# The origin of synthons and supramolecular motifs: beyond atoms and functional groups

Rahul Shukla, Emmanuel Aubert, Mariya Brezgunova, Sébastien Lebègue, Marc Fourmigué, Enrique Espinosa

► To cite this version:

Rahul Shukla, Emmanuel Aubert, Mariya Brezgunova, Sébastien Lebègue, Marc Fourmigué, et al. The origin of synthons and supramolecular motifs: beyond atoms and functional groups. International Union of Crystallography journal, 2025, 12 (3), 10.1107/s2052252525001447. hal-05049396

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Submitted on 28 Apr 2025

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Distributed under a Creative Commons Attribution 4.0 International License
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Received 20 December 2024

Accepted 17 February 2025

Edited by A. Martín Pendás, Universidad de Oviedo, Spain

This article is part of a collection of articles on Quantum Crystallography, and commemorates the 100th anniversary of the development of Quantum Mechanics. It is dedicated to Dr Slimane Dahaoui and Professor János G. Ángyán, who passed away before the preparation of this article.

**Keywords:** chalcogen bonding; halogen bonding; hydrogen bonding; electrophilic-nucleophilic interactions; electron density; Laplacian of electron density; topological analysis; crystal engineering.

CCDC reference: 2424586

**Supporting information:** this article has supporting information at www.iucrj.org

# The origin of synthons and supramolecular motifs: beyond atoms and functional groups

Rahul Shukla,ª,ᵇ Emmanuel Aubert,ª Mariya Brezgunova,ª Sébastien Lebègue,ª Marc Fourmiguéᶜ and Enrique Espinosaª*

A four-membered $R_2^2(4)$ supramolecular motif formed by S···S and S···I chalcogen-bonding interactions in the crystal structure of 4-iodo-1,3-dithiol-2-one ($C_3HIO_2S$, IDT) is analysed and compared with a similar $R_2^2(4)$ motif (stabilized by Se···Se and Se···O chalcogen bonds) observed in the previously reported crystal structure of selenaphthalic anhydride ($C_8H_4O_2Se$, SePA) through detailed charge density analysis. Our investigation reveals that the chalcogen-bonding interactions participating in the $R_2^2(4)$ motifs observed in the two structures have the same characteristic orientation of local electrostatic electrophilic···nucleophilic interactions while involving different types of atoms. We carried out Cambridge Structural Database searches for synthons and supramolecular motifs involving chalcogen-, halogen- and hydrogen-bonding (ChB, XB and HB) interactions. Geometrical characterizations and topological analyses of the electron density $ρ(r)$ and its negative Laplacian function [$L(r) = -\nabla^2ρ(r)$] indicate that all the bonding interactions forming the motifs are driven by local electrophilic···nucleophilic interactions between complementary charge concentration (CC) and charge depletion (CD) sites present in the valence shells of the atoms, regardless of the atoms and functional groups involved. The graph-set assignment $G_d^a(n)$ ($G = C, R, D$ or $S$), formerly developed by Etter [Acc. Chem. Res. (1990), **23**, 120–126] for HB interactions, is a convenient way to describe the connectivity in supramolecular motifs based on electrophilic···nucleophilic interactions (such as ChB, XB and HB interactions), exchanging the number of atomic acceptors (a) and donors (d) with the number of nucleophilic (n: CC) and electrophilic (e: CD) sites, and the number of atoms building the motif *n* by *m*, leading to the new graph-set assignment $G_e^n(m)$ ($G = C, R, D$ or $S$). Geometrical preferences in the molecular assembly of synthons and other supramolecular motifs are governed by the relative positions of CC and CD sites through CC···CD interactions that, in most cases, align with the internuclear directions within a <15° range despite low interaction energies. Accordingly, beyond atoms and functional groups, the origin of recurrent supramolecular structures embedded within different molecular environments is found in the local electrostatic complementarity of electrophilic and nucleophilic regions that are placed at particular geometries, driving the formation and the geometry of synthons and supramolecular motifs by directional and locally stabilizing electrostatic interactions.

## 1. Introduction

Hydrogen bonding is the most commonly observed intermolecular interaction in crystals of organic compounds containing hydrogen atoms of acidic character. The use of rules about the formation of hydrogen bonds can aid in the design and analysis of multi-component crystals of organic compounds, such as co-crystals (Tiekink & Zukerman-Schpector, 2017). However, so far, the formation of a co-

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OPEN ACCESS

Published under a CC BY 4.0 licence

<footnote>ªCRM2, Université de Lorraine, CNRS, Nancy F-54500, France, ᵇDepartment of Chemistry (NCI Laboratory), GITAM (Deemed to be University), 530045 Visakhapatnam, Andhra Pradesh, India, and ᶜInstitut des Sciences Chimiques de Rennes, Université Rennes 1, UMR CNRS 6226, Campus de Beaulieu 35042, France. *Correspondence e-mail: enrique.espinosa@univ-lorraine.fr</footnote>
crystal cannot be predicted using these rules, and it can only be verified after experimental analysis. Strategies put in place to build up co-crystals are mainly based on the formation of supramolecular building blocks called synths (Desiraju, 1995), which are defined as recurring intermolecular structural units found in crystal phases. Hence, studies on the competition between different supramolecular building blocks have been carried out to facilitate the prediction of co-crystal formation (Etter, 1991). The results of these studies suggest that the most energetically stable synthon is the one that appears in the arrangement of the co-crystal formed (Blagden et al., 2008). These hypotheses have been verified experimentally through comparisons of single-crystal structures (Vishweshwar et al., 2006).

A study carried out using the Cambridge Structural Database (CSD) (Allen, 2002) and the CONQUEST (version 1.17) software demonstrated that most co-crystals form preferentially by making use of heterosynthons rather than homosynthons (Groom & Allen, 2014). An homosynthon is characterized by intermolecular interactions between the same functional group, such as carboxylic acid···carboxylic acid or amide···amide interactions. An heterosynthon is characterized by intermolecular interactions between different but complementary functional groups, such as carboxylic acid···amide or carboxylic acid···pyridine. Since carboxylic acids are found in a large number of organic molecules and active pharmaceutical ingredients, they are among the most studied functional groups in crystal engineering (Desiraju, 1991; Shan et al., 2002a; Shan et al., 2002b; Vishweshwar et al., 2005). Statistical analyses carried out using the CSD (Allen et al., 1999) and involving structures that only contain carboxylic acid functional groups have shown that the main molecular association follows the formation of the supramolecular homosynthon carboxylic acid···carboxylic acid. However, in the presence of competing functional groups such as amide or pyridine groups, carboxylic acid···pyridine and carboxylic acid···amide heterosynthons were found to be more favoured (Steiner, 2001; Vishweshwar et al., 2003a; Vishweshwar et al., 2003b; Nangia, 2010). This empirical information on the complementarity between functional groups and their supramolecular building blocks could lead to guidelines for the design of co-crystals. Such guidelines would facilitate the selection of co-formers (namely, the appropriate molecules participating in the formation of co-crystals), which could then be used in experimental screens targeting forms of multi-component solids (Issa, 2011). The formation of co-crystals can be induced through the use of hydrogen-bond donors and acceptors that are part of the molecular entities forming the co-crystal, as well as the way they may interact through hydrogen bonding (Blagden et al., 2007). After a thorough study of preferential arrangements and HB patterns found in a large number of organic crystals, Etter made several observations to aid in the design of hydrogen bonds in solids and applied a graph-set assignment to define the morphology of hydrogen-bonded arrays differentiating the type of donors and acceptors that are present (Etter, 1990). These graph-set symbols are of the form $G_d^n$, where G = C, R, D or S,

denoting chain, ring, dimer (or other finite set) or intramolecular HB patterns, respectively, while the subscript *d* and superscript *a* indicate the number of donors and acceptors used in each motif, and *n* is the number of atoms in the unit.

The graph-set assignment $G_d^n$ is a very convenient way to describe the connectivity in supramolecular motifs based on electrophilic···nucleophilic interactions, generalizing the description of HB patterns to additional ones that originate from other types of non-covalent interactions. Indeed, after the initial use of synths based on HB interactions, other supramolecular building units have been identified based on halogen bonds (Cavallo et al., 2016; Fourmigué, 2009), and more recently on chalcogen bonds (Scilabra et al., 2019; Vogel et al., 2019; Gleiter et al., 2018; Dhaka et al., 2024; Dukhnovsky et al., 2024). In all these cases, new supramolecular architectures exhibit specific electrophilic and nucleophilic regions at donor and acceptor molecules that lead to highly directional interactions. Electrophilic (charge-depleted: CD) sites in halogen bonds and chalcogen bonds are associated with $\sigma$-hole regions (Clark et al., 2007; Politzer & Murray, 2017) and are typically revealed by a plot of the molecular electrostatic potential (MESP) on isosurfaces of electron density in the external parts of molecules, which become significantly positive, as with acidic hydrogen atoms that are involved in HB interactions. On the other hand, good nucleophilic (charge concentration: CC) sites are typically associated with lone-pair regions of Lewis bases involved in HB, XB and ChB interactions, displaying negative MESP values and therefore ensuring the electrostatic complementarity with donor partners. Although additional types of non-covalent electrophilic···nucleophilic interactions have been described in the literature (Alkorta et al., 2020), this work will focus on ChB and XB interactions, and HB interactions to a lesser extent.

The IUPAC defined the chalcogen bond as a net 'attractive interaction between an electrophilic region associated with a chalcogen atom in a molecular entity and a nucleophilic region in another, or the same, molecular entity' (Aakeroy et al., 2019). While similar to the halogen bond as per the definition (Desiraju et al., 2013), characterizing a chalcogen bond can be complex in comparison. This is because the anisotropic distribution of $\rho(r)$ around the $Ch_{sp^3}$ atom can result in multiple CD sites suitable for ChB interactions, which can compete and sometimes merge (Shukla et al., 2020). In comparison, halogen atoms have only one CD region suitable for an XB interaction. This is the reason why intermolecular chalcogen bonds do not always form along the covalent bond direction of the chalcogen atom, as observed in halogen bonds. In the past few years, there has been a steady increase in both experimental and theoretical studies focusing on ChB interactions. This is because, in addition to their ability to form strong intermolecular and intramolecular interactions in crystal structures, chalcogen bonds also present potential applications in the fields of catalysis, organic synthesis and material design, among other fields (Mahmudov et al., 2017; Bamberger et al., 2019; Dhaka et al., 2020; Beau et al., 2023). The formation of supramolecular synths mediated by ChB interactions is also a very common phenomenon. However,
this feature is relatively less explored compared with motifs
involving hydrogen and halogen bonds. Investigations on
chalcogenated molecules have shown the formation of robust
Ch···O interactions with the electrophilicity of the chalcogen
atom increasing in the order O < S < Se < Te (Brezgunova *et al.*, 2013), which parallels the observed behaviour of X···O
interactions along the series of halogen atoms F < Cl < Br < I (Geboes *et al.*, 2015). Other studies have shown that the
characteristics of the Ch···O interaction remained similar
(Scilabra *et al.*, 2019) even when one type of chalcogen atom
was replaced with another.

In the current study, the crystal structure of 4-iodo-1,3-di-
thiol-2-one (C<sub>3</sub>HIOs<sub>2</sub>, hereafter called IDT) is investigated
via theoretical charge density analysis. The presence of
hydrogen, chalcogen and halogen atoms in the small IDT
molecule allows an in-depth investigation of HB, ChB and XB
interactions present in the crystal structure of this molecule. A
significant structural aspect of IDT on which we focus is the
formation of a four-membered motif assembled from S···S
and S···I chalcogen bonds. Considering the expected posi-
tions of electrophilic and nucleophilic regions around the
atoms involved, the motif in IDT is extremely similar to the
recurrent R<sub>2</sub><sup>2</sup>(4) motif in selenaphthalic anhydride (SePA)
(Brezgunova *et al.*, 2013), which is formed by Se···Se and
Se···O chalcogen bonds (see the scheme below). This feature
raises the question of the origin of similar supramolecular
motifs involving different atoms. Is the origin of the motif
associated with the atom or the functional group involved in
the formation of the interactions building the supramolecular
structure, or with the appropriate orientation of particular
electrophilic and nucleophilic regions present in the inter-
acting atoms? The formation of a similar motif in IDT and
SePA strongly suggests that the latter holds true. Hereafter,
the graph-set assignment G<sub>d</sub><sup>a</sup>(n) developed by Etter (1990) for
HB interactions is generalized to any non-covalent interaction
(such as HB, XB or ChB interactions) using the new notation
G<sub>e</sub><sup>n</sup>(m) (G = C, R, D or S), where the number of atomic
acceptors a and donors d are exchanged for the number of
nucleophilic n (CC) and electrophilic e (CD) sites, and the
number of atoms building the motif n for m (to avoid a
misunderstanding with the number of nucleophiles).

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With the aim of identifying the structural parameters that
correspond to the geometrical preferences shown in synthons
(and in a more general way, in the formation of structurally
similar non-covalent interactions), a detailed CSD search has
been carried out for other supramolecular R<sub>2</sub><sup>2</sup>(4), R<sub>3</sub><sup>3</sup>(3) and
bifurcated intermolecular motifs, as well as for intramolecular
motifs. In addition, to investigate the origin of recurrent non-
covalent inter-/intramolecular motifs and their geometries in

depth, the topology of L(r) = -∇²ρ(r) has been also investi-
gated for selected motifs to determine local nucleophilic (CC)
and electrophilic (charge depletion, CD) sites in the valence
shells of the atoms and to quantify their geometric orientation
with respect to internuclear directions; this procedure has
already been applied in previous work and described by the
angle between the CC···CD and internuclear directions
(Brezgunova et al., 2013; Shukla et al., 2020). Overall, the
investigation carried out in this study establishes that face-to-
face CC···CD interactions drive atomic orientations and are
definitively more important than the atoms or functional
groups involved in the formation of different supramolecular
synthons or motifs.

2. Experimental and theoretical methods

**2.1. Synthesis and crystal growth**

4-Iodo-1,3-dithiol-2-one (C<sub>3</sub>HIOS<sub>2</sub>, IDT) was synthesized from the corresponding thione 4-iodo-1,3-dithiol-2-thione (Le Gal *et al.*, 2016) in CH<sub>3</sub>Cl/AcOH with Hg(OAc)<sub>2</sub>, as shown in earlier work (Domercq *et al.*, 2001). The sublimation method was used to obtain IDT single crystals of good quality (70°C sublimation temperature).

2.2. X-ray diffraction

Low-temperature high-resolution single-crystal X-ray
diffraction measurements were performed using an Mo Kα
radiation source (λ = 0.71073 Å) on an Enraf-Nonius
diffractometer with a Kappa-CCD detector at *T* = 100 (4) K
(Oxford Cryosystems N₂ cooling device). The data collection
strategy was determined and data reduction was carried out
with *CrysAlisPro CCD/RED*. After absorption correction, the
measured reflections were then sorted, scaled and merged
using the *SORTAV* program (Blessing, 1995). The structures
were solved with *SHELXS* (Sheldrick, 2008) and refined with
*SHELXL* (Sheldrick, 2015) incorporated in the *OLEX2*
program (Dolomanov *et al.*, 2009). The molecular packing of
IDT was drawn using *Mercury* (Macrae *et al.*, 2020). See Table
S1 in the supporting information for data collection and
structure refinement details.

2.3. Computational electron density

Owing to the presence of several heavy atoms (namely, two
sulfur atoms and one iodine atom) in a small organic molecule
that crystallizes in the triclinic system with the non-centro-
symmetric space group *P*1, the experimental dataset for IDT
was of limited quality for experimental charge density analysis
(Fig. S1 of the supporting information). For this reason, only
periodic theoretical calculations were performed on the
crystal structure of IDT based on the experimental geometry
and obtained after the independent atom model (IAM)
refinement. *Ab initio* periodic calculations using density
functional theory (DFT) were then performed on the crystal
structure of IDT with the *Vienna Ab initio Simulation Package*
<figure><img src="image_7.png" /><figcaption>Figure 1</figcaption></figure>

Maps calculated in the molecular plane and in the two perpendicular planes bisecting the C—S—C angles containing the S-atom lone pairs (inset figures) of IDT (theoretical model): (a) residual electron density at the resolution range 0 ≤ (sin θ/λ) ≤ 0.9 Å⁻¹, (b) static deformation density Δρ(r) and (c) L(r) = -∇²ρ(r). Contours for maps (a) and (b) are at the ±0.05 e Å⁻³ level: full lines in blue are positive, dotted lines in red are negative. Contours for (c) in e Å⁻⁵ are on a logarithmic scale: red lines are positive and blue lines are negative.

(VASP) (Kresse & Furthmüller, 1996a; Kresse & Hafner, 1993; Kresse & Hafner, 1994; Kresse & Furthmüller, 1996b). More precisely, we used the functional of Perdew, Burke and Ernzerhof (Perdew et al., 1996) as the exchange–correlation functional, and to ensure convergence a value of 900 eV was set for the plane-wave expansion of the wavefunction, as well as a k-points grid of 16 × 12 × 8 to sample the first Brillouin zone. The valence electron density was represented on a regular grid comprising 160 × 224 × 280 points along the crystallographic axes and was used to compute the structure factors. Note that the comparison of a previous experimental charge density model for C₆Cl₆ with the corresponding periodic ab initio theoretical DFT model obtained with VASP, using the same method as in the present work, led to extremely close results in intermolecular regions (Aubert et al., 2011).

DFT calculations were also undertaken at the B3LYP/
Def2TZVPP level of theory on isolated molecules (monomers,
dimer, trimers) in order to characterize the intermolecular
interactions. The molecular structures were extracted from
crystal structures and the Gaussian 16 program package was
used for the calculations (Frisch et al., 2019). Topological
analyses were also performed using AIMAll (Keith, 2019).

2.4. Multipolar refinement

The theoretical multipolar refinement was performed using
the MoPro/MoProviewer software package (Jelsch et al., 2005;
Guillot et al., 2014). In the multipolar refinements against the
theoretically calculated structure factors (sin θ/λ<sub>max</sub> =
1.0 Å<sup>-1</sup>), the Slater-type radial functions were expanded up to
the hexadecapole level (l = 4) for the I (n<sub>l</sub>, ξ: 8, 8, 8, 8 for l = 1,
2, 3, 4; 4.84 bohr<sup>-1</sup>) and S atoms (n<sub>l</sub>, ξ: 4, 4, 6, 8 for l = 1, 2, 3, 4;
3.8513 bohr<sup>-1</sup>), and up to octapole level (l = 3) for C (n<sub>l</sub>, ξ: 2, 2,
3 for l = 1, 2, 3; 3.0 bohr<sup>-1</sup>) and O atoms (n<sub>l</sub>, ξ: 2, 2, 3 for l = 1, 2,

3; 4.5 bohr⁻¹). In the fitting against theoretical data, core
electrons were omitted from the MoPro atomic definitions,
since the VASP structure factors correspond to valence elec-
trons only. The multipolar models fitted against the theoretical
structure factors converged to the agreement factors wR(F) =
0.023 and R(F) = 0.041 (Table S1). The residual density map of
the best theoretical model shows residual peaks centred at the
I and S atoms [Fig. 1(a)]. In the same plane, the static defor-
mation density Δρ(r) and L(r) = -∇²ρ(r) maps of the theo-
retical multipolar model of IDT are shown in Figs. 1(b) and
1(c), respectively. The Δρ(r) map shows that the highest
density accumulation is on the C2–C3 bond (0.6 e Å⁻³) and
three is a polarized electron distribution towards the C atoms
along the C–S and C–I bonds. The lone pairs of S1 merge in
a banana-shaped distribution (their separation is not observed
at any contour level), whereas those of S2 are separated [see
inset figures in Fig. 1(b)]. However, it is noticeable that a
polarization of the electron density takes place towards one of
the lone pairs in both S atoms. This effect could be explained
by the participation of the S atoms in different intermolecular
interactions above and below the molecular plane (S1···O1,
S2···O1 and S1···I1 contacts, which result in the stacking of
the molecules in columns). The multipolar model shows the
depletion of the electron density (δ⁺) extending along the
C–S bonds (Δρ varies from −0.25 to −0.10 e Å⁻³). In
general, the deformation density map of the S atom exhibits
very similar features to those observed earlier for the Se
atom in selenophtalic anhydride SePA (Brezgunova et al.,
2013). On the other hand, the deformation density of
the I atom in IDT is qualitatively close to those previously
described for Cl and Br atoms (Bui et al., 2009; Aubert et
al., 2011; Brezgunova et al., 2012), namely a δ⁺ region on
iodine located on the prolongation of the C3–I1 bond
and δ⁻ regions in the plane perpendicular to the bonding
direction.
## 2.5. The topology of $\rho(\mathbf{r})$ and $L(\mathbf{r})$ functions

Within the QTAIM framework (Bader, 1990), topological analysis of $\rho(\mathbf{r})$ is performed in order to extract significant information on bonding interactions present in molecular crystals. Accordingly, we have evaluated the topological and local energetic properties of $\rho(\mathbf{r})$ at bond critical points (BCPs) for a detailed description of the intermolecular and non-covalent intramolecular interactions investigated in this study. Topological analysis of $L(\mathbf{r}) = -\nabla^2\rho(\mathbf{r})$, with the determination of its own CPs [different from those of $\rho(\mathbf{r})$], has also been performed in order to identify CD and CC regions present in the valence shells of the atoms participating in the interactions. The local electrostatic complementarity of CD and CC regions interacting through space will help in characterizing the electrophilic-nucleophilic interactions (CD···CC) which are the origin of preferred orientations in molecular assemblies.

In the valence shells of atoms, $(3,-3)/(3,+3)$ CPs correspond to 3D nucleophilic/electrophilic sites [the $L(\mathbf{r})$ distribution is locally concentrated/depleted at the CP along the three main directions], whereas the interpretation of saddle $(3,+1)/(3,-1)$ CPs remains more complex because it depends on the relative positions of other $(3,-3)/(3,-1)/(3,+1)/(3,+3)$ CPs around them. This feature is a consequence of the continuity of the $L(\mathbf{r})$ function in space, leading to alternating local maxima and minima either along directions or on surfaces. For instance, a $(3,-1)$ CP can be found as a maximum/minimum along a 1D gradient field line of the $L(\mathbf{r})$ distribution linking two $(3,+1)$ or two $(3,-3)$ CPs. On the other hand, a $(3,+1)$ CP can be found as a maximum/minimum along a 1D gradient field line of the $L(\mathbf{r})$ distribution linking two $(3,+3)$ or two $(3,-1)$ CPs.

The saddle $(3,-1)$ and $(3,+1)$ CPs correspond to the local 1D depletion/2D concentration and 2D depletion/1D concentration, respectively, along the three main directions of the $L(\mathbf{r})$ distribution at the CP. Thus, in surfaces including two $(3,-3)$ CPs, a $(3,+1)$ CP appears as a CD site in the valence shell of the atom where the interaction access towards the nucleus is more favourable for a nucleophile, whereas a $(3,-1)$ CP appears in between two $(3,-3)$ CPs along the gradient vector line of the $L(\mathbf{r})$ distribution linking them. Accordingly, $(3,-1)$ CPs generally perform less well than $(3,+1)$ CPs as electrophilic centres, but this is however modulated by their observed $L(\mathbf{r})$ values. The quality of $(3,-1)$ CPs as electrophilic centres also depends on the relative positions of the $(3,-3)$ CPs: the more distant from each other they are, the better is the electrophilic quality of the $(3,-1)$ CP. Therefore, if the $(3,-3)$ CPs are separated far enough, the $(3,-1)$ CP marks the interaction access direction towards the nucleus for a nucleophile at the intersection of the perpendicular plane with the gradient field direction of the $L(\mathbf{r})$ distribution linking the $(3,-3)$ CPs. On the other hand, significant overlap of the electron distributions associated with the two $(3,-3)$ CPs leads us to consider the $(3,-1)$ CP as a nucleophilic indicator of the simultaneous contributions of both $(3,-3)$ CPs, in particular if the former is placed in the intermolecular interaction plane rather than the latter two.

For $S_{sp^3}$ atoms, it is common to observe the lone pairs overlapping each other in the region where a $(3,-1)$ CP is exhibited, whereas for $S_{sp^3}$ atoms their open valence-shell structure – attributed to large $\sigma$-hole regions – results in a $(3,-1)$ CP simultaneously positioned in between two $(3,-3)$ CPs (lone pairs) and two $(3,+1)$ CPs, lying approximately at the intersection of the lone-pair plane and the plane containing both $\sigma$ holes in a region of significant depletion of electron density. As shown in this work, the last trend is observed for $S_{sp^3}$ atoms and the $(3,-1)$ CP is considered to be a CD site, while due to the closer proximity of the $(3,-3)$ CPs (lone pairs) of the $S_{sp^3}$ atoms, the $(3,-1)$ CP takes the role of a CC site in IDT because it is placed in the intermolecular interaction plane, representing the accommodation of the contribution of each lone pair that is also involved in another more straightforward interaction [see the interlayer interactions in Fig. 2(b)]. For $O_{sp^3}$ atoms, the overlap of lone pairs is even more significant because they are closer to each other (Brezgunova et al., 2013). In that case, due to their proximity, the two $(3,-3)$ CPs can contribute as two nucleophilic centres involved in the same intermolecular interaction, without consideration of the less performant $(3,-1)$ CP between them.

## 3. Cambridge Structural Database searches

The Cambridge Structural Database (CSD) ConQuest module (version 2021.1.0) was used to perform a search for the intermolecular and non-covalent intramolecular interactions focused on in this study. In addition to several geometrical parameters that have been defined to characterize the interactions, we also applied some constraints for all the searches performed in this study. Hence, only structures whose 3D coordinates are fully determined and error free were involved in the search query. Furthermore, disordered structures, polymers, ionic and powder structures were excluded from the search. Finally, to ensure that only high-quality supramolecular motifs were part of the working set of crystal structures, the agreement *R* factor of the crystal structures, which represents the goodness of fit between the crystallographic model and the experimental diffraction data, was kept at $\le 0.1$ for all searches.

## 4. Results and discussion

### 4.1. Crystal structure of IDT

IDT crystallizes in the triclinic system (P1 space group) with one molecule in the unit cell (see Table S1 for crystallographic data as well as data for spherical and multipolar refinements). In the crystal structure, IDT molecules form layers where the molecules are connected by two types of bifurcated interactions [Fig. 2(a)]. Along the c-axis direction, each molecule is connected to neighbouring ones by relatively short $S_2 \cdots S_1$ and $S_2 \cdots I_1$ ChB interactions [3.8308 (1) and 3.8035 (9) Å, respectively], forming chains. The value of the reduction ratio (RR), which measures the penetration (RR < 1) or separation (RR > 1) of van der Waals (vdW) spheres, reaches 1.06 and
**Table 1**

Structural parameters (see Fig. 4) characterizing $Ch(\delta^+) \cdots (\delta^-)Y$ (Ch = S, Se; $Y = O, S, I$) chalcogen-bonding interactions in IDT and SePA.

Parameters with units: distance (d) $Ch \cdots Y$ ($Y = Ch, X$) (Å); RR, defined as the $Ch \cdots Y$ distance over the sum of vdW radii (dimensionless); contact angles $C_{1A} - Ch_1 \cdots Y, \zeta_{1A}$ (°), $C_{1B} - Ch_1 \cdots Y, \zeta_{1B}$ (°), $Ch_1 \cdots Y - C_{2A}, \zeta_{2A}$ (°) and $Ch_1 \cdots Y - C_{2B}, \zeta_{2B}$ (°); molecular angles $C_{1A} - Ch_1 - C_{1B}, \alpha_1$ (°) and $C_{2A} - Ch_2 - C_{2B}, \alpha_2$ (°); degree of planarity angle in the $\sigma_i$ plane $\phi_i = \zeta_{iA} + \zeta_{iB} + \alpha_i$, where $i = 1, 2$ (°); $\zeta_1 = \max(\zeta_{1A}, \zeta_{1B})$ and $\zeta_2 = \max(\zeta_{2A}, \zeta_{2B})$. vdW radii = 1.52, 1.80, 1.90 and 1.98 Å for O, S, Se and I, respectively.

<table><thead><tr><th>Compound</th><th>Ch(δ<sup>+</sup>)...(δ<sup>-</sup>)Y<sup>†</sup></th><th>d</th><th>RR</th><th>ζ<sub>1A</sub>/ζ<sub>1B</sub></th><th>α<sub>1</sub></th><th>φ<sub>1</sub></th><th>ζ<sub>2A</sub>/ζ<sub>2B</sub></th><th>α<sub>2</sub></th><th>φ<sub>2</sub></th><th>ζ<sub>1</sub> - ζ<sub>2</sub></th><th>φ<sub>1</sub> - φ<sub>2</sub></th></tr></thead><tbody><tr><td rowspan="2">IDT</td><td>S<sub>1</sub><sup>i</sup>...S<sub>2</sub><sup>iii</sup></td><td>3.8308 (1)</td><td>1.06</td><td>161.4/97.9</td><td>96.0</td><td>355.3</td><td>126.6/135.4</td><td>96.6</td><td>358.6</td><td>26.0</td><td>-3.3</td></tr><tr><td>S<sub>2</sub><sup>iii</sup>...I<sub>1</sub><sup>i</sup></td><td>3.8035 (3)</td><td>1.01</td><td>171.0/84.9</td><td>96.6</td><td>352.5</td><td>92.7</td><td>-</td><td>-</td><td>78.3</td><td>-</td></tr><tr><td rowspan="2">SePA</td><td>Se<sub>1</sub><sup>i</sup>...Se<sub>1</sub><sup>ii</sup></td><td>3.8220 (2)</td><td>1.01</td><td>166.3/79.1</td><td>87.4</td><td>332.8</td><td>87.4/122.0</td><td>87.4</td><td>296.8</td><td>44.3</td><td>36</td></tr><tr><td>Se<sub>1</sub><sup>i</sup>...O<sub>1</sub><sup>ii</sup></td><td>3.3552 (1)</td><td>0.98</td><td>119.0/145.4</td><td>87.4</td><td>351.8</td><td>111.2</td><td>-</td><td>-</td><td>34.2</td><td>-</td></tr></tbody></table>

1.01 for the $S_2 \cdots S_1$ and $S_2 \cdots I_1$ ChB interactions, respectively. The molecules are also assembled in the layers by HB ($O_1 \cdots H_2$) and XB ($O_1 \cdots I_1$) interactions between the chains described above, with distances [2.235 Å and 2.9342 (3) Å, respectively] that are significantly shorter than the sum of their corresponding vdW radii (RR = 0.82 and 0.84). The relatively short distance between the layers (3.339 Å) is a result of the intra-column $S_1 \cdots I_1$, $S_{1,2} \cdots O_1$ and $S_2 \cdots C_2$ ($I_1 \cdots \pi$) contacts [Fig. 2(b)] between stacked molecules that are slipped within each column.

## 4.2. Chalcogen-bonding interactions

### 4.2.1. Comparison between chalcogen bonding in IDT and SePA

The ChB interactions in the crystal structure of IDT show features very similar to those observed in the crystal structure of SePA (Fig. 3) (Brezgunova et al., 2013). Indeed, despite different atoms and relative positions of the interacting molecules, IDT and SePA exhibit similar types of intermolecular contacts involving two $Ch_{sp^3}$ atoms and form a geometrically similar synthon-type fragment that is based on a

cyclic four-centre motif. Based on the generalized graph-set notation, the four-membered fragments observed in IDT and SePA (Figs. 2 and 3) can be classified as $R_2^2(4)$ supramolecular motifs, with two electrophilic regions and two nucleophilic regions in the four-membered rings.

Table 1 presents the observed $Ch \cdots Y$ ($Y = Ch, X$, where $X$ represents a halogen) distances in IDT and SePA, which are compared with the corresponding sums of the vdW radii by means of the RR value, as well as the contact angles $\zeta_1$ and $\zeta_2$, indicating the directionality of the interactions (Fig. 4). From the calculated RR parameters, it is observed that Se atoms in the $Se \cdots Se$ contact approach closer than the S atoms in the $S \cdots S$ contact. This trend has already been noted for halogen atoms, where the heavier bromine atoms approach closer in $Br \cdots Br$ contacts than the lighter chlorine atoms in $Cl \cdots Cl$ contacts (Brezgunova et al., 2012).

The structural angles $\zeta_1$ and $\zeta_2$ (Table 1) allow us to roughly estimate the expected locations of $\delta^+$ and $\delta^-$ regions in Ch atoms that are involved in the formation of $\delta^+ \cdots \delta^-$ interactions (Fig. 4). The magnitudes of the angles show several differences in the interaction geometries. Thus, for $S_1 \cdots S_2$, $Se_1 \cdots Se_1$ and $S_2 \cdots I_1$ interactions, one of the two $\zeta_1$ angles

<figure><img src="image_8.png" /><figcaption>**Figure 2**</figcaption></figure>

Crystal structure of IDT. (a) View from above of layers showing the four-membered fragment $R_2^2(4)$ involving two ChB interactions ($S \cdots S$ and $S \cdots I$ in blue) and a V-type supramolecular motif involving HB (grey) and XB (orange) interactions. (b) Side view of layers showing intercolumn contacts in green.

<footnote>† Symmetry codes. IDT: (i) x, y, z; (ii) x, y, z; (iii) x, y, -1 + z. SePA: (i) x, y, z; (ii) 1/2 - x, -1/2 + y, 3/2 - z.</footnote>
<figure><img src="image_9.png" /><figcaption>Figure 3</figcaption></figure>

Crystal structure of SePA. (a) Side view projected on the *ac* plane showing the four-membered $R_2^2(4)$ fragment involving two ChB interactions (Se···Se and Se···O in blue) and intracolumn interactions (green). (b) View from above projected on the *bc* plane showing two $R_2^2(10)$ fragments, each involving two HB interactions (grey).

tends to be close to 180° (linearity), predicting the location of the $δ^+$ region close to the direction of the C—Ch bond. In contrast, for $Se_1...O_2$, the $ζ_1$ values are close to each other, indicating that the location of the $δ^+$ region is expected to be approximately along the direction bisecting the C—Se—C angle in the $σ_1$ plane (Fig. 4), as pointed out in the earlier study of SePA (Brezgunova et al., 2013). On the other hand, the inverse situation is observed with the $ζ_2$ parameter. Indeed, for $Se_1...Se_1$, $S_2...I_1$ and $Se_1...O_2$, $ζ_2$ ranges between 90 and 110°, which approximately corresponds to the expected angular location of the lone pairs ($δ^−$ regions) in I, O and Se atoms. In the case of the $S_1...S_2$ contact, the $ζ_{2A}$ and $ζ_{2B}$ values are close to each other, indicating that the $δ^−$ region is roughly located along the direction bisecting the C—$S_2—C$ angle in the $σ_2$ plane. It is important to highlight that the observation of a region of either $δ^+$ or $δ^−$ character along the direction bisecting the C—$Ch_{sp^3}—C$ angle is the consequence of the angular opening of the $Ch_{sp^3}$ lone pairs. Thus, a $δ^−$ region is often observed for lighter chalcogens (O, S), whereas a region of $δ^+$ character is more likely to be observed for heavier chalcogens (Se, Te), in which the lone pairs are more separated from each other.

A in-depth structural analysis of chalcogen–chalcogen interactions is needed for the description of geometrical features beyond the standard geometrical contact angles $ζ_1$ and $ζ_2$, also taking into account the relative orientation of molecules participating in the interactions. This is because not all Ch···Ch contacts involve electrophilic···nucleophilic ($δ^+...δ^−$) ChB interactions, so it is important to differentiate between several cases. For an $sp^3$-hybridized Ch atom, the $σ$ plane (defined as the C—Ch—C plane) represents the region where the chalcogen atom is expected to develop $δ^+$ regions. On the other hand, the $π$ plane, which bisects the $α$(C—Ch—C) angle and is perpendicular to the $σ$ plane, represents the region where the lone pairs of Ch should show participation with $δ^−$ regions [Fig. 4(a)]. Accordingly, the $ζ_i$

and $α_i$ angles, and the relative position of the $σ_i$ and $π_i$ planes of both molecules ($i$ = 1, 2) geometrically characterize the relative orientation of the $Ch_1...Ch_2$ contact [Fig. 4(b)]. In fact, if $Ch_1$ is participating via a $δ^+$ region in the $C_{1A/1B}—Ch_1...Ch_2$ interaction, $Ch_2$ should be close to the $σ_1$ plane, meaning that the magnitude of $φ_1$ (defined as $φ_1 = α_1 + ζ_{1A} + ζ_{1B}$) should approach 360°. Similarly, if $Ch_2$ participates via a $δ^+$ region in the interaction, then $Ch_1$ should be close to the $σ_2$ plane and $φ_2 \simeq 360°$. Other significant geometrical parameters are $ζ_1 = \max(ζ_{1A}, ζ_{1B})$ and $ζ_2 = \max(ζ_{2A}, ζ_{2B})$, which characterize the directionality of the $Ch_1...Ch_2$ interaction. Hence,

<figure><img src="image_10.png" /><figcaption>Figure 4</figcaption></figure>

(a) Schematic of the expected orientation of electrophilic ($δ^+$) and nucleophilic ($δ^−$) regions around the Ch atom within the C—Ch—C $σ$ plane and in the perpendicular $π$ plane. (b) Structural angles used in the characterization of the C—$Ch_1...Ch_2—C$ interactions ($Ch_1/Ch_2 = S/Se/Te$).
<caption>**Table 2**</caption>

Structural and topological parameters for $Ch(\delta^+) \cdots (\delta^-)Y$ (Ch = S, Se; $Y = O, S, Se, I$) chalcogen-bonding interactions in IDT and SePA.

$\alpha$ is the angle between the CD···CC and internuclear directions. Parameters with units: $\alpha$ (°), topological and local energetic properties $\rho$ (e Å⁻³), $\nabla^2\rho$ (e Å⁻⁵), G and V (kJ mol⁻¹ bohr⁻³), and $|V|/G$ (dimensionless), calculated at BCPs using the AIMAll software (Keith, 2019) with interacting dimers calculated at experimental geometries. vdW radii = 1.52, 1.80, 1.90 and 1.98 Å for the O, S, Se and I atom, respectively.

<table><thead><tr><th>Compound</th><th>Ch(δ<sup>+</sup>)···(δ<sup>-</sup>)Y<sup>†</sup></th><th>ρ</th><th>∇<sup>2</sup>ρ</th><th>G</th><th>V</th><th>|V|/G</th><th>-E<sub>int</sub><sup>‡</sup></th><th>α<sup>§</sup></th></tr></thead><tbody><tr><td rowspan="3">IDT</td><td>S<sub>1</sub><sup>i</sup>···S<sub>2</sub><sup>iii</sup></td><td>0.028</td><td>0.32</td><td>6.6</td><td>-4.2</td><td>0.64</td><td>2.1/-</td><td>10.1</td></tr><tr><td>S<sub>2</sub><sup>iii</sup>···I<sub>1</sub><sup>i</sup></td><td>0.048</td><td>0.45</td><td>10.0</td><td>-7.6</td><td>0.76</td><td>3.8/-</td><td>8.7</td></tr><tr><td>Dimer E<sub>int</sub></td><td></td><td></td><td></td><td></td><td></td><td>6.4/5.9/5.9</td><td></td></tr><tr><td rowspan="3">SePA</td><td>Se<sub>1</sub><sup>i</sup>···Se<sub>1</sub><sup>ii</sup></td><td>0.041</td><td>0.36</td><td>8.1</td><td>-6.3</td><td>0.78</td><td>3.2/4.7</td><td>17.3/15.0</td></tr><tr><td>Se<sub>1</sub><sup>i</sup>···O<sub>1</sub><sup>ii</sup></td><td>0.050</td><td>0.60</td><td>12.9</td><td>-9.4</td><td>0.73</td><td>4.7/5.9</td><td>11.7</td></tr><tr><td>Dimer E<sub>int</sub></td><td></td><td></td><td></td><td></td><td></td><td>9.4/8.3/7.9/10.6</td><td></td></tr></tbody></table>

based on the parameters $\phi_1, \phi_2, \zeta_1$ and $\zeta_2$, chalcogen-chalcogen bonding (where regions of different electronic nature $\delta^+ \cdots \delta^-$ are facing each other) and chalcogen contacts involving regions of similar electronic nature. The importance of these parameters and their use will be further discussed during the analysis of the CSD search results below.

### 4.2.2. Topological analysis of $\rho(r)$ in chalcogen-bonding regions of $R_2^2(4)$ motifs in IDT and SePA

Based on the topological analysis of $\rho(r)$ (Bader, 1990), bonding interactions between atoms are identified by the existence of a bond path between their nuclei and the concomitant BCP at the intersection of the bond path with the interatomic zero-flux surface $S(r) [\nabla\rho(r) \cdot n(r) = 0, \forall r \in S$, with n being the unit vector $\perp S$ at r]. Chalcogen-bonding interactions in IDT and SePA were thus identified by the observed bond paths and BCPs in their $S_1 \cdots S_2, S_2 \cdots I_1, Se_1 \cdots Se_1$ and $Se_1 \cdots O_2$ regions (Fig. 5).

In order to quantitatively characterize the intermolecular interactions observed in IDT and SePA, we focus on the topological and energetic properties of $\rho(r)$ at their BCPs. Table 2 presents the values of the electron density $\rho$ and the Laplacian $\nabla^2\rho$, as well as those of the local electron kinetic (G) and potential (V) energy densities at the BCPs of the selected interactions. For the sake of comparison between IDT

and SePA, as well as for a coherent comparison with data throughout this work, values are reported for interacting dimers calculated at the DFT B3LYP/Def2TZVPP level of theory using experimental geometries (experimental data for SePA, and periodic theoretical VASP data for IDT and SePA are presented in Table S2 of supporting information, showing quite similar values). For the four intermolecular interactions, the magnitudes of $\rho$ and $\nabla^2\rho$ are low ($0.028 < \rho < 0.050$ e Å⁻³, $0.32 < \nabla^2\rho < 0.62$ e Å⁻⁵) (Table 2) and typically fall into the range determined (theoretically and experimentally) for other weak intermolecular interactions, such as weak H···O (Espinosa et al., 1999), H···N (Mata et al., 2007) and H···F (Espinosa et al., 2002) hydrogen bonds, and weak X···X halogen-bonding interactions (Brezgunova et al., 2012).

The ratio $|V|/G < 1$ classifies the four contacts as ‘pure’ closed-shell interactions of weak intensity (Espinosa et al., 2002). Although the empirical estimation of the interaction energy $E_{int}$ (kJ mol⁻¹) = $V$ (kJ mol⁻¹ bohr⁻³)/2 (Espinosa et al., 1998) was previously derived for weak-to-medium HB interactions, it has also been used to provide a reasonable estimate for other weak XB (C₆Br₅OH, C₆Cl₅OH) and ChB (SePA) interactions, which were thus compared in the same framework to HB interactions in the same crystal structures (Brezgunova et al., 2012; Brezgunova et al., 2013). In order to gauge the goodness of the estimates for halogen bonds and chalcogen bonds, we have also calculated the $E_{int}$ values from other relationships found in the literature and derived for XB

<figure><img src="image_11.png" /><figcaption>**Figure 5**</figcaption></figure>

Intermolecular Ch···Ch and Ch···Y contacts (Ch = S, Se; $Y = O, I$) with their bond paths (dotted lines) and their corresponding BCPs (small green circles) between the interacting atoms in the dimers of (a) IDT and (b) SePA.

<footnote>† See Table 1 for symmetry codes. ‡ For individual interactions, $-E_{int}$ (kJ mol⁻¹) is estimated as (left) $-V/2$ and (right) $-0.375V + 2.366$ [for ChB interactions involving Se atoms, see Bauzá & Frontera (2020)]. The interaction energy of the dimers (difference between the energy of the dimer and those of the monomers) has been calculated at the B3LYP-D3/Def2TZVPP level of theory: values (in kJ mol⁻¹) correspond to $-E_{int\_dimer}/-E_{int\_dimer\_corrected\_BSSE}/-\Sigma V/2/\Sigma E_{int\_Bauzá & Frontera, 2020)}$. § In the case of the $Se_1^i \cdots Se_1^{ii}$ interaction, one CC seems to interact simultaneously with two CD sites, leading to two $\alpha$ angles.</footnote>
and ChB interactions (Bauzá & Frontera, 2020). Interaction energies in both approaches are similar to each other (except for the S···S and S···I interactions, which cannot be estimated from the latter reference) and fall within a narrow range of small magnitudes (−*E*<sub>int</sub> = 2–6 kJ mol<sup>−1</sup>, Table 2). The addition of individual interaction contributions to estimate the interaction energy of the system in which they are embedded compares very well to the interaction energy of each dimer calculated at the B3LYP-D3/Def2TZVPP level of theory (Table 2), which exhibits low *E*<sub>int</sub> magnitudes (~6 kJ mol<sup>−1</sup> for IDT and between 8 and 10 kJ mol<sup>−1</sup> for SePA). Low interaction energies contrast with the formation of similar supramolecular motifs embedded in different crystalline environments, despite the different atoms and functional groups involved.

Comparing the estimated *E*<sub>int</sub> values derived for interac-
tions involving homochalcogens, the Se···Se interaction is
roughly 30% more energetic than S···S (3.8 kJ mol<sup>-1</sup> versus
2.7 kJ mol<sup>-1</sup>, as averaged from experimental and theoretical
values). The observed tendency, supported by the calculated
|V|/G magnitudes (Table 2), is in accordance with theoretical
studies (Bleiholder *et al.*, 2007), showing that the strength of
these contacts decreases in the order Te···Te > Se···Se >

S···S > O···O and reflects the tendency discussed earlier for
X···X interactions [−*E*<sub>int</sub> = 4.9 ± 1.2 kJ mol<sup>−1</sup> for Br···Br
versus −*E*<sub>int</sub> = 4.3 ± 1.1 kJ mol<sup>−1</sup> for Cl···Cl (Brezgunova *et
al.*, 2012)]. It is notable that, paralleling the increase of
polarizability from chalcogen to halogen atoms (along the
same periodic table row), the estimated magnitude *E*<sub>int</sub> of
individual interactions contributing to the interaction energy
of motifs increases from S···S to Cl···Cl and from Se···Se to
Br···Br.

The deformation of the electron density distribution Δρ(**r**),
which is defined as the difference between the crystalline
electron density model and the IAM [Δρ(**r**) = ρ<sub>cryst</sub>(**r**) −
ρ<sub>IAM</sub>(**r**)], aims to show the redistribution of electrons from
isolated atoms to their configuration in the crystal environ-
ment as a consequence of all intra- and intermolecular inter-
actions. In Fig. 6, the theoretical 3D static Δρ(**r**) map is plotted
in the chalcogen-bonding regions of IDT and SePA. In both
crystal structures, the map clearly shows δ<sup>−</sup> (Δρ > 0, blue) and
δ<sup>+</sup> (Δρ < 0, red) regions directed towards each other in the
intermolecular regions S<sub>2</sub>···I<sub>1</sub> and Se<sub>1</sub>···Se<sub>2</sub>, while a less clear
situation is observed for the S<sub>1</sub>···S<sub>2</sub> and Se<sub>1</sub>···O<sub>2</sub> contacts
involving regions located just in front of the Ch atoms.
Paralleling the progressive separation of the lone pairs along

<figure><img src="image_12.png" /><figcaption>Figure 6</figcaption></figure>

Static deformation density Δρ(r) maps in intermolecular regions of (a) IDT and (b) SePA. Isosurfaces are drawn at ±0.05 e Å⁻³ levels: δ⁻ and δ⁺ isosurfaces are shown in blue and red, respectively. The blue isosurface in front of the S2 atom corresponds to a δ⁻ region in the plane bisecting the C1–S2–C2 angle perpendicularly at S2. Maps and relevant topological CPs of the function L(r) [L(r) = −∇²ρ(r)] for (c) IDT and (d) SePA: CC sites correspond to (3,−3) CPs (yellow) for Se, I and O atoms, and to the (3,−1) CP (green) for S atoms; CD sites correspond to the (3,−1) CP (green) for the Se atom, and to the (3,+1) CPs (pink) for S and Se atoms. All the represented CPs are close to interaction planes. Bond paths (dotted lines) and BCPs (small green circles) associated with the synthon are shown in (c) and (d) and drawn with the AIMAll software (Keith, 2019).
the series O < S < Se < Te (Brezgunova et al., 2013), a $δ^−$ region is more likely to be observed with a banana shape in the $π$ plane for O and S atoms, while a $δ^+$ region is instead seen with a banana shape in the $σ$ plane from the contributions of the $σ$ holes roughly along the C—Ch directions for Se and Te atoms. The former scenario corresponds to S₁ in IDT, whereas the polarization of the electron distribution towards one lone pair in S₂ leads to the splitting of the $δ^−$ banana-shape distribution, permitting the emergence of a $δ^+$ region [see Fig. 1(b) and insets]. In the plane of the $R_2^2(4)$ motif [Fig. 6(a)], the S₂···S₁ ChB interaction ($δ^−···δ^+$) involves a depleted region $δ^+$ of S1 roughly along the C1—S1 bond (close to the S1—C3 BCP) and a small $δ^−$ concentration region for S2 (resulting after splitting) close to the intersection of the $σ$ and $π$ planes (in the vicinity of the $δ^−$ banana-shape distribution). In SePA, the Se atom also exhibits a banana-shape distribution in the $π$ plane [Fig. 6(b)], but due to the increased separation of the lone pairs with respect to S atoms, a small $δ^+$ region appears in the $σ$ plane, relatively close to the $δ^−$ distribution in the $π$ plane.

In order to clarify these observations, the interactions that are focused on have been further characterized using the topological CPs of the function $L(r)$ [Figs. 6(c) and 6(d)]. In the valence shells of atoms, (3,−3) CPs lying outside covalent bonds indicate 3D CC sites and are associated with lone pairs, whereas (3,+1) CPs are mostly found on (or close to) intermolecular interaction planes (along the C—X bonding directions for halogen atoms, and in the $σ$ plane roughly along the C—Ch$_{sp^3}$ bonding directions for chalcogen atoms). The (3,+1) CPs are typically associated with CD sites, because the function $L(r)$ is depleted along two main directions on surfaces where (3,−3) CPs remain. On the other hand, topological CPs of the (3,−1) type indicate that the function $L(r)$ is depleted along only one main direction that links two (3,−3) CPs, also as a consequence of the continuity of the function in space. Accordingly, close to the $π$ plane of Ch$_{sp^3}$ atoms, a (3,−1) CP is exhibited between two (3,−3) CPs that correspond to the CC sites of the lone pairs. Note that the separation between the two (3,−3) CPs and the sign of the function $L(r)$ in the region of the (3,−1) CP are irrelevant for the topological emergence of this CP. Therefore, (3,−1) CPs can show as either weak CC or weak CD sites because this feature only depends on the separation of the (3,−3) CPs, which are associated with the relative position of the lone pairs and therefore to the contribution of a small region of either $δ^−$ or the $δ^+$ character in the vicinity of the intersection of the $σ$ and $π$ planes. Hence, the (3,−1) CP of the S2 atom in Fig. 6(c) represents a CC site, whereas in the case of the Se1 atom in Fig. 6(d), it represents a CD site. Accordingly, in both crystal structures, the synthon shows facing CD···CC interactions, while aligning the corresponding electrophilic···nucleophilic interactions with internuclear directions, and are observed close to bond paths. Indeed, the angle between the directions $α(\text{CD}_1···\text{CC}_2; \text{at}_1···\text{at}_2)$ is small (10.1, 8.7, 11.7 and 17.3° for S···S, S···I, Se···O and Se···Se, respectively), as previously observed in another crystal structure involving ChB interactions (Shukla et al., 2020). Note that, while a high similarity is observed

between the positions of CC and CD sites within the same motif found in SePA and IDT, due to the extended $δ^+$ region around the Se atom in the molecular $σ$ plane a further (3,+1) CP is also observed on the other side of the bond path [upper position in Fig. 6(d)]. This CP remains roughly along the same C—Se direction and belongs to the same $σ$-hole region, with $α = 15.0°$. Accordingly, the CC site seems to interact simultaneously with two CD sites of the same Se atom, with $α = 17.3$ and 15°. This simultaneous interaction of one CC site with two CD sites observed on either side of the same bond path is perhaps at the origin of slightly higher $α$ values than those typically observed with all the other interactions found in this work (<15°), as a consequence of the accommodation of two CD···CC interactions. Altogether, the reported results support the assumption that the relative orientation of atoms involved in intermolecular interactions, and therefore the supramolecular motifs they form, are driven by the local electrophilic and nucleophilic regions found in the valence shells of atoms, which are governed by specific CD and CC sites determined by the topological CPs of the function $L(r)$.

### 4.2.3. CSD search on $R_2^2(4)$ supramolecular motifs

Fig. 7 shows the geometrical parameters and criteria used for the CSD search. Results indicate that the $R_2^2(4)$ supramolecular motif is primarily present with the sulfur atom in the Ch₁ and Ch₂ positions (Ch₁ = S₁ and Ch₂ = S₂) with either a halogen atom (X = F/Cl/Br/I) (219 unique motifs) [Figs. 7(a) and 7(c)] or a chalcogen atom (Ch₃ = O/S/Se) (513 unique motifs) [Figs. 7(b) and 7(d)]. Focusing on the S₁···S₂ interaction with X in the $R_2^2(4)$ motif [Fig. 8(a)], 57 hits present $φ_1 = φ_2$ and $ζ_1 = ζ_2$. These motifs are chalcogen···chalcogen contacts similar to those previously reported as halogen···halogen type-I contacts (Desiraju & Parthasarathy, 1989). These motifs (set 1) are all located exactly at the origin of the $φ_1 - φ_2$ versus $ζ_1 - ζ_2$ plot (represented in black). In addition, 54 motifs (set 2) with $-20° < φ_1 - φ_2 < 20°$ and $-10° < ζ_1 - ζ_2 < 10°$ (represented in red) can be also considered as type-I contacts, because they show both similar directionality ($ζ_1 \simeq ζ_2$) and relative situation of the S₁ and S₂ atoms with respect to the $σ_1$ and $σ_2$ planes ($φ_1 \simeq φ_2$). A further 31 motifs (set 3) show both $φ_1$ and $φ_2 < 320°$ (represented in light blue). The significant difference of $φ_1$ and $φ_2$ with respect to 360° implies that neither S₂ nor S₁ is close to the $σ$ plane of the other S atom, indicating that their $δ^+$ regions are not involved in their contacts and therefore suggesting that a primarily molecular stacking builds the motifs. The remaining 77 motifs show typical behaviour for chalcogen bonds involving electrophilic and nucleophilic regions in the interaction ($δ^+···δ^−$). In 31 of these motifs (set 4), $φ_1 > φ_2$ ($φ_1 - φ_2 > 0$) and $ζ_1 > ζ_2$ ($ζ_1 - ζ_2 > 0$) (represented in green) are observed. A positive magnitude of $φ_1 - φ_2$ implies that S₂ is in the $σ_1$ plane of S₁, while a positive magnitude of $ζ_1 - ζ_2$ implies that S₁ is participating via a $δ^+$ site, therefore indicating an $S_1^{δ^+}···S_2^{δ^-}$ interaction. For 27 motifs (set 5), both $φ_1 - φ_2$ and $ζ_1 - ζ_2$ are negative (represented in dark blue) and they correspond to $S_1^{δ^-}···S_2^{δ^+}$
<figure><img src="image_13.png" /><figcaption>Figure 7</figcaption></figure>

$R_2^2(4)$ (4) supramolecular motifs used for the CSD search: $Ch_1/Ch_2 = S/Se/Te$, $X = F/Cl/Br/I$, $Ch_3 = O/S/Se$ (no fragments were found with $Ch_3 = Te$). Geometrical criteria used in the search for motifs: distances $d = Ch_1 \cdots Ch_2/Ch_2 \cdots X/Ch_2 \cdots Ch_3 \le \text{sum (vdW)} + 0.4 Å$, structural angles $\angle C-Ch_1 \cdots Ch_2/\angle C-Ch_2 \cdots X/\angle C-X \cdots Ch_2/\angle C-Ch_2 \cdots Ch_3/\angle C=Ch_3 \cdots Ch_2$ within the range 60–180°. For $C_{1A/1B}-Ch_1 \cdots Ch_2-C_{2A/2B}$ interactions: $\zeta_{1A/1B} = \angle C_{1A/1B}-Ch_1 \cdots Ch_2$ and $\zeta_{2A/2B} = \angle C_{2A/2B}-Ch_2 \cdots Ch_1$. For $C_{2A/2B}-Ch_2 \cdots X/Ch_3-C_{1B}$ interactions: $\zeta_{1A/1B} = \angle C_{2A/2B}-Ch_2 \cdots X$ and $\zeta_2 = \angle C_{1B}-X/Ch_3 \cdots Ch_2$. Note that, in addition to $Ch_1 \cdots Ch_2$ interactions, the nomenclature $\zeta_{1A/1B}$ and $\zeta_{2A/2B}$ also requires $Ch_2 \cdots X$ interactions to be consistent with that of Table 1. X-atom vdW radii = 1.47, 1.75, 1.85 and 1.98 Å for F, Cl, Br and I, respectively. Ch-atom vdW radii = 1.52, 1.80 and 1.90 Å for O, S and Se, respectively.

interactions by invoking similar reasons. In the remaining 19 motifs (set 6), $\phi_1 - \phi_2 < 0$ and $\zeta_1 - \zeta_2 > 0$ (represented in orange). Here, while the positive $\zeta_1 - \zeta_2$ value means that $S_1$ is participating in the interaction with a $\delta^+$ region, a negative $\phi_1 - \phi_2$ value implies that $S_1$ is in the $\sigma_2$ plane of $S_2$. This is the case for IDT ($\phi_1 - \phi_2 < -3.3°$ and $\zeta_1 - \zeta_2 > 26.0°$, Table 1), which corresponds to a ChB situation where $S_2$ is participating with a $\delta^-$ region roughly located in the vicinity of its $\sigma_2$ plane, along the direction bisecting the $C_{1A}-S_2-C_{1B}$ angle, and influenced by the contribution of one lone pair that is polarized in this region.

In order to extend the scope of our analysis, we also performed a detailed CSD search for motifs represented in Figs. 7(b) and 7(d), with $Ch_1 = Ch_2 = S$ and $Ch_3 = O/S/Se$ [Fig. 9(a)]. The search resulted in 513 unique motifs that were analysed similarly to Fig. 8(a). In terms of the previously defined subsets of data, the analysis shows the presence of 130 motifs belonging to set 1 (black data, all of them placed at the origin of the graph), 104 to set 2 (red data), 69 to set 3 (light blue data), 91 to set 4 (green data), 87 to set 5 (dark blue data) and 32 to set 6 (orange data), leading to a data distribution which is very similar to that depicted in Fig. 8(a). Also, as in Fig. 8(a), sets 4–6 in Fig. 9(a) represent the motifs formed with

$Ch_1 \cdots Ch_2$ ChB interactions, while sets 1–3 concern type-I and stacking contacts. Note that searching with $Ch_1/Ch_2 = S/Se/Te$ (excluding $Ch_1 = Ch_2 = S$) and either $X = F/Cl/Br/I$ or $Ch_3 = O/S/Se/Te$ resulted in very few hits (only 43 and 8 unique motifs, respectively) and hence no in-depth analysis was performed for this dataset, as it was too small.

Overall, the observations made here with respect to S··S ChB interactions and contacts are supported by the geometrical parameters $\phi_1 - \phi_2$ and $\zeta_1 - \zeta_2$ (Fig. 8). Hence, while sets 1 to 3 correspond to S··S contacts of type I (roughly $|\phi_1 - \phi_2| < 20°$ and $|\zeta_1 - \zeta_2| < 10°$, red data) and stacking geometries (mainly with $15° < |\phi_1 - \phi_2| < 60°$ and $|\zeta_1 - \zeta_2| > 30°$, light blue data, even if some data points can spread out of these limits), sets 4 and 5 are associated with ChB $\delta^+ \cdots \delta^-$ interactions (either both $\phi_1 - \phi_2$ and $\zeta_1 - \zeta_2$ are positive or negative, green or dark blue data). The particular S··S chalcogen contacts in set 6 ($\phi_1 - \phi_2 < 0$ and $\zeta_1 - \zeta_2 > 0$, orange data) correspond to $\delta_2^- \cdots \delta_1^+$ ChB interactions. However, they do not have counterpart $\delta_2^+ \cdots \delta_1^-$ ChB interactions in the region where $\phi_1 - \phi_2 > 0$ and $\zeta_1 - \zeta_2 < 0$ due to the presence of the $Ch_2 \cdots X$ contacts, which involve the corresponding electrophilic region of $Ch_2$ and the nucleophilic region of X in the $\delta_2^+ \cdots \delta_X^-$ ChB interaction, as observed in IDT.
<figure><img src="image_14.png" /><figcaption>Figure 8</figcaption></figure>

(a) Scatter plot of $\zeta_1 - \zeta_2$ versus $\phi_1 - \phi_2$ with $\text{Ch}_1 = \text{Ch}_2 = \text{S}$ and $X = \text{F/Cl/Br/I}$ [Figs. 7(a) and 7(c)]}, see text for colour code. Frequency plots of geometrical angles: (b) $\zeta_{1A/1B} = \angle \text{C}_{2\text{A}/2\text{B}} - \text{S}_2 \cdots X$ defined in Fig. 7(c) for the whole set of 219 motifs, (c) $\zeta_{1A/1B} = \angle \text{C}_{2\text{A}/2\text{B}} - \text{S}_2 \cdots X$ defined in Fig. 7(c) for the 77 motifs showing $\text{Ch}_1 \cdots \text{Ch}_2$ ChB interactions, (d) $\zeta_{2A} = \angle \text{C}_{1\text{B}} - X \cdots \text{S}_2$ ($X = \text{F/Cl/Br/I}$) defined in Fig. 7(c) with $X = \text{F}$ (yellow), $X = \text{Cl}$ (orange), $X = \text{Br}$ (red) and $X = \text{I}$ (purple).

The high similarity between Figs. 8(a) and 9(a) seems to indicate that the structural features involved in the $R_2^2(4)$ motifs that were analysed are equivalent when either halogen or chalcogen atoms are present at the analogous position ($X$ or $\text{Ch}_3$) in the $R_2^2(4)$ motif. Despite this significant trend, plotting the frequency of the $\text{C}_{2\text{A}}/\text{C}_{2\text{B}} - \text{S}_2 \cdots X$ [Fig. 8(b)] and $\text{C}_{2\text{A}}/\text{C}_{2\text{B}} - \text{S}_2 \cdots \text{Ch}_3$ [Fig. 9(b)] angles for all 219 and 513 motifs, respectively, observed for each dataset does not reveal any particular angular preference. However, selecting the 77 and 210 motifs that we consider to be ChB interactions within each dataset, a clear pattern appears in both frequency plots. Two peaks are found in the 90–100° and 160–170° regions for $R_2^2(4)$ motifs with $X$ [Fig. 8(c)] and two others appear in the 80–90° and 140–150° regions for $R_2^2(4)$ motifs with $\text{Ch}_3$ [Fig. 9(c)], which correspond to the expected angular geometries of $\text{C}_{2\text{B}} - \text{S}_2 \cdots X/\text{Ch}_3$ and $\text{C}_{2\text{A}} - \text{S}_2 \cdots X/\text{Ch}_3$, respectively, associated with the $\delta^+$ region of the S atom along the $\text{C}_{2\text{A}}-\text{S}_2$ direction. These peaks in frequency are similar to those previously reported for a CSD search on S/Se/Te···O ChB interactions (Brezgunova et al., 2013). Furthermore, a third lower-frequency peak appears in the ranges 120–130°/110–120° [Figs. 8(c) and 9(c)] for each dataset, which mainly corresponds to a $\delta^+$ region (smaller than the $\delta^+$ regions that are approximately along C–S bonding directions) placed in the $\sigma$ plane along the direction bisecting the $\text{C}_{2\text{A}}-\text{S}_2-\text{C}_{2\text{B}}$ angle

and making a ChB interaction with $X/\text{Ch}_3$. In this case, we have not, however, excluded the possibility of finding motifs where a $\delta^-$ region appears to be involved instead of a $\delta^+$ region, making a type-I interaction between S and $X/\text{Ch}_3$ atoms, even if this situation should be, in principle, less favourable for the stability of the motif. Figs. 8(d) and 9(d) show the frequency plots for the $\text{C}_{1\text{B}}-X/\text{Ch}_3 \cdots \text{S}_2$ angles [Figs. 7(c) and 7(d)], depicted separately for each X or $\text{Ch}_3$ atom type. They point the expected angular geometry at which the lone pairs of the $X/\text{Ch}_3$ atoms are involved in the interaction. Accordingly, while the peak of the frequency plot is observed at 80–90° for $X = \text{Cl}$, Br and I, and for $\text{Ch}_3 = \text{S}$ and Se, the peak shifts towards 110–120° for $X = \text{F}$ and to 100–110° for $\text{Ch}_3 = \text{O}$.

To conclude, the geometrical analysis above shows that the S···S ChB interaction in IDT belongs to set 6 of the CSD search results ($\phi_1 - \phi_2 < 0$ and $\zeta_1 - \zeta_2 > 0$), whereas the Se···Se ChB interaction in SePA belongs to set 1 ($\phi_1 - \phi_2 > 0$ and $\zeta_1 - \zeta_2 > 0$) (Table 1). Both occur simultaneously with a further ChB interaction, involving either a halogen or chalcogen atom as the acceptor. Overall, both ChB interactions build a supramolecular $R_2^2(4)$ motif, the geometry of which fits with the expected positions of the electrophilic and nucleophilic regions of the atoms in the interaction. Additionally, the electronic descriptors that characterize the electrophilic (CD)
<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /><figcaption>Figure 9</figcaption></figure>

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

(a) Scatter plot of ζ₁ − ζ₂ versus φ₁ − φ₂ with Ch₁ = Ch₂ = S and Ch₃ = O/S/Se [Figs. 7(b) and 7(d)] (no fragments were observed with Ch₃ = Te), see text for colour code. Frequency plots of geometrical angles: (b) ζ₁A/IB = ∠C₂A/₂B−S₂···Ch₃ defined in Fig. 7(d) for the whole set of 513 motifs, (c) ζ₁A/IB = ∠C₂A/₂B−S₂···Ch₃ defined in Fig. 7(d) for the 210 motifs showing Ch1···Ch2 ChB interactions, (d) ζ₂A = ∠C₁B−Ch₃···S₂ (Ch₃ = O/S/Se) defined in Fig. 7(d) with Ch₃ = O (yellow), Ch₃ = S (orange) and Ch₃ = Se (red) (no fragments were observed with Ch₃ = Te).

and nucleophilic (CC) sites in the valence shells of the atoms
are observed in a CD···CC interaction within the supramo-
lecular R<sup>2</sup><sub>2</sub>(4) motif, facing each other closely along the inter-
nuclear directions. These trends suggest that the formation
and the geometry of the synthon in the crystal structures of
IDT and SePA are exhibited regardless of the molecule and
are highly dependent on the appropriate orientation of CC
and CD sites present in the motif. Hence, with the aim of
extending this investigation, hereafter we analyse other
supramolecular motifs involving different intermolecular and
non-covalent intramolecular interactions.

4.3. Other synths and motifs

4.3.1. Triangular $X_3$ synths [$R_3^3(3)$ motifs]

Previous studies on the crystal structures of the halogenated
molecules hexachlorobenzene, C₆Cl₆ (HCB), hexabromo-
benzene, C₆Br₆ (HBB), pentachlorophenol, C₆Cl₅OH (PCP),
and pentabromophenol, C₆Br₅OH (PBP), have shown the
formation of triangular X₃ synths (Bui et al., 2009; Brez-
gunova et al., 2012; Aubert et al., 2011), which can be labelled
as R<sup>3</sup><sub>3</sub>(3) ring motifs following the new graph-set notation,
where each halogen atom simultaneously plays an amphoteric
role involving one electrophilic and one nucleophilic region in
the X₃ synthon. The bonding pattern in these motifs was
established to be driven by local electrostatic electro-

philic···nucleophilic (δ⁺···δ⁻) interactions. In terms of
geometry, the main difference between a standard single
halogen···halogen bond and a triangular XB interaction in
the X₃ synthon is the relative orientation of the electrophilic
(δ⁺) and nucleophilic (δ⁻) regions involved in the formation of
the halogen bonds. Thus, in a standard single halogen
···halogen bond, δ⁺ and δ⁻ sites are roughly orthogonal to
each other, resulting in an angular difference |Δξ| = |ξ₁ − ξ₂| ≈
90° [Fig. 10(a)]. On the other hand, in the case of X₃ synths,
the angular difference |Δξ| is significantly less and ideally close
to 60° in order to simultaneously accommodate three elec-
trophilic (δ⁺) and nucleophilic (δ⁻) regions [Fig. 10(b)].

Table 3 presents the geometrical parameters of the X···X
interactions within X₃ synths in C₆Cl₆, C₆Cl₅OH, C₆Br₆ and
C₆Br₅OH. The RR parameter ranges from 0.95 to 1.05, indi-
cating intermolecular distances between the interacting atoms
that are close to the sums of their vdW radii. In addition, the
magnitude of |Δζ|, which ranges from 47.9 to 59.1° in all but
two interactions in C₆Cl₅OH, further confirms the character-
istic XB interactions δ⁺···δ⁻ under investigation. The two
interactions that lie out of the expected |Δζ| range in C₆Cl₅OH
concern a specific molecular orientation, different to those
found in the other compounds, which is due to a particular
competition between XB and HB interactions.

All the reported X···X interactions in C₆Cl₆, C₆Cl₅OH, C₆Br₆ and C₆Br₅OH (see Fig. 11) were found to be of ‘pure’
<caption>**Table 3**</caption>

Halogen-bond geometries of X₃ synthons in C₆Cl₅ (HCB), C₆Cl₅OH (PCP), C₆Br₆ (HBB) and C₆Br₅OH (PBP).

α is the angle between the CD···CC and internuclear directions. Parameters with units: d (Å), angles (°), RR (dimensionless). vdW radii = 1.75 and 1.85 Å for Cl and Br atoms, respectively.

<table><thead><tr><th>Molecule</th><th>X(δ<sup>+</sup>),···(δ<sup>-</sup>)X<sup>†</sup></th><th>d</th><th>RR</th><th>ζ<sub>1</sub></th><th>ζ<sub>2</sub></th><th>|Δζ|</th><th>α</th></tr></thead><tbody><tr><td rowspan="3">C<sub>6</sub>Cl<sub>6</sub></td><td>Cl<sub>1</sub><sup>i</sup>,···Cl<sub>2</sub><sup>ii</sup></td><td>3.4466 (1)</td><td>0.98</td><td>175.0</td><td>116.7</td><td>58.3</td><td>7.6</td></tr><tr><td>Cl<sub>2</sub><sup>ii</sup>,···Cl<sub>3</sub><sup>iii</sup></td><td>3.4701 (1)</td><td>0.99</td><td>174.7</td><td>124.2</td><td>50.5</td><td>9.3</td></tr><tr><td>Cl<sub>3</sub><sup>iii</sup>,···Cl<sub>4</sub><sup>i</sup></td><td>3.6662 (1)</td><td>1.05</td><td>171.2</td><td>123.3</td><td>47.9</td><td>7.3</td></tr><tr><td rowspan="3">C<sub>6</sub>Cl<sub>5</sub>OH</td><td>Cl<sub>4</sub><sup>i</sup>,···Cl<sub>2</sub><sup>ii</sup></td><td>3.4095 (1)</td><td>0.97</td><td>175.1</td><td>78.3</td><td>96.8</td><td>13.5</td></tr><tr><td>Cl<sub>2</sub><sup>ii</sup>,···Cl<sub>3</sub><sup>iii</sup></td><td>3.6476 (2)</td><td>1.04</td><td>126.4</td><td>110.3</td><td>16.1</td><td>10.8</td></tr><tr><td>Cl<sub>3</sub><sup>iii</sup>,···Cl<sub>4</sub><sup>i</sup></td><td>3.6197 (2)</td><td>1.03</td><td>177.5</td><td>122.1</td><td>55.4</td><td>5.5</td></tr><tr><td rowspan="3">C<sub>6</sub>Br<sub>6</sub></td><td>Br<sub>1</sub><sup>i</sup>,···Br<sub>2</sub><sup>ii</sup></td><td>3.5412 (2)</td><td>0.96</td><td>174.2</td><td>115.1</td><td>59.1</td><td>12.2</td></tr><tr><td>Br<sub>2</sub><sup>ii</sup>,···Br<sub>3</sub><sup>iii</sup></td><td>3.5551 (4)</td><td>0.96</td><td>176.7</td><td>123.8</td><td>52.9</td><td>10.5</td></tr><tr><td>Br<sub>3</sub><sup>iii</sup>,···Br<sub>4</sub><sup>i</sup></td><td>3.7761 (2)</td><td>1.02</td><td>171.2</td><td>122.8</td><td>48.4</td><td>10.8</td></tr><tr><td rowspan="3">C<sub>6</sub>Br<sub>5</sub>OH</td><td>Br<sub>2</sub><sup>i</sup>,···Br<sub>3</sub><sup>iii</sup></td><td>3.5066 (2)</td><td>0.95</td><td>173.3</td><td>117.3</td><td>56.0</td><td>10.3</td></tr><tr><td>Br<sub>3</sub><sup>iii</sup>,···Br<sub>4</sub><sup>iii</sup></td><td>3.6576 (2)</td><td>0.99</td><td>173.0</td><td>122.6</td><td>50.4</td><td>9.0</td></tr><tr><td>Br<sub>4</sub><sup>iii</sup>,···Br<sub>2</sub><sup>i</sup></td><td>3.7127 (3)</td><td>1.00</td><td>175.7</td><td>120.7</td><td>55.0</td><td>11.7</td></tr></tbody></table>

closed-shell type, since they showed $|V|/G < 1$ at their corresponding BCPs (Brezgunova et al., 2012). The local properties of $ρ(r)$ at BCPs indicate that the Cl···Cl and Br···Br interactions are weak, as shown by the small magnitudes of $ρ$ and $∇²ρ$ (0.028 < $ρ$ < 0.058 e Å⁻³ and 0.38 < $∇²ρ$ < 0.62 e Å⁻⁵ for Cl···Cl contacts, and 0.042 < $ρ$ < 0.066 e Å⁻³ and 0.41 < $∇²ρ$ < 0.66 e Å⁻⁵ for Br···Br contacts, including both experimental and theoretical data). According to the local electronic properties at the BCPs, it was found that Br($δ^+$)···($δ^−$)Br interactions are more intense than Cl($δ^+$)···($δ^−$)Cl, owing to the larger electrophilic $δ^+$ character of the heavier Br atom, even if the nucleophilic $δ^−$ power of the lone pairs is smaller in the Br atom than for the lighter Cl atom.

The CSD search for homo-X₃ synthons ($X = Cl/Br/I$) resulted in 855 motifs and therefore in a total of 2565 X···X interactions (see the caption for Fig. 10 for the geometrical criteria). In Fig. 12, the peak in frequency observed for $|Δζ|$ in the 0–10° range mainly corresponds to type-I halogen···halogen contacts, regardless of the type of halogen atom involved [Figs. 12(d)–12(f)]. In addition, the frequency plot for $|Δζ|$ shows an extended maximum around 40–50° for $X =$

Cl (1887 Cl···Cl interactions) and a clearly defined maximum at 50–60° for $X = Br$ and $I$ (546 Br···Br and 132 $I···I$ interactions), as expected for XB interactions taking place in X₃ synthons (Fig. 10). On the other hand, the frequency distribution of the X···X distances shows a peak for each type of halogen atom, appearing at 3.5–3.8, 3.6–3.9 and 3.8–4.0 Å for $X = Cl$, Br and $I$, respectively [Figs. 12(a)–12(c)]. These correspond approximately to the ranges $1 < RR_{Cl} < 1.3$, $0.9 < RR_{Br} < 1.2$ and $0.8 < RR_{I} < 1$ (vdW radii = 1.75, 1.85 and 1.98 Å for $X = Cl$, Br and $I$, respectively), following the expected increase in interaction strength along the series Cl···Cl < Br···Br < $I···I$, which parallels the increasing polarizability Cl < Br < $I$ of the halogen atoms.

The characterization of the topological CPs of the function $L(r)$ shows that the CD···CC interactions are almost collinear with internuclear directions. Indeed, for the 12 X···X interactions found in the X₃ synthons ($X = Cl, Br$) of the four crystal structures, the ranges for the angle between the two directions $α(CD₁···CC₂; at₁···at₂)$ are 7.3–7.6, 10.5–12.2, 5.5–13.5 and 9.0–11.7° for HCB, HBB, PCP and PBP, respectively. This result further supports the fact that the relative orienta-

<figure><img src="image_19.png" /><figcaption>**Figure 10**</figcaption></figure>

Geometrical representation of X···X halogen bonds ($X = Cl/Br/I$) (a) for a single interaction ($ζ₁ ≃ 180°$, $ζ₂ ≃ 90°$) and (b) within a triangular X₃ synthon ($ζ₁ ≃ 180°$, $ζ₂ ≃ 120°$). (c) Ch···Ch chalcogen bonds (Ch = S/Se/Te) shown within a triangular Ch₃ synthon. $Δζ$ is expected at roughly 90 and 60° in (a) and (b), whereas in (c) it is difficult to estimate due to the presence of multiple $δ^+/δ^−$ sites in Ch₃p³ atoms [see Fig. 4(a)]. CSD searches for X₃ and Ch₃ synthons [R₃₃(3) motifs] involve the following criteria: distances X···X and Ch···Ch ≤ sum (vdW) + 0.4 Å, and angles $∠C-X···X$ and $∠C-Ch···Ch$ within the ranges 100–180° and 60–180°, respectively. X-atom vdW radii = 1.75, 1.85 and 1.98 Å for Cl, Br and $I$, respectively. Ch-atom vdW radii = 1.80, 1.90 and 2.06 Å for S, Se and Te, respectively.

<footnote>† Symmetry codes: C₆Cl₆: (i) x, y, z; (ii) 1/2 – x, 1/2 + y, 1/2 – z; (iii) –1/2 – x, –1/2 + y, 1/2 – z; (iv) –1 + x, 1 + y, z. C₆Cl₅OH: (i) x, y, z; (ii) x, 3 – y, –1/2 + z; (iii) –x, y, 1/2 – z; (iv) –x, 3 – y, –z. C₆Br₆: (i) x, y, z; (ii) 1.5 – x, 1/2 + y, 1/2 – z; (iii) –1/2 + x, 1/2 – y, 1/2 + z; (iv) 2 – x, 1 – y, –z. C₆Br₅OH: (i) x, y, z; (ii) 2 – x, 1/2 + y, 1 – z; (iii) 1 – x, 1/2 + y, 1 – z; (iv) –1 + x, 1 + y, z.</footnote>
<figure><img src="image_20.png" /><figcaption>Figure 11</figcaption></figure>

Maps and topological CPs of the function $L(\mathbf{r}) [=-\nabla^2 \rho(\mathbf{r})]$ for (a) HCB, (b) PCP, (c) HBB and (d) PBP. $L(\mathbf{r})$ plots are calculated in the planes defined by the positions of the three atoms involved in each synthon. CC and CD sites correspond to (3,−3) CPs (yellow) and (3,+1) CPs (pink) for all Cl and Br atoms. Intermolecular Cl···Cl and Br···Br contacts are shown with their bond paths (dotted lines) and the corresponding BCPs (small green circles) between the interacting atoms.

<figure><img src="image_21.png" /><figcaption>Figure 12</figcaption></figure>

Frequency distributions for X···X (X = Cl/Br/I) XB interactions within homo-X₃ synthons. For X = Cl, Br and I, the X···X distance and the |Δζ| angular orientation are represented in (a) and (d), (b) and (e), and (c) and (f), respectively. The motif shown in Fig. 10(b) was used for the CSD search with the geometrical parameters d(X···X) ≤ sum(vdW) + 0.4 Å and ζ₁ and ζ₂ angles within the range 100–180°. vdW radii = 1.75, 1.85 and 1.98 Å for Cl, Br and I atoms, respectively.
tion of atoms involved in intermolecular interactions, and therefore the supramolecular motifs they form, are driven by the local electrophilic···nucleophilic interactions between CD and CC sites, as previously observed in IDT, SePA and other crystal structures involving ChB interactions (Shukla *et al.*, 2020).

Triangular $R_3^3(3)$ motifs involving chalcogen atoms are also found in the literature. For instance, they appear in some of the crystal structures of the families of 3H-1,2-benzodithiole-3-one and 3H-1,2-benzodithiole-3-thione heterocycles, and their selenium analogs (Shukla *et al.*, 2020). In order to expand the investigation of $X_3$ synthons ($X = Cl, Br, I$) [Fig. 10(b)] to $Ch_3$ synthons [Fig. 10(c)], we also performed a detailed CSD search for $R_3^3(3)$ motifs involving $Ch = S, Se$ and $Te$ atoms in $sp^3$ hybridization (Fig. 13). The search resulted in 1071, 56 and

55 $R_3^3(3)$ motifs with $Ch = S, Se$ and $Te$ atoms, leading to 3213 $S···S, 168 Se···Se$ and 165 $Te···Te$ interactions, respectively. The maxima in the frequencies for $S···S, Se···Se$ and $Te···Te$ distances [Figs. 13(a)–13(c)] are seen at 3.8–4.0, 3.9–4.0 and 4.1–4.2 Å, corresponding to 1.06 < $RR_S$ < 1.11, 1.03 < $RR_{Se}$ < 1.05 and 1.00 < $RR_{Te}$ < 1.02 (vdW radii = 1.80, 1.90 and 2.06 Å for $Ch = S, Se$ and $Te$, respectively). The peak in frequency observed for $|Δξ|$ in the 0–10° range (for $Ch = S/Te$) corresponds mainly to type-I $Ch···Ch$ contacts [Figs. 13(d) and 13(f)]. Besides this peak, the $|Δξ|$ frequency plots show an extended maximum at 20–30° for $Ch = Se$, a small maximum at 30–40° for $Ch = S$ and a very well defined maximum at 60–70° for $Ch = Te$. The RR results are in line with those of $X_3$ synthons, whereas the frequency plots of $|Δξ|$ do not show peaks at high $|Δξ|$ angles for all $Ch$ atoms that could be

<figure><img src="image_22.png" /><figcaption>Figure 13</figcaption></figure>

Frequency distributions in $Ch···Ch$ ($Ch = S/Se/Te$) ChB interactions within homo-$Ch_3$ synthons. For $Ch = S, Se$ and $Te$, the $Ch···Ch$ distance and the $|Δξ|$ angular orientation are represented in (a) and (d), (b) and (e), and (c) and (f), respectively. The motif shown in Fig. 10(c) was used for the CSD search with the geometrical parameters $d$ ($Ch···Ch$) ≤ sum(vdW) + 0.4 Å and $ξ_1$ and $ξ_2$ angles within the range 60–180°. vdW radii = 1.80, 1.90 and 2.06 Å for S, Se and Te atoms, respectively.
<caption>**Table 4**</caption>

Structural parameters, topological and energetic properties at BCPs, and estimated interaction energies for $X^{δ+}...δ⁻Y$ ($X = H, I; Y = O, Cl$) interactions in the V-type motifs present in the crystal structures of IDT and PCP.

$α$ is the angle between the CD···CC and internuclear directions. Parameters with units: $d$ (Å), $RR$ (dimensionless), $ξ₁$ and $ξ₂$ (°), $α$ (°), and topological properties as in Table 2. For individual interactions, $-E_{int}$ (kJ mol⁻¹) is estimated as (left) -V/2 and (right) -0.556V - 2.697 [for XB interactions involving I atoms, see Bauzá & Frontera (2020)]. The interaction energies in IDT and PCP dimers have been calculated at the B3LYP-D3/Def2TZVPP level of theory: values (in kJ mol⁻¹) correspond to $-E_{int_system}/-E_{int_system_corrupted_BSSE}/-ΣV/2/-ΣE_{int}$ (Bauzá & Frontera, 2020). vdW radii = 1.20, 1.52, 1.75 and 1.98 Å for H, O, Cl and I atoms, respectively.

<table><thead><tr><th>Compound</th><th>X(δ<sup>+</sup>)···(δ<sup>-</sup>)Y</th><th>d</th><th>RR</th><th>ξ<sub>1</sub></th><th>ξ<sub>2</sub></th><th>ρ</th><th>∇<sup>2</sup>ρ</th><th>G</th><th>V</th><th>|V|/G</th><th>-E<sub>int</sub></th><th>α</th></tr></thead><tbody><tr><td rowspan="3">IDT</td><td>C2–H2···O1–C1</td><td>2.235</td><td>0.82</td><td>158.7</td><td>137.9</td><td>0.089</td><td>1.25</td><td>28.4</td><td>-22.6</td><td>0.80</td><td>11.3/-</td><td>8.5</td></tr><tr><td>C3–I1···O1–C1</td><td>2.9342 (3)</td><td>0.84</td><td>170.3</td><td>135.5</td><td>0.112</td><td>1.49</td><td>35.6</td><td>-30.6</td><td>0.86</td><td>15.3/14.3</td><td>1.8</td></tr><tr><td>Dimer† E<sub>int</sub></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>33.4/31.6/26.6</td><td></td></tr><tr><td rowspan="3">PCP</td><td>O1–H1···O1–C6</td><td>2.018</td><td>0.74</td><td>151.3</td><td>125.4</td><td>0.136</td><td>1.69</td><td>43.6</td><td>-41.2</td><td>0.95</td><td>20.6/-</td><td>6.5/15.7</td></tr><tr><td>O1–H1···Cl5–C5</td><td>2.943</td><td>1.00</td><td>114.7</td><td>89.3</td><td>0.038</td><td>0.51</td><td>10.8</td><td>-7.7</td><td>0.71</td><td>3.8</td><td>7.0</td></tr><tr><td>Dimer E<sub>int</sub></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>24.8/22.3/24.4</td><td></td></tr></tbody></table>

† For the calculation of the interaction energy of the motif, the IDT trimer is considered to be a dimer formed by the molecule involving an O atom in the V-type motif and the supramolecular rigid unit formed by the two assembled molecules that involve the I and H atoms in the V-type motif.

systematically associated to electrophilic···nucleophilic interactions, as in $X₃$ synthons. However, as discussed in Section 4.2.3 and due to the presence of multiple $δ⁺/δ⁻$ sites in $Ch_{sp}³$ atoms [Fig. 4(a)], the structural descriptors associated with $Ch^{δ+}...δ⁻$ Ch ChB interactions need to be handled with care. According to our previous analysis of $Ch···Ch$ contacts, $|Δξ| ≥ 50°$ mainly encompasses electrophilic···nucleophilic ($δ⁺...δ⁻$) ChB interactions, even if some type-I and stacking interactions can still be found in this particular region [Figs. 8(a) and 9(a)]. Hence, due to the very well defined frequency maxima occurring at $|Δξ| = 60–70°$, Te is found to be the most suitable amongst the chalcogens for forming $Ch₃$ synthons.

On the other hand, besides $X₃$ synthons and $Ch₃$ synthons, other triangular $R₃(3)$ motifs based on pnictogen-bonded cyclic trimers ($PH₂Y₃$) ($Y = F, Cl, OH, CN, NC, CH₃, H$ and $BH₂$) with $C₃h$ symmetry and bonding energies ranging from -17 to 63 kJ mol⁻¹ have also been described in the literature from theoretical calculations (Alkorta et al., 2013). However, they are beyond the scope of this study, which mainly focuses on ChB, XB and HB interactions, and will not be addressed here.

### 4.3.2. Bifurcated V-type motifs

The most common V-type atomic motifs are found in HB interactions H···Y ($Y = O, N$), bifurcated at either Y or H. They involve local $δ⁺...δ⁻$ interactions, where $δ⁺$ corresponds to a CD region along the extended bonding direction of H and $δ⁻$ corresponds to a lone-pair region of Y. Accordingly, several very common situations can appear: (i) the $δ⁺$ region of a single H atom interacts with $δ⁻$ regions of two Y atoms, (ii) a single $δ⁻$ region of one Y atom interacts with each $δ⁺$ region of two H atoms, and (iii) two $δ⁻$ regions of a single Y atom interact with $δ⁺$ regions of two H atoms. Hereafter we will see that V-type motifs can also be found with other type of atoms, as long as they contribute with appropriate $δ⁺$ or $δ⁻$ regions and have a convenient angular disposition in the $δ⁺...δ⁻$ interactions building the motif.

In the crystal structure of IDT, a bifurcated V-type motif involving HB (H···O) and XB (I···O) interactions has been identified [Figs. 2(a) and 14(a)]. Table 4 presents the structural parameter characteristics of this motif. Here, the O atom forms a bifurcated interaction with H and I atoms, showing almost equal $ξ₂$ angles ($∠C–O···H/I = 137.8/137.5°$) that are

<figure><img src="image_23.png" /><figcaption>**Figure 14**</figcaption></figure>

Maps and topological CPs of the function $L(r) = -∇²ρ(r)$ for (a) IDT and (b) PCP. CC sites correspond to (3,−3) CPs (yellow) for O and Cl atoms, CD sites correspond to either (3,+3) (violet) CPs for H atoms, or (3,−1) (dark green) CPs for H and I atoms. Intermolecular HB and XB interactions ($X^{δ+}...δ⁻O$, with $X = H, I$) are shown with their bond paths (dotted lines) and the corresponding BCPs (small light-green circles) between the interacting atoms. Planes are defined by the interacting atoms in (a) and by the CPs of $L(r)$ focused on in (b).
larger than those typically observed for the location of the oxygen lone pairs in sp² hybridization (~120°). This can be explained by the need to respond to the arrangement of two neighbouring molecules involved in the intermolecular interactions. On the other hand, as expected, the angle ζ₁ for C—I···O is closer to linear geometry (170.3°) than for C—H···O (158.6°). With respect to the RR parameter, the two interactions present very similar values (0.82 and 0.84).

Fig. 14(b) shows another bifurcated V-type motif involving O—H···O—C and O—H···Cl—C interactions, previously observed in the reported crystal structure of pentachlorophenol (C₆Cl₅OH, PCP) (Brezgunova et al., 2012). The O—H···O—C interaction is a short hydrogen bond (RR = 0.74), with structural angles of ζ₁ = 151.3° and ζ₂ = 125.4° indicating the expected electrophilic and nucleophilic regions close to the O—H bonding direction and around the oxygen lone pair in sp² hybridization. The O—H···Cl—C interaction exhibits a distance close to a vdW contact (RR = 0.99), with structural angles of ζ₁ = 114.7° and ζ₂ = 89.3°, suggesting that the δ⁺ region of the H atom is involved in a lateral interaction with the δ⁻ region of the Cl atom lone pair that is perpendicular to the C—Cl bonding direction (Table 4).

The bond paths and BCPs of the V-type motifs found in the trimer of IDT and in the dimer of PCP are depicted in Fig. 14, along with the relevant CC and CD sites found from the topological analysis of the function L(r). Structural data, electron properties at BCPs, estimated interaction energies and the angular descriptor α between the CC···CD and internuclear directions are presented in Table 4.

In both bifurcated V-motifs the interactions are of 'pure' closed-shell type (|V|/G < 1) (Table 4) (Espinosa et al., 2002). In IDT, the topological (ρ, ∇²ρ) and local energetic properties (G, V, |V|/G) at BCPs are larger for O···I than for O···H, indicating a stronger interaction in the former. In addition, from the estimated energetic contributions to the dimer interaction energy (Eᵢₘₜ), the O···I bonding is more energetic than O···H. On the other hand, in PCP, the magnitudes of ρ, ∇²ρ, G, V and |V|/G are significantly larger for H···O than for H···Cl (Table 4), in particular when looking at their estimated energy contributions to the interaction energy of the dimer (Eᵢₘₜ). As in the previous sections dealing with R²₃(4) and R³₃(3) motifs, the characterization of the topological CPs of the function L(r) in the V-type motifs shows local electrophilic···nucleophilic interactions (CD···CC) that are remarkably well aligned with internuclear directions. Indeed, α < 10° for the four interactions in the V-type motifs. A second value of α is also given for the H···O interaction in PCP to emphasize that the π plane containing both lone pairs is in fact directed towards H (the second α value corresponds to the second CC site of O). It is also noticeable that, despite the very weak H···Cl interaction (pointed out by all the topological properties at the BCP), the angle α is lower than 10°. This result seems to indicate that directionality is not necessarily linked to a significant interaction energy. A similar finding is observed, for instance, in X₃ synthons. In the I···O interaction of IDT, a (3,+1) CP of L(r) is also plotted in Fig. 14(a), which is found further inside the electron shell than the (3,−1) CP

associated with the CD site of I. The two CPs are connected by a gradient line of L(r) that indicates the direction of electrophilicity of the atom, while the angle α is very similar for both of them. Their joint representation aims to show that, in cases of heavier atoms such as I, the CD site is better described by a (3,−1) CP of L(r) in a region of large depletion of electron density rather than the usual (3,+1) CP, which is found in a region of significant electron concentration [∇²ρ(r) < 0].

### 4.3.3. Intramolecular interactions

The results of CSD searches for intramolecular HBs and ChB interactions are shown in Fig. 15. Differing from the former notation of Etter (1990), where the graph-set notation S(n) denotes an intramolecular HB pattern of n members and subscript d and superscript a do not appear because they equal 1 in all cases, in the new graph-set notation involving CC and CD sites, it is of interest to keep both the subscript e and superscript n to describe the number of electrophilic and nucleophilic sites in the interaction, as shown later.

The most common non-covalent intramolecular interactions concern H···O hydrogen bonds, forming S¹₁(6) motifs. S¹₁(5) motifs involving H···O hydrogen bonds are also observed, but are in less number. Supporting this observation, a CSD search for these motifs gave rise to 3596 S¹₁(5) and 9793 S¹₁(6) hits. On the other hand, a similar search involving H···Br hydrogen bonds resulted in 295 S¹₁(5) and 10 S¹₁(6) hits. Based on the total number of hits, these results indicate that O is more commonly observed as a hydrogen-bond acceptor than Br for either the S¹₁(5) or the S¹₁(6) motif. In the case of Br, the larger number of hits involving S¹₁(5) motifs [with respect to S¹₁(6) motifs] may indicate that larger atoms accommodate better with the geometry of five-membered rings than smaller atoms, such as O, for which the intramolecular non-covalent interaction appears to be favoured within a six-membered ring geometry, as shown by the number of hits for S¹₁(6) and S¹₁(5) motifs involving H···O contacts. A similar feature is observed in intramolecular chalcogen bonding, where larger donor atoms (such as Ch = S, Se with rᵢₗW = 1.80, 1.90 Å, respectively) favour the observation of a greater number of five-membered rings with respect to six-membered rings. Indeed, the search for intramolecular Ch···O chalcogen bonds resulted in 1501 and 183 hits for S¹₁(5) and S¹₁(6) motifs, respectively, with Ch = S, whereas the search resulted in 152 and 5 hits for S¹₁(5) and S¹₁(6) motifs with Ch = Se. Hence, with S, Se and Br atoms, the number of S¹₁(6) motifs are only 12, 3 and 3% of the number of observed S¹₁(5) motifs with the same type of atoms, respectively, whereas the opposite is observed for O atoms where the number of S¹₁(5) motifs are 37% of the number of S¹₁(6) motifs.

Fig. 16 shows the frequency distribution of the ζ₁ and ζ₂ angles defined in Fig. 15 for H···O and H···Br HB interactions forming S¹₁(5) and S¹₁(6) motifs. For both types of hydrogen bonds, the frequency peaks shift towards larger angles from S¹₁(5) (ζ₁ = 100–110° and ζ₂ = 80–90° for H···O, and 110–120° and ζ₂ = 60–70° for H···Br) to S¹₁(6) motifs (ζ₁ = 140–150° and ζ₂ = 100–110° for H···O, and ζ₁ = 130–140° and
<caption>**Table 5**</caption>

Structural parameters, topological and energetic properties at BCPs, and estimated interaction energies for intramolecular interactions $X(\delta^+) \cdots (\delta^-)Y(X = H, C, Se, Br; Y = O, C, Br)$ in PBP, GOHJAQ and AHEQIN.

$\alpha$ is the angle between the CD···CC and internuclear directions. Parameters with units: $d$ (Å), $\zeta_1$ (°), $\zeta_2$ (°), $\alpha$ (°), topological properties as in Table 2. Interaction energies $-E_{int}$ (kJ mol⁻¹) are estimated as in Tables 2 and 4.

<table><thead><tr><th>Compound</th><th>X(δ<sup>+</sup>)···(δ<sup>-</sup>)Y</th><th>d</th><th>RR</th><th>ζ<sub>1</sub></th><th>ζ<sub>2</sub></th><th>ρ</th><th>∇<sup>2</sup>ρ</th><th>G</th><th>V</th><th>|V|/G</th><th>-E<sub>int</sub></th><th>α</th></tr></thead><tbody><tr><td>PBP</td><td>O···H···Br···C</td><td>2.156</td><td>0.71</td><td>146.1</td><td>62.9</td><td>0.235</td><td>1.70</td><td>58.2</td><td>-70.1</td><td>1.20</td><td>35.1/-</td><td>15.0</td></tr><tr><td rowspan="2">AHEQIN</td><td>C···Se···O···C</td><td>2.561</td><td>0.75</td><td>170.3/76.6</td><td>103.0</td><td>0.212</td><td>2.35</td><td>64.9</td><td>-65.7</td><td>1.01</td><td>32.9/27.0</td><td>3.1</td></tr><tr><td>C···H···C(π)···N</td><td>2.354</td><td>0.81</td><td>110.7</td><td>90.3</td><td>0.101</td><td>1.22</td><td>28.9</td><td>-24.6</td><td>0.85</td><td>12.3/-</td><td>13.8</td></tr><tr><td rowspan="2">GOHJAQ</td><td>C···Br···O···C</td><td>2.909</td><td>0.86</td><td>174.5</td><td>115.7</td><td>0.101</td><td>1.38</td><td>31.9</td><td>-26.4</td><td>0.83</td><td>13.2/12.0</td><td>5.1</td></tr><tr><td>C···C(π)···Br···C</td><td>3.516</td><td>0.99</td><td>98.4</td><td>134.1</td><td>0.040</td><td>0.46</td><td>10.1</td><td>-7.6</td><td>0.76</td><td>3.8/-</td><td>12.9</td></tr></tbody></table>

$\zeta_2 = 70–80°$ for H···Br). A similar result is observed for the corresponding frequency distribution of the $\zeta_{1A/1B}$ and $\zeta_2$ angles defined in Fig. 15 for S···O and Se···O ChB interactions (Fig. 17). Indeed, they shift to larger angles from $S_1^1(5)$ (for S···O: $\zeta_{1A} = 160–170°$, $\zeta_{1B} = 70–80°$ and $\zeta_2 = 90–100°$; for Se···O: $\zeta_{1A} = 160–180°$, $\zeta_{1B} = 70–80°$ and $\zeta_2 = 90–110°$) to $S_1^1(6)$ motifs (for S···O: $\zeta_{1A} = 170–180°$, $\zeta_{1B} = 80–90°$ and $\zeta_2 = 110–120°$; for Se···O: $\zeta_{1A} = 170–180°$, $\zeta_{1B} = 80–90°$ and $\zeta_2 = 90–100°$), even if the very few cases of $S_1^1(6)$ motifs with Se···O interactions cannot be considered statistically significant. While the $\zeta_{1A}$ angle of ~180° in both S···O and Se···O interactions mostly seems to indicate that the electrophilic region along the C—Ch bond [in both $S_1^1(5)$ and $S_1^1(6)$ motifs] is responsible for the chalcogen bond, the electrophilic region along the O—H bonding direction is clearly better oriented in $S_1^1(6)$ motifs ($\zeta_1 = 140–150°$) than in $S_1^1(5)$ motifs ($\zeta_1 = 100–110°$), in line with the previous observation that showed a larger number of hits with the former motif. Additionally, in both $S_1^1(5)$ and $S_1^1(6)$ motifs involving either HB or ChB interactions, the $\zeta_2$ angle approximately corresponds to the expected position of a lone pair of the acceptor atom (O or Br) in its particular hybridization.

The crystal structure of PBP (Brezgunova et al., 2012) exhibits an intramolecular H···Br HB interaction [Fig. 18(a)]. As presented in Table 5, the interaction shows a significantly low reduction ratio parameter $RR = 0.75$, while the associated structural angles $\zeta_1$ and $\zeta_2$ (146.1 and 62.9°) indicate an HB interaction with an O—H$^{δ+}$ electrophilic region well oriented towards the nucleophilic region of the Br lone pair, forming an $S_1^1(5)$ motif [Figs. 16(c) and 16(g)]. In line with the large $\zeta_1$ angle, the short HB distance and the small $RR$ value, the H···Br interaction exhibits an incipient degree of covalence $|V|/G >1$ with a significant electron density magnitude at the BCP ($\rho = 0.232 e Å^{-3}$).

For comparison with other intramolecular HB patterns, we have also performed topological analysis on intramolecular chalcogen and hydrogen bonding [Fig. 18(b)], and halogen and tetrel bonding [Fig. 18(c)]. Thus, two $S_1^1(5)$ motifs sharing a C—Se moiety (CSD code AHEQIN; Jones et al., 2002) and a pair of $S_1^1(11)$ and $S_1^1(9)$ motifs intersecting on a secondary $S_2^2(4)$ motif (GOHJAQ, Widner et al., 2014) were studied. Note that all of them are found in the molecular planes. The scheme below shows the expected positions of the electrophilic and nucleophilic regions building the two $S_1^1(5)$ motifs in

<figure><img src="image_24.png" /><figcaption>**Figure 15**</figcaption></figure>

CSD searches performed for non-covalent intramolecular interactions involving (a) H···O hydrogen bonds belonging to $S_1^1(5)$ motifs, (b) H···O hydrogen bonds belonging to $S_1^1(6)$ motifs, (c) H···Br hydrogen bonds belonging to $S_1^1(5)$ motifs, (d) H···Br hydrogen bonds belonging to $S_1^1(6)$ motifs, (e) Ch···O chalcogen bonds (Ch = S, Se) belonging to $S_1^1(5)$ motifs with $X$ = any atom, and (f) Ch···O chalcogen bonds (Ch = S, Se) belonging to $S_1^1(6)$ motifs with $X$ = any atom. Dashed lines crossing the bonds represent bonds of any type (single, double, aromatic etc.). Geometric criteria used for the CSD search were: distances H···O/H···Br/Ch···O ≤ sum(vdW radii), angles $\zeta_1 = \angle O-H···O/\angle O-H···Br$, $\zeta_2 = \angle C=O···H/\angle C=O···Br/\angle C=O···Ch$, $\zeta_{1A} = \angle X-\text{Ch}···O$ and $\zeta_{1B} = \angle C-\text{Ch}···O$ ranging from 60 to 180° (vdW radii = 1.20, 1.52, 1.80, 1.90 and 1.85 Å for H, O, S, Se and Br atoms, respectively).
AHEQIN, and the $S_1^1(11)$ and $S_1^1(9)$ motifs [intersecting on a secondary $S_2^2(4)$ motif] in GOHJAQ, as discussed below. From the structural parameters (Table 5), the significantly low RR values demonstrate that these intramolecular interactions are very short (except for the tetrel bond, TrB), while the $\zeta_1$ and $\zeta_2$

angles further confirm the expected geometry of the electrophilic···nucleophilic interaction involved in the intramolecular chalcogen and halogen bonding under investigation. In Fig. 18(c), the V-type bifurcated interaction at the amphoteric halogen atom involves its electrophilic σ-hole region along the

<figure><img src="image_25.png" /><figcaption>Figure 16</figcaption></figure>

$\zeta_1$ frequency distribution for HB interactions: (a) $S_1^1(5)$ H···O, (b) $S_1^1(6)$ H···O, (c) $S_1^1(5)$ H···Br and (d) $S_1^1(6)$ H···Br. $\zeta_2$ frequency distribution for HB interactions: (e) $S_1^1(5)$ H···O, (f) $S_1^1(6)$ H···O, (g) $S_1^1(5)$ H···Br and (h) $S_1^1(6)$ H···Br.
C–Br bonding direction in a halogen bond (C–Br$^{δ+}...δ−}$O) and its nucleophilic lone-pair region in the tetrel bond (C–C$^{δ+}...δ−}$Br), leading to an S<sub>2</sub><sup>2</sup>(4) motif. The existence of these non-covalent intramolecular interactions is established by the

presence of bond paths and the concomitant BCPs (Fig. 18). In AHEQIN and GOHJAQ, the three intramolecular XB, HB and TrB interactions are of ‘pure’ closed-shell type (|V|/G < 1), whereas the ChB interaction shows an incipient degree of

<figure><img src="image_26.png" /><figcaption>Figure 17</figcaption></figure>

$\zeta_{1A/1B}$ frequency distribution for ChB interactions: (a) $S_1^-(5)$ S...O, (b) $S_1^-(6)$ S...O, (c) $S_1^-(5)$ Se...O and (d) $S_1^-(6)$ Se...O interactions. $\zeta_2$ frequency distribution for ChB interactions: (e) $S_1^-(5)$ S...O, (f) $S_1^-(6)$ S...O, (g) $S_1^-(5)$ Se...O and (h) $S_1^-(6)$ Se...O.
<figure><img src="image_27.png" /><figcaption>Figure 18</figcaption></figure>

Maps and topological CPs of the function $L(r)$ [= −∇²ρ(r)] for (a) H···Br in PBP, (b) Se···O and H···C in AHEQIN and (c) Br···O and C···Br in GOHJAQ. CC sites correspond to (3,−3) CPs (yellow) for O and Br atoms and to (3,−1) CPs (dark green) for the C atom; CD sites correspond to (3,+1) (pink) and (3,−1) CPs (dark green) for H atoms, (3,+1) CPs (pink) for the C atom, (3,−1) CPs (dark green) for the Se atom and (3,+1) CPs (pink) for the Br atom. Intramolecular HB, ChB, XB and TrB interactions [$X(δ⁺)···(δ⁻)Y$ with X = H, Se, Br; Y = O, Br] are shown with their bond paths (dotted lines) and their corresponding BCPs (small light-green circles) between the interacting atoms.

covalence (|V|/G > 1). The topological parameters at the BCP of the Se···O chalcogen bond in AHEQIN are roughly similar to those calculated for the H···Br hydrogen bond in PBP, suggesting similar strength. In comparison, the intramolecular XB (Br···O) and TrB (C···Br) interactions in GOHJAQ are observed to be significantly weaker (Table 5).

<figure><img src="image_28.png" /></figure>

As previously pointed out, the assignment of CC and CD sites to specific CPs of the function $L(r)$ should be taken with care. Hence, in addition to the CPs that are associated with CC and CD sites, surrounding CPs are plotted in Fig. 18 for discussion. Nucleophilic sites are clearly identified by the (3,−3) CPs that are associated with the atomic lone pairs of Br and O atoms, whereas in $\pi$ systems they appear as (3,−1) CPs, such as in the H···C interaction of AHEQIN. On the other hand, $\pi$ systems also develop electrophilic sites that are described by (3,+1) CPs, such as in the C···Br interaction of GOHJAQ. Because of the development of (3,−1) and (3,+1) CPs in $\pi$ systems, the local electrostatic complementarity of electrophilic···nucleophilic interactions also takes place in $\pi$-$\pi$ interactions and drives the mutual arrangement of these systems. This trend, being beyond the scope of this work, has not been investigated in depth here and will be addressed in future research. The electrophilic site of an H atom is typically described by a (3,+3) CP that appears along the X−H bond direction. Concomitantly, it is very common to find two (3,+1) CPs, one on each side of this (3,+3) CP, such as in AHEQIN. These (3,+1) CPs are typically involved in lateral HB interactions, as observed in the H···C interaction of this compound and in the orientation of the (3,+1)···(3,−3) CPs with the internuclear direction H···O of GOHJAQ. In the case of PBP, and due to the strong H···Br interaction that pulls the O−H group toward the intramolecular region, the electron distribution around the H atom follows the effect of the

surrounding atoms, leading to the coalescence of the (3,+3) and (3,+1) CPs, which disappear while the observed (3,−1) CP emerges in the interaction with the (3,−3) CP of the Br atom. The $\sigma$-hole interaction of Se with the lone pair of O in AHEQIN involves a (3,−1) CP that behaves as a CD site because the lone pairs of the Se atom are sufficently separated, as explained in previous sections. This feature permits the development of an extended $\sigma$ plane of electrophilic character in front of the O atom where, in addition to the (3,−1) CP, we also found two (3,+1) CPs, one on each side of the former, as observed in SePA and other chalcogenated molecules (Shukla et al., 2020). In GOHJAQ, the $\sigma$ hole of Br shows an electrophilic region more directed toward the lone pair of the O atom. The corresponding CD site is assigned to a (3,+1) CP because the (3,−1) CP found for the heavier I atom in IDT does not appear here for Br.

The topological CPs of the function $L(r)$ in the intramolecular motifs analysed again show that CD···CC interactions are almost collinear with internuclear directions ($\alpha$ ≤ 15° for all of them, see Table 5). Note that, in addition to the observations made for intermolecular motifs and synths, they also indicate that local electrophilic···nucleophilic interactions between CD and CC sites facing each other drive the atomic orientation in intramolecular motifs.

## 5. Conclusions

It is quite difficult to predict the geometrical preferences of intermolecular interactions involving chalcogen atoms because the position of their electrophilic ($\delta^+$) and nucleophilic ($\delta^−$) regions can appear enlarged and/or shifted depending on the chalcogen atom type and on its atomic environment. Indeed, in addition to a $\sigma$-hole region that can be found enlarged in the $\sigma$ plane (encompassing a wider range of contact angles than, for instance, in XB interactions, and therefore blurring the expected directionality of the ChB interactions along bonding directions), the relative position of its lone pairs in the $\pi$ plane can lead to either a $\delta^+$ or a $\delta^−$ region close to the intersection of the $\pi$ and $\sigma$ planes. The structural angles are very useful for characterizing the geometrical particulars of their intermolecular contacts and therefore for analysing electronic interactions involving chal-
cogen atoms in sp³ hybridization. To this end, the geometrical descriptors $Δζ = ζ₁ − ζ₂$ and $Δφ = φ₁ − φ₂$ defined in this work and based on (i) the intermolecular contact angles $ζᵢ = max(ζᵢA, ζᵢB)$, (ii) the intramolecular angles $αᵢ = CᵢA − Chᵢ − CᵢB$ and (iii) the planarity degree angle in the $σᵢ$ plane $φᵢ = ζᵢA + ζᵢB + αᵢ (i = 1, 2)$, have shown their usefulness. With this respect, the $Δφ$ versus $Δζ$ plot is a very convenient way to differentiate between different Ch···Ch contacts, and in particular to assess $δ⁺· · · δ⁻$ ChB interactions.

The CSD searches and frequency plots of geometrical descriptors of synths and other supramolecular motifs highlight the particular orientations of intermolecular interactions in all the supramolecular structures investigated in this work. These specific orientations match the expected positions of electrophilic ($δ⁺$) and nucleophilic ($δ⁻$) regions in either ChB, XB or HB interactions.

Molecular $δ⁺$ and $δ⁻$ regions are observed in the deformation $Δρ(r)$ maps in the external part of the molecules. The electronic sites responsible for these features are found in the valence shells of the atoms and are assigned by the critical points of the $L(r)$ function, which determine their either CD or CC character along their three main topological directions. The topological analyses of $ρ(r)$ and $L(r)$ functions point out that the observation of particular supramolecular motifs does not depend on the type of atom and functional group involved in donor and acceptor sites, and therefore on the bonding type (such as, for instance, ChB, XB, HB or TrB). Indeed, once relevant electrophilic and nucleophilic regions are placed facing each other along the internuclear directions of the intermolecular interactions that assemble the structural motif, the motif forms in a similar way. As an example, the supramolecular four-membered motif observed in IDT and SePA is electronically equivalent in the two crystal structures, building a synthon that is independent of the atoms involved.

The proposed graph-set assignment $G_n^e(m) (G = C, R, D$ or S) is a very convenient way to describe the connectivity in motifs based on electrophilic···nucleophilic interactions, where *n* and *e* denote the number of nucleophilic (CC) and electrophilic (CD) sites, and *m* is the number of atoms building the motif. In all the $R_2^2(4)$, $R_3^3(3)$, V-type, and $S_1^1(6)$, $S_1^1(5)$ and $S_2^2(4)$ motifs explored, involving either inter- or intramolecular ChB, XB, HB or TrB interactions, the orientation of atoms and functional groups is systematically driven by local electrostatic electrophilic···nucleophilic interactions between CD···CC sites, as suggested by the small $α$ angle between CD···CC and the internuclear directions (in most cases $α < 15°$). Hence, CC and CD sites drive the relative positions of molecules by orienting their atoms. They are thus at the origin of particular molecular assemblies, governing the geometrical preferences of synths and other supramolecular motifs despite the fact that they can exhibit modest interaction energies. According to the features described in this work, the local complementary nature of CD···CC interactions makes them the building blocks of recurring supramolecular motifs, even if made from different atoms and functional groups and embedded in different molecular environments.

This work will be followed by further investigations dealing with descriptors measuring the nucleophilic/electrophilic power of CC/CD sites and the interaction between them. In addition to synths and supramolecular motifs, we would also like to extend this analysis to $π···π$ stacking interactions in the same framework. In our future work, a central point of interest will concern the sensitivity of the geometrical position of CC/CD sites, and their nucleophilic/electrophilic power, to molecular environments and conformations.

## Acknowledgements

We thank the PMD2X X-ray diffraction facility of the Université de Lorraine for X-ray diffraction measurements. RS also thanks the Gandhi Institute of Technology and Management (GITAM, a Deemed University) for infrastructure and research facilities. We thank Julien Lieffrig (Rennes) for the preparation of IDT.

## Funding information

This work has been supported by the French National Agency for Research (grant Nos. ANR-17-CE07-0025 and ANR-21-CE07-0014). RS thanks the ANR for 1 year and 4 month postdoctoral contracts. The EXPLOR mesocenter is thanked for providing access to their computing facility (project No. 2021CPMXX2483).

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