Definition of the Halogen Bond (IUPAC Recommendations 2013): A Revisit Pradeep R. Varadwaj,* Arpita Varadwaj, Helder M. Marques, and Koichi Yamashita Cite This: Cryst. Growth Des. 2024, 24, 5494−5525 Read Online ACCESS Metrics & More Article Recommendations ABSTRACT: This Article revisits the “Definition of the Halogen Bond (IUPAC Recommendations 2013)” [Desiraju, G. R. et al. Pure Appl. Chem. 2013, 85 (8), 1711−1713], recommendations that fail to include the fundamental, underlying concept of (electrophilic) σ- and p-/π-hole theory and orbital-based charge transfer interactions that accompany halogen bond formation. An electrophilic σ-hole, or p-/π-hole, is an electron-density-deficient region of positive polarity (and positive potential) on the electrostatic surface on the side of halogen along, or orthogonal to, a covalently bonded halogen in a molecular entity that leads to the development of a noncovalent interaction�a halogen bond� when in close proximity to an electron-density-rich nucleophilic region on the same or another identical or different molecular entity, with which it interacts. This Article re-examines the characteristic features of the halogen bond and lists a wide variety of donors and acceptors that participate in halogen bonding. We add caveats that are essential for identifying halogen bonding in chemical systems, necessary for the appropriate use of the terminologies involved. Illustrative examples of chemical systems that feature inter- and intramolecular halogen bonds and other noncovalent interactions in the crystalline phase are given, together with a case study of some dimer systems using first-principles calculations. We also point out that the π-hole/belt (or p-hole/belt) that may develop on the surface of a halogen derivative in halogenated molecules may be prone to forming a π-hole/belt (or p-hole/belt) halogen bond when in close proximity to nucleophiles on another similar or different molecular entity. ■ INTRODUCTION Noncovalent interactions are a broad family of attractive interactions that occur locally in many chemical systems.1−8 They are important in the supramolecular assembly and shaping of crystals in the solid state and are categorized into different flavors based on their character and the identity of the chemical elements that participate in their formation. These interactions are chemical synthons of variable strength, from very weak to a strength comparable to that of a coordinate bond, or indeed a covalent bond.9−14 Their strength is determined based on the nature of the participating electron-density-donating and electron-density-accepting molecules/fragments/atoms.15 They are players in the formation of dimers, trimers, tetramers, oligomers, and supramolecular systems. They often feature directional properties, but not (always) when they are the forced consequence of a true (primary) interaction(s). Weak noncovalent interactions are weak forces that typically occur between neutral molecular entities, while stronger interactions appear when one of the participating sites (electron density donor) has a negative charge (a polarity opposite to that of the electron density acceptor). The former interactions in the gas-phase have been investigated using a variety of spectroscopic techniques (e.g., rotational,16,17 vibrational,18,19 and anion photoelectron spectroscopy20 andmass spectrometry21), where- as strongly bonded interactions are ion−molecule or ion-pair adducts that have been reported primarily in the crystalline phase. Although chemical reactions are widely understood as a result of the making and breaking of chemical bonds,22 noncovalent interactions, while generally weaker than covalent bonds, also develop during the course of a chemical reaction. They cause the assembly of molecular entities at surfaces, leading to the formation of stable materials with applications in optoelectronics, catalysis, and sensing.23 The recently proposed definition of a pnictogen bond (PnB)24 states that these are “weak attractive interactions between an electrophilic region on a pnictogen atom in a molecular entity (wherein the pnictogen is involved in other stronger bonds) and a nucleophilic region in another, or the Received: February 15, 2024 Revised: May 18, 2024 Accepted: May 20, 2024 Published: June 24, 2024 Articlepubs.acs.org/crystal © 2024 American Chemical Society 5494 https://doi.org/10.1021/acs.cgd.4c00228 Cryst. Growth Des. 2024, 24, 5494−5525 D ow nl oa de d vi a U N IV O F T H E W IT W A T E R SR A N D o n Ju ly 4 , 2 02 4 at 1 1: 42 :2 3 (U T C ). Se e ht tp s: //p ub s. ac s. or g/ sh ar in gg ui de lin es f or o pt io ns o n ho w to le gi tim at el y sh ar e pu bl is he d ar tic le s. https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Pradeep+R.+Varadwaj"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdf https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Arpita+Varadwaj"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdf https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Helder+M.+Marques"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdf https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Koichi+Yamashita"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdf https://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.cgd.4c00228&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?goto=articleMetrics&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?goto=recommendations&?ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=tgr1&ref=pdf https://pubs.acs.org/toc/cgdefu/24/13?ref=pdf https://pubs.acs.org/toc/cgdefu/24/13?ref=pdf https://pubs.acs.org/toc/cgdefu/24/13?ref=pdf https://pubs.acs.org/toc/cgdefu/24/13?ref=pdf pubs.acs.org/crystal?ref=pdf https://pubs.acs.org?ref=pdf https://pubs.acs.org?ref=pdf https://doi.org/10.1021/acs.cgd.4c00228?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as https://pubs.acs.org/crystal?ref=pdf https://pubs.acs.org/crystal?ref=pdf 00664068 Highlight 00664068 Highlight same, molecular entity”. (A molecular entity is defined as “any constitutionally or isotopically distinct atom, molecule, ion, ion- pair, radical, radical ion, complex, conformer, etc., identifiable as a separately distinguishable entity”25). This definition is misleading given that PnBs are not and cannot always be regarded as “weak attractive interactions”, since they can be of the van der Waals type, weak, strong, or even very strong depending on the energy strength of the interaction.9 For example, the pnictogen bond in [X3Sb···F− (X = F, Cl, Br)] should not be regarded as a weak interaction given it comprises an appreciable amount of covalency.9 This is applicable to halogen bonds as well,12,15 considering that they feature a variety of bond strengths. The experimental and computational recognition of inter- and/or intramolecular noncovalent interactions formed by elements of groups 14−17 of the periodic table in chemical systems, especially when they behave as electrophiles, has gained significant momentum over the past decade. Revised definitions, characteristic features, footnotes, and illustrative examples containing electron density donors and acceptors have been proposed. These noncovalent attractive interactions have been termed tetrel bonds (TtBs), group 14;10,26,27 pnictogen bonds (PnBs), group 15;28−30 chalcogen bonds (ChBs), group 16;31−33 and halogen bonds (XBs), group 17.2,34,35 This classification is useful to identify how an element of a particular group behaves in maintaining an attractive engagement but with a specific name, as unambiguously demonstrated by Cavallo and workers in their unique piece “Naming interaction from the electrophilic site”.36 Clearly, integrating all types of noncovalent interactions into three classes (σ-hole interactions,37−39 π-hole interactions,40,41 and p-hole interactions42−44) does not allow us to determine which specific element, and from which specific group of the Periodic Table, is involved in the formation of a specific type of noncovalent interaction. The subdivision of the noncovalent interactions based on the elements in a group acting as an electrophile, e.g., phosphorus bond (group 15), allows one to unequivocally capture the noncovalent bond formation ability, as well as the chemical reaction profile, of that specific element (for example, “fluorine chemistry”45 or “iodine chemistry”46). Halogen bonds were often abbreviated as XBs,2,3,14,47−49 although recently the abbreviation HaB has come into use.50−54 Formal definitions became desirable with the increasing appreciation of the significance of noncovalent interactions in areas as diverse as crystal engineering, chemistry; physics; molecular biology; crystallography; and polymer, supramolec- ular, medicinal, and materials sciences, among others. The definition of the hydrogen bond (HB) was revised in 2011, accompanied by a series of characteristics and features.55 A similar definition was subsequently applied to elements of groups 14−17. For instance, when transferred to HaBs, PnBs, and ChBs, the definition proposed for HBs was virtually unchanged (except for obvious terms such as halogen/ chalcogen atom or halogen/chalcogen bond), yet the number of characteristics were significantly reduced without any in- depth explanation, and the original literature featuring the characteristics of HaBs and ChBs was not referenced. Therefore, the semi-formal definitions and characteristics of HaB34 and ChB31 still require a revisit. The concepts underlying the electrophilic nature of σ-37,56,57 or π-holes41,58,59 have greatly assisted as umbrella terms in recognizing the occurrence of noncovalent interactions in many chemical systems.57,60−62 These holes generally appear on the electrostatic surfaces of molecular or arene moieties along or orthogonal to the outer extensions of covalently bonded atoms, respectively. This distinctive conceptual framework39,56,63−67 surprisingly has been overlooked as a possible characteristic of HaBs34 and ChBs,31 although it has been widely applied for the rationalization of these noncovalent interactions. We briefly incorporated the underlying concept of σ- and π-holes in our recently proposed definitions of PnB28 and TtB.26 Subsequent to our proposals for PnB, the IUPAC working group proposed a definition of the PnB that incorporated these concepts.24 Therefore, given the importances of these concepts in many studies focusing on noncovalent interactions, it is apparent that the previously proposed IUPAC definitions and characteristic features of the halogen and chalcogen bonds may be incomplete without the inclusion of the concept of an electrophilic σ-hole and an electrophilic π-/p-hole (or even π-/p-belt). An electrophilic σ-hole appears in a region on the electrostatic surface of an atom A in a molecule R−A (where R is the remainder part of the molecular entity), which has been attributed to be the result of an anisotropy of the atom’s charge density distribution.39 It is not only electron-density-deficient (and associated with a positive electrostatic potential) but also appears on the side of A opposite to the outer extension of a covalent or coordinate bond, where A is, for example, a tetrel, pnictogen, chalcogen, or halogen derivative. A visual represen- tation of the electron-density-deficient (electrophilic) and electron-density-rich (nucleophilic) regions (green/cyan/blue and red, respectively) on the electrostatic surface of covalently bonded halogen atoms in some simple molecules is presented in Figure 1. It is this electrophilic σ-hole on the halogen atom in molecules that has the capacity to act as a HaB donor (HaBD) in sustaining an attractive noncovalent engagement when in close proximity to the negative (nucleophilic) site on an interacting partner entity that acts as an HaB acceptor (HaBA). Occasionally an electrophilic π-/p-hole (π-/p-belt) may be observed in halogen-containing molecules.68,69 The halogen atom in molecules such as FCN and FCCCN is entirely electrophilic, i.e., both the lateral and axial portions of the electrostatic surfaces of fluorine in these molecules are electrophilic.68 The lateral portions of the electrostatic surface arise from the p-type orbitals; they are deficient in electron density. Past studies68,70,71 have demonstrated that the axial regions generally have a larger electrophilicity than the lateral regions and are prone to the formation of halogen bonds with nucleophiles when in close proximity. This concept is also applicable, for instance, to oxygen-centered ChBs,11,72 as well as triel and aerogen bonds.176 For example, there are two positive regions on the outer surface of boron in BF3 that appear orthogonal to the B−F bond, caused by its empty p-type orbital. One might refer to them either as π-holes or p-holes.43,73 The π-/p-belt appears around covalent bonds, while the π-hole may appear on the surface of covalently bonded atoms or in the junction region of a pair, or array, of atoms in a molecular entity. Some have called the π-/p-belt around a covalent bond a “π- ringhole”,29,59 although what is present is not a “hole” but rather a “π-/p-belt”. Interestingly, both σ- and π-holes in molecular entities have been experimentally observed using Kelvin probe force microscopy.74,75 The definition and features discussed in the IUPAC paper defining the HaB overlook the importance of the noncovalent bonding capacity of the heaviest halogen, astatine (At). When in molecules, At has the capacity to participate in simple and supervalent halogen bonding interactions with nucleophiles in Crystal Growth & Design pubs.acs.org/crystal Article https://doi.org/10.1021/acs.cgd.4c00228 Cryst. Growth Des. 2024, 24, 5494−5525 5495 pubs.acs.org/crystal?ref=pdf https://doi.org/10.1021/acs.cgd.4c00228?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as neighboring molecules.76,77 Astatine can behave as a halogen bond donor�possibly a stronger one than iodine�owing to its much more electrophilic (σ-hole) character.78 Similarly, a number of studies68,69,79−86 have been reported that demon- strate the ability of covalently bonded fluorine in molecules to form a halogen bond (or counterintuitive interactions) upon donating a σ-hole on the fluorine to the Lewis base of the interacting molecular entity. Nevertheless, the ten features listed in ref 34 alone may be insufficient for rationalizing HaBs, and citations to the original literature highlighting these features are missing. The IUPAC recommendations34 are merely a short overview of HaBs. No illustrative examples are given; thus, the recommendations may not be sufficient to identify chemical instances where halogen bonding occur. Furthermore, the recommendations34 do not mention the possibility that halogen bonding can also be formed by hypervalent halogen derivatives and cations containing halogen atoms, as well as by electrophilic π-/p-holes (π-/p-belt) on halogen derivatives in molecular entities. Many crystal structures have been reported that provide evidence for this (see the illustrative examples below). Furthermore, the IUPAC recommendation34 is also silent on the occurrence of antielectrostatic halogen bonds,87−90 as well as those that have been reported as negative−negative and positive−positive halogen-centered noncovalent interactions involving halogen atoms in the same91,92 or a neighbor- ing68,79,81,93−95 (interacting) molecular entity.91,92,96 This Article revisits and expands upon the IUPAC definition of the halogen bond.34 We list a number of notes and characteristic features, keeping essentially the format of the original IUPAC recommendations (and transferable in principle to any noncovalent interaction), that are likely to assist when exploring halogen bonds in chemical systems. We also list a rich variety of halogen bond donors and halogen bond acceptors, as well as caveats that should be borne in mind when classifying an attractive interaction as a halogen bond. It is customary not to confuse the terms “donor” and “acceptor” in this context with those that have been widely used in chemistry as “electron donor” and “electron acceptor”. In current scenario, a HaBD refers to the donor of a “halogen bond” that is an “electron density acceptor” or simply an “electron acceptor”. Similarly, a HaBA should be understood as an acceptor of a “halogen bond”, which is an “electron density donor” or simply an “electron donor”. This view is applicable to all kinds of noncovalent interactions, regardless of whether it is a hydrogen bond, chalcogen bond, or tetrel bond, pnictogen bond, among others. Nevertheless, illustrative examples retrieved from crystal structures deposited in the Cambridge Structural Database (CSD)100 are presented. A first-principles-based case study focusing on simple dimer systems is also presented to validate some of the recommended notes and characteristic features of the halogen bond and to further a basic understanding of this type of noncovalent interaction. The concept of a π-/p-hole (or π-/p-belt) halogen bond formed by halogen’s π-/p-hole (or π-/ p-belt) in molecules is introduced. Some of the annotations may seem repetitive, but this is to clarify the terminology. We interchangeably use terms such as “bond” or “interaction” to mean the same thing, even though some99 have suggested that terms such as “σ-, π-, and p-hole bonds” should be read as “σ-, π-, and p-hole interactions”. In our opinion, the terms “bond” and “interaction” have the same meaning; a “covalent bond”, for example, is unequivocally a “covalent interaction” in a pair of two atoms in a molecular entity. π- or p-type interactions/bonds occur when electrophilic π- or p-type orbitals are involved. Based on the non-negligible covalent character of the p-hole bond, we made no attempt to distinguish it from the π-hole bond. ■ DEFINITION The IUPAC definition34 of the halogen bond is as follows: “A halogen bond occurs when there is evidence of 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”.We recommend that this is expanded to read as follows: A halogen bond (HaB) develops in a chemical system when a net attractive engagement occurs between an electron-density-def icient (electrophilic) region on the electro- static surface of a halogen atom in a molecular entity and a close- lying electron-density-rich (nucleophilic) region on the electrostatic surface of the same or another identical or dif ferent molecular entity. Figure 1. Visual representation of the electrophilic and nucleophilic regions (δ+ and δ−, respectively) on the electrostatic surface of a halogen atom in some simple molecules. Top, from left: HBr, F2, and FCN. Bottom, from left: CH3Br, CF3Cl, and C6H5Cl. The electrophilic regions (δ+) on the halogen atom on the side of X opposite to the extension of the R−X (X = halogen) covalent bonds are typically referred to as (positive) σ-holes, which may be involved in attractive engagements with the nucleophilic regions on the surface of the interacting partner molecules to form halogen bonds. R is the remaining part of the molecule. The most electrophilic and nucleophilic regions are colored blue and red, respectively. The molecular graph obtained from the application of the quantum theory of atoms in molecules (QTAIM97,98) is superimposed with the molecular electrostatic surface potential (MESP) in each case. The potential was mapped with the 0.001 au (electrons bohr−3) isoelectronic density envelope of each system, and the [ωB97X-D/aug-cc-pVTZ] level of theory was used. Atom labeling is shown for each case. Crystal Growth & Design pubs.acs.org/crystal Article https://doi.org/10.1021/acs.cgd.4c00228 Cryst. Growth Des. 2024, 24, 5494−5525 5496 https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig1&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig1&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig1&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig1&ref=pdf pubs.acs.org/crystal?ref=pdf https://doi.org/10.1021/acs.cgd.4c00228?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as ■ RECOMMENDED NOTES FOR IDENTIFYING A HALOGEN BOND Note 1. The definition is general and, in principle, is transferable to any noncovalent interaction, including HBs, TtBs, ChBs, PnBs, triel and aerogen bonds,101 etc., obviously replacing the term “halogen atom” with the appropriate term for the attractive interaction being referred to. Note 2: A HaB, like an HB, is a noncovalent interaction between interacting sites of opposite (local) polarity. It is not recognized as such when the HaBD site X is not apparently identifiable as having an electrophilic region but engages in an attractive interaction with a nucleophilic region in the HaB acceptor site Y, a view that is transferable to other attractive interactions such as the PnB (see Note 4 of the definition of PnB).102 The electrophilic region on the halogen atom in a halogen-containing molecule may be induced when placed in the vicinity of any strong electrostatic field of the interacting partner molecular entity.95 The electrophilic and nucleophilic regions stand out on the outer electrostatic surfaces of a HaBD and HaBA, respectively. Note 3. A HaB is represented by the structural motif R−X···Y, where X (X = F, Cl, Br, I, At) is the HaB donor, a halogen atom (which may or may not be hypervalent) that must feature an electrophilic region on its outer electrostatic surface, and R is the remainder part of the molecule containing the HaBD. The HaBD can be seen either in an electrically neutral molecule or in a fragment of a molecular cation, which may or may not be a π- system; Y is an HaB acceptor, which may be a lone-pair region in a molecule, a molecular anion, or an atomic anion and must possess a nucleophilic region. Note 4. A HaB is either intermolecular3 or intramolecular103 and cannot simultaneously possess both characteristics: when it develops in the same molecular entity containing the electro- phile X and nucleophile Y, it is intramolecular; when it occurs between two molecular entities (one with a HaB donor X and the other with a HaBA acceptor Y) that are either identical or different, it is intermolecular. Note 5. A HaB can be very strong,104,105 strong,12 of medium strength,12,106 weak,107,108 or of the van der Waals type108,109 depending on the binding (or interaction) energy of the interaction. The bond strength of the HaB, in many instances, is comparable to that of a HB, TtB, ChB, or PnB. It should not always be assumed to be a weak interaction,24 since it appears in different flavors depending on the strength of the interaction. Note 6. The combination of Notes 2 and 3 may read “a HaB is an attractive interaction between HaB donor site X and HaB acceptor site Y of opposite charge capacity (Xδ+ and Aδ−)”; here, δ+ and δ− symbolically refer to the positive and negative local charge polarity on the interacting regions on the electrostatic surfaces of X and Y, respectively (see Figure 1). This also applies to HBs, TtBs, ChBs, PnBs, and any other noncovalent interaction as far as their definitions are concerned (i.e., a positive site on the noncovalent donor atomA attracts a negative site on the noncovalent acceptor atom Y when in close proximity, where A refers to a triel, tetrel, pnictogen, chalcogen, halogen, or aerogen atom, among others). Note 7. The definition of the HaB requires that an electrophile on a HaB donor X attracts a nucleophile on a HaB acceptor Y; however, it is not necessarily the case that regions of opposite charge polarity on the electrostatic surfaces of interacting molecules will always attract each other to form a HaB when in close proximity. The actual sites on X and Y that interact attractively are determined by the spatial rearrangement that corresponds to the maximization of the attractive (electrostatic) interaction between X and Y. Note 8. The surface charge polarities of HaB donor site on X andHaB acceptor site on Ymay be determined by examining the extrema (local maxima and minima) of the potential on the electrostatic surfaces of the interacting molecular entities. The HaBA Y is often (but not always!) characterized by a local minimum of (negative) potential, and the HaB donor site X is characterized by a local maximum of (positive) potential. This is also applicable to other noncovalent interactions, such as ChBs and PnBs; however, formation of a PnB with a PnB donor site Pn, characterized by a local minimum of (positive) potential,110 and a PnB acceptor site Y, characterized by a local maximum of (negative) potential, is not unlikely (for example, the N�P···F− H dimer). Note 9. An intermolecular HaB is likely to follow a type II geometric topology of a noncovalent bonding interaction; a type II topology, which relates to ∠R−X···Y, is often linear or quasi- linear (but may be nonlinear) and satisfies the local differential charge polarity condition (see Note 6).3,111,112 An intra- molecular HaB does not generally follow the same geometric topology of bonding; it is often nonlinear, following a type I geometry (∠R−X···Y < 140°); if an electrophilic π-/p-hole (or π-/p-belt) on a halogen derivative in a molecule is involved in making up aHaBwith aHaBA Y, R−X···Y is often an orthogonal HaB interaction and is nonlinear (there can be exceptions!). Note 10. The formation of a HaB between interacting sites may result from an attractive engagement between an electro- philic σ-hole region characterized by a positive electrostatic potential on the side of HaB donor X opposite to the R−X bond extension and a nucleophilic site on Y. A HaB may also occur when an attractive interaction develops between the lateral electrophilic site(s) on X in R−X and the nucleophilic site on Y (see Notes 7−8). Note 11. An electrophile on covalently bonded halogen atom X in HaBD need not always have the characteristic of a σ-hole but can have the characteristics of a π-/p-hole instead. An electrophilic σ-hole is a region of lower electronic density on X, not a region of electrostatic potential,37,113,114 which may appear linearly along or off the outer extension of the R−X covalent bond axis;115 its exact location depends on the nature of R (e.g., its electronegativity and electron-withdrawing capacities). It is often observed that the stronger the electron-withdrawing capacity of R, the greater the electrophilicity on the side of X opposite to the outermost extension of the R−X covalent bond. An electrophilic π-/p-hole (or π-/p-belt) in a molecule containing the HaBD may appear on the outer surface of X, orthogonal to the R−X covalent bond, which may have the capacity to attract a nucleophile Y on the same or a different molecule to form an R−X···Y π-/p-hole (or even π-/p-belt) halogen bond (see examples in following sections).110 Note 12. It should not always be assumed that regions of higher electron density on HaBA Y will have negative electrostatic potentials and that regions of lower electron density on HaBD will have positive ones, given that the electrostatic potential reflects the effects of the nuclei as well as the electrons.37 It is the local potentials�not the σ-holes(or π-/ p-holes)�that are responsible for the development of halogen bonding.56 A nucleophilic σ-hole (or simply a negative σ-hole, or a σ-hole accompanied by a negative electrostatic potential) may also appear on the outer electrostatic surface on the side of X in R−X (as on F in H−F), which is often weakly nucleophilic Crystal Growth & Design pubs.acs.org/crystal Article https://doi.org/10.1021/acs.cgd.4c00228 Cryst. Growth Des. 2024, 24, 5494−5525 5497 pubs.acs.org/crystal?ref=pdf https://doi.org/10.1021/acs.cgd.4c00228?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as compared to the lateral sides of the same atom X. If the weakly nucleophilic σ-hole on X (frequently fluorine) forms an attractive noncovalent interaction with an electron density donor site on Y, this may not be recognized readily as a HaB, since the halogen atom in the HaBD moiety X in the isolated molecular entity acts as a nucleophile. However, a nucleophilic σ-hole (as a HaBA) on a covalently bonded halogen molecule may attract an electrophilic σ-hole on the halogen in another molecule to form a HaB. The electrophilic and nucleophilic natures of σ-holes on atom X in R−X are characterized by the positive and negative signs of the local most maximum of electrostatic potential, respectively.81,82 The positive character of the σ-hole on X increases going from the lighter to the heavier (more polarizable) halogen atoms within the group 17 and as the remainder of the molecule becomes more electron- withdrawing116 (viz. F2 > Cl2 > Br2 > I2 (> At2)). Positive and negative π-/p-holes on X in a HaBD are characterized by the positive and negative signs of the potential, respectively; they represent a maximum or (even sometimes a minimum) of potential depending on the extent of the electron density delocalization on the surface of X. Note 13. Halogens, and especially Br, I and At, may be hypervalent in molecules; they may concurrently form multiple HaBs with more than one HaBA site Y on the molecules with which they interact.117,118 This is especially true when the HaB donor atom X is entirely electrophilic or part of a cation; the HaB donor atom X may also form multiple HaBs when it manifests both π-/p- and σ-holes and interacts simultaneously with more than one nucleophile, a hypothesis that may be transferrable to ChB/PnB donors inmolecules (seeNote 5 of the definition paper of the PnB34). Note 14. Two halogen sites on two different molecules in close proximity may involve in an attractive engagement to form a HaB; in this case, one of them would act as a HaB donor X and the other as a HaBA Y (viz. X−X···Y−Y′; X, Y, Y′ = halogen). Note 15. A halogen bondmay occur between theHaB donor X and the HaB acceptor Y within a neutral molecule, or between two neutral molecules in close proximity. It may also occur between a neutral molecule with a HaB donor X and an anion (or a negative π-/p-belt as in HC�CH or a π-hole on an arene moiety (C6H6) with negative π-density) containing Y, or between the HaB donor X in a molecular cation and a nucleophile (lone-pair or negative π-density) on Y in a neutral molecule, or between two molecules of opposite charge polarity with a HaB donor X in the cation and a HaB acceptor Y in the anion (i.e., an ion-pair). Note 16. An electrophilic σ-hole (or π-/p-hole) on a HaB donor X in molecules need not always form a halogen bond when in close proximity to an HaBA Y. For example, the weak σ- hole on Cl in HCl does not form a HaB with the nucleophile on the lateral portion of F in HF when the latter faces the σ-hole on Cl. The placement of electron-withdrawing substituents on the Lewis base Ymay reverse the sign of the electrostatic potential in its lone pair or π-bond region to positive, and this may enable it to engage in the formation of a HaB with the positive σ-hole of a Lewis acid. A reverse scenario may also be likely in certain circumstances, as a negative σ-hole is likely to form a HaB with the negative lone pair region of a HaBA Y.95 The highly negative σ-hole may become less negative because of electron-with- drawing substituents at the peripheral sites of a halogenated molecule.81 A positive σ-hole on covalently bonded halogen X may be introduced in an anion in the presence of cation that enables it to engage attractively with a HaBA site Y, developing a halogen bond between them, as observed in the case of a tetrel derivative in an anion.119 Note 17. An attractive noncovalent interaction between an electrophilic (or nucleophilic) region on a halogen atom in one molecular entity and an electrophilic (or nucleophilic) region in the same or a neighboring interacting molecular entity may not be considered to be a halogen bond if both carry the same charge polarity (seeNotes 2, 6, and 7 and the definition).91,92 This could arise for several reasons, for example, as the forced consequence of primary interactions (HB, PnB, or HaB) and/or the dominant role of polarization/dispersive forces. It can also be caused by the heterogeneous distribution of charge density on the surfaces of interacting atomic basins or by charge transfer interactions between interacting sites. An attraction caused by the latter is referred to as “antielectrostatic” halogen bonding,87−90 a term that should not be confused with the definition of halogen bonding. It should be borne in mind that polarization is a physical observable, while charge transfer between orbitals, in this context, arises from a mathematical model;120,121 some have questioned the “false claims” regarding the observation of orbitals,122−124 while others are of the view that charge transfer is indistinguishable from polarization38,121,125 but occurs when a shift in electron density from a nucleophile to an electrophile passes through a (somewhat arbitrary) boundary between them. Note 18. It is sometimes incorrectly assumed that “electron- rich” and “electron-poor” regions have negative and positive electrostatic potentials, respectively, and that the electrostatic potential follows the electronic density. This is often, but not always, the case. For example, the internuclear regions of covalent bonds usually have accumulated electron density, but the electrostatic potential in these regions is generally positive and is due to the proximity of the nuclei (also see Note 12).126 ■ RECOMMENDED FEATURES FOR CHARACTERIZING A HALOGEN BOND On the formation of a typical halogen bond R−X···Y between two interacting molecular entities R−X and Y: (a) A Coulombic engagement (attraction) may occur locally between the interacting regions onHaB donor X andHaB acceptor Y. (b) The sign of the binding energy (also the interaction energy, complexation energy, or stabilization energy) is likely to be negative to signify an energetically favorable interaction (also see Note 5); this energy refers to the difference of the sum of the total electronic energies of the isolated HaBD R−X and HaBA Y moieties from the total electronic energy of the halogen bonded system R−X···Y. (c) An energy decomposition analysis, for instance, using symmetry adapted perturbation theory (SAPT),127 may indicate the energetic contributions to the interaction energy of the HaB arise from electrostatics, exchange, induction (polarization and/or charge transfer), and long- range dispersion. The role of an individual energy component of the HaB may vary depending on the nature and the extent of the interaction between HaBD X and HaBA Y (in accord with the fifth feature in ref 34), although the interaction energy is not readily dissected into individual components. Dispersion is not a measurable quantity, even though its prevalence has been d i s cu s sed and ju s t i fied many t imes . Others121,128−130 have demonstrated that dispersion and polarization are an integral part of an electrostatic Crystal Growth & Design pubs.acs.org/crystal Article https://doi.org/10.1021/acs.cgd.4c00228 Cryst. Growth Des. 2024, 24, 5494−5525 5498 pubs.acs.org/crystal?ref=pdf https://doi.org/10.1021/acs.cgd.4c00228?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as interaction and that they emerge from the Hellmann− Feynmann theorem,131,132 which asserts that forces acting on nuclei in a molecule or molecular complex are entirely Coulombic in nature. (d) The distance between the HaBD site X and the HaBA site Y tends to be smaller than the sum of the van der Waals (vdW) radii of the respective interacting atomic basins but larger than the sum of their covalent bond radii; deviation from the former criterion is likely, since the known vdW radii of atoms are only accurate to within ±0.2 Å37,133−135 (the first part of d accords with first feature in ref 34). This criterion may not apply to π-/p- hole (or π-/p-belt) HaB if multiple atoms describe the HaBD entity (viz. the bonding region of X2). (e) TheHaBD site X tends to approach the HaBA Y along the outer extension of a σ-covalent bond, R−X. The angular deviation from the R−X bond extension is often less pronounced in HaBs than in HBs, ChBs, and PnBs; the directionality of these interactions is driven by electro- statics and the location of the σ-hole (along or off the R− X bond axis),115 although charge transfer and lone-pair repulsion contribute non-negligibly to the linearity of HaBs.136,137 (f) The angle of interaction, ∠R−X···Y, tends to be linear or quasi-linear when the approach of the electrophilic site on X is along the R−X σ-covalent bond extension, but can be nonlinear or bent when the HaB occurs between the lateral portion of an entirely electrophilic HaBD site X (as in a molecular cation, for example) and the nucleophilic region on Y, as well as when the same HaBD X is simultaneously involved in secondary interactions with the same or a different HaBA Y. Part of f accords with the third feature proposed in ref 34; however, this feature fails to account for the directionality of the π-/p-hole (or π-/p- belt) halogen bonds formed by the electrophilic π-/p-hole (or π-/p-belt) hosted by a bonded halogen derivative in molecules and the nucleophile on HaB Y. Accordingly, the angle of interaction, ∠R−X···Y, tends to be nonlinear (60° < ∠R−Y···A < 135°) when the approach of the electrophilic site on X is orthogonal the R−X σ-covalent bond extension (as in Cl3Br···CO and Cl3Br···N2). 110 (g) When the nucleophilic region on the HaBA entity Y is a lone-pair orbital or a (negative) π-/p- region, the HaBD entity X tends to approach HaBA entity Y along the axis of the lone-pair or orthogonal to the π-/p-hole (or bond) plane regardless of the nature of the halogen bond (also see e). (h) The length of the R−X covalent bond opposite to theHaB (called the halogen bond donor distance) is typically longer than that in the isolated (unbound) HaBD entity; this accords with the second feature proposed in ref 34. However, this may not always be the case (e.g., shortening of the halogen donor bond R−X may be seen);138−141 geometric deformation to other parts of the HaBD/HaBA entities may occur upon the formation of a linear (or an orthogonal) halogen bond.110 (i) The infrared absorption (IR) and Raman scattering observables of both R−X and Y are affected by HaB formation; compared to the harmonic frequency of the same bond in the isolated molecule, the vibrational frequency of the R−X bond may be red-142−144 or blue- shifted141,145,146 depending on the extent of the interactions involved.15 New vibrational modes associ- ated with the formation of the (R−)X···Y intermolecular halogen bond may also be observed, as for HBs, TtBs, ChBs, and PnBs, in accordance with the seventh feature in ref 34. (j) The nuclear magnetic resonance (NMR) chemical shifts of nuclei in both R−X and Y are typically affected as found for R−Ch···YChBs; the isotropic coupling constant of the HaB donor in the complex system tends to decrease relative to that of the isolated HaB donor,27,103,118,147−149 as observed for HBs, TtBs, ChBs, and PnBs. This accords with the second feature in ref 34. (k) The UV−vis absorption bands of the HaBD chromo- phore may experience a shift to shorter wave- lengths;150−152 the binding energies of the peaks associated with X with the X-ray photoelectron spectrum (XPS) of the R−X···Y complex shift to lower energies relative to unbonded X, in accordance with the eighth and tenth features, respectively, in ref 34. (l) A bond path and a bond critical point between HaBD X and HaBA Y may be found when an electron density topology analysis based on the quantum theory of atoms in molecules (QTAIM)97,98 is carried out, together with the appearance of other charge density-based signatures such as those associated with the sign and magnitude of the Laplacian of the charge density and the total energy density at bond critical points.15 This may be in accordance with the sixth feature in ref 34. (m) Isosurface volumes (colored greenish, blue, or blue-green between HaBD X and HaBA Y, representative of attractive interactions134,135,153,154) may be seen if a noncovalent index analysis (NCI) based on reduced density gradients is performed;155−157 similar isosurface features may also emerge when an independent gradient model (IGM),156,157 an IGM based onHirshfeld partition of molecular density (IGMH), or an interaction region indicator (IRI) analysis is performed.158,159 Feature l may fail in some chemical systems, especially in the weak bonding regime,68,119,160−163 but the isosurface analysis is expected to recover inter- and/or intramolecular interaction between interacting atomic basins.13,161,164 (n) At least some transfer of charge density from the frontier HaBA orbital to the frontier HaBD orbital may occur (viz. from a (filled) lone-pair type orbital (n) to an empty σ*-/ π*-type anti-bonding orbital);12 when the transfer of charge density between the orbitals is significant, the formation of a dative (covalent) interaction is likely.9 The occurrence of the phenomenon IUPAC recommended for HBs is also applicable to TtBs, ChBs, and PnBs; the nature of charge transfer (hyperconjugation) may be assessable upon computing the second-order perturba- tion theory based stabilization energy using natural bond orbital (NBO)15,140,165,166 and/or block-localized wave function (BLW) method approaches.167,168 (o) The halogen bond strength typically increases with a given HaBA Y, as the electronegativity of X decreases in the order F > Cl > Br > I (> At) and the electron- withdrawing ability of R increases; there may be an exception when the chemical environment alters the nature of the reactivity between the HaBD and HaBA moieties (in accord with the fourth feature in ref 34). (p) The halogen bond strength may increase for a specific HaBA Y and R of the R−X entity as the polarizability of the X atom increases ((At >) I > Br > Cl > F). This is Crystal Growth & Design pubs.acs.org/crystal Article https://doi.org/10.1021/acs.cgd.4c00228 Cryst. Growth Des. 2024, 24, 5494−5525 5499 pubs.acs.org/crystal?ref=pdf https://doi.org/10.1021/acs.cgd.4c00228?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as analogous to the effect observed in the case of TtB (Pb > Sn >Ge > Si > C), ChB (Te > Se > S >O),169 and PnB (Bi > Sb > As > P > N); if a secondary interaction (e.g., hydrogen bond, halogen bond, chalcogen bond, tetrel bond, pnictogen bond, etc.) is involved either with the HaB bond donor or the acceptor, the order of interaction strength may alter. (q) The strength of a halogen bond170 can be ultrastrong (i.e., interaction/binding energy > −40 kcal mol−1), very strong (−25 < energy ≤ −40 kcal mol−1), strong (−25 < energy < −15 kcal mol−1), moderately strong (−5 < energy < −15 kcal mol−1), weak (−3 < energy < −5 kcal mol−1), very weak (−1 < energy < −3 kcal mol−1), or of the vdW type (−0.01 < energy ≤ −1.0 kcal mol−1).26,28,108 Chemical systems with the HaB energies falling into different categories depend largely on the reactivity of the HaBD X and HaBA Y sites in the interacting molecular entities. For example, if an anion Y attracts an electrophilic region on X in R−X, the interaction energy can be of the ultrastrong type (e.g., bond energies for FI···F− and II···F− are −69.0 and −75.0 kcal mol−1, respectively12); the interaction energy can be categorized as very strong and moderately strong when the identities of HaBD X and HaBA Y are changed (e.g., bond energies of the ion−molecule interactions IF···I−, II···I−, and IF···Cl− are −37.4, −16.9 and −14.5 kcal mol−1, respectively).12 VdW interactions are expected between neutral molecules when X and Y have weakly electrophilic and nucleophilic regions on their electro- static surfaces, respectively (e.g., as in HCl···N2 and HCl··· O2); when the interaction energy is appreciable (> −15 kcal mol−1), a non-negligible degree of covalency in halogen bonds is likely.15,49,171,172 (r) The electrophilicity and nucleophilicity of specific regions on the halogen atom inmolecular entities may be assigned using the sign of the local most maxima and minima of potential (VS,max and VS,min, respectively).13,66,68,173,174 Signatures such as the positive and negative signs of VS,max or VS,min (VS,max > 0 or VS,min > 0 and VS,max < 0 or VS,min < 0, respectively) may be used to determine the electro- philicity and nucleophilicity on the surface of the halogen atom X in R−X. The electrophilic and nucleophilic σ- and π-holes126,175,176 (or even π-/p-type belts) on atom X (or around the bonding region in a pair of halogen atoms) may be characterized by VS,max > 0 and VS,max < 0, respectively. It is often observed that the σ-hole on the surface of halogen atom X in R−X covalent bond is characterized by VS,max > 0; when VS,max < 0, a negative σ- hole on X in R−X is inferred. This view is transferable to π-/p-holes (or π-/p-belts) as well. (s) Similar insight as in rmay be gained about the character of a σ-hole from an analysis of the extended transition-state method with natural orbitals for chemical valence (ETS- NOCV);177−180 in addition, this approach may also be used to evaluate the charge transfer between the halogen bond donor and acceptor orbitals,181,182 as well as to gain insight into the electrostatics, exchange-correlation, Pauli’s exchange-repulsion, and orbital interaction en- ergies of a halogen bond. ■ SOME EXPERIMENTALLY AND THEORETICALLY IDENTIFIED HALOGEN BOND DONORS AND ACCEPTORS The list of HaB donors and acceptors is vast. Some of them are from theoretical studies reported by a number of research groups, while others are taken from structures deposited in the CCDC.100 The list below is not comprehensive, but illustrative. The HaB donor entity X in R−X may be • the axial outer portion on the side of halogen atom X in hydrogen halides HX (X = Br, Cl, I, At) and haloalkanes (CH3X, CH2X2, 183 CHX3 (X = Cl, Br, I, At),184 CX4 (X = F, Cl, Br, I, At), and CnF2n+1I); • the axial outer portion on the side of X in OX2 185 and in dihalogen molecules X2 and XX′ (X, X′ = F, Cl, Br, I, At); • the axial outer portion on the side of X in NX3, 186 as well as XCN and XCCCN (X = F, Cl, Br, I, At);68 • the axial outer portion on the side of halogen X in haloethene C2X4, 187 C6H5X, and C6X6 (X = Cl, Br, I); • the axial outer portion of halogen X in −NO2 substituted arene moieties (as in 1,3,5-triiodo-2,4,6-trinitrobenz- ene,188 2-chloro-1-iodo-4-nitronaphthalene,189 and 1,3,5-trichloro-2,4,6-trinitrobenzene);190 • the axial outer portion of halogen in haloalkynes, such as the arene derivatives (C2I2, 191 haloprogin (C9H4- Cl3IO),192 and 1-halo-2-phenylacetylene (C8H5X (X = Br, I)),193 1-fluoro-4-(iodobutadiynyl)benzene (C10H4- FI),194 2,6-bis(iodoethynyl)pyridine (C9H3I2N),195 3- iodo-2-propynyl-N-butylcarbamate,196 3-(iodoethynyl)- benzoic acid (C9H5IO2), 197 2-(bromoethynyl)-1,3-di- chlorobenzene (C8H3BrCl2), 198 1,4-difluoro-2,5-bis- (iodoethynyl)benzene (C10H2F2I2), 199 1,4-bis(iodo- ethynyl)benzene (C10H4I2), 200 2,3-bis(bromoethynyl)- 1,4-dimethoxybenzene,201 2,2′,4,4′,6,6′-hexafluoro- 3,3′,5,5′-tetrakis(iodoethynyl)biphenyl (C20F6I4), 202 1,3,5-tris(bromoethynyl)benzene (C12H3Br3), 203 1,1′,1″,1‴-methanetetrayltetrakis[4-(iodoethynyl)benz- ene] (C33H16I4), 204 1,3,5-trifluoro-2,4,6-tris(iodoethyn- yl)benzene (C12F3I3), 205 1,4-bis(5-chloro-pent-4-ynyl- oxy)benzene (C16H16Cl2O2), 206 2,6-bis(iodoethynyl)- pyridine (C9H3I2) , 195 2,3,5 ,6-tetrafluoro-1,4- bis(iodoethynyl)benzene (C10F4I2), 207 and 3-(iodo- ethynyl)pyridine (C7H4IN));197 • hypervalent halogen derivative in molecules, as in (dichloro-trifluoromethyl)iodine (CCl2F3I), 208 dichloro- (phenyl)iodane (C6H5Cl2I), 209 o-(dichloriodo)nitro- benzene (C6H4Cl2INO2), 210 p-(dichloriodo)nitrobenz- ene (C6H4Cl2INO2), 210 2-(dichloroiodo)pyridine (C5- H4Cl2IN),211 bis(pentafluorophenyl)iodonium trifluoroacetate (C14F13IO2), 212 trifluoromethyl-tetra- fluoro-iodine (CF7I), 213 and pentafluorophenyl-tetrakis- (fluoro)iodine (C6F9I)); 214 • the halogen in imide and amide derivatives such as N,N′- dibromoethanedi-imidoyl-difluoride (C2Br2F2N2) 215 and 1-chloropyrrolidine-2,5-dione (C4H4ClNO2); 216 1,3-di- bromo-5,5-dimethylimidazolidine-2,4-dione (C5H6Br2- N2O2), 217 N-bromosuccinimide (C4H4BrNO2), 218 N- chloro-N-(2,6-dichlorophenyl)trichloroacetamide (C8- H3Cl6NO),219 1-iodopyrrolidin-2-one (C4H6INO),220 1-chloro-1H-1,2,3-benzotriazole (C6H4ClN3), 221 N,N,N′-trichlorobenzamidine (C7H5Cl3N2), 222 N,N-di- chloromethylsulfonamide (CH3Cl2NO2S), 223 N-chloro- N-methoxyurea (C2H5ClN2O2), 224 1,3-dichloro-5,5-di- Crystal Growth & Design pubs.acs.org/crystal Article https://doi.org/10.1021/acs.cgd.4c00228 Cryst. Growth Des. 2024, 24, 5494−5525 5500 pubs.acs.org/crystal?ref=pdf https://doi.org/10.1021/acs.cgd.4c00228?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as methylhydantoin (C5H6Cl2N2O2), 225 1,3-dichloro-2,4- imidazolidinedione (C3H2Cl2N2O2), 225 N-chloro-N- phenyl-2-chloroacetamide (C8H7Cl2NO),219 and 1,3- dichloro-1,3-diazetidine-2,4-dione (C2Cl2N2O2); 226 • the halogen derivative in systems containing boron such as hexachloroborazine (B3Cl6N3), 227 (naphthalene-1,8- diyl)bis(dichloroborane) (C10H6B2Cl4), 228 1-carba-2,- 3,4,5,6,7,8,9,10,11,12-undecachlorododecaborate (CHB11Cl11), 229 and 2,3,4,5,6-pentachloro-7,8,9,- 10,11,12-hexaiodoaza-closo-dodecaborane (HB11Cl5I6- N);230 • the halogen derivative in cations, e.g., fluoroammonium (FNH3 +),231 3-(iodoethynyl)pyridin-1-ium (C7H5- IN+),232 5-bromosulfenyl-1,3,2,4-dithiadiazolium (CBrN2S3+), 233 2-(iodoethynyl)pyridinium (C7H5- IN+),232 2-chlorodibenzo[b,d]bromol-5-ium (C12H7- BrCl+),234 1,2,3,4-tetrafluorodibenzo[b,d]iodol-5-ium (C12H4F4I+), 235 bis(pentafluorophenyl)iodonium (C12- F10I+), 236 [4-(ethoxycarbonyl)phenyl](phenyl)iodanium (C15H14IO2 +),237 and bis(4-chlorophenyl)iodanium (C12H8Cl2I+). 238 The HaB acceptor entity Y may be • a lone-pair on an atom in a molecular entity (a Lewis base), with many possibilities including the lateral portions of covalently bonded halides in HX, CH3X, and CX4 (X = F, Cl, Br, I); N in pyridines, amines, or even in N2; O in H2O, O2, H2CO, CO, CO2, and an ether or carbonyl group; covalently bonded halogens in mole- cules; As in AsMe3; a chalcogen in a heterocycle such as a thio-, seleno-, and tellurophene derivatives, as well as fused polycyclic derivatives thereof; furoxans, 2,5-thi- adiazoles N-oxides, sulfoxide, aryl sulfoxides, and tellur- azoles N-oxides; O, S, and/or N in derivatives of macrocyclic aza- and/or thia-crown-ethers such as 18- crown-6, 18-aza-crown-6, 15-crown-5, N-phenylaza-15- crown-5, and 21-crown-7, cyclam, [2.2.2]cryptand, 1,4,7- triazacyclononane, monothiadibenzo[24]crown-8-ethers, dithiadibenzo[24]crown-8-ethers, trithiadibenzo[24]- crown-8-ethers, tetrathiadibenzo[24]crown-8-ethers, etc.; • an anion, such as the halide anions X−, OH−, NO3 −, CF3SO3 −, tetraphenylborate C24H20B−, CN−, Cl3−, I3−, Br3−, Cl2I−, Br2I−, Br3I2−, I2Cl−, I42−, I5−, Cl3I2−, I8−, Br3Cl4−, NO3 −, ClO4 −, 5-oxotetrazole (CHN4O−), N3 −, BF4 −, AuCl4−, PF6 −, AsF6 −, pentazolide (N5 −), 5,5′- bistetrazolates (C2N8 2−), p-tosylate (C7H7SO3 −), hexa- Figure 2. Ball-and-sick (and/or mixed capped stick) models of halogen-centered intermolecular close contacts observed between atomic basins of interacting molecules in some crystals. (a) N,N,N-trimethyl-N-(2-chloro-ethyl)ammonium trichloride,239 (b) tris(1,3,6,8-tetrakis(methylthio)pyren- ium) tris(triiodide) heptaiodine,240 (c) bis(η6-benzene)-ruthenium(II) bis(tetrafluoroborate)nitromethane solvate,241 (d) methylphosphanium bromide,242 (e) trimethylselonium aqua-tetrachloro-oxo-molybdenum,243 (f) guanidinium tetrafluoroborate,244 (g) rac-1-methyl-1,2-diphenyl-1,2- dihydronaphtho[1,8-cd][1,2]diphosphol-1-ium tetrafluoroborate,245 (h) chloro-(tris(thiazol-2-yl)phosphine)gold(I),246 and (i) 2,2′,2″-nitrilotris- (ethan-1-aminium) tris[tetrafluoroborate].247 For clarity, some of the molecules in the crystal were deleted, such as bis(η6-benzene)-ruthenium(II) in (c), for example. The CSD reference code in each case is shown in uppercase letters, and selected bond distances and angles are in Å and degrees, respectively. Labeling of selected atoms is shown in each case. Crystal Growth & Design pubs.acs.org/crystal Article https://doi.org/10.1021/acs.cgd.4c00228 Cryst. Growth Des. 2024, 24, 5494−5525 5501 https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig2&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig2&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig2&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig2&ref=pdf pubs.acs.org/crystal?ref=pdf https://doi.org/10.1021/acs.cgd.4c00228?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as bromo-pentamethyl-1-carbadodecaborane (C6H16B11- Br6−), closo-dodecaborate (H12B12 2−), and polyatomic oxyanions such as C2O4 2−, ReO4 −, AsCl4−, SbF6 −, SbCl4−, BiCl4−, GaCl4−, ZnCl42−, SiX6 2−, GeX6 2−, SnX6 2− and PbX6 2− (X = F, Cl, Br), PbI64−, SnCl3−, SnI3−, GeCl3−, GeBr3−, GeI3−, Br4Sn2−, I4Sn2−, Cl4Pb2−, I5Pb3−, B2Cl62−, CHB11Cl11−, B12Br122−, B12I122−, B12Cl122−, CH6B11Br6−, etc.; • a (negative) π-/p-belt containing system (species featuring a double or triple bond, for example, the midpoints of the C�C and C�C bonds in H2C�CH2 and HC�CH, respectively) and the negative π-hole regions of arene moieties of any kind, such as the centroid regions of arenes (for example, C6H6, C6H5OH, C6H5F, C6H5NHCH3, C6H5NHOH, and C6(NH2)6; the C�C bonding regions in fullerene C60 and C70; N in NO3 −, etc.). What follows are illustrative crystal systems in which the packing between the molecular building blocks is solely or partly driven by halogen bonding of various types. They include intermolecular and intramolecular HaBs discussed in Notes 4 and 15. We begin by providing examples of chemical systems that may appear to have halogen bonds but actually do not. We applied some theoretical approaches in cases where conclusions were difficult to reach. Considering that different studies use different levels of theory and basis sets to study halogen bonds, we have chosen a similar strategy but opted for the most frequently used theoretical methods to explore the reactivity of molecular entities, subject to their sizes and available computa- tional resources. ■ ILLUSTRATIVE CRYSTAL SYSTEMS NOT FEATURING HALOGEN BONDING It is often found that the halogen derivative in molecules can be engaged attractively with a similar or different neighboring molecule, contributing to the solid-state structure of many crystals. However, the engagement is not always driven by halogen bonding. For example, the C···Cl close contact in the crystal of N,N,N-trimethyl-N-(2-chloro-ethyl)ammonium tri- chloride (Figure 2a) is not a halogen bond; it is a charge-assisted tetrel bond. The S···I close contacts in the crystal of [3(C20H18S4+),3(I3−),7(I2)] (Figure 2b) are not HaBs; they are charge-assisted ChBs. The N···F close contact in [C12H12Ru2+,2(BF4 −),CH3NO2] is not a HaB; it is a charge- assisted PnB, since N has an electrophillic π-/p-hole and the F in BF4 − is a HaBA (Figure 2c). The C···Br and P···Br close contacts in the crystal of [CH6P+,Br−] (Figure 2d) are not HaBs; they are a charge-assisted tetrel bond and a pnictogen bond, respectively. The Se···Cl close contact in the crystal of [C3H9Se+,H2Cl4- MoO2 −] (Figure 2e) is not a HaB; it is a charge-assisted ChB. The C···B and C···F close contacts in [CH6N3 +,BF4 −] (Figure 2f) are charge-assisted TtBs; they are not halogen bonds, since the boron/fluorine atom in the anion in BF4 − is a HaBA. The P··· F close contact in the crystal of [C23H19P2 +,BF4 −] (Figure 2g) is not a halogen bond; it is a charge-assisted pnictogen bond. The P···Cl close contact between the building blocks responsible for the crystal of [C9H6AuClN3PS3] (Figure 2h) is a pnictogen bond, not a halogen bond. Similarly, the N···F close contact in [C6H21N4 3+,3(BF4 −)] is not a halogen bond; it is a charge- assisted PnB because the N is electrophillic in the C6H21N4 3+ cation so is a pnictogen bond donor (PnBD) (Figure 2i). In the crystal of [C11H24N+,C6H5F5I−,C2H3N] (not shown; CSD ref NACSEQ248), the three interacting molecular building blocks are packed such that two I···F close contacts occur between a pair of close C6H5F5I− ions. The I···F close contact distance, 3.392 Å, is significantly shorter than the vdW radii of I and F (2.04 Å (I) + 1.47 Å (F) = 3.51 Å);249 the C−I···F angle is 149.2°, which suggests the presence of a directional interaction. An analysis of the geometric feature alone is insufficient to determine whether the I···F close contact is a HaB. However, as we will show below, and have demonstrated recently else- where,119 the I···F close contact could be regarded as HaB given that the interaction between the anion and the cation in the crystal is likely to play an important role in polarizing the electrostatic field of the anion; the induction of a positive potential on the surface of the I in C6H5F5I− along the C−I bond extension may occur, which shall interact attractively with the lateral portion of F in a neighboring C6H5F5I−. This speculative scenario for the occurrence of halogen bonding in the crystal is very different from that found in the crystals of trifluoromethyl- tetrafluoro-iodine (CF7I) 213 and pentafluorophenyl-tetrakis- (fluoro)iodine (C6F9I) 214 (vide inf ra). ■ ILLUSTRATIVE CRYSTAL SYSTEMS FEATURING HALOGEN BONDING Halogen Bonding in Anion-Molecule Systems in Crystal Adducts. Some examples of chemical systems where close contacts occur that might not be readily identified as halogen bonds are given in Figure 3. The Cl···Cl close contact in the crystal of tetraethylammon- ium tetrachloroiodate [Cl4I−,C8H20N+]250 (Figure 3a) develops along the outer extensions of the I−Cl bond axes between two Cl atoms belonging to two neighboring [Cl4I−] anions, and the angle of interaction, ∠I−Cl···Cl, is 180.0°. The inorganic framework (···ICl4−···Cl4I−) of the crystal features Cl···Cl close contacts (Figure 3a), which are stabilized by an extensive number of Cl···H hydrogen bonds (not shown) due to the presence of the organic counterpart. The latter contacts are likely to cause changes to the charge density distribution around the chlorine atoms in the anion, forcing the Cl in the anions to Figure 3. Illustration of X···X close contacts between inorganic halide frameworks in some organic−inorganic ion-pair adducts in the crystalline phase. The CSD reference in each case is shown in uppercase letters, and selected bond distances and angles are in Å and degrees, respectively. (a) Tetrachloroiodate [Cl4I−,C8H20N+],250 (b) catena-(18-crown-6 oxonium clathrate heptaiodide) [(C12H24O6)n,n- (H3O+),n(I7−)],251 (c) bis(bromotris(4-fluorophenyl)phosphonium) b r om i n e n o n a b r om i d e t r i b r om i d e [ 2 (C 1 8H 1 2 B r F 3 - P+),Br9−,Br3−,Br2], 252 and (d) bis(triphenylphosphine)iminium hexa- kis(chlorobromo)chloride (C36H30NP2 +,Br6Cl7−).253 For clarity, the organic cations, viz. C8H20N+ in (a), [(C12H24O6)n,n(H3O+)] in (b), 2(C18H12BrF3P+) in (c), and C36H30NP2 + in (d), have been omitted. Labeling of selected atoms is shown in each case. Crystal Growth & Design pubs.acs.org/crystal Article https://doi.org/10.1021/acs.cgd.4c00228 Cryst. Growth Des. 2024, 24, 5494−5525 5502 https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig3&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig3&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig3&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig3&ref=pdf pubs.acs.org/crystal?ref=pdf https://doi.org/10.1021/acs.cgd.4c00228?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as interact with each other constructively. The 1D chain-like inorganic framework [···ICl4−···Cl4I−] stabilized by Cl···Cl close contacts is probably the forced consequence of the primary hydrogen bonding interactions. At first glance, the Cl···Cl close contacts might not be regarded as HaBs, considering that they appear between two entirely negative sites. However, their engagements display linearity (type II, the angle of interaction), satisfying feature f, and the intermolecular distance between the two Cl atoms, 3.344 Å, is less than twice the vdW radius of Cl (3.64 Å),249 satisfying feature d of a halogen bond. These two features are not sufficient to determine whether or not the halogen···halogen contacts in the crystal can be characterized as halogen bonds and whether they are the result of electrostatic polarization caused by hydrogen bonds (and the cation); this is surely a topic for a future investigation. The I···I close contacts between the I7− anions in the crystal of catena-(18-crown-6 oxonium clathrate heptaiodide), (C12H24O6)n,n(H3O+),n(I7−)251 (Figure 3b), may not merely be considered as attractive interactions between the entirely negative I7− sites that cause the development of the inorganic framework. From the geometry of the I7− anion alone, it may be inferred that the anion is an assembly between an I3− anion and two I2 molecules, which is driven by a two σ-hole HaBs. The attractive interaction occurs between the electrophilic σ-hole on the surface of an I atom opposite to the I−I bond extension in the I2 molecule and the nucleophile on the central I atom of the I3− anion. The I7− anions are also halogen bonded to each other via covalently bonded σ-holes (r(I···I) = 3.974 and 4.043 Å) of I2 that are common to the [I5−] framework. As noted above, the formation of the I7− anion, and the interaction between these ions, contributes to the development of the inorganic frame- work; and the interactions occur in the presence of the polarizing field of the oxonium cation, which plays a critical role the assembly through hydrogen bonding. The Br···Br close contacts between a pair of Br9− anions caused by a Br2 molecule as a spacer in the crystal of [2(C18H12BrF3P+),Br9−,Br3−,Br2] 252 (Figure 3c) are halogen bonds, with r(Br···Br) = 3.280 Å and ∠Br−Br···Br9− = 177.9°. Similarly, the Br···Br close contacts between the Br3− anion and the Br2 molecule responsible for rigid framework of Br9− are also halogen bonds. This is not surprising, since each outer end of the Br2 molecule that has an electrophilic σ-hole assists in the development of the Br9− anion framework via a (covalent) halogen bond and the other end of the same molecule halogen bonds with the Br3− cation [r(Br···Br) = 3.156 Å], contributing to the development of the inorganic framework. The latter are quasi-linear, and the Br···Br intermolecular distances are less than twice the vdW radius of Br (3.73 Å).249 The Cl···Cl and Cl···Br close contacts between Br6Cl7− anions in the bis(triphenylphosphine)iminium hexakis(chlorobromo)- chloride (C36H30NP2 +,Br6Cl7−) crystal253 (Figure 3d) are halogen bonds. The inorganic anion, Br6Cl7−, is an assembly between a Cl− anion and six Cl−Br molecules; this is driven by the positive σ-holes onHaBD halogen, each on the side of the Br atom lying opposite to the Cl−Br bond extension in Cl−Br. In addition, the Br6Cl7− anions are linked to each other via Cl···Cl and Cl···Br halogen bonds, in which the electrophilic σ-hole on the side of the Cl atom opposite to the Br−Cl bond extension donates the halogen bond and the lateral portions of the Cl and Br atoms behave as acceptors (r(Cl···Cl) = 3.207 Å, ∠Br−Cl··· Cl = 172.2°; r(Cl···Br) = 3.861 Å; ∠Br−Cl···Br = 163.5°). The Xn − (n = 3, 5, 7, 9) anions can be viewed as the result of an attractive engagement between an halide anion and two or more dihalogen (X2) molecules, and are driven by HaBs. Accordingly, the Br9− anion (Figure 3c) is actually an assembly of a Br− anion with four Br2 molecules. That is, a single Br− anion (HaBA) (covalent) halogen bonds with four neighboring electrophilic σ- holes; each resides on the side of a Br atom opposite to the Br− Br covalent bond extension in a Br2 molecule (HaBD), resulting in the formation of the Br9− anion. Since the formal charge of Br9− and Br3− is −1, their presence as counterions stabilizes the organic cation, (viz. C18H12BrF3P+ in Figure 3c), leading to the formation of an organic−inorganic hybrid crystalline material. The crystal, tripropylammonium nonabromide [C12H28N+,Br9−] (CSD ref ODAQER254), is another example (not shown), where Br···Br HaB occurs between the Br atoms of close-lying Br9− inorganic anions, which is driven by the presence of the organic cation; in this case, r(Br···Br) = 3.395 Å and ∠Br−Br···Br = 173.3°. The chemical systems outlined above (viz. Br6Cl7− and Xn −), and those illustrated in Figure 3, are stabilized by σ-hole centered halogen bonds,68,255,256 validating the expanded definition, as well as Notes 1−4, 6−11, and 15 and features a and d−f. The 2D-like layers formed by Cl13− anions are separated by organic spacers in the crystal of bis(triphenylphosphine)- iminium tridecachloride [C36H30NP2 +,Cl13−] (CSD ref PIG- CIU257), producing an inorganic−organic hybrid material. The inorganic layers are linked through Cl···Cl HaBs, with r(Cl···Cl) = 3.964 Å and ∠Cl−Cl···Cl = 161.1°. These close contacts are longer than those observed in the crystal of bis(N,N,N- trimethylanilinium)dodecachloride [2(C9H14N+,Cl122−] (CSD ref PIGDER257), where r(Cl···Cl) = 3.00−3.45 Å and∠Cl−Cl··· Cl = 168.1°−174.9°. Both the angular and bond distance features are in agreement withNotes 1−4, 6−11, and 15, features a and d−f, and the definition of a halogen bond, since Cl13− may be viewed as consisting of an anion attractively assembled with six Cl2 molecules, [Cl−···(Cl2)6]. The HaB interactions above may to some extent resemble those investigated theoretically for cesium tetrel halide perov- skite oligomers [Cs+·TtX3 −]n (n = 2, 3, 4)67 and [CH3NH3 +· TtX3 −]2 (Tt = Ge, Sn, Pb; X = Cl, Br, I) ion-pair dimers.119 Upon the formation of the [Cs+·TtX3 −] ion-pairs, the cesium cation polarizes TtX3 − through Coulombic and charge transfer interactions, creating electrophilic σ-holes on the surface of Tt. These σ-holes on an ion-pair then attract the negative halogen sites on another ion pair(s) in close proximity, leading to the formation of [Cs+·TtX3 −]n oligomers. This explains why, in the presence of Cs+, the [TtX3 −] anions attract each other, leading to the formation of inorganic cage-like 3D structures in the solid state. This result complements Note 16 in the sense that an electrophilic σ-hole can be induced in an anion, which can then interact with a nucleophile. Hypervalent Halogen as a Halogen Bond Donor for Halogen Bonding. The iodine atom is hypervalent in molecular CF7I 213 and C6F9I 214. These neutral molecules are the building blocks of their corresponding crystalline materials. The MESP plots of the two entities show that both the axial and lateral portions of covalently bonded I are electrophilic (see Figure 4a and b, respectively, top). The [ωB97X-D/def2- TZVPPD]-level analysis suggests that there is no σ-hole on the side of the covalently bonded I atom opposite to the C−I bond extension. Instead, a p-type hole is evident; it is, however, characterized not by a VS,max but by a positive VS,min of 37.9 kcal mol−1 in CF7I (see feature r). Additionally, there are four maxima of potential (filled tiny red circles) on I that surround the p-hole, each described by a VS,max of 41.4 kcal mol−1; they Crystal Growth & Design pubs.acs.org/crystal Article https://doi.org/10.1021/acs.cgd.4c00228 Cryst. Growth Des. 2024, 24, 5494−5525 5503 pubs.acs.org/crystal?ref=pdf https://doi.org/10.1021/acs.cgd.4c00228?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as each appear on the surface of I but in the junction (nonbonding) region between a pair of F atoms. The strengths of the corresponding extrema of potential in C6F9I are 36.2 and 38.8 kcal mol−1, respectively. The chemical situation in CF7I is very similar to that observed in the case of the P�N molecule, in which a σ-hole was not found on the electrostatic surface of the molecule on the side of P opposite to the N�P bond extension but instead a positiveminimumof potential with its origin from a p-type orbital (VS,min > 0).110 The packing in the CF7I 213 and C6F9I 214 crystals is driven by many C−I···F nonlinear halogen bonds that follow a type II topology of noncovalent bonding (see Note 9). They are the result of Coulombic attraction between HaB donor I in one molecule and the HaB acceptor F in the adjacent molecules with which the former interacts (in agreement with feature a). The hypervalent I atom is a multicentered HaB donor site (see Note 13), forming several I···Y (Y = Cl, O) noncovalent interactions between the building blocks in the crystals of o-(dichloriodo)- nitrobenzene (Figure 4c) and p-(dichloriodo)nitrobenzene (Figure 4d), respectively. Similarly, along with other attractive interactions, the crystal structure of tetrafluoro[4-(pentafluoro- l6-sulfanyl)phenyl]-l5-iodane (C6H4F9IS) (CSD ref UNILIP258) shows reasonably strong I···F close contacts between the five- coordinate hypervalent I atom in one molecule and the lateral portion of a F atom in an interacting partner molecule (r(I···F) = 2.906 Å and ∠C−I···F = 144.5°), providing stability to the supramolecular assembly. That hypervalent halogen in molec- ular entities can halogen bond with nucleophiles in an interacting partner molecule has also been reported else- where.259 These conclusions validate several Notes (for example, Notes 3, 6, 9, and 13−15) and features a and d−f. An interesting feature of chemical bonding that develops between the engaging molecules, for instance, in CF7I, is the π-/ p-hole halogen bond that emerges from the donation of the halogen’s π-/p-hole to the interacting nucleophile (F); this is quasi-linear, following a type II geometric bonding topology. This may contrast with the conventional view that π-/p-hole bonds are orthogonal interactions and nonlinear, as discussed elsewhere110 and observed in other instances, which are discussed below. Intramolecular Halogen Bonding in Crystals. Shown in Figure 5 are a few instances in which intramolecular I···O halogen bonding interactions occur; they are not chalcogen bonds, since carbonyl oxygen serves as a HaB acceptor site Y and the covalently bonded I atom is the HaB donor site X. The HaBs are either nonlinear in C10H9ClINO3 260 (see ∠C−I···O in Figure 5a) or quasi-linear in C9H7F3INO3S 261 and C15H14INO3 262 (see∠N−I···O in Figure 5b and c, respectively). The I···O close contact in o-nitrodiphenyliodonium iodide (CSD ref ENIGEN210) is not a chalcogen bond; it is an intramolecular halogen bond (r(I···O) = 2.735; ∠C−I···O = 157.5°). The hypervalent I(III) motif in bis(pentafluorophen- yl)iodonium trifluoroacetate (CSD ref BIHFIK212) (Figure 5c) does not form a chalcogen bond with nearest-neighbor O and F atoms; it forms I···F and I···O intramolecular halogen bonds. The electrophilic σ-hole on the extension of the C−I and N−I covalent bonds in this molecule cannot be visualized since it is annihilated during the formation of noncovalent bonds. The F··· O, Cl···N, and F···N close contacts in crystals C6H4FN5O6, 263 C15H13ClN2O,264 and C16H3F7N2S 265 shown in Figure 5d−f, respectively, are examples of intramolecular HaBs formed with HaB acceptors O, N, and N, respectively. The occurrence of one of the F···N halogen bonds in Figure 5f is a result of crystal packing, as our calculations suggested that the molecule is nonplanar in the gas phase. The illustrations validate several Notes 4 and 13, including Note 3. Halogen Bonding in Charge-Assisted Systems (viz. Ion-Pairs) in Crystals. Further examples of the occurrence of halogen bonds in crystalline materials are shown in Figure 6. They occur between ions in adducts. The bond distance and bond angles for the I···F, Br···Cl, I···I, I···Cl, and Br···I close contacts in the ion-pairs shown, respectively, in Figure 6a−e are charge-assisted halogen bonds. They are quasi-linear, and the intermolecular X···Y contact distance in each case is less than the sum of the vdW radii of X and Y. The remaining I···F close contact in Figure 6a that occurs between two cationic species (phenyl-trifluoro-iodine), is probably a σ-hole centered lump− hole interaction.266,267 Whether or not it can be referred to as a HaB requires a detailed theoretical investigation. Examples of chemical systems containing various halogen bonds are shown in Figure 7. The Br···Br, I···I, and I···I close Figure 4. (Top) The molecular skeletal framework (left) and 0.001 au isoelectronic density-mapped molecular electrostatic surface potential graph (right) of (a) trifluoromethyl-tetrafluoro-iodine (CF7I); 213 and (b) pentafluorophenyl-tetrakis(fluoro)iodine (C6F9I), 214 obtained with [ωB97X-D/def2-TZVPPD]. The blue region on the outer surface of covalently bonded I shows the dispersed nature of its electrophile, composed of I’s π-/p-hole. Selected maxima and minima of potential (VS,max and VS,min; in kcal mol−1) on the surface of covalently bonded I are shown as filled tiny circles in blue and red, respectively. (a and b) Nonlinear I···F halogen bonding interactions in the crystals of these systems. (c and d) HaB environment in the crystals of o-(dichloriodo)- nitrobenzene (C6H4Cl2INO2) 210 and p-(dichloriodo)nitrobenzene (C6H4Cl2INO2), 210 respectively. The CSD reference in each case is depicted in uppercase letters, and selected bond distances and angles are in Å and degree, respectively. Hanging contacts in red are marked in (d). Crystal Growth & Design pubs.acs.org/crystal Article https://doi.org/10.1021/acs.cgd.4c00228 Cryst. Growth Des. 2024, 24, 5494−5525 5504 https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig4&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig4&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig4&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig4&ref=pdf pubs.acs.org/crystal?ref=pdf https://doi.org/10.1021/acs.cgd.4c00228?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as contacts between the building blocks in the crystals shown in Figure 7a−c, respectively, are a result of halogen bonding formed when the HaB donor X in a neutral molecule is in close proximity to the HaB acceptor Y in an anionic entity. The I···Cl, I···Cl/I···F, and I···Cl close contacts shown in Figure 7d−f, respectively, are halogen bonds, but they are formed when the HaB donor X in a cationic molecule is in close proximity to the HaB acceptor Y in an anionic entity (i.e., an ion-pair). Of the two halogen bonds marked in Figure 7e, the I···Cl HaB is intermolecular and the I···F HaB is intramolecular. Halogen Bonding in Neutral Molecular Systems in Crystals. The Br···N, I···Cπ, I···O, Br···N, I···O, and I···N close contacts shown in Figure 7g−k are HaBs formed between neutral molecules as building blocks in the crystals. They are the result of attraction between the electrophile on the HaB donor X in a neutral molecule and a lone-pair region on HaB acceptor Y in a neighboring neutral molecule. Of the two I···O halogen bonds shown in Figure 7i, one is quasi-linear and the other is bent because of the nature of the skeletal framework of the molecule containing the HaB acceptor. The I···O intramolecular HaB is shorter than that of the intermolecular HaB (r(I···O) = 2.356 vs 2.770 Å; Figure 7k). All the intermolecular HaBs in these systems are directional in a sense that a positive site on the covalently bonded halogen attacks a negative site during the process of HaB formation, obeying feature a, and the angle of approach of the electrophile is greater than 170°. There are two exceptional cases to the angle of approach of the electrophile, notable of Figure 7e and i. The approach angle is nonlinear in both, with the approach being intramolecular in the former and intra/intermolecular in the latter. For the latter, the nonlinearity in the intermolecular HaB arises as a result of the two neighboring C�O groups of the −C6H2O3 fragment in C12H7IO3 being simultaneously engaged attractively with the hypervalent I atom in the making of the two I···O HaBs. Although the hypervalent I atom is capable of donating two σ- holes, one of them is involved in making two I···O HaBs, one linear (∠C−I···O= 170.6°/174.6°) and one nonlinear (∠C−I··· O= 135.5°/130.6°) (one pair shown); this is similar to what was observed for the system in Figure 7f, where the iodine atom is hypervalent but carries a charge of +1. Moreover, the C12H7IO3 molecule may also contain a pair of intramolecular I···O HaBs, which can be captured from the r(I···O) values of 3.187−3.189 and 3.192−3.205 Å (not shown) that are less than the sum of the vdW radii of I and O, i.e., 3.59 Å (rvdw(I) = 2.04 Å and rvdw(O) = 1.55 Å). These intramolecular HaBs are nonlinear (viz. ∠C−I··· O = 86.4−98.9° and 68.3−70.3°), as expected. Halogen Bonding via Arene-Based Halogen Bond Acceptors in Crystals. Crystalline systems in which the packing is driven by cation−π and neutral−πHaBs, among other noncovalent interactions, are shown in Figure 8. Here, π means the delocalized charge density regions on electrostatic surface of an arene moiety that act as the nucleophilic site Y. In all four examples in Figure 8, the centroid region of the arene moiety (marked by a tiny sphere in red) in the interacting partner entity serves as the HaB acceptor Y for the HaB donor X in the entity with which it interacts. For example, the I···π(arene) close contact in [C12H10I+,C24H20B−]284 (Figure 8a) is a charge- assisted HaB between the ions in an ion-pair; the iodine atom is hypervalent and positively charged and donates two σ-centered halogen bonds. The I···π(arene) and Br···π(arene) close contacts in crystals shown in Figure 8b−d occur between two identical neutral molecules. In these cases, it is very difficult to use feature d to validate the concept of “intermolecular distance is smaller than the sum of the vdW radii of respective atoms that are bonded with each other” because theHaB acceptor site is not just a single C atom as shown in the case of fullerene C70 and I2 (Figure 7h) but the centroid of an array of C atoms. However, the HaBs in all these systems are directional, and obeying feature a. Figure 5. Illustration of intramolecular C−I···O and N−I···O halogen bonding interactions observed in crystals of (a) 1-chloro-2- carbomethoxymethyl-1,3-dihydro-3-oxo-1,2-benziodazole (C10H9ClINO3), 260 (b) (N-(trifluoromethanesulfonyl)imino)(2-acetylphenyl)-λ3-iodane (C9H7F3INO3S), 261 (c) 1-[[(4-methoxyphenyl)methyl]amino]-1λ3,2-benziodoxol-3(1H)-one (C15H14INO3), 262 (d) 5-fluoro-2,4,6-trinitro-1,3- benzenediamine (C6H4FN5O6), 263 (e) 2-benzylidene-1-(4-methylphenyl)hydrazine-1-carbonyl chloride (C15H13ClN2O),264 and (f) 6,7,9-trifluoro- 2-(2,3,5,6-tetrafluorophenyl)[1,3]thiazolo[5,4-c]isoquinoline (C16H3F7N2S). 265 Selected intramolecular I···O bond distances and ∠C−I···O (or ∠N−I···O) bond angles are in Å and degrees, respectively. Halogen bonds are represented as dotted lines. The CSD reference in each case is shown in uppercase letters. Labeling of selected atoms is shown in each case. Crystal Growth & Design pubs.acs.org/crystal Article https://doi.org/10.1021/acs.cgd.4c00228 Cryst. Growth Des. 2024, 24, 5494−5525 5505 https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig5&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig5&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig5&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig5&ref=pdf pubs.acs.org/crystal?ref=pdf https://doi.org/10.1021/acs.cgd.4c00228?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as Figure 9 shows HaBs that develop when the nucleophilic region on the HaBA Y is a (negative) π-region and when the HaBD X approaches it orthogonally (or near orthogonally) to the C�C π-bond plane. The X···π (acetylenic C�C) HaBs between the interacting moieties are quasi-linear in all cases, as evidenced by the angles of interaction, i.e., 175.0° < ∠C− X···π(C�C) (X�Cl, Br, I) < 177.5°, and also obey feature a. The small deviation of the angle of approach indicates that the HaB donor atom I/Br is not not covalently bonded to the midpoint of the C�C bond but rather to a region in the vicinity of a carbon atom that manifests relatively larger nucleophilicity. ■ A CASE STUDY USING FIRST-PRINCIPLES CALCULATIONS Whether an electrophilic σ-hole region on a halogen atom in a molecule is able to form a halogen bond depends not only on the strength of its potential but also on the nature of the interacting nucleophile and the chemical environment developed between them. Consequently, calculating the electrostatic potential on the interacting monomer entities provides a good first approximation to an understanding of the possible development of an attractive noncovalent interaction before its full character- ization (see feature r).115 The same insight may be gained when the ETS-NOCV approach is employed.177 To exemplify this, we considered an H−Cl molecule. It has an electrophilic σ-hole on the surface of the Cl atom, which appears on the side of Cl opposite to the outermost extension of the H− Cl covalent bond and may serve as an HaBD site X. We considered the nucleophiles (lone-pair region) on the halogen in three other simple molecules, i.e., HF, F2, and Cl2, which could serve as a HaBA site Y. The electrophilic and nucleophilic regions on the electrostatic surfaces of the four molecules can be inferred from the MESP plots shown in Figure 10a−d. AIMAll292 and MultiWfn293,294 were used, and the wave functions were generated using their respective optimized ground state geometries obtained with Gaussian 16.295 Second- order Møller−Plesset perturbation theory (MP2),296,297 together with Dunning’s all-electron correlated basis set, aug- cc-pVTZ, was employed. The charge density on the electrostatic surface of the halogen is anisotropic regardless of the molecular entities examined (HF, HCl, F2, and Cl2). For instance, the potential on the axial and lateral sites of F along and around the H−F covalent bond extension is negative but anisotropic (VS,max = −18.9 kcal mol−1; Figure 6. Charge-assisted halogen bonding in some ion-pair adducts. (a) Phenyl-trifluoro-iodine hexafluoroantimonate,248 (b) bis(4- bromopyridinium) tetrachloro-copper(II),268 (c) diiodo-(1,2-bis(diphenylphosphino)benzene)-gold(III) triiodide,269 (d) tetrakis(4-iodopyridin- 1-ium) bis(μ-chloro)-octachloro-dibismuth,270 and (e) bis(4-bromo-1,3-diethylimidazol-2-ylidene)-bis(iodo)-gold bis(4-bromo-1,3-diethylimida- zol-2-ylidene)-gold bis(iodide).271 For clarity, selected ions C5H5BrN+, C5H5IN+, and I− were deleted from (b−e), respectively. Halogen bonds are represented as dotted lines in red. The CSD reference in each case is shown in uppercase letters. Crystal Growth & Design pubs.acs.org/crystal Article https://doi.org/10.1021/acs.cgd.4c00228 Cryst. Growth Des. 2024, 24, 5494−5525 5506 https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig6&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig6&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig6&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig6&ref=pdf pubs.acs.org/crystal?ref=pdf https://doi.org/10.1021/acs.cgd.4c00228?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as VS,min = −20.4 kcal mol−1, Figure 10a). The F atom in H−F features a nucleophilic σ-hole (VS,max < 0) (see Note 12), and the VS,min represents the lone-pair region on F that dominates. In the case of the other three molecules shown in Figure 10b−d, the strength of the electrophilic σ-hole (see Note 11) on the electrostatic surface of the halogen increases in the order: H−Cl (9.0 kcal mol−1) < F−F (16.5 kcal mol−1) < Cl−Cl (25.5 kcal mol−1). We then built four 1:1 dimer models (Figure 10e−h), that were fully relaxed at the [MP2/aug-cc-PVTZ] level of theory. The resulting optimized geometries of the corresponding binary systems are shown in Figure 10i−l, in which, the positive σ-hole (HaBD) in one molecule is engaged attractively with a nucleophile (HaBA) on the partner molecule (see Notes 1−4 and 11) and the nature of attraction between them is intermolecular (Note 4). The final geometry of the dimers is very similar to the starting geometry for all cases, except for FH···ClH (cf. Figure 10e and Figure 10I represent initial and final (optimized) geometries, respectively). In Figure 10e, the electrophilic σ-hole on Cl in HCl was placed with its orientation toward the nucleophilic lone-pair density on F on HF. This arrangement between the two molecules did not cause any Coulombic engagement between them, despite the electrophilic σ-hole on Cl in HCl facing toward a nucleophile F on HF. The HF molecule had rather adjusted the positions of its atomic constituents during the energy-minimization process so as to maximize its Coulombic interaction with the nucleophile on the Cl atom in HCl. This led to the determination of the optimum geometry of Figure 7. Illustration of the occurrence of halogen bonding between building blocks in some crystalline materials. (a) Tris(1,10-phenanthroline)-iron bis(tribromide) hemikis(dibromine) [C36H24Fe N6 2+,2(Br3−),0.5(Br2)], 272 (b) bis(2,2′:6′,2″-terpyridine)-cobalt bis(iodide) tetrakis(1,3,5-trifluoro- 2,4,6-tris(iodo)benzene) methanol solvate [C30H22CoN6 2+,4(C6F3I3),CH4O,2(I−)],273 (c) di(isoquinolin-2-yl)iodanium tris(iodine) triiodide [C18H14IN2 +,I3−,3(I2)], 274 (d) diphenyliodonium chloride [C12H10I+,Cl−], 275 (e) bis(2-fluorophenyl)iodonium chloride [C12H8F2I+,Cl−], 276 (f) bis(diphenyliodonium) tetrachloro-platinum [2(C12H10I+),Cl4Pt2−],277 (g) bis(acetonitrile) bromine [2(C2H3N),Br2]; 278 (h) C70 fullerene di-iodine [I2,C70], 279 (i) 3,6-dioxo-2-(phenyliodaniumyl)cyclohexa-1,4-dien-1-olate [C12H7IO3], 280 (j) 3,4,5-tribromo-2,6-dimethylpyridine [C7H6Br3N],281 (k) 1-(1-diazo-2,2,2-trifluoroethyl)-1,2-benziodoxol-3(1H)-one [C9H4F3IN2O2], 282 and (l) 2,3,5,6-tetrafluoro-4-iodopyridine toluene solvate [C7H8,C5F4IN].283 For clarity, some molecules in (a−d), (f) and (g) are omitted. Halogen bonds are represented as dotted lines in red. The CSD reference in each case is shown in uppercase letters, and selected halogen bond distances and bond angles are in Å and degrees, respectively. Labeling of selected atoms is shown in each case. Crystal Growth & Design pubs.acs.org/crystal Article https://doi.org/10.1021/acs.cgd.4c00228 Cryst. Growth Des. 2024, 24, 5494−5525 5507 https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig7&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig7&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig7&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig7&ref=pdf pubs.acs.org/crystal?ref=pdf https://doi.org/10.1021/acs.cgd.4c00228?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as ClH···FH (Figure 10i), which is driven by a hydrogen bond. This validates Note 7, as well as Notes 6 and 16, rationalizing a pair of neutral molecules forming complexes, as well as features a and g, revealing the overriding importance of Coulombic forces and the nature of the approach of the electrophile toward the lone-pair region. For chemical systems in Figure 10j−l, the σ-hole-centered lone-pair type interaction leading to the formation of the HaB may be seen:HCl···FH in Figure 10j, HCl···F2 in Figure 10k, and HCl···Cl2 in Figure 10l. The formation of a HaB in HCl···FH in Figure 10j accords with the hypothesis in Note 12 that a nucleophilic σ-hole on F in HF attracts an electrophilic σ-hole on Cl in HCl. In all cases, the interaction energy, ΔE, is negative, in agreement with feature b. The quasi-linear nature of the directionality associated with the intermolecular interactions in the binary systems is consistent with Note 9; that two halogen atoms in two different molecules can be attractively engaged to form a halogen bond is in line with Note 14, including the validation of features a, b, and d−g. Some previous studies have demonstrated that an electro- philic σ-hole in a molecule can attract an electrophilic σ-hole on another interacting molecule, thus forming a halogen···halogen interaction. An attractive interaction, albeit weak, develops between them as a result of a marginal difference in charge density between the interacting regions,68,298 which may also involve some charge transfer between the HOMO and LUMO orbitals. These halogen···halogen interactions are not halogen bonds as far as the definition is concerned, and it is not easy to guess which atom is an electrophile and which one is a nucleophile. These have been referred to as “counterintuitive” interactions79,84,95 or “unconventional bonds”.93 The stability of these complexes arises largely from the dispersion and polarization contributions to the interaction energy.80,84 Similarly, the intramolecular halogen···halogen contacts ob- served in perhalogenated ethanes, X3C−CY3 (X, Y = F, Cl),91 and hexahalogenated benzene derivatives (viz., C6X6 (X =Cl, Br, I)), along with their seven fully mixed hexahalogenated benzene analogues,92 should not be regarded as halogen bonds as per the definition and insofar as Notes 2, 6, 7, and 17 and feature a are concerned. Nevertheless, in all four dimers of Figure 10, the intermolecular bond distance is smaller than the sum of the vdW radii of the noncovalently bonded atomic basins, and the intermolecular interactions are directional (cf. Note 9 and feature e). The appearance of dotted bond paths and nonzero Figure 8. Illustration of mixed ball-and-stick and capped stickmodels of (a) diphenyliodonium tetraphenylborate [C12H10I+,C24H20B−],284 (b) trifluoro[2-[(4-methoxyphenyl)iodaniumyl]phenyl]borate [C13H11- BF3IO],285 (c) (6,8-dibromo-3-sulfanyl-2H-1-benzopyran-2-one- O,S)-triphenyl-tin [C27H18Br2O2SSn], 286 and (d) 1-bromo-3-(2-phen- ylethenyl)benzene [C14H11Br]. 287 Halogen bonds are represented as dotted lines in red. The CSD reference in each case is shown in uppercase letters, and selected halogen bond distances and bond angles are in Å and degrees, respectively. The tiny sphere at the center of the arene moiety in molecules (a−d) represents the centroid. Labeling of selected atoms is shown in each case. Figure 9. Illustration of the halogen bonding interaction between neutral molecules formed between HaBD X and the acetylenic (negative) π-density onHaBA Y in some crystals. (a) 2,6-Dichloro-3-ethynylpyridine (C7H3Cl2N),288 (b) (3R)-5-(2-iodo-3,4,5-trimethoxyphenyl)-1-(trimethylsilyl)pent- 1-yn-3-ol (C17H25IO4Si), 289 (c) 2,2′,4,4′,6,6′-hexafluoro-3,3′,5,5′-tetrakis(iodoethynyl)biphenyl (C20F6I4), 202 (d) (R)-1-methyl-2-(iodoethynyl)- ferrocene (C13H11FeI), 290 (e) 9-[3-(2-bromopyridin-4-yl)prop-2-yn-1-yl]-9H-carbazole (C20H13BrN2), 291 (f) 5,6,11,12-tetrakis(phenylethynyl)di- benzo[b,h]biphenylene bromoform solvate (C52H28,2(CHBr3)). 184 Selected atom types, bond distances (Å), and bond angles (degree) are shown; the CSD ref code for each case is depicted in uppercase letters. Crystal Growth & Design pubs.acs.org/crystal Article https://doi.org/10.1021/acs.cgd.4c00228 Cryst. Growth Des. 2024, 24, 5494−5525 5508 https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig8&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig8&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig8&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig8&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig9&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig9&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig9&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig9&ref=pdf pubs.acs.org/crystal?ref=pdf https://doi.org/10.1021/acs.cgd.4c00228?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as charge density (ρb) values at the bond critical points (bcps) between the interacting molecules (cf. Figure 10m−p) provide evidence of the presence of noncovalent closed-shell inter- actions (feature l), and the positive signs of the Laplacian of the charge density (∇2ρb) at these bcps confirm that they are closed- shell interactions.299−305 These results are in agreement with the results of IGM-δginter that reveal (attractive) isosurfaces between atomic basins corresponding to the interacting monomers in each dimer configuration (feature m). The isosurfaces are colored bluish-green for the weak attractive interaction in FH··· ClH (see Figure 10q) and green for the vdW-type interaction in HCl···FH, HCl···F2, and HCl···Cl2 in (cf. Figure 10r−t). An evaluation of the dissected interaction energy of each dimer was performed at the [SAPT2 + 3(CCD)/aug-cc-pVTZ] level of theory; this was based on the wave function and density functional descriptions of themonomers and the dimers, and the interaction energy is the difference between the two. (CCD refers to the coupled-cluster double equations306 that account for dispersion, and SAPT is symmetry-adapted perturbation theory.307) This approach has been successful in explaining intermolecular interactions in a variety of chemical systems.308 SAPT, coded in PSI4,309 decomposes the net interaction energy into four components: electrostatics, exchange, induction (polarization), and dispersion terms. Our [SAPT2 + 3(CCD)/aug-cc-pVTZ]-based results are summarized in Table 1; they were computed using the [MP2/ aug-cc-pVTZ] geometry of each dimer. From the results, it is apparent that the energy due to dispersion supersedes the individual component energy arising from electrostatics and induction for the three halogen bond systems (Figure 10j−l). All three attractive components complement the exchange (repulsion) energy without affecting the negative sign of the overall interaction energy (see features b and c). In the case of the hydrogen bonded dimer FH···ClH (Figure 10i), the component energy due to electrostatics is larger than that arising due to induction or dispersion, revealing the greater importance of the former compared to the latter two. The nature of the total interaction energy, ΔE(SAPT2 + 3(CCD)), agrees well with the MP2-level BSSE-corrected interaction energy, ΔE[MP2/aug-cc-pVTZ], for each dimer (features b and c), where BSSE is the basis set superposition error accounted for by the counterpoise procedure of Boys and Bernardi.310 Since the ΔE of each halogen bonded dimer is less than −1.0 kcal mol−1, each can be classified as a vdW dimer. By contrast, FH···ClH can be classified as a weakly hydrogen bonded dimer since its interaction energy is greater than −1.0 kcal mol−1 (see feature q). We have not examined the NMR, UV−vis, and vibrational features of the intermolecular complexes investigated and are thus unable to comment on features i−k. Our second-order perturbation theory analysis of the Fock matrix in NBO suggests that the second-order energy E(2) can explain the nature of the orbital interactions involved between Figure 10. [MP2/aug-cc-pVTZ]-computed potential on the electro- static surfaces of (a) HF, (b) HCl, (c) F2, and (d) Cl2, mapped on their respective 0.001 au (electrons bohr−3) isoelectronic density envelopes. The tiny circles in red and blue represent VS,max and VS,min, respectively, and values in the color bar are in kcal mol−1. (e−h) Initial configurations of selected dimers of HCl with (e and f) HF, (g) with F2, and (h) with Cl2) used for energy-minimization. (i−l) Energy- minimized geometries of the corresponding dimers from (e−h), respectively; selected bond distances and bond angles are in Å and degrees, respectively, and the uncorrected and BSSE-corrected interaction energies (ΔE and ΔE(BSSE)) are in kcal mol−1. (m−p) QTAIM-based molecular graphs of the corresponding dimers. Atoms are shown as large spheres; bond paths are shown as solid and dotted lines that represent covalent and noncovalent interactions, respectively; bond critical points are shown as tiny spheres between atomic basins; and the charge density (ρb) and the Laplacian of charge density (∇2ρb) values at selected bcps are given in a.u. (q−t) IGM-δginter isosurfaces (colored blue or green) of the corresponding dimers. Table 1. SAPT2 + 3(CCD)-Level Decomposed Energy Components (in kcal mol−1) Arising from Electrostatics, Exchange- Repulsion, Induction, and Dispersion Interactions Obtained on [MP2/aug-cc-pVTZ] Relaxed Geometries of Some Selected Dimers of HCl with HF, F2 and Cl2 a system figure electrostatics exchange induction dispersion ΔE(SAPT2 + 3(CCD)) ΔE[MP2/aug-cc-pVTZ] FH···ClH Figure 10(i) −3.54 5.08 −2.42 −2.09 −2.97 −2.80 HCl···FH Figure 10(j) −0.21 0.73 −0.13 −0.74 −0.35 −0.32 HCl···F2 Figure 10(k) −0.23 0.73 −0.04 −0.85 −0.39 −0.39 HCl···Cl2 Figure 10(l) −0.55 1.74 −0.17 −1.76 −0.74 −0.89 aIncluded are the [MP2/aug-cc-pVTZ]-level basis set superposition error (BSSE) corrected interaction energies, ΔE[MP2/aug-cc-pVTZ], for the corresponding systems for comparison with ΔE(SAPT2 + 3(CCD)). Crystal Growth & Design pubs.acs.org/crystal Article https://doi.org/10.1021/acs.cgd.4c00228 Cryst. Growth Des. 2024, 24, 5494−5525 5509 https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig10&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig10&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig10&ref=pdf https://pubs.acs.org/doi/10.1021/acs.cgd.4c00228?fig=fig10&ref=pdf pubs.acs.org/crystal?ref=pdf https://doi.org/10.1021/acs.cgd.4c00228?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as the “filled” (donor) Lewis-type NBOs and “empty” (acceptor) non-Lewis NBOs, shedding some light on the formation of the dimers in Figure 10i−l. E(2) values for the dominant charge transfer delocalizations, viz., n(3)Cl → σ*(H−F), n(1)F → σ*(Cl−H), n(3)F → σ*(Cl−H), and n(3)Cl → σ*(Cl−H) explaining the dimers FH···ClH, HCl···FH, HCl···F2, and HCl··· Cl2, are 6.39, 0.32, 0.37, and 0.59 kcal mol−1, respectively, where n and σ* represent the lone-pair and antibonding orbitals, respectively. The trend in the nature of energy of the charge transfer interaction accords with the ΔE[MP2/aug-cc-pVTZ] values for the same dimers (cf. Table 1). The orbital-based hyperconjugative interactions reflect that the σ-type antibond- ing orbital associated with the σ-hole portion of the molecule (HaBD) is the acceptor of charge density from lone-pair donors (HaBA), validating feature n. A further example is illustrated in Figure 11 to validate Note 16. As far as the definition is concerned,34 the fluorine in FCN should not form a halogen bond with the lone-pair on nitrogen on another identical molecule. This is based on the (somewhat dated) presumption that the lone-pairs on fluorine are electron- density-rich and that when both the negative sites on N and F on the two interacting molecules come in close proximity, they repel each other. That fluorine in molecular entities can behave as an electrophile becomes apparent after applying the MESP model (as Murray et al.115,311,312 and Scheiner313 have noted previously). Its application enables us to demonstrate that fluorine in FCN is entirely positive, and the net electron density is concentrated on the electrostatic surface of the bonded nitrogen atom (Figure 11a). The surface of covalently bonded fluorine features a maximum and