Multidentate halogen bond acceptors: from fluorides to iodides. Anticooperativity in halogen-bonded clusters

Abstract

A survey of the Cambridge Structural Database together with a statistical analysis of its results has been conducted in order to investigate the frequency of occurrence of halide anions as halogen bond acceptors of different denticity. The results show that for the majority of studied motifs (C–I)_n⋯Y⁻ (Y = F, Cl, Br and I) the number of halogen bond donors n ≤ 4, and for the fluoride anion there are no motifs containing more than four ligands in the crystal structure. To assess the impact of denticity of halides as acceptors on interaction energy and its nature, computational studies have been performed for model halogen-bonded complexes (F₃C–I)_n⋯Y⁻ (Y = F, Cl, Br, and I) with different number of halogen bond donors. A canonical energy decomposition analysis (canonical EDA) reveals the trends in interaction energy and its components when increasing the number of halogen-bonded ligands. Moreover, the canonical EDA allows to establish the factors making the adduct (F₃C–I)₅⋯F⁻, containing the structural motif which does not occur in the crystal structure, different from analogous complexes. Additionally, the non-additivity of interactions in the model systems and its source have been studied.

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Introduction

One can hardly overestimate the role of halide anions in chemical and biochemical processes. To mention only a few: halides are important reagents in organic synthesis,¹ they play a role in organocatalysis,² serve as components of synthons used in crystal engineering,^3–5 and take part in self-assembly processes.^1,6–9 Halide anions can also constitute a basis of supramolecular organic conductors.¹⁰ Moreover, they have the ability to form coordination polymers,¹¹ and their encapsulation in other coordination polymers may enhance the desired properties such as photoluminescence.¹² Halides play a crucial role in the synthesis of anisotropic noble metal nanostructures.^13,14 They are important components of persovskite solar cells, also the lead-free ones, and ionic liquids based on halides may serve as passivation layers for highly stable perovskite solar cells.¹⁵ Furthermore, in biology the transport of halide anions through membranes is of vital importance for living organisms, for example cystic fibrosis is caused by the presence of mutations in genes encoding membrane proteins responsible for chloride transport.¹⁶ The synthetic anion transporters, often mimicking biological processes, have found applications not only in medicine but also in material sciences.¹⁷ The roles mentioned above are connected in some way with anion recognition processes which are usually associated with hydrogen bonding. However, one should not forget that anion recognition may also be based on halogen bonding,^18–21 especially for halides which are very efficient halogen bond acceptors.²² Due to this fact it is possible to synthesise halide anions receptors^23–25 and transporters¹⁷ based on halogen bonding.

The halogen bonding with halides as acceptors is important in crystal engineering.^6,8,26 Generally, contacts C–X⋯Y⁻ (X, Y = F, Cl, Br or I) are common in the crystal structure with the only exception of F⁻.²⁷ Interestingly, although the halogen bonds formed with fluoride anions as acceptors were proved to be very strong,^27,28 one can mention only several crystal structures in which the C–X⋯F⁻ motif occurs.^28–31 Recently, a systematic study devoted to the contacts C–X⋯Y⁻ (X, Y = F, Cl, Br or I) present in the crystal structure and to the model systems containing this structural motif has been performed.²⁷ The mentioned study is focused on the general features of C–X⋯Y⁻ contacts when changing halogen bond acceptors (halides) and donors but makes no distinction between monodentate and multidentate halogen bond acceptors. In the crystal structure, one can easily find motifs in which halide anions are multidentate halogen bond acceptors, which means they accept more than one halogen bond at the same time.^1,32–37

Most of the studies devoted to various aspects of halogen bonding is mainly focused on the bond donors. However, in the case of halides acting as acceptors when forming very strong halogen bonds, the studies on halogen bonding in the context of acceptors are needed, especially since halide anions are widely used in engineering of functional materials,³⁸ not only in the solid state^{3–5,37,39–42} but also in liquids.⁴³ Understanding interactions is crucial for developing rational engineering strategies. Since halides often are multidentate halogen bond acceptors, one may ask how the presence of many halogen bond donors affects the nature and strength of interactions and what is the impact of non-additivity effects, which may substantially modify the bond strength.⁴⁴

The aim of the present study is to examine halogen bonding in the dent of denticity of halide anions as halogen bond acceptors. Since, based on the previous studies,²⁷ it was proved that from amongst C–X halogen bond donors, C–I is both, most common in the crystal structure and the most efficient one, the corresponding (C–I)_n⋯Y⁻ (Y = F, Cl, Br and I) motifs were chosen as the subject of the research. The purpose of the first, crystallographic part of the present study is a statistical analysis of the crystal structures containing (C–I)_n⋯Y⁻ (Y = F, Cl, Br and I) motifs. In the second, computational part, the adducts (F₃C–I)_n⋯Y⁻ (Y = F, Cl, Br, and I) are chosen as model systems to investigate interaction energy and its components in the context of denticity of halides as halogen bond acceptors, taking into account the aspect of non-additivity of interactions. Furthermore, since in the previous studies it was shown that the properties of halogen bonds with fluoride anions differ from those with heavier halides,^27,28 another aim of the present paper is to verify whether fluoride anions are exceptional also in the context of their denticity.

Experimental

Survey of the cambridge structural database

The CSD (Version 5.46, November 2024)⁴⁵ was searched for structural motifs (C–I)_n⋯Y⁻ (Y = F, Cl, Br and I; n = 1, 2,⋯,8), using ConQuest Version 2024.3.0. The upper limit for the I⋯Y⁻ distance was set at the sum of van der Waals radii +0.4 Å and the C–I⋯Y⁻ angle value was in the range of 120–180°, similarly as in the previous studies devoted to halide anions as halogen bond acceptors.^27,46 At this point it should be mentioned that van der Waals radii determined by Alvarez⁴⁷ were used throughout this work, in accordance with the values used in software by Cambridge Structural Data Centre (CCDC) since December 2024. Halide anions (Y⁻) were defined either as halogens with no atoms covalently bonded to them or as bonded by any type of bond with an atom of alkali or alkaline earth metals. Iodine atoms from the donor groups were restricted to monovalent species; carbon atoms bonded to them were of any type of hybridisation. The search was limited to single-crystal structures with no errors.

Computational methods

All calculations were performed using Amsterdam Density Functional (ADF) program as implemented in the Amsterdam Modelling Suite (AMS, version 2023.101).^48,49 The density functional theory (DFT) calculations were performed by applying the generalised gradient approximation (GGA) functional BP86⁵⁰ in combination with the D3 dispersion correction⁵¹ and Becke–Johnson (BJ) damping.⁵² The BP86 functional⁵⁰ was previously tested against the CCSD(T) level for halogen-bonded adducts containing Cl⁻ anion⁵³ and was used to perform the canonical energy decomposition analysis for halogen bonded systems containing chosen halide ions.⁵⁴ At this point one should also notice that the empirical potential absorbs the basis set superposition error (BSSE) so there is no need to examine it separately. Relativistic effects were taken into account by using the zeroth-order regular approximation (ZORA). The orbitals (with no frozen core) were expanded in QZ4P Slater basis set,⁵⁵ since this basis set was proved to be sufficient for proper description of a small fluoride anion.⁵⁶ This computational level was previously used for description of bonding interactions with halide ions.^27,56 The structures of (F₃C–I)_n⋯Y⁻ (Y = F, Cl, Br, and I) were optimised and the optimisations were followed by the harmonic vibrational analysis at the same computational level to confirm that the stationary points correspond to the potential energy surface minima.

The interaction energy, ΔE_int, was decomposed basing on the Kohn–Sham molecular orbital model. This energy decomposition scheme, known as canonical energy decomposition analysis (canonical EDA), allows to decompose the ΔE_int term as:⁵⁷

ΔE_int = ΔV_elstat + ΔE_Pauli + ΔE_oi + ΔE_disp (1)

ΔV_elstat refers to Coulomb interactions between unperturbed fragments, ΔE_Pauli corresponds to a repulsion between overlapping occupied orbitals of the fragments, ΔE_oi refers in turn to all attractive orbital interactions, comprising both donor–acceptor interactions and polarisation. Finally, the ΔE_disp term denotes the dispersion. Moreover, the steric interaction term, ΔE_steric, can be defined as:

ΔE_steric = ΔV_elstat + ΔE_Pauli (2)

ΔE_steric comprises overall energy associated with mixing of electronic densities of fragments, with no polarisation and donor–acceptor interactions.

One may also consider ΔE_int in the context of many-body expansion, according to which interaction energy of a systems consisting of more than two parts is the sum of interactions of all its possible subsystems. For example for a system consisting of three units (1, 2 and 3), the interaction energy, ΔE_int, is defined as a sum of two-body interactions – all interactions in pairs, ΔE₁₂, ΔE₁₃, ΔE₂₃, and the three-body term, ΔE₁₂₃:

ΔE_int = ΔE₁₂ + ΔE₁₃ + ΔE₂₃ + ΔE₁₂₃ (3)

For bodies i and j (i < j; i, j ∈ {1, 2, 3}) two-body terms are defined as follows:

ΔE_ij = E_ij − (E_i + E_j) (4)

where E_i is the energy of the i-th body and E_ij is the energy of the system ij. The three-body term in turn is:

ΔE₁₂₃ = E₁₂₃ − (E₁ + E₂ + E₃) – (ΔE₁₂ + ΔE₁₃ + ΔE₂₃) (5)

All energies in eqn (3)–(5) are calculated in the optimised geometry of the three-body system.

For systems consisting of more units the interaction energy is defined analogously. All non-pairwise interactions reflect non-additivity of interactions. If the character of non-pairwise terms is stabilising, one says of interaction cooperativity or synergy, and if it is destabilising, the effect is called anticooperativity. For a three-body system ΔE₁₂₃ is the only non-additive term but for systems consisting of more units, the non-additive term comprises all non-pairwise interactions, e.g. for a four-body system the non-additive term is the sum of interaction energies of all triads (there are four triads being subsystems of a quartet) and the four-body term. Generally, one may define the interaction non-additivity term, ΔE_n-a, as the difference between the interaction energy of the studied many-body system and the sum of interaction energies of all possible pairs formed by the units it consists of, e.g. for a three-body system ΔE_n-a is:

ΔE_n-a = ΔE_int – (ΔE₁₂ + ΔE₁₃ + ΔE₂₃) (6)

Eqn (6) shows that calculation of ΔE_n-a for a three-body systems requires calculation of the interaction energy of the triad and of all possible pairs being its subsystems in the optimised geometry of the triad.

Results and discussion

(C–I)_n⋯Y⁻ motifs in the CSD

A CSD search yielded 981 structural motifs (C–I)_n⋯Y⁻ (Y = F, Cl, Br and I; n = 1, 2,⋯,8), found in 762 crystal structures, meeting the geometrical criteria mentioned in the Experimental section of the article; in some structures more than one motif occurs. Interestingly, the majority of motifs contains C(sp²)–X as a halogen bond donor, although the type of hybridisation of the carbon atom was not limited to sp² during the search. All the motifs are included in the present study, irrespective of whether in the crystal structure there are many motifs of the same or different n value. The number of motifs (C–I)_n⋯Y⁻ together with percentages are shown in Table 1, the lists of CSD refcodes of structures containing motifs of a given type are collected in Table S1 in the SI.

Table 1 Number of motifs (C–I)_n⋯Y⁻ found in the CSD; percentages calculated with reference to the total number of motifs containing the given type of anion, in parentheses^a

n	F^−	Cl^−	Br^−	I^−
a Percentages in each column separately sum up to 100%.
1	0 (0.0%)	92 (38.5%)	81 (33.6%)	207 (41.9%)
2	4 (57.1%)	90 (37.7%)	84 (34.9%)	151 (30.6%)
3	1 (14.3%)	27 (11.3%)	34 (14.1%)	79 (16.0%)
4	2 (28.6%)	28 (11.7%)	32 (13.3%)	40 (8.1%)
5	0 (0.0%)	1 (0.4%)	4 (1.7%)	6 (1.2%)
6	0 (0.0%)	1 (0.4%)	3 (1.2%)	10 (2.0%)
7	0 (0.0%)	0 (0.0%)	0 (0.0%)	0 (0.0%)
8	0 (0.0%)	0 (0.0%)	3 (1.2%)	1 (0.2%)

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The results presented in Table 1 clearly indicate that, as it has been demonstrated recently for C–X⋯Y⁻ contacts (X, Y = F, Cl, Br, and I),²⁷ (C–I)_n⋯F⁻ motifs are extremely rare in the crystal structure, whilst (C–I)_n⋯I⁻ are most common making up 50.4% of the total number of motifs. When one considers studied motifs in the context of the number of C–I donors (ligands) bonded to a chosen halide anion (n), it is evident that motifs C–I⋯Y⁻ and (C–I)₂⋯Y⁻ are most common in the crystal state, and generally motifs (C–I)_n⋯Y⁻ for n = 1, 2, 3, and 4, constitute altogether 97.0% of the total number of studied systems. In the crystal structure one finds no motifs containing 7 ligands. The examples of motifs (C–I)_n⋯Y⁻ representing the variety of the number of halogen bond donors (differing in n values) are shown in Fig. 1.

Fig. 1 Motifs (C–I)_n⋯Y⁻ (n = 1, 2, 3, 4, 5, 6, 8) present in the crystal structure, CSD refcodes given below; I⋯Y⁻ contacts: blue dotted line, C: dark grey, H: light grey, N: lavender, F: neon yellow, Cl: green, Br: orange, I: purple.

The mean values of I⋯Y⁻ distance and C–I⋯Y⁻angle, with the corresponding root mean standard deviations (RMSD), for different types of motifs (C–I)_n⋯Y⁻ are given in Table 2 and Table S2 in the SI, respectively. Since the number of motifs (C–I)_n⋯Y⁻ with n ≥ 5 is low, further statistical analysis of distances and angles is limited to adducts with n ≤ 4. Taking into account the values of standard deviations, one may notice that there are no statistically significant differences between the mean values of the I⋯Y⁻ distance and the number of ligands bonded to a halide anion (see Table 2). A similar observation can be made for the mean values of the C–I⋯Y⁻angle (Table S2 in the SI). However, the mean values and RMSD are known to be sensitive to outliers⁵⁸ and due to this reason median values and median absolute deviations (MAD) which are more resilient to outliers⁵⁸ are also used in this study. The median and MAD values for I⋯Y⁻ distance and C–I⋯Y⁻angle are collected in Tables S3 and S4 in the SI. Also in the case of median values, one finds no interdependence between the distance I⋯Y⁻ (or C–I⋯Y⁻angle) and the number of ligands present in the studied motif. However the data shown in Table S4 in the SI show that median values of the C–I⋯Y⁻ angle for (C–I)_n⋯Y⁻ (for n ≤ 4) are close to 170°, within MAD, suggesting that C–I⋯Y⁻ contacts in the crystal structure are usually close to linearity.

Table 2 Mean values and RMSD, in parentheses, of the I⋯Y⁻ distance in motifs (C–I)_n⋯Y⁻, n ≤ 4, found in the CSD, in Å

n	F^−	Cl^−	Br^−	I^−
1	—	3.255 (0.195)	3.322 (0.209)	3.528 (0.199)
2	2.539 (0.069)	3.136 (0.121)	3.268 (0.127)	3.520 (0.165)
3	2.543 (0.000)	3.123 (0.112)	3.287 (0.088)	3.524 (0.125)
4	2.603 (0.056)	3.180 (0.139)	3.321 (0.116)	3.615 (0.172)

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When considering structural properties of C–I⋯Y⁻ contacts, it is important to refer to a halogen bond definition. According to the IUPAC definition, a halogen bond of a general scheme R–X⋯Y⁵⁹ exhibits two main geometrical features: the X⋯Y distance tends to be smaller than the sum of van der Waals radii and the R–X⋯Y angle tends to be 180°. To approach this definition, the data from the CSD were further limited to those in which the I⋯Y⁻ distance is smaller than the sum of van der Waals radii and the C–I⋯Y⁻ angle values are in the range 160° to 180°. More than 92.2% of studied contacts meet these conditions. The number of structures fulfilling the tightened geometrical criteria, together with the corresponding percentages are collected in Table S5 in the SI.

C–I⋯Y⁻ interactions in (C–I)_n⋯Y⁻ motifs

The survey of the CSD allowed to establish that motifs (C–I)_n⋯Y⁻ with n ≤ 4 make up 97.0% of the total number of motifs (C–I)_n⋯Y⁻ with any number of halogen bond donors. Due to this reason adducts (F₃C–I)_n⋯Y⁻ (Y = F, Cl, Br and I) with n ≤ 5 were chosen as model systems for further interaction energy studies. Such set of model systems allows to investigate changes in interaction energies when increasing the number of halogen bond donors, especially that it covers the border between n = 4 and n = 5 but at the same time the set is consistent and does not generate a problem of minima of different symmetries appearing for systems with larger number of halogen bond donors.

The optimised structures of studied complexes have the following symmetries: for n = 1 − C_3v, for n = 2 − C_2v, for n = 3 − C_3v, and for n = 4 − T_d. The structures of adducts (F₃C–I)₅⋯Y⁻ have no symmetry but the halogen bond donor atoms of iodine are in positions very close to vertices of right square pyramids. One may notice that, whilst in (F₃C–I)₅⋯F⁻ the fluoride anion sits above the plane of iodine atoms in ligands, for (F₃C–I)₅⋯Y⁻ (Y = Cl, Br, I) the halide anion is below the plane. Although in crystals the spatial arrangement of ligands is affected not only by studied halogen bonding but also by other interactions, a similar spatial arrangement with the Br⁻ ion below the plane is present in the structural motif of the crystal structure with the refcode SARKEE, shown in Fig. 1. Moreover, as concerns the structural features of studied complexes, the distance I⋯Y⁻ increases with the number of halogen bond donors for each type of anion Y⁻. The values of distances I⋯Y⁻ in the adducts (F₃C–I)_n⋯Y⁻ are given in Table S6 in the SI.

When investigating the interactions in complexes (F₃C–I)_n⋯Y⁻ it is important to analyse the bonding between halides and halogen bond donors, eliminating the impact of interactions between the donors. This aim can be achieved by treating all halogen bond donors bonded to a halide as a whole and analysing the values of ΔE_int and its components. Fig. 2a presents the relationship between the interaction energy, ΔE_int, in (F₃C–I)_n⋯Y⁻ and the number of halogen bond donors, for Y = F, Cl, Br and I. The values of interaction energy, ΔE_int, and its components are collected in Table S7 in the SI. In Fig. 2a one may notice that for all studied halides the absolute value of interaction energy increases with the number of halogen bond donors and the differences between interaction energies diminish at the same time. This observation indicates that the mean interaction energy, ΔE_int, per number of halogen bonds formed in the system, decreases with the number of ligands (Fig. S1 in the SI). This means that in the crystal structure the formation of many halogen bonds to many monodentate acceptors may be energetically more favourable than the formation of same number of halogen bonds to one multidentate acceptor. This finding is in line with the results of the CSD survey showing that motifs of the low n value, namely C–I⋯Y⁻ and (C–I)₂⋯Y⁻ are most common in the crystal structure. However, one should take into account that in crystals there are usually many competing interactions affecting the crystal packing. The behaviour of ΔE_int is similar for all studied halide anions. However, it is important to stress that stabilisation is significantly stronger for fluorides as halogen bond acceptors than for other halides, as it was previously demonstrated for adducts F₃C–X⋯Y⁻ (X, Y = F, Cl, Br and I) with one halogen bond donor.²⁷

Fig. 2 Energy decomposition analysis, in kcal mol⁻¹; F⁻: grey, Cl⁻: green, Br⁻: red, I⁻: blue.

To understand the changes of ΔE_int, it is crucial to analyse its components. For all studied interactions the main stabilising components are: the Coulomb attraction, ΔV_elstat, and the ΔE_oi term comprising donor–acceptor interactions together with polarisation. Since the behaviour of these components for (F₃C–I)₅⋯F⁻ deviates from the general trends found for other studied adducts, the properties of (F₃C–I)₅⋯F⁻ are described separately in the next paragraph. The absolute values of ΔV_elstat and ΔE_oi increase with the number of halogen bond donors (Fig. 2b and c, respectively). In all the cases, the ΔV_elstat component predominates ΔE_oi and for a given halide anion, the ratio ΔV_elstat/ΔE_oi increases with the number of halogen bond donors in the adduct (Table S7 in the SI). The Pauli repulsion term, ΔE_Pauli, increases with the number of halogen bond donors (Fig. 2d). The last analysed component of ΔE_int, namely the dispersion, ΔE_disp, increases the stability of studied systems but it is significantly less pronounced than other terms. The absolute values of ΔE_disp increase linearly with the number of ligands (Fig. 2e), making the dispersion term more significant (but still relatively weak) for greater systems, whilst remaining negligible for the small ones. Additionally, one may notice that the strength of Coulomb, attractive orbital interactions and Pauli repulsion decreases in the following order: F⁻ > Cl⁻ > Br⁻ > I⁻, whilst for dispersion one finds the opposite trend – especially for the fluoride anion ΔE_disp is practically negligible which can be explained with low polarisability of F⁻.

One may observe that for (F₃C–I)₅⋯F⁻ the stabilisation due to both Coulomb attraction and orbital interactions is weaker than for (F₃C–I)₄⋯F⁻ (Fig. 2b and c, respectively). Also the ratio ΔV_elstat/ΔE_oi for (F₃C–I)₅⋯F⁻ is smaller than in the case of (F₃C–I)₄⋯F⁻. At this point, it is important to stress that the described general tendencies in ΔV_elstat and ΔE_oi, the main stabilising factors for adducts (F₃C–I)_n⋯Y⁻ are not kept only in the case of (F₃C–I)₅⋯F⁻, the system containing the structural motif (C–I)₅⋯F⁻ which does not occur in the crystal structure. Also in the case of ΔE_Pauli, there is an exception of (F₃C–I)₅⋯F⁻, for which Pauli repulsion is weaker than in the case of (F₃C–I)₄⋯F⁻. This effect compensates weaker electrostatic and attractive orbital interactions for (F₃C–I)₅⋯F⁻ and also due to this overall stabilisation in (F₃C–I)₅⋯F⁻ is stronger than in (F₃C–I)₄⋯F⁻.

The described ΔE_int together with its components refers only to interactions between halide anions and molecules containing halogen bond donors, treated as a whole. However, to analyse non-additivity of interactions, also the interactions between the ligands should be taken into account. To avoid confusion, all energies comprising not only the interactions between the halogen bond acceptor and the donors (as in the case of ΔE_int and its components) but also the interactions between the ligands are denoted with the index “BL”, for example ΔE_int,BL. The values of ΔE_int,BL and its components are given in Table S8 in the SI. The trends found for ΔE_int,BL and its constituents are similar to those described in detail for ΔE_int, with the exception of ΔE_disp,BL which does not exhibit linear relationship with the number of halogen bond donors. However, similarly to ΔE_disp, absolute values of ΔE_disp,BL are relatively small in comparison with other components of ΔE_int and increase with increasing number of ligands. At this point, one may focus on non-additivity of interactions, ΔE_n-a, which is defined as the difference between ΔE_int,BL and the interaction energy of all two-body interactions of two types: between the anion and the ligands, and between the ligands. It is also worth mentioning that the two-body interactions are dominated by the anion-ligand component (Table S9 in the SI), for example for (F₃C–I)₄⋯F⁻ the energy of all F₃C–I⋯F⁻ interactions is −175.5 kcal mol⁻¹, whilst the corresponding energy for all interactions between F₃C–I ligands amounts only to −5.0 kcal mol⁻¹.

The values of ΔE_n-a indicate that the adducts (F₃C–I)_n⋯Y⁻ exhibit the anticooperative effect which rises nearly linearly with the increasing value of n (Fig. 3 and Table S9 in the SI). Anticooperativity means that the sum of many-body interactions in clusters (F₃C–I)_n⋯Y⁻ is destabilising and diminishes stabilisation due to pairwise interactions.

Fig. 3 ΔE_n−a, in kcal mol⁻¹; F⁻: grey, Cl⁻: green, Br⁻: red, I⁻: blue.

Since the Coulomb attraction is additive by definition, it does not affect ΔE_n-a. The values of ΔE_n-a are meaningful and positive because of the impact of the ΔE_oi term – the reduction of Pauli repulsion due to many-body interactions is practically negligible (Table S10 in the SI). One may notice (Fig. 3) that the slope of a trend line for F⁻ (23.8) is markedly larger than for other halide anions (12.2, 10.7, 8.7 for Cl⁻, Br⁻ and I⁻, respectively), proving that for the fluoride anion many-body terms, which are destabilising, grow more rapidly with increasing number of halogen bond donors. This finding additionally supports the conclusion previously formulated for chosen complexes containing halides,^27,28 that the properties of interactions in complexes with fluoride anions as halogen bond acceptors differ from those present in adducts of halide anions of a different type.

Conclusions

The survey of the Cambridge Structural Database together with the statistical analysis of the results allowed to establish that in the crystal structure one found structural motifs (C–I)_n⋯Y⁻ (Y = Cl, Br and I) containing up to eight halogen bond donors. No structures with seven ligands were observed. (C–I)_n⋯F⁻ were confirmed to be very rare in the crystal structure. For the fluoride anion only the structures with n ≤ 4 were found. It was demonstrated that generally, the motifs (C–I)_n⋯Y⁻ (Y = F, Cl, Br and I) with the number of halogen-bonded ligands not greater than four comprised 97% of all motifs found in the CSD.

The computational analysis performed for the model complexes shown that the greater the number of halogen bond donors bonded to a halide anion the more stabilising the interaction was. However, when ΔE_int per number of halogen bond donors was taken into account, it appeared that the greater the system, the weaker the stabilisation per ligand. The canonical energy decomposition analysis allowed to establish that the absolute values of ΔE_int increased with the number of halogen bond donors mainly due to the increasing impact of Coulomb interactions, ΔV_elstat, and attractive orbital interactions, ΔE_oi. Moreover, the ratio ΔV_elstat/ΔE_oi in majority of the cases increased with the number of ligands. The only exception from the trends found for ΔV_elstat, ΔE_oi and their ratio was the adduct (F₃C–I)₅⋯F⁻ for which stabilisation due to electrostatic and orbital interactions was weaker than in the (F₃C–I)₄⋯F⁻ complex.

Analysis of ΔE_int in the context of many-body expansion allowed to establish that the model systems exhibited large anticooperative effect traced to destabilising changes of the ΔE_oi component of non-pairwise interactions. The anticoopeartive effect increased linearly with the number of ligands. Interestingly, the increase was shown to be about two times stronger for fluoride anions than for the rest of halides, once more proving that fluorides are exceptional among halides as halogen bond acceptors.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information is available. See DOI: https://doi.org/10.1039/d5cp02845k.

Acknowledgements

Calculations were carried out using resources provided by the Wroclaw Centre for Networking and Supercomputing (https://wcss.pl), grant no. 118, and the Polish high-performance computing infrastructure PL-Grid (HPC Centre: ACK Cyfronet AGH), grant no. PLG/2025/018106.

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Footnote

† Dedicated to Professor Resnati, celebrating a career in fluorine and noncovalent chemistry on the occasion of his 70th birthday.

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