Se Donors with Dihalogens as a Source of Information for

Article pubs.acs.org/crystal

Adducts of S/Se Donors with Dihalogens as a Source of Information for Categorizing the Halogen Bonding Published as part of the Crystal Growth & Design virtual special issue on Halogen Bonding in Crystal Engineering: Fundamentals and Applications M. Carla Aragoni, Massimiliano Arca, Francesco A. Devillanova,* Francesco Isaia, and Vito Lippolis Dipartimento di Scienze Chimiche e Geologiche, Università degli Studi di Cagliari, S.S. 554 bivio per Sestu, 09042 Monserrato Cagliari, Italy ABSTRACT: The great variety of products ensuing from the reactions between chalcogen donors and dihalogens and their assemblies in the crystal lattice provides a wide experimental basis useful to disembroil the ongoing debate on how to define the halogen bonding. In this paper we present a critical analysis/study of the structural features retrieved from the Cambridge Structural Database (CSD) for linear three-body systems involving either halogens, X−X−X (X = Br, I), or halogen(s) and chalcogen(s) atoms, E−X− Y, X−E−Y, and E−X−E (E = S, Se; X = Y = Cl, Br, I; X = I, Y = Cl, Br, I). The relative elongations (δ) of the two bonds in the examined three-body systems with respect to the sum of the relevant atomic radii can be fitted by a common nonlinear least-squares equation derived from the bond-valence model. The similarities observed in the structural features suggest a common nature of the chemical bond in all systems considered and indicate that the charge transfer and the 3c-4e models can be successfully applied to all the cases considered to explain the nature of the chemical bonding.

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INTRODUCTION It is well-known that the reaction between molecules containing chalcogen donor atoms, E (E = S, Se), and dihalogens, XY (X = Y = I, Br; X = I, Y = Br, Cl), can afford a great variety of products including neutral charge-transfer (CT) adducts featuring an almost linear E−X−Y moiety, and insertion adducts containing a “T-shaped” X−E−Y fragment.1−12 According to the notation introduced by Martin and coworkers,13,14 these adducts are respectively referred to as 10-X-2 and 10-E-3 hypervalent compounds, indicating that the central atom is formally associated with five electron pairs (10 electrons), among which 2 or 3, respectively, are bond pairs.15,16 Both types of adducts feature the central atom in a hypervalent state, the two different three-body systems (E−X− Y and X−E−Y) being linear and about 10−12% longer than the sum of the corresponding covalent radii.15 The chemical bond in linear E−X−Y and X−E−Y fragments, as well as in trihalides X3−,15 can be described by using the 3c-4e bonding scheme,14 according to which these moieties are characterized by a total bond order of 1, with each one of the two bonds exhibiting bond orders varying from 0 to 1 (see Figure 1 for selected examples).15 However, besides the adducts containing the E− X−Y and X−E−Y fragments, other different structural archetypes were established by X-ray structural analysis and vibrational spectroscopy for the products of the reactions of chalcogen donors with dihalogens, depending both on the acid/ © 2012 American Chemical Society

base nature of the reactants and the experimental conditions used.1−12 In an attempt to evaluate whether the different products obtainable from these reactions could ensue from a common intermediate species, Husebye et al.10 proposed the cation [>C−E−X]+ as a transitional species. This cation could undergo a nucleophile attack on either the chalcogen or the halogen site, and, depending on the nature of the nucleophile, the formation of the above-mentioned adducts, the formation of dications [>C−E−E−CC−E−X−E−CC−E−X]+ assumed as a theoretical transitional species can help in predicting the nature of the final product.2a,11b

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RESULTS AND DISCUSSION It has been shown that the reaction between chalcogen donors and dihalogens can yield a plethora of products. Among these a recurrent structural motif is the presence of linear three-body systems, recognizable either as fundamental molecular conReceived: October 7, 2011 Revised: April 5, 2012 Published: April 23, 2012 2769

dx.doi.org/10.1021/cg201328y | Cryst. Growth Des. 2012, 12, 2769−2779

Crystal Growth & Design

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Table 1. Number of Fragments (Structures) in Selected Linear (Angle > 165°) Three-Body Systems Found in the CSD21 with Interatomic Distances Ranging from the Sum of the Covalent Radii up to That of Van der Waals Radii I S X−X−X E−X−X X−E−X E−E−X E−X−E E−E−E

Br Se

S

Se

181 (127) 43 (32) 7 (6) 13 (7) 7 (6) 85 (58)

11 (11) 8 (7) 85 (29)

d − (rB + rC) d − (rA + rB) = AB ; δ BC = BC rA + rB rB + rC

10 (10) 10 (7) 194 (86) 42 (18) 4 (3)

8 (7) 56 (24)

155 (68) 23 (13) 2 (2)

0

stituents or as supramolecular assemblies in competition with other intermolecular interactions, in the crystal lattice.1−12,18−20 In order to identify the existing sequences of chalcogen and halogen atoms involved in linear three-body systems, a search on the Cambridge Structural Database (CSD)21 was performed on the fragments A−B−C (A, B, C = S, Se, Cl, Br, I) by imposing linearity (A−B−C angle > 165°) and bond distance values ranging between single bonds and the sum of the van der Waals radii of the involved atoms (Table 1). Occurrences were found in the CSD for almost all the considered combinations, and Figure 1 reports the scatter plots of the two bond distances (dAB vs. dBC) for some selected systems showing a considerable incidence. It is important to point out that the imposed CSD search conditions do not take in consideration the charge borne by the fragment, so that, for example, the structural data relative to the tri-iodine systems (Figure 1a) not only include discrete I3− anions but also all the sequences of three iodine atoms following the imposed conditions. It is important to stress that among the considered threebody systems, those featuring a central halogen atom are currently classified as cases in which a halogen bonding occurs.22 Thus, information obtained from the analysis of the data in the CSD can help obtain a deeper insight into the nature of the halogen bond in its widest definition within an A−X−B system (A, B elements, X halogen). The scatter plots shown in Figure 1 indicate that the two bond distances in the considered three-body systems are correlated and follow similar trends, although the bond values directly depend on the nature of the atoms involved. In order to quantitatively compare all retrieved data, it is possible to consider for each couple of A−B and B−C distances (dAB and dBC, respectively) in an A−B−C three-body system their normalized elongations with respect to the sum of the covalent radii of the atomic species involved (rA, rB, and rC): δAB

Se

1618 (1084) 147 (104) 1 (1) 36 (17) 12 (11) 109 (81)

Cl

S

sAB = e(dAB− dAB) / kAB

(2)

where d0AB, calculated as a sum of listed empirical parameters,28,29 represents the A−B distance in isolated systems with sAB = 1, and dAB is the distance in a perturbed system (sAB < 1). kAB is a parameter which only marginally depends on the nature of the atomic species A and B and shows values of about 0.37 Å for most bonds.29a By assuming that in A−B···A systems, the relationship sA−B + sB···A = 1 holds, it can be shown that23 0

0 dAB = dAB − kAB ln[1 − e−(dAB− dAB) / kAB]

(3)

By extending this equation to A−B···C three-body systems, the following equation can be written: 0

0 dAB = dAB − kAB ln[1 − e−(dBC− dBC) / kBC]

(4)

If d0AB and d0BC are approximated to the sum of covalent radii, rA + rB and rB + rC, respectively,30 and eq 1 is introduced in eq 4, eq 5 can be obtained: δAB = −

kAB 0 dAB

0

ln[1 − e−δBCdBC/ kBC] (5)

On the condition that kAB 0 dAB

=

kBC 0 dBC

=k (6)

which implies that the relationship δAB = f(δBC) should be symmetric with respect to the straight line of equation δAB = δBC (the symmetry of δAB = f(δBC) with respect to the bisector of the I quadrant is required because in a A−B···C three-body system A and C can be swapped). Eq 5 can be simplified in eq 7: δAB = −k ln[1 − e−δBC/ k]

(7)

Equation 7 provides a direct simplified relationship between δAB and δBC in A−B−C systems following a bond-valence model, dependent on the single adimensional parameter k and independent of the nature of the atomic species A, B, and C. Therefore, eq 7 would allow for the direct comparison of δAB and δBC values in three-body systems featuring different composing atoms. In the following, A−B−C systems will be analyzed on the basis of the nature of the composing atoms. E−X−Y Fragments. These fragments are mainly found in CT adducts of sulfur and selenium compounds, and, among the consistent number of structures reported, many examples pertain to CT adducts formed by sulfur donors (E = S) and diiodine (X = Y = I). In the past we proposed a classification of these CT complexes into three categories: (i) weak or medium-

(1)

In analogy with previous analysis of systems featuring a hydrogen bonding, several model functions f(δ) could be adopted for correlating δAB and δBC. In particular, the O−H and H···O distances in O−H···O systems have been fitted23 by adopting an expression directly derived from the bond valence model,24−29 which has been widely applied as a tool for the interpretation and prediction of bond lengths in inorganic crystals.25 Notably, this model, which was rationalized in terms of the molecular orbital theory,26 has been successfully applied not only to ionic interactions, but also to covalent compounds, including those characterized by metallic bonding.27 According to this model, the bond-valence24c sAB and the length dAB of an A−B bond are related by the approximated equation: 2770



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Figure 1. Scatter plots of the experimental bond distances (Å) for selected A−B−C (A, B, C = S, Se, Cl, Br, I) three-body systems obtained from a CSD21 search by imposing the linearity of the fragments (angle > 165°) and interatomic distances lower than the sum of van der Waals radii of the involved species: (a) I−I−I 1618 (1084); (b) Br−Br−Br 181 (127); (c) S−I−I 147 (104); (d) Se−I−I 43 (32); (e) Cl−Se−Cl 155 (68); (f) Br− Se−Br 194 fragments (86 structures).

weak adducts, in which the S···I2 interaction can be seen as a perturbation induced by the donor on the diiodine molecule. In these systems the I−I bond order nI−I, defined according to original Pauling’s equation31 as a function of the distance dI−I

between the iodine atoms ranges from values slightly lower than 1 to about 0.6 (dI−I < 2.86 Å). (ii) Very strong adducts in which the donor−acceptor interaction is so strong that nI−I becomes lower than 0.4 (dI−I > 3.01 Å). (iii) Strong adducts 2771



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Figure 2. Structural data of the S−I−I fragments found in the CSD reported as scatter plot of δ1 vs δ2 where δ1 = δS−I and δ2 = δI−I (see eq 1). The solid curve represents the least-squares fit of the data adopting eq 7 as a model. The red point has not been included in the fitting. Fitted parameter k = 0.161; rmsd = 0.036; normalized rmsd = 0.133.

Figure 4. Structural data of the Se−X−Y fragments overlapped with those of the structural data reported in the scatter plot of Figure 3 depicted as dots [S−X−Y (·); Se−I−I (red open circles); Se−I−Br (red open squares); Se−I−Cl (red plus signs); Se−Br−Br (red open triangles)] reported as scatter plot of δ1 vs δ2 where δ1 = δSe−X and δ2 = δX−Y (see eq 1). The solid curve represents the least-squares fit of all data adopting eq 7 as a model. Data with δX−Y > 0.35 along with the red point in Figure 2 have been omitted from the fitting. Fitted parameter k = 0.158; rmsd = 0.034; normalized rmsd = 0.089.

spectroscopy.15,32 In fact, the first class of compounds shows FT-Raman spectra characterized by only one peak due to the νI−I stretching vibration falling in the low frequency region at frequencies lower than 213 cm−1 (gas phase) depending directly on the entity of the donor−acceptor interaction between the S donor molecule and diiodine. In the spectra of the very strong adducts, no peaks assignable to the iodine− iodine stretching vibration are found, thus supporting a description of these very polarized systems as [>C−S−I]+···I− CT adducts. For strong adducts, FT-Raman spectra are characterized by three peaks in the low frequency region as expected for a S−I−I three-body system. The present class of compounds, where a continuous variation of dS−I vs dI−I bond lengths (Figure 1c) is observed in the condensed phases, shows close structural analogies with systems featuring hydrogen bonding situations. In his review of the hydrogen bonding in the solid state, Steiner observed that, having defined X−H as the donor group and A as the hydrogen bonding acceptor, “the hydrogen bond phenomenon is a very broad one: there are dozens of different X−H···A interactions that occur commonly in the condensed phases” and that “dissociation energies span more than two orders of magnitude, about 0.2−40 kcal·mol−1”, concluding that “the nature of the interaction is not constant but includes electrostatic, covalent, and dispersion contributions in varying weights”.33 Therefore, while an electrostatic model could satisfactory explain the chemical bonding in unbalanced S−I−I fragments in which one of the two bond distances approach the sum of the relevant van der Waals radii, the other bond being substantially a single covalent bond, it becomes more and more inadequate to describe the chemical bonding on approaching more balanced

Figure 3. Structural data of the S−X−Y fragments [S−I−Br (red open circles); S−I−Cl (red open squares); S−Br−Br (red open triangles)] reported as scatter plot of δ1 vs δ2 where δ1 = δS−X and δ2 = δX−Y (see eq 1). The least-squares fit (eq 7) of the data provides k = 0.156 (rmsd = 0.028; normalized rmsd = 0.103). The solid curve represents the least-squares fit of data including the systems featuring the S−I−I fragments (Figure 2): k = 0.160; rmsd = 0.035; normalized rmsd = 0.100. The red point in the scattergraph depicted in Figure 2 has not been considered in the overall fit.

embracing all the intermediate cases characterized by quite balanced bond orders (0.4 < nI−I < 0.6; 2.86 Å < dI−I < 3.01 Å).1,3a,31 This classification is supported by FT-Raman 2772



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Figure 6. Structural data of the E−X−E fragments overlapped with those of the structural data reported in the scatter plot of Figure 5 depicted as dots [E−X−Y (·); X−E−Y (·); E−X−E (○)] reported as scatter plot of δ1 vs δ2 where δ1 = δE−X and δ2 = δX−E (see eq 1). Data for GIGBED, TUNCAG, and VIYRIE were neglected since they feature atomic positions with mixed occupancies. Because of the peculiar structure of the bromoselenate(I) anion [Se16Br18]2− in MUHGUR the two points circled in blue were also neglected. The solid curve represents the least-squares fit of all data (excluding bluecircled data and those not considered in the fitting of Figures 2, 4, and 5) adopting eq 7 as a model. Fitted parameter k = 0.157; rmsd = 0.049; normalized rmsd = 0.066.

Figure 5. Structural data of the X−E−Y fragments overlapped with those of the structural data reported in the scatter plot of Figure 4 depicted as dots [E−X−Y (·); Br−S−Br (red open triangles); I−S−I (red open circles); Cl−S−Cl (red open squares); I−Se−I (green open circles); I−Se−Br (red solid circles); Br−Se−Br (green open triangles); Cl−Se−Br (green solid circles); Cl−Se−Cl (green open squares)] reported as scatter plot of δ1 vs δ2 where δ1 = δX−E and δ2 = δE−Y (see eq 1). The solid curve represents the least-squares fit of all data adopting eq 7 as a model. The data with a red circle around them and those not considered in the fitting of Figures 2 and 4 have not been taken into account in the overall fit. Fitted parameter k = 0.157; rmsd = 0.050; normalized rmsd = 0.067.

we obtain the scatter plot shown in Figure 4, in which the solid line represents the least-squares fit of the data according to eq 7. All δE‑X/δX‑Y data with few exceptions, share the same correlation (k = 0.158; rmsd = 0.034), with those related to selenium containing systems gathering on the right-hand side of the scatter plot in agreement with the stronger donor ability of selenium donors as compared to the sulfur congeners. X−E−Y Fragments. These fragments are mainly found in T-shaped 10-E-3 adducts between chalcogenone donors and dihalogens featuring the central chalcogen atom in a hypervalent state. This class of compounds represents the only other possibility to linearly arrange one chalcogen and two halogen atoms. In Figure 5 all data found in the CSD for all the combinations X−E−Y (E = S, Se; X, Y = I, Br, Cl) are reported as a scattergraph of the parameters δX−E and δE−Y. The data relative to the systems E−X−Y previously discussed have also been introduced in the diagram as dots. All data from E−X−Y and X−E−Y systems, with few exceptions, share the same correlation curve following application of eq 7 (k = 0.157; rmsd = 0.050). E−X−E Fragments. Among the products that can be obtained from the reactions of chalcogen donors and dihalogens, E−X−E fragments are mainly found in [>C−E− X−E−C 0.35; see text) adopting eq 7 as a model. Fitted parameter for I− I−I fragments: k = 0.150, rmsd = 0.010, normalized rmsd = 0.026; for all data: k = 0.152; rmsd = 0.042; normalized rmsd = 0.057.

Figure 7. Structural data of the Br−Br−Br fragments overlapped with those of the structural data reported in the scatter plot of Figure 6 depicted as dots [E−X−Y (·); X−E−Y (·); E−X−E (·); Br−Br−Br (○)]. The data are reported as scatter plot of δ1 vs δ2 where δ1 = δBr1−Br2 and δ2 = δBr2−Br3 (see eq 1). Data for NOFYUC have not been considered since they feature Br−Br bond distances shorter than the sum of two bromine covalent radii; the point circled in green corresponds to the tribromide in TIJLII whose structure was solved with an R factor of 11.08%. The solid curve represents the leastsquares fit of all data (excluding the circled point as well as those not considered in the fitting of Figures 2 and 4−6) adopting eq 7 as a model. Fitted parameter for Br−Br−Br fragment: k = 0.164, rmsd = 0.029, normalized rmsd = 0.048; for all data: k = 0.158; rmsd = 0.046; normalized rmsd = 0.061.

for E−X−Y and X−E−Y fragments (see above), where the terminal halogen atoms of the three-body systems can be easily involved in intermolecular contacts. X−Y−Z Trihalogen Fragments. A survey of the crystal structures deposited into the CSD containing any linear sequence of three halogen atoms, having each of the two interatomic distances spanning from the sum of the covalent radii to the sum of the van der Waals radii provided the results collected in Table 2. While no examples of I−Br−Cl and Br− Cl−Cl sequences were found, all the other combinations occur, the I−I−I systems being the most numerous followed by Br− Br−Br, Cl−I−Cl, and Br−I−Br ones (Table 2). For our purposes, the discussion can be limited to triiodine and tribromine sequences, which are the most numerous. In these cases also, the structural data, expressed as δBr−Br and δI−I (eq 1) share the same correlation found for the data corresponding to the three-body systems discussed above and reported as dots in Figures 7 and 8, respectively. Remarkably, a certain number of data, mainly belonging to triiodine fragments, spread out in

systems discussed above, a correlation holds between the two E−X bond distances: on reinforcing one bond, a lengthening of the other is observed, so that the total length of the E−I−E framework is almost independent of the nature of the organic fragments bearing the chalcogens. Accordingly, the structural data relative to these fragments reported as δE−X vs δX−E (eq 1) can be fitted along with those related to the three-body systems described above (eq 7; k = 0.157; rmsd = 0.049; Figure 6). With the exception of two points, all the other points related to E−X−E systems gather in the restricted area typical of systems having fairly well balanced bonds. Two main reasons account for this: (i) the potential energy surfaces (PESs) calculated for the [HS−I−SH]− and [HSe−I−SeH]− model compounds are steeper than those calculated for CT and “T-shaped” adducts (see below); (ii) the organic framework incorporating the chalcogen donor can shield the E−X−E fragment from further intermolecular interactions, differently from what can happen 2774



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Figure 9. Potential energy surfaces (PESs) calculated for X2, X3− and for the model adducts [HE−X−X]− [E = S, Se; X = I (a), Br (b)]. d(X−X) − d(X2)eq represents the difference between the X−X bond lengths d(X−X) with respect to the optimized ones d(X2)eq in the free dihalogens.

share the correlation defined by the points corresponding to all the other three-body systems considered so far (k = 0.152; rmsd = 0.042 for the cumulative fitting curve in Figure 8). These experimental observations represent the main reason why the 3c-4e or CT models in our opinion are more adequate to describe the “halogen bond” in linear systems featuring a central halogen atom than a purely electrostatic model based on the interaction between the positive electrostatic potential on the outer side of the halogen (σ-hole) and the negative site of a Lewis base (LB), which remains important in any case in driving the approach of LB to the halogen site.39 The use of the 3c-4e model to describe linear three-body systems belonging to

the regions of the scatter plot corresponding to very unbalanced bonds. It is evident that for these three-body systems the correlation between the two bonds, expected according to the 3c-4e model, is lost, one of the bonds being longer than expected and the total bond order being lower than 1. In our opinion, this can be reasonably explained by considering that the influence of the surrounding chemical environment on the chemical bonding within the three-body systems becomes stronger and stronger on moving toward bond distances that approach the sum of van der Waals radii. This notwithstanding, the great majority of triiodine systems (δI−I ≤ 0.35, corresponding to dI−I ≤ 3.6 Å; 87% of the data) 2775



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H (−0.00220 au), at the Se−I bond critical point (BCP), and the calculated Wiberg index (0.23) for this very polarized bond indicate a partial covalent nature for it. Analogous results were obtained for adducts featuring Se−X−Y moieties (X = Y = I; X = I, Y = Br, Cl) with QTAIM parameters at the BCPs of the Se−X and X−Y bonds, indicating a 3c-4e nature also for these systems. In order to better understand the reasons why the considered three-body systems feature such bonding variability, potential energy surfaces (PESs) were calculated at the DFT level for some representative model systems (see the Experimental Section). For the sake of comparison, the corresponding surface calculations were extended to dihalogen molecules (X2). In Figure 9, the PES curves calculated for X2, X3−, and the model CT adducts [HS−X−X]− and [HSe−X−X]− are depicted (X = I, a; X = Br, b). The PESs calculated for the three-body systems present a wide flat region around the energy minima as compared to the PES curves calculated for the 2c-2e systems X2. Because of the flat potential holes, distortions imposed by the organic framework or weak packing interactions of few kcal mol−1 are sufficient to impose the small energy variations required to move the three-body systems from the equilibrium distances. PES curves calculated for the model systems [X−HE−X]− (E = S, Se; X = Cl, Br, I) feature similar trends as those discussed above for trihalides (Figure 10). Se−Se−Se Fragments. Recently, analogies and differences between polychalcogenides and polyhalides, mainly tritellurides and triiodides, have been comparatively discussed with the help of quantum chemical DFT calculations, and it was shown that homo- and heteronuclear trichalcogen systems behave as threebody systems strictly related to those discussed above.41 The main difference between isoelectronic (22 e) X3− trihalides and E 3 4− trichalcogenides is the overall charge, with the consequence that trihalides are stable anions, while trichalcogenides cannot exist without a delocalization of the negative charge. This is the reason why linear trichalcogen fragments can only be found when the chalcogen atoms are bonded to organic fragments or are part of metal complexes. As a study case, we have searched the CSD looking for Se− Se−Se linear systems. All data found are reported in Figure 11 as δSe−Se parameters, together with the data relative to all the other systems previously considered (Figure 8), showing that all share a common correlation following application of eq 7 (k = 0.153, rmsd = 0.043). Also for Se−Se−Se fragments, several points in the scatter plot belong to symmetric or slightly asymmetric systems (higher covalent contribution); however, the points corresponding to very asymmetric systems (higher electrostatic contribution) are equally numerous. As observed in systems featuring hydrogen bonding,33 also in Se−Se−Se three-body systems there is no indication of a critical distance at which the bond switches from the substantially covalent to the predominantly electrostatic nature. However, also in this case, although the electrostatic interaction can explain the very unbalanced situations satisfactorily, it becomes more and more inadequate to explain the nature of the chemical bonding in more symmetric cases. Interestingly, the trend of the calculated PES curve for the [H2Se−HSe−SeH2]+ model compound (Figure 12) shows that also in this case few kcal mol−1 are enough to displace the three-body system from the point of minimum energy.

Figure 10. Potential energy surfaces (PESs) calculated for model Tshaped adducts [X−HE−X]− systems (E = S, Se; X = Cl, Br, and I). d(X−E) − d(X−E)eq represents the differences between the HE−X bond lengths d(X−E) with respect to the optimized ones d(X−E)eq.

Figure 11. Structural data of the Se−Se−Se fragments overlapped with those of the structural data reported in the scatter plot of Figure 8 depicted as dots [E−X−Y (·); X−E−Y (·); E−X−E (·); X−X−X (·); Se−Se−Se (○)]. The data are reported as a scatter plot of δ1 vs δ2 where δ1 = δSe1−Se2 and δ2 = δSe2−Se3 (see eq 1). Fitted parameter for all data (excluding those not considered in the fittings depicted in Figures 2 and 4−8): k = 0.153; rmsd =0.043; normalized rmsd =0.057.

chalcogen-dihalogen adducts has been recently supported by applying the quantum theory of atoms in molecules (QTAIM) to a series of different adducts of selone donors with dihalogens and pseudo-halogens among which are some very polarized Tshaped compounds containing the I−Se−Cl, I−Se−Br, and I− Se−CN fragments.12 In all three cases, the three-center delocalization index δ(A,B,C) introduced by Ponec and coworkers40 to better distinguish between hypervalent 3c-4e compounds (A−B−C) and 2c-2e systems (A−B) within the QTAIM framework indicate for all three compounds a 3c-4e bond nature [δ(I,Se,X) = −0.203, −0.243, and −0.074 for X = Cl, Br, and CN, respectively]. In particular, in the case of the adduct with ICN featuring the fragment I−Se−CN, both the calculated negative value of the local electronic energy density, 2776



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Figure 12. Potential energy surface (PES) calculated for the hypothetical model compound [H2Se−HSe−SeH2]+. d(Se−Se) − d(Se−Se)eq represents the differences between the Se−Se bond lengths d(Se−Se) with respect to the optimized one d(Se−Se)eq.

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CONCLUSIONS Sequences of three aligned halogen, chalcogen, or mixed halogen/chalcogen atoms represent recurrent motifs either as a functional group in some archetypes of products ensuing from the reaction of dihalogens and chalcogen donors, or as supramolecular assemblies in many other solid products, including polyhalides. Sequences for almost all possible combinations of three aligned chalcogen/halogen atoms are found in the CSD, some of them being very numerous. The analysis of the retrieved data indicates that all systems must be considered strictly correlated, sharing the same nature in terms of chemical bonding. Except for the case of the E−X−E fragment, all the other linear three-body systems here considered show a continuous variation of the distances of the two bonds from balanced situations up to very unbalanced ones without indications of critical distances at which the bonds switch from the substantially covalent to the predominantly electrostatic nature. Indeed, by expressing all bond distances as relative variation δ with respect to the sum of the covalent radii of the involved atomic species, all data belonging to systems as varied as CT adducts of chalcogen donors with halogens and interhalogens (Figures 2−4), hypervalent chalcogen T-shaped adducts (Figure 5), halonium complexes of chalcogen donors (Figure 6), sequences of three halogen atoms (Figures 7−8), can be fitted with a single semiempirical equation resulting from the bond-valence model. Remarkably, the same correlation can be extended to polychalcogenides, as demonstrated for the compounds featuring Se−Se−Se fragments, confirming the analogies in the electronic structures of all the considered systems. It is important to point out that many among the three-body systems considered here display a central halogen atom and therefore represent peculiar cases of arrangements in which a halogen bonding is operating. If we had to limit the presence of a halogen bonding to the cases in which one of the two bonds A−X, X−B is close to the sum of the relevant van der Waals radii, an electrostatic model could be adequate to the description of this interaction. However, the lack of discontinuity in the correlation between the two distances in the classes of three-body arrangements considered renders it

mandatory to consider the presence of a halogen bonding also in the cases featuring balanced A−X and X−B distances. Under such circumstances, both the CT and the 3c-4e bond models seem to be more appropriate to describe the nature of the halogen bonding, since the different match in the energies of the combining orbitals is responsible for the different covalent and electrostatic contributions.

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EXPERIMENTAL SECTION Structural data were retrieved from CSD by means of the software Conquest v5.32.21 The nonlinear least-squares fit42 of experimental data was carried out adopting eq 7 as a model (initial guess of k = 0.37). Theoretical calculations were carried out on dihalogens X2, trihalides X3− (X = Cl, Br, and I), hypervalent [X−HE−X]− systems (E = S, Se; X = Cl, Br, and I), charge transfer (CT) adducts HE·X2− (E = S, Se; X = Br and I) and, for the sake of comparison, on the 22-electron threebody system [H2Se−HSe−SeH2]+ with the commercial suite of programs Gaussian 09 package.43 On the grounds of the results reported previously and comparing different functionals in closely related systems,2b,44 the mPW1PW functional45 was adopted along with the Schäfer, Horn, and Ahlrichs basis set46 for hydrogen and the completely uncontracted basis sets LANL0847 for halogen and chalcogen species with effective core potentials (ECPs), supplemented by d-type polarization functions. In a few cases, such as for [X−HE−Cl]− (E = S, Se; X = Cl, Br), a quadratically convergent SCF procedure was needed. For all species, the molecular geometry was optimized (with the tight cutoffs on forces and step size) and verified by a frequency calculation, carried out by determining the second derivatives of the energy with respect to the Cartesian coordinates of the nuclei. For three-body systems of the type X−Y−Z, PESs were subsequently carried out by calculating the total electronic energy at geometries obtained by systematically scanning the variation of the X−Y and Y−Z bond distances, with the geometrical constraint of keeping constant the X−Z distance. All other bonds, such as chalcogen−hydrogen bonds, were not subject to any constraints. All calculations were carried out with an E4 Workstation equipped with four quadcore Opteron processors and 16 GB of RAM. Molden 5.048 and 2777



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GaussView 5.049 were exploited for analyzing the results of the calculations.

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hypervalent does not necessarily require the involvement of a d orbital from the central E atom in order to explain the bond nature of the bonding in the X−E(R)−X system.14 (17) Arca, M.; Demartin, F.; Devillanova, A. F.; Garau, A.; Isaia, F.; Lippolis, V.; Piludu, S.; Verani, G. Polyhedron 1998, 17, 3111−3119. (18) (a) Nakanishi, W. In Handbook of Chalcogen Chemistry; Devillanova, F. A., Ed.; RSC Publishing: Cambridge, 2007; Chapter 10.3, pp 644−668; (b) Bigoli, F.; Deplano, P.; Devillanova, F. A.; Girlando, A.; Lippolis, V.; Mercuri, M. L.; Pellinghelli, M. A.; Trogu, E. F. Inorg. Chem. 1996, 35, 5403−5406. (c) Devillanova, F. A.; Garau, A.; Isaia, F.; Lippolis, V.; Verani, G.; Cornia, A.; Fabretti, A. C.; Girlando, A. J. Mat. Chem. 2000, 1281−1286. (19) (a) Arca, M.; Demartin, F.; Devillanova, A. F.; Garau, A.; Isaia, F.; Lippolis, V.; Verani, G. J. Chem. Soc., Dalton Trans. 1999, 3069− 3073. (b) Aragoni, M. C.; Arca, M.; Devillanova, A. F.; Isaia, F.; Lippolis, V.; Mancini, A.; Pala, L.; Slawin, A. M.; Woollins, J. D. Chem. Commun. 2003, 2226−2227. (c) Blake, A. J.; Devillanova, A. F.; Gould, R. O.; Li, W.-S.; Lippolis, V.; Parsons, S.; Radek, C.; Schröder, M. Chem Soc. Rev. 1998, 27, 195−206. (d) Svensson, P. H.; Kloo., L. Chem. Rev. 2003, 103, 1649−1684. (20) For example, in the crystal packing of [>C−E−E−C

Se Donors with Dihalogens as a Source of Information for

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