3Br, and CF3I molecules all have a positive σ-hole region, while CH3Cl does not have a σ-hole. The σ-holes in the CH3Br and CH3I molecules are much weaker. The calculation also showed that the progressive introduction of F atoms to CH3I raised the interaction energy from −10.5 (CH3I···NH3) to −26.8 kJ·mol−1 (CF3I···NH3).115 In addition, as shown in Figure 16, the introduction of electron-withdrawing groups such as −F and −CN can significantly tune the surface electrostatic potential of the σ-hole on halogen atoms.61 This can enhance the strength of the halogen bond. Politzer et al.125 also noted that the introduction of fluorine substitutions can dramatically affect the halogen-bond strength: the interaction energy of the C6F5Cl···acetone complex is 102% greater than that of the C6H5Cl···acetone. Therefore, perfluorohalogenated alkenes and their analogues are good halogen-bond donors. When they interact with suitable halogen-bond acceptors, the strength of the resulting halogen bond is greater than a hydrogen bond.7 The strengths of the π-hole bond are also correlated with the magnitudes of the positive surface electrostatic potential of the π-

hole and negative surface electrostatic potential in the electronrich site, respectively (cf. Figures 4 and 11a). However, the strength of the halogen bond is affected also by several chemical factors. In terms of halogen-bond donors, the main factors are summarized as follows. (1) The characteristic effect of the halogen atom. As the electronegativity of the X atom (X = F, Cl, Br, and I) becomes smaller, the corresponding polarizability becomes stronger. Consequently, the strength of the halogen bond formed by different halogen atoms decreases in the order of I > Br > Cl > F. Resnati et al.115 obtained the interaction energies of CF3X···NH3 (X = Cl, Br, and I) complexes using MP2 calculations: −26.8 kJ· mol−1 for CF3I···NH3, −19.7 kJ·mol−1 for CF3Br···NH3, and −9.6 kJ·mol−1 for CF3Cl···NH3. Because the surface electrostatic potential surrounding the F atom (the most electronegative element) is negative in most cases, it is difficult to form a halogen bond with this compound. It is therefore the least likely to function as a halogen-bond donor. However, some theoretical calculations and experimental results indicate that F atoms can indeed work as halogen-bond donors and interact with electronrich elements to form halogen-bond complexes under specific circumstances including F2 or CN−F,43,116−120 although their strengths are much weaker than other halogens. In another example, F atoms in the −CF3 moiety of CF3SO2OCOF or 3-nitro-trifluoroacetylbenzene molecules have a positive surface electrostatic potential on their central surface and can interact with lone electron pair-containing neutral atoms and anions due to the presence of a powerful electron-withdrawing group.43 Similar to I2,121 calculations indicate that F2 can also function as a halogen-bond donor and form the halogen bond.43,116,122 In addition, the surface electrostatic potential of X in XF molecules follows the order F 5083

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Figure 17. Increasing Vs,max of the π-hole for triazines/fluorinated benzenes with different groups: (a) 1,3,5-triazine, Vs,max = 61.2 kJ·mol−1; (b) trifluoro1,3,5-triazine, Vs,max = 151.9 kJ·mol−1; (c) cyan-1,3,5-triazine, Vs,max = 217.1 kJ·mol−1; (d) nitro-1,3,5-triazine, Vs,max = 254.6 kJ·mol−1; (e) fluorobenzene, Vs,max = −8.8 kJ·mol−1; (f) 1,3,5-trifluorobenzene, Vs,max = 9.6 kJ·mol−1; and (g) hexafluorobenzene, Vs,max = 76.7 kJ·mol−1. All results are recalculated at the M06-2X/aug-cc-pVTZ level of theory by the authors’ group.

neutral species, the strength of the σ-hole bond and π-hole bond also increases as the electronegativity of the electron-rich atom increases (such as Cl, Br, I, N, O, S, etc., except for F atoms). For example, the halogen bond became stronger in the order N > O, S in perfluorocarbons127 and O > N > S in hydrocarbons.128 In addition, for a given electron-rich atom, the hybridization state and steric hindrance also affect the strength of the halogen bond. Taking the N atom as an example, the effect follows the order sp3 (amine) > sp2 (pyridine) > sp (nitrile) and the strength of the halogen bond formed by various amines decreases in the order tertiary amine > secondary amine > primary amine such as 1azabicyclo[2.2.2]octane and diazabicyclo[2.2.2]octane, which can act as the strongest halogen-bond acceptor due to the exposed lone electron pair on the N atom without steric hindrance. In some cases, the interaction strength of a tertiary amine with a halogen atom may be weaker than that of a secondary amine due to steric hindrance.

hole and negative surface electrostatic potential of the electronrich site (cf. Figures 5 and 6). The magnitude of the π-hole is dependent on the substituent groups or atoms bound to the π system. The electron charge density and polarization of the negative sites also dramatically affect the strength of the π-hole bond. The aromatic ring (π-hole bond donor) should have a large positive surface electrostatic potential in order to form a strong πhole bond for a given bond acceptor. Common electronwithdrawing groups such as −F, −CN, and −NO2 all increase the surface electrostatic potential of aromatic π-hole systems. As illustrated in Figure 17, the magnitude of the π-hole becomes greater as the electron-withdrawing substituent group becomes stronger. In the 1,3,5-triazine and trifluoro/cyano/nitro-1,3,5triazine molecules they are 61.2, 151.9, 217.1, and 254.6 kJ· mol−1, respectively. In addition, the magnitude of the π-hole also becomes greater as the number of F substituents increases, e.g., for fluorinated benzene, −8.8 (−F), 9.6 (−3F), and 76.7 (−5F) kJ·mol−1. Therefore, as the electron-withdrawing ability and number of substituent groups increase, the π-hole becomes more positive and the resulting π-hole bond is stronger. For example, the interaction energies of the π-hole bond complexes between molecules (in Figure 17a and b) and Cl− are −20.1 and −61.9 kJ· mol−1 as computed at the MP2/6-31+G*//MP2/6-31+G* level, respectively.16 In addition, the magnitude of several inorganic πhole molecules, e.g., 1,3,5,2,4,6-triazatriborinine, borthiin, boroxine, and hexazine, are 117.2, 133.9, 159.0, and 368.2 kJ mol−1, respectively, and the corresponding energies of the π-hole bond complexes with Cl− are −46.0, −46.4, −62.8, and −63.2 kJ mol−1.84 The electron-donating properties of the σ-hole bond and πhole bond acceptors are also an important consideration. Anions are usually better bond acceptors than the neutral species,124,126 indicating the great potential of the σ-hole bond and π-hole bond in anion coordination chemistry. The more dissociated an ion pair is the stronger is the σ-hole bond and π-hole bond formed. To be more specific, for the anion species, smaller anions such as F− and Cl− have greater polarizing abilities and lead to shorter equilibrium distances in the σ-hole···anion and the π-hole···anion complexes. Therefore, they possess more negative energies and stronger σ-hole bonds and π-hole bonds.26,114 (The examples and the relevant literature are described in section 6.) For the

4. TYPES OF σ-HOLE BOND AND π-HOLE BOND ACCEPTORS On the basis of the properties of the bond donor, the halogen bond, chalcogen bond, pnicogen bond, and tetrel bond are subsets of the σ-hole bond mentioned above, and the iodine bond, bromine bond, and chlorine bond are subsets of the halogen bond.129 However, the properties of the bond acceptors in the σ-hole bond and π-hole bond are important, too.130 4.1. n-Type Bond Acceptors

The bond acceptors with a lone pair possessing atom (e.g., N atom of a pyridine or an amine, O atom of a carbonyl group) play an important role in assembling supramolecular structures or functional materials. For example, the supramolecular halogenbond cocrystals assembled mainly by the C−I···N, C−I···F, as well as π−π interactions exhibit strong violet-blue photoluminescence or unique white light emission and two-dimensional optical waveguide properties.131 Also, C−Br···O halogen bond is thought to be an important factor that enhances phosphorescence of bromobenzaldehyde compounds in crystals by more direct spin−orbital coupling.132 Halogen atom substituents in halogen-bond donor molecule can also function as special n-type bond acceptors due to anisotropic charge distributions on the halogen atoms. The 5084

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Figure 18. Proposed structures of the C−X···π interactions. (a, b, c, and f) Above the bond model, (d) above-the-center model, and (e) above-thecarbon model.

Figure 19. 1,4-DITFB and bent 3-ring-N-heterocyclic hydrocarbons cocrystals assembled via C−I···N and C−I···π halogen bonds emit green, orange yellow, and orange phosphorescence.161

(XF, XCN, XCCH, and XCF3, X = F, Cl, Br, and I) to determine the bond type, i.e., the π-hole···lp bond or X···π halogen bond. Borazine readily formed both the π-hole···lp bond with a halogenated molecule and X···π halogen bond with a stronger halogen bond donor. The π-hole···lp bond may be changed into the X···π halogen bond with an increase in the interaction strength.

contacting interaction along the negative belt of each halogen atom is named a Type I halogen−halogen interaction; it is a normal van der Waals interaction of the dispersion−repulsion type due to close packing of the polarized nonspherical halogens with no need to invoke a specific attractive force. Importantly, the σ-hole of a halogen atom can interact with the negative belt region of the surface electrostatic potential of another halogen atom on the equatorial position perpendicular to the C−X axis. The halogen-bond pattern is named a Type II halogen−halogen interaction and is a typical halogen bond. As an expansion of the Type II interaction, triangular trihalogen interactions are named ,Type III halogen−halogen interactions.133−141 Furthermore, halogen−halogen interactions combined with hydrophobic interactions are very useful. For example, both hydrophobic 3-bromo- and 3-iodo-carbazole can form nano/ microsized crystal particles via self-assembly in aqueous solution as mediated by halogen−halogen and hydrophobic interactions.142 These interactions can stabilize the triplet state of luminescent molecules, inhibit oxygen quenching, and increase phosphorescence intensity. For the π-hole bond, Sarkhel et al.143 first noticed the interactions between lone electron pairs of oxygen atom in DNA, RNA, and protein molecules and electron-deficient or positively polarized aromatic or nitrogen heterocyclic rings. In crystals, Mak et al.144 constructed two supramolecular frameworks based on mononuclear Cu(II) building blocks and confirmed four types of unusual intermolecular π-hole···OC interactions between carbonyl and pyridyl moieties. This may be significant for the construction of inorganic−organic hybrid frameworks using a combination of coordination binding and noncovalent interactions. Borazine or “inorganic benzene” has properties that are different from benzene, despite the fact that they have similar structures and electronic properties. Li et al.145 studied the complexes formed by borazine and four halogenated molecules

4.2. π-Type Bond Acceptors

The π-type σ-hole bond and π-hole bond acceptors appear important because of their good luminescent, conducting properties or others in materials field. Studies of the halogen bond involving π-type bond acceptors can be traced back at least to the late 1940s, when Benesi and Hildebrand studied the socalled π−σ* charge transfer complexes formed by iodine and benzene or its derivatives.5 The π-type bond acceptors include not only ethylene, ethyne, cyclopropene, and carbonyl compounds with simple multiple bonds (e.g., CC, CC, and CO, etc.) but also aromatic compounds with conjugated π electrons (e.g., benzene, pyridine, furan, thiophene, etc.). Calculations and crystal data indicate that halogen atoms tend to rest in sites that are perpendicular to the double or triple bonds along the direction of the σ-hole to form T-shaped structures146−151 (Figure 18a, 18b, and 18c). For interactions between halogen atoms and aromatic compounds, the C−X axis is also likely to be perpendicular to the plane of the aromatic ring but is comparatively complex. Hassel and Strømme152,153 first confirmed that Br2 is positioned above the benzene ring centroid in a cocrystal of benzene/Br2 (Figure 18d). Later, Kochi et al.154 found that Br2 was actually located above the rim of the benzene based on observations of Br2-benzene and Br2-methylbenzene cocrystals. They described eq 2 to estimate the “above-thecarbon/bond/center” structure (Figure 18e and 18f) 5085

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Figure 20. C−Br···π, C−H···π, and π-hole···π bonds and π−π delocalization in the 1,4-DBrTFB/phenanthrene cocrystal and the corresponding phosphorescent photo under 365 nm light.50

Figure 21. Radical monomers in cocrystals composed of 1,2-/1,4-DITFB and plots of χmT vs T with the best fit result of the 1D Bonner−Fisher model or S = 1/2 dinuclear model (solid line) for 1, 2, and 3. Reprinted with permission from ref 76. Copyright 2013 American Chemical Society.

η=1+

orange phosphorescence, respectively (Figure 19). This is due to different degrees of spin−orbital coupling due to a differential C−I···π halogen bond in strength and position.161 In addition to the common π-type bond acceptors, planar or linear anions with delocalized π bonds such as NO3− or N3− can also interact with aromatic π-holes through the π-hole···π bond.16,162 For organic π-type bond acceptors, the π-hole bond still has not as yet received much attention relative to the σhole···π bond represented by the C−X···π halogen bond. More than two decades ago it was noted that the cocrystal structure of C6H6 and C6F6 had an alternating arrangement of C6H6 and C6F6 in a face-to-face geometry.163 Williams164 used the molecular electric quadrupole moment model to show that the interactions between C6H6 and C6F6 were electrostatic rather than a π → π*/σ* charge transfer. Moreover, their strong intermolecular polarization caused an induced dipole moment of 0.44 D, almost l/8 of an electron transferred over a typical intermolecular spacing of 3.7 Å. This was an additional contribution to the binding interaction. However, from another perspective, the interactions between C6H6 and C6F6 can be more intuitively explained as a π-hole···π bond. As shown in Figure 20, the π-hole of 1,4-DBrTFB and the σhole of Br may indeed interact with the conjugated π system of phenanthrene to form a π-hole···π and σ-hole···π bond, respectively, in the magenta phosphorescent cocrystal composed of 1,4-DBrTFB and phenanthrene.50 In general, pyrene dimers

2 d12 − D2 d12 − D2 +

d 2 2 − D2

(2)

where d1 and d2 refer to the distances between the halogen atoms and the nearest two carbon atoms in the benzene ring, d1 < d2 and D refers to the shortest distance between the halogen atom and the benzene ring or C−C bond. If the halogen atom is located above a C atom (d1 = D) then η = 1; if the halogen atom is located above the C−C center/bond (d1 = d2) then η = 2. Shen et al.155 reported that the C−I···π halogen bond also obeyed this rule in cocrystals of 1,4-DITFB with biphenyl, naphthalene, and phenanthrene. In addition, the calculations also indicated that the “above-the-carbon” or “above-the-bond” geometries had the lowest energy and most stable conformations.156,157 In general, the strength of the halogen bond formed with a π-type acceptor is weaker than that with an n-type acceptor for a given halogenbond donor. The C−I···π halogen-bond and other weak interactions have been used together to successfully assemble organic phosphorescent cocrystals of 1,4-/1,2-DITFB (halogen-bond donor) and conjugated polycyclic aromatic hydrocarbons or heterocyclic arenes (halogen-bond acceptor).155,158−160 An interesting example is that the cocrystals assembled from 1,4-DITFB and three bent 3-ring-N-heterocyclic hydrocarbons (phenanthridine, benzo[f ]quinoline, and benzo[h]quinoline; mainly via C−I···N and C−I···π halogen bonds) emit green, orange-yellow, and 5086

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Figure 22. (a and b) Competition between the π-hole···π/lp and C−I···π/lp bonds. (c) Direction of the charge transfer in complexes in which the two bonds coexist. (a) Reprinted with permission from ref 179. Copyright 2012 AIP Publishing LLC. (b) Reprinted with permission from ref 180. Copyright 2012 Wiley-VCH Verlag GmbH & Co. KGaA. (c) Reprinted with permission from ref 181. Copyright 2012 American Chemical Society.

The free radical as a π-hole bond acceptor also should be useful in crystal engineering, magnetic functional materials, and even biological systems, e.g., internal interactions between various free radicals (N−O•, O2−•, OH•) and the π-holes in the body.

are very easily formed via π−π stacking, and their interaction energies are from ca. −49.4 (3.4 Å separation) to −39.4 kJ·mol−1 (3.6 Å separation).165 However, the calculated energies of the πhole···π bonds in the DITFB/pyrene cocrystals were −53.0 (1,4DITFB/pyrene) and −58.7 kJ·mol−1 (1,2-DITFB/pyrene). This implies that the π-hole···π bond may overcome the π−π stacking of pyrenes to modulate its crystal structure, phosphorescent spectra, and decay kinetics further.159,166

4.4. Anion-Type Bond Acceptors

Halides and pseudohalogen anions (Cl−, Br−, I−, CN−, SCN−) are important anion-type σ-hole and π-hole bond acceptors. In addition, other more complicated anions can work as bond acceptors including inorganic NO3−, SO42−, ClO4−, and PO43− and organic −COO− and −SO3−171 as well as the chiral Dcamphorsulfonate anion.172 The investigation on anion-type bond acceptors is one of the hottest topics in both the σ-hole bond and the π-hole bond based on anion recognition which will be discussed in detail later in section 6.

4.3. Free-Radical-Type Bond Acceptors

Organic nitroxide radicals (N−O•) as σ-hole bond acceptors due to a number of advantageous characteristics including stability, optical transparency, higher electron density, and good solubility are very useful in emerging fields such as spintronics and quantum computing, etc. Moreover, the free-radical-type bond acceptors involving N−O• have attracted significant attention especially in the assembly of molecular magnetic materials.167−169 Morishima et al.167,168 provided the earliest reports of interactions between N−O• and halogenated molecules based on 13C NMR results and explained them in terms of spin delocalization or charge transfer interactions using molecular orbital calculations. Schollhörn et al.169 synthesized a novel crystalline material with one-dimensional, infinite, supramolecular chains using halogen-bond interactions between N−O• and 1,4-DITFB. Later, halogen-bond paramagnetic complexes were also detected in several halocarbon solvents,170 and the formation of the halogen-bond complexes was characterized by the marked broadening of the electron-spin resonance lines of N−O•. These results might be quite helpful in the identification of halides other than fluorine using the electron-spin resonance signal changes of N−O•. Pang et al.76 showed that in cocrystals of 1,4/1,2-DITFBs and 4-benzoyloxy-2,2,6,6-tetramethylpiperidine-1-oxy (BTEMPO) free radicals (Figure 21) the distances between free radicals are longer (6.308 Å) or shorter (3.426 Å) than that (6.128 Å) in BTEMPO single crystal. However, the antiferromagnetic coupling between free radicals in cocrystals was strengthened relative to that in a single crystal of BTEMPO. This is attributed to the spin density delocalization of the free radical → σ*(C−X). This result provides new ideas for creating novel molecular magnets and expands the application of halogen bonds in the assembly of functional materials because of the interaction modulated by a halogen bond.

5. INTERPLAY BETWEEN THE σ-HOLE BOND AND π-HOLE BOND Common noncovalent interactions including hydrogen-bond, halogen-bond, π-hole···anion/lp/π, or cation−π interactions173 have always coexisted in complexes in the form of competitive or cooperative interactions and play an important role in supramolecular chemistry, molecular biology, crystal engineering, and related fields.26 Understanding these relationships is significant for the design of novel materials or supramolecular systems. Experiments and theoretical calculations have recently confirmed the cooperative effects between the π-hole···anion bond and the hydrogen bond or the π-hole···π bond174−176 as well as between the halogen bond and the hydrogen bond or lithium bond,177,178 etc. Several recent articles reported on the interplay (cooperation, competition, and orthogonality) of the σ-hole bond and πhole bond. Wang et al.179,180 confirmed the formation of the C−X···π/lp and π-hole···π/lp bonds in solution based on the movement of opposite directions in the chemical shifts of the 13C NMR bonded to the halogen atoms upon addition of bond acceptors. The C−X···π/lp and π-hole···π/lp bonds are competitive (Figure 22a and 22b). DFT calculations supported this conclusion. In binary liquid mixtures of C6F5X (X = Cl, Br) and C6D6 it was observed that there was no C−Cl/Br···π bondonly the πhole···π bond in the system. In contrast, the C6F5I−C6D6 system had only the C−I···π bond and no π-hole···π bond, that is, the 5087

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Figure 23. Single-crystal structures of the cocrystal: (left) packing diagram of an infinite structure formed by the σ-hole···N, π-hole···F bonds, and F−F contacts; (right) σ-hole···N, π-hole···F bonds, and F−F contacts in the cocrystal. Bond distances are shown in Angstroms. Color codes: C, gray; H, white; N, blue; F, light blue; I, purple. Reprinted with permission from ref 185. Copyright 2013 Wiley-VCH Verlag GmbH & Co. KGaA.

C−I···π bond was stronger than the π-hole···π bond but the C− Cl/Br···π bond was weaker than the π-hole···π bond. This group also found that only the C−I···lp and a few C−Br··· lp rather than the C−Cl···lp bond can compete successfully with the π-hole···lp bond in binary systems of C6F5X and different deuterated solvents with lps (such as CD3CN, CD3COCD3, CD3OD, DMSO[D6], etc.). Lu et al.181 concluded that the direction of charge transfer for the halogen bond and π-hole bond coexisted in the same complex and explains the energetic effects between the two interactions. As shown in Figure 22c, the heteroatomic cyclic molecule (from Frontera’s work182) is the πhole bond donor and accepts the charge from X−. It simultaneously is a halogen-bond acceptor and donates charge to the FX molecules. The different direction of charge transfer for the two bonds would strengthen these interactions. This results in a cooperative effect. In contrast, the 1,4-DITFB molecule as the π-hole and halogen-bond donor accepts the charge from both of the negative sites (X− and lp of NY3). The same direction of charge transfer for the two bonds leads to the additive and diminutive effects. Yan et al.183 reported that 19F NMR chemical shifts of C6F5Br and C6F5I all shifted to higher field with an increase in Cl− concentration, whereas the chemical shifts of C6F6 and C6F5Cl shifted to lower fields in acetonitrile. The results show that C6F5X (X = Br and I) molecules were prone to form the halogen bond with Cl−, and the corresponding association constants and interaction energies were 0.18 and 38.0 M−1 and −61.9 and −93.3 kJ·mol−1, respectively. The C6F5X (X = F and Cl) with Cl− formed the π-hole···Cl− bond complexes with corresponding association constants and interaction energies of 0.11 and 0.23 M−1 and −58.0 and −59.4 kJ·mol−1, respectively. This means that the σ-hole···Cl − bond and π-hole···Cl − bond are competitive, and there is a large difference in the association constant of C6F5I···Cl− relative to the others. This can be used to separate iodoperfluorobenzene from mixtures containing hal-

operfluorobenzene analogues via solid-phase abstraction. Zhao et al.184 indicated that triethylphosphine oxide interacted with C6F6 and C6F5Cl through the π-hole···OP bonds and with C6F5I through the σ-hole···OP bond. These two interactions were comparable and should coexist competitively in C6F5Br. Gao et al.185 assembled a cocrystal with repeated 8-F-atom units as the basic structural motif based on a combination of the bifurcated C−I···N···I−C σ-hole bonds and antiparallel double π-hole···F bonds between 1,2-DITFB and acridine; the cocrystal structure is shown in Figure 23. The combination of the σ-hole and the π-hole bonds or together with other weak interactions could play a significant role in assembling the function materials, molecular recognition, and so on.

6. APPLICATION OF THE σ-HOLE BOND AND π-HOLE BOND IN ANION RECOGNITION Various useful crystal materials can be designed using a halogen bond including temperature-sensitive, magnetic, or optically crystalline materials.124,132,186−193 The halogen bond provides a new method for understanding the recognition mechanism of chemical and biological molecules,194−200 attracts great interest in drug design,201−203 and has potential applications in chemical sensing and molecular recognition.204−208 In comparison to the halogen bond (σ-hole bond), applications of the π-hole bond in functional materials are still relatively rare but the number of studies is increasing,185 and the importance of the π-hole···anion bond in anion recognition and the π-hole···lp bond in biochemistry or drug design has been confirmed.22,209−211 This section summarizes the typical examples of anion recognition by the simple/macrocyclic σ-hole bond and π-hole bond donors as well as other applications associated with anion recognition. 6.1. Recognized by the Simple Bond Donors

The simple σ-hole bond and π-hole bond donors should be more important in the exploration of the origination of both the σ-hole 5088

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association ability for a given bond donor is Cl− > Br− > I−, which is a typical electrostatically attractive sequence. To evaluate the ability of an organic diiodinated ammonium salt to reversibly encapsulate diiodoperfluoroalkanes (DIPFA)196 and dihalogens,215−217 Resnati et al.196 studied the interactions of nonporous α,ω-bis(trimethylammonium)alkane dihalides with I(CF2)mI, I2, and Br2 through the halogen bond. The process was highly selective for the DIPFA-forming X−···I− Y−I···X− (X = I) trimeric supramolecular dianions that were matched in length to the chosen dication, as depicted in Figure 25a. This process can be reversed at higher temperatures and lower vapor pressures, which provides useful information for the synthesis of fluoro-containing resins and surfactants. In addition, bis(trimethylammonium)hexane diiodide displayed a sizematching dynamic response to I2, leading to the formation of poorly stable and rare [I4]2− (I−···I−I···I−) polyiodide-containing crystalline species under extreme conditions (cf. Figure 25b).215 The [I2Br4]2− and [I2Cl4]2− mixed analogs were also formed by thermally inducing crystal-to-crystal elimination of one I2 molecule.217 Hexamethonium halides have also been shown to act as functional solids for clathration and storage of dihalogens. Interactions between the multidentate halogen-bond donor TIE and the halide anions provide a basis for improving anion recognition and the assembly of multidimensional functional materials. Wang et al.77 used various experimental techniques and calculations to show that the stoichiometries of TIE with X− were all 1:1 in acetonitrile, and the association constants (Ka(C−I···Cl−/Br−/I−)) were 69.5, 57.0, and 38.1 M−1, respectively. This implies that the ability of X− to form a halogen bond follows the order Cl− > Br− > I− due to Cl− having a higher electron density. XRD revealed that the stoichiometries of the interactions between TIE and Cl−/I− were the same in solution and in cocrystal form (Figure 26). By contrast, the TIE···Br− complex is influenced by solvent. For example, the stoichiometry of the TIE/Br− cocrystal was always 3:1 from evaporating acetonitrile, dichloromethane, or a mixture of dichloromethane−ethanol (5:1) at room temperature, and the structure was tetragonal. The stoichiometry was 1:1, and the structure was anorthic in acetone. In addition, the calculation results in the gas phase showed that the strength of the interactions decreased in the order C−I···Cl− (−127.7 kJ· mol−1) > C−I···Br− (−111.0 kJ·mol−1) > C−I···I− (−102.8 kJ· mol−1). This is consistent with the experimental results in solutions and indicates that the C−I···X− interaction was driven mainly by electrostatic forces. For the π-hole bond, early in the last century, obvious color changes were observed when the anions were added to solutions containing electron-deficient aromatic compounds (Figure 27).

bond and the π-hole bond, although their performance is unsatisfactory in the selective recognition of anions in most cases. For the σ-hole bond, Resnati et al.126 confirmed that the ability to form a halogen bond follows the polarizability of the halide ion, i.e., I− > Br− > Cl−. For example, when ICF2CF2I interacts as a halogen-bond donor with X− (X = Cl, Br, and I) in CDCl3 solution, the values of the 19F NMR shift variations (Δδ = δICF2CF2I − δICF2CF2I···X−) were 2.17, 3.10, and 3.54 ppm, respectively. Kochi et al.212,213 studied the halogen-bond interactions between CBr4/CHBr3 and halide/pseudohalogen anions using UV spectroscopy and crystallography. The typical association constants of CBr4 and X− (X = Cl, Br, and I) in CH2Cl2 solution were 3.0, 2.8, and 3.2 M−1, respectively. This indicates the association ability follows the order I− > Cl− > Br−. However, Shen et al.214 showed via UV−absorption spectra that the strong C−I···X− halogen bond of 1,2-diiodoperfluoroethane (DIPFE), 1,4-diiodoperfluorobutane (DIPFB), and 1,6diiodoperfluorohexane (DIPFH) with halide anions occurs in acetonitrile and confirmed a 1:1 stoichiometry of DIPFE, DIPFB, or DIPFH with halide anions. The association constants Ka(C−I···Cl−/Br−/I−) were 98.2, 66.5, and 45.7 M−1 for DIPFE, 173.4, 121.9, and 68.6 M−1 for DIPFB, and 251.7, 149.2, and 81.3 M−1 for DIPFH. Color changes are observed immediately upon addition of colorless halide solutions to the pink DIPFA solutions especially for DIPFE (cf. Figure 24). More noticeably,

Figure 24. Color changes of DIPFE before and after interacting with colorless halide anions in chloroform solvent (1, 0.1 M DIPFE alone; 2, 0.1 M DIPFE···Cl−; 3, 0.1 M DIPFE···Br−; 4, 0.1 M DIPFE···I−). Reprinted with permission from ref 214. Copyright 2011 PCCP Owner Societies.

the association constants of the halogen-bond complexes for the same X− are closely associated with the alkyl chain length of the DIPF alkanes, that is, the longer the alkyl chain length the stronger the halogen-bond complex. The results indicate that the

Figure 25. (a) Crystal packing of the complex between [(CH3)3N+·(CH2)12·N+·(CH3)3]·I22− and C6H12I2 involving the I−···I−Y−I···I− superanion. (b) Structure of a complex between bis(trimethylammonium)hexane diiodide and I2 involving the [I4]2− anion. (a) Reprinted with permission from ref 196. Copyright 2009 American Association for the Advancement of Science. (b) Reprinted with permission from ref 215. Copyright 2010 The Royal Society of Chemistry. 5089

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Figure 26. Halogen-bond cocrystals assembled by TIE and halide anions (from CH3CN): (a) TIE···Cl−, (b) TIE···Br−, and (c) TIE···I−.77

Figure 27. Structures of some π-hole bond donors, and photographs of the chromogenic reactions between p-CA or p-BA and halide ions. The experiment was repeated according to ref 75, and photographs were taken under ambient light by the authors’ group.

Figure 28. Recognition of halide anions using halogen-bond supramolecular systems developed by Beer et al. (a) Reprinted with permission from ref 206. Copyright 2010 Wiley-VCH Verlag GmbH & Co. KGaA. (b) Reprinted with permission from ref 221. Copyright 2010 American Chemical Society. (c and d) Reprinted with permission from ref 222. Copyright 2011 Wiley-VCH Verlag GmbH & Co. KGaA. (e) Reprinted with permission from ref 223. Copyright 2012 Wiley-VCH Verlag GmbH & Co. KGaA. (f) Reprinted with permission from ref 224. Copyright 2012 American Chemical Society.

5090

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Figure 29. Anion recognition based on (a) multidentate halogen bonds, (b) cooperation between the halogen bond and the hydrogen bond, and (c) bidentate halogen bonds using the ethynylene and diynylene-linked iodoperfluoroarenes developed by Taylor et al. (a) Reprinted with permission from ref 225. Copyright 2010 Wiley-VCH Verlag GmbH & Co. KGaA. (b) Reprinted with permission from ref 226. Copyright 2011 American Chemical Society. (c) Reprinted with permission from ref 227. Copyright 2013 Wiley-VCH Verlag GmbH & Co. KGaA.

Br− > Cl−.220 The association constants of the complexes obtained by UV absorption titration experiments were 0.172 (Cl−), 0.343 (Br−), and 1.004 (I−) M−1 for cyanuric chloride complexes and 0.370 (Cl−), 0.688 (Br−), and 1.011 (I−) M−1 for 1,3,5-triazine complexes, respectively. They seem apparently to be the order of charge transfer ability of halide to π-hole bond donors. However, it can be concluded by combining energy decomposition analysis and natural bond orbital analysis that the π-hole···X− bond and σ-hole···X− bond are electrostatically attractive in nature regardless of the order of I− > Br− > Cl− or converse based on combining analysis of calculation and experiments.

The interactions between electron-deficient aromatic compounds and anions were attributed to charge transfer complexation218 or nucleophilic aromatic substitution reactions,219 which should result in strong polarization according to the present πhole bond concept. Hay et al.98 studied a series of interactions between electron-deficient aromatic compounds and X− using crystal structures and calculations and noticed that three different types of complexes were formed when X− is positioned above the plane of the arenes: strongly covalent σ complexes, weakly covalent charge transfer complexes, and noncovalent anion−π complexes. A C−H group in the arene allows another type of interaction to form, i.e., C−H···X− hydrogen bond. Kochi et al.75 explored the recognition capability of several πhole bond donors for X− using UV spectral titration. Taking the π-hole bond donor pyrazine-2,3,5,6-tetracarbonitrile (TCP) as an example, the association constants of TCP···Br − /I − complexes were 7 and 3 M−1, respectively, that is, the π-hole··· X− bond abilities of TCP to Br−/I− follow the order Br− > I−. In addition, the strength order of the π-hole bond of cyanuric chloride and 1,3,5-triazine with tetrapropylammonium halide (Pr4N+·X−) using UV absorption and 13C NMR titration experiments in acetonitrile confirmed that the bond abilities of cyanuric chloride/1,3,5-triazine with X− all follow the order I− >

6.2. Recognized by the Macrocyclic Bond Donors

Comparatively speaking, the macrocyclic σ-hole and π-hole bond donors possess more advantages over simple bond donors due to the multidentate bonding ability and size or geometric matching with anion to a novel macrocyclic molecular structure. For the σ-hole bond, Beer et al.206,221 constructed serial pseudorotaxane assemblies for anion recognition. A supramolecular pseudorotaxane with a threading structure of throughspace interactions between 2-bromo-1,3-dihexyl-4,5-dimethyl1H-imidazol-3-ium chloride as the hosts and macrocycles as the 5091

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Figure 30. (a) Macrocyclic anion receptors synthesized by Wang et al. and their association constants with Bu4N+ halides in CH3CN. (b) UV−vis (top) and fluorescence (bottom) titrations of 1 with Bu4N+·F−. (c) X-ray crystal structures of the π-hole···anion/lp complexes with different active sites. (a and c) Reprinted with permission from ref 114. Copyright 2011 Wiley-VCH Verlag GmbH & Co. KGaA. (b) Reprinted with permission from ref 22. Copyright 2008 Wiley-VCH Verlag GmbH & Co. KGaA.

guests (Figure 28a) can recognize Cl− by the C−Br···Cl− halogen bond and N−H···Cl− hydrogen bond.206 Similarly, an analogous iodotriazolium halide salt (Figure 28b) was selected as the host molecule. It showed superior halide anion recognition capability in CDCl3/CD3OD/D2O.221 The 1H NMR titration experiments showed high selectivity to I− (Ka = ca. 2.2 × 103 M−1). Later, they directly synthesized a host molecule with two active sites (Figure 28c) using a bromoimidazole derivative and identified its ability to recognize halide anions in a mixed CD3OD/D2O solvent.222 The 1H NMR titration experiments indicated that the trend of halogen-bond strength was Br− > I− ≫ Cl−; the corresponding Ka values were 889, 184, and Br− > I− ≫ TsO−, NO3−, HSO4−. For example, the association constants Ka obtained using 19F NMR titration in acetone (Figure 29a−d) with the above anions were 1.9 × 104, 3.8 × 103, 7.6 × 102, 10, I−, and thus, the recognition of anions can be realized using the cooperative effects of halogen bonds and hydrogen bonds. Recently, alkynyl and bialkynyl groups were designed and synthesized as linkers for 2-iodoperfluoroarene halogen-bond donors227 as shown in Figure 29c. The 19F NMR titration experiments in acetone showed that the bond abilities of host molecule 1 with Bu4N+ salts decreased on the order of Cl− > Br− > I− > NO3−, HSO4− (the corresponding Ka values were 1.2 × 103, 8.5 × 102, 3.5 × 102,