Factors Controlling Asymmetrization of the Simplest Linear I3â and I42

Article pubs.acs.org/crystal

Factors Controlling Asymmetrization of the Simplest Linear I3− and I42− Polyiodides with Implications for the Nature of Halogen Bonding Published as part of the Crystal Growth & Design virtual special issue on Halogen Bonding in Crystal Engineering: Fundamentals and Applications Gabriele Manca, Andrea Ienco, and Carlo Mealli* Istituto di Chimica Composti OrganoMetallici ICCOM-CNR, Via Madonna del Piano 10, 50019 Sesto Fiorentino (Florence), Italy S Supporting Information *

ABSTRACT: This paper investigates geometric and electronic features of linear I3− and I42− anions, as building blocks of larger polyiodides. Most experimental structures are quasi D∞h, although one lateral linkage is occasionally elongated with I···I separations approaching those of I···I−R− species, typical of halogen bonding (HalB). Hirshfeld surfaces from crystal data highlight solid state effects depending on the distribution of the counterions around I3− or I42− units. Corresponding experimental asymmetries have been mimicked with density functional theory calculations through different surroundings of positive point charges. The consequent deformations are interpreted in terms of the s/p rehybridizations occurring at the central I atom(s) of the populated frontier σ* wave functions. The origin is a charge-induced variation of the orbital energies at lateral iodides (electronegativity), hence by their the donor power in a nucleophilic attack. The calculations also provide energy information on I2 + I− or I2 + 2I− additions, and, in solvent, the intrinsic energy stability of I42− is for the first time validated. In the absence of positive charge perturbations, the 1− charge of a remote iodide polarizes I3− and promotes incipient electrostatic attraction, which is quickly accompanied by electron transfer with a generalized σ delocalization throughout I42−. Implicit orbital overlap supports a covalent picture, or better to say hypervalency, given the electron richness of the central atoms. Molecular electrostatic potential (MEP) surfaces are expected to show σ holes in support of the purely electrostatic HalB model, typically proposed for I···I−R− systems. However, the computed surfaces show little evidence of σ holes in the equilibrium adducts I3−, I42− and I···I−R− suggesting that HalB cannot be purely electrostatic.

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INTRODUCTION Self-assembly, hierarchical order, supramolecules are relevant in chemistry, not only for the beautiful structural motifs but also for the technological relevance,1 as the properties of the building blocks propagate or transform in the aggregates (e.g., magnetism, catalytic activity, chemical sensitivity2). Interactions are generally weak, including π-stacking, van der Waals and/or dispersion forces, hydrogen bonding (HyB)3 and, as recently pointed out, more directional halogen bonding (HalB).4 The general formulation of the latter is D···X−Y, where Y−X is the donor of the halogen atom X, D a generic Lewis base (including a X− halide)5 and Y is an aryl or alkyl group, better if with electron withdrawing substituents, which strenghten the HalB. The electrostatic or covalent nature of HalB is still debated, but its directionality suggests direct involvement of one X p orbital in collinear interactions. Synthetic strategies have been developed to enhance the strength of the HalB,6 which appears important also for biosystems, where the molecular folding of proteins is affected.7 It is also relevant in material science, crystal engineering, nonlinear optics, molecular recognition, and more.8 Particularly suited to HalB is the iodine’s high polarizability,9 which is exploited in the formation of polyiodides. The electric conductivity of the latter10 is © 2012 American Chemical Society

attributable to a Grotthus type diffusion mechanism similar to that of proton transfer in water.11 The simplest I3− polyiodide normally features two equal I−I linkages, shorter than in comparable HalB systems. Its formation is likely due to I− + I2 addition, starting with I2 polarization and subsequent electrostatic interaction, which evolves into actual electron transfer at shorter separations. Indeed, the I−/I3− redox couple is a fundamental component in dyesensitized solar cells (DSSC)12 in ionic liquid electrolytes.13 Polyiodides have the general formula Inx, with the x charge varying from −1 to −4 and the n nuclearity reaching the number of 29.14 The building blocks I1−4x assemble in zigzag or cyclic arrangements also through quasi perpendicular interactions. The latter, indicated as second class HalB,15 imply simultaneous engagement of two orthogonal p orbitals of one I atom. A simple example is the cyclic polyiodide I102−16 (Figure 1), where the basic linear units are all present with typical I−I separations. For instance, two horizontal and slightly elongated I2 molecules (2.75 Å vs the 2.73 Å in the isolated species17) are Received: September 2, 2011 Revised: February 15, 2012 Published: February 15, 2012 1762

dx.doi.org/10.1021/cg201154n | Cryst. Growth Des. 2012, 12, 1762−1771

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RESULTS AND DISCUSSION

Extension of the Pimentel−Rundle MO Model for Symmetric I3−. In 1951, a qualitative three center/four electron model (3c/4e−) was proposed (PR model) for D∞h triiodide,25 but only considering the p atomic orbitals. which coincide with the molecular axis (Scheme 1 with exclusion of Scheme 1. Basic MOs for a Symmetric I3− Unita

2−

Figure 1. Cyclic I10 polyiodide, resulting from the interaction between pairs of I2 molecules and I3− anions.

engaged in lateral interactions of the HalB type, the 3.44 Å distances being similar to those of I42− and I···I−R− adducts. Another description, still consistent with second class HalB,15 can be that of lateral I3− units perpendicularly interacting with two I2 molecules. Although simple, I102− still raises many questions about the interplay between electronic/electrostatic components. Isolated I3− units act as counterions in many structures. Most often, they are symmetric (D∞h) with ∼0.2 Å elongated linkages with respect to the I2 precursor, although also asymmetries up to 0.3 Å may be observed, as in [1-methyl cytosinium][I3]18 (MCYTRI in the Cambridge Datafile19). In these cases, the weaker linkage compares with typical HalB, almost suggesting that the I− + I2 addition is frozen before the ultimate D∞h structure. At the latter, about half electron has been transferred from the incoming iodide to the remote opposite atom, while the central atom remains practically uncharged as in I2. The electron redistribution seems to indicate significant covalency (hypervalency), rather than purely electrostatic bonding. Analogous considerations can be made for the linear I42− dianions found in about 10 crystal structures.20 Most of them are symmetric (D∞h) with the central I−I linkage about ∼0.1− 0.2 Å longer than in free I2 and lateral separations of about ∼3.4 Å. Two I42− structures are instead asymmetric, an example being the salt [V(CNCH3)6][I4]20h with sequential I−I distances of 3.17, 2.85, 3.52 Å. The largest value is close to the limits of I···I−R− HalB systems. Therefore, the factors for I42− asymmetrization are important also for the interpretation of HalB. In this paper, we employ various computational tools to analyze the mentioned problem. First, the effects of different distributions of counterions around a given anion are examined by computing Hirshfeld surfaces21 derived from experimental crystal data. Then, the asymmetrization trends for both I3− and I42− species are simulated by density functional theory (DFT) optimizations using different sets of surrounding positive point charges, which mimic the crystalline environments. Useful information is derived from the computed energy formation of the linear adducts with evidence for a stabilizing σ delocalization, hence electron transferring from the incoming nucleophile. This also applies to I42− and excludes a justification of the adduct only in terms of a pure charge transfer model, as previously done.22 Perturbation theory rules are used to describe wave function topologies and their evolution depending on the electronegativity variations of the terminal atoms. Finally, the MO pictures for I3− and I42−, as well as some I···I−R− system, is correlated to the molecular electrostatic potential (MEP) surfaces, whose depletions (σ holes)23 are often used to justify the presence/absence of HalB interactions24 without properly addressing the underlying factors.

a

The orbitals in the dashed boxes are additive with respect to the original Pimentel and Rundle model.25

the dashed boxes). However, also s orbitals are important for the σ system and, in particular, the antibonding contribution of the central one to the frontier populated level (∼5% at the DFT level). This counterbalances its bonding contribution in the lower 1Σg+ (the s orbitals appear in dashed boxes to highlight the differences with the PR model). A MOOP diagram (overlap population MO by MO),26 not shown, confirms the negative contribution of 2Σg+ to σ bonding. The formation of two I−I single bonds would require two vacant antibonding levels instead of one, so that the bond orders can only be 0.5. The central atom must be hypervalent, being counted >8 electrons. Already Hoffmann et al. analyzed the problem in depth, also through accurate DFT calculations for I3 − and other isoelectronic species. The contribution of the central s orbital was highlighted also through a mathematical treatment of the applied perturbation theory,27 although no hint was made on the key role of the latter for asymmetrization (vide infra). In a previous paper on X2Y− trihalogens, the same author had underlined the hypervalent character of these 22 electrons molecules.28 To summarize, 12 electrons fully populate the two π orthogonal systems (thus being the source of some electronic repulsion), while the remaining 10 belong to the σ system formed by six atomic orbitals (one s and one p per atom). Two low lying combinations (not shown in Scheme 1) may be taken as out-pointing lone pairs, so that the inner I−I−I region consists of four levels with six delocalized electrons. At variance with the originally proposed 3c/4e− model, the 4c/6e− one appears more general with the understatement that “c” refers to orbitals rather than atoms. We already proposed such a different model for related linear D−I−I adducts, in which D is a sulfur base.29 Scheme 1 will be our reference MO model also for monitoring the evolution of the wave functions, upon electronegativity perturbations at the terminal atoms of trihalides. The experimentally observed I3− asymmetrization was satisfactorily reproduced by DFT calculations using different distributions of the positive charges (vide infra). The different bond lengths correlate to a s/px rehybrization at the central atom (mainly in the 2Σg+ level). A similar picture 1763



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also applies to the I42− asymmetrization, as well as to the HalB hypervalency trends in typical I···I−R− systems. Basic Information from DFT Optimizations of I3−. The number of discrete I3− anions in the CCDC files19 depends on the criteria fixed to dismiss external weak I···I interactions, which typically give rise to extended polyiodides. At the 3.7 Å limit, the genuine I3− species are reduced to about 150, most of them having equivalent I−I linkages of ∼2.90 Å,30 although the distances can be different as 3.14 and 2.74 Å, as occurs in (3,5bis(ethylamino)-1,2-dithiolylium) tri-iodide.31 Symmetry unconstrained DFT optimizations, in the gas phase, invariably produce D∞h species with ∼0.1 Å overestimated distances. The latter are commonly attributed to the usage of pseudopotentials,32 although also the full basis set 321G* (available for iodine in Gaussian0933) provides similar results (see Supporting Information). Other methods, such as Coupled Cluster (CC34) or Moeller−Plesset MPn,35 can better perform but have not been used because we are more interested in general trends than precise simulations. Instead, we tested different functionals, such as B3LYP,36 M05-2X,37 and B2PLYP-D,38 the last including dispersion forces,37,38 which should not be determinant for the present linear molecules with no 1,3 contact. Geometry and energy comparisons are presented in Table 1 for both gas phase and in-solvent (CHCl3)

Scheme 2. Effects of the +1 Point Charge over the Atomic Orbitals of a Single Iodide at Different Distances

direction of the charge being about 0.3 eV more stable than its orthogonal partners. This implies a higher electronegativity for the px orbital, hence its minor donor power along the dipole. Scheme 2 refers to gas-phase data, but the trends are similar in a solvent such as CHCl3 (PCM model40), although the gaps are reduced by a factor of ∼0.7 at 4 Å. Confirmation also comes

Table 1. Geometric and Energetic Comparisons for Symmetric I3− (Gas-Phase and CHCl3 solvent) as Obtained from Different DFT Functionals (See Computational Details) gas phase

CHCl3 solution −

from MEP surfaces23 for a single iodide (see Figure 2). The drawing a refers to an infinite separation of a 1+ point charge (at the left side), while in b and c the distances are 7.0 and 4.0 Å, respectively. Electron density progressively accumulates on the side of the positive charge, so that the potential is depleted in the opposite direction (the color becomes more bluish). Such a σ hole excludes nucleophilic attack of I− toward the I2 molecule along the dipole’s axis. Instead, the uniformly distributed red color along the orthogonal belt confirms equivalent donor power in all the orthogonal directions. The point already indicates the preferential distributions of charges around I3− and possibly justifies two orthogonal interactions (second class)15 observed in polyiodides (e.g., I102− in Figure 1). Figure 3a shows the MEP of the I2 molecule perturbed by a collinear 1− point charge at 4.0 Å.41 The charge corresponds to that of the approaching iodide anion from the right side.

I2 + I−

I2 + I

a

Figure 2. Isodensity MEP surfaces (0.04 electrons Bohr−3) for a single I−: (a) no external positive charges; (b) left side 1+ point charge at 7 Å; (c) left side 1+ point charge at 4 Å. MEP values range between −0.12 and −0.09 hartree (from red to blue color).

functional

I−I (Å)

ΔGa

ΔEa

I−I (Å)

ΔGa

ΔEa

B3LYP M05−2X B2PLYP-D experiment33

3.04 2.98 3.03 2.90

−26.9 −26.9 −25.1

−33.4 −33.8 −31.7

3.03 2.97 3.01

−12.3 −12.3 −10.4

−18.8 −19.1 −17.3

Energies in kcal mol−1.

optimizations. The M05-2X functional, which accounts for medium range electron correlation, provides shorter but still overestimated I−I distances. Formation of I3−, as a I2 + I− adduct, is always energetically favored with only minor differences between functionals, especially concerning ΔG values. Importantly, stabilization of the adduct is more than halved in solvent (compare the ΔG value of −12.3 vs. −26.9 kcal mol−1), a difference to be considered also for the I42− formation (vide infra). A reasonable justification is that the solvent reduces the electrostatic attraction, since the anion's charge better diffuses through the bulk of the medium. Given the sufficient consistency of the different functionals in Table 1, the following data only refer to B3LYP36 calculations. Electrostatic Potential Effects of the Positive Charges. The distribution of counterions has been addressed by other authors to affect the geometry of polyiodides.39 To better understand the origin of the problem, Scheme 2 compares the DFT energies for the orbitals of a single iodide at different separations from the +1 point charge. Starting from infinite distance, the sets of s and p orbital are equally stabilized till 7.0 Å (∼1.3 eV). Then, the effect becomes more directional and increases at shorter distances. At 4.0 Å, the degeneration of the three p orbitals is removed, the one in

Figure 3. Molecular electrostatic potential (MEP) plots for (a) the I2 molecule associated to a right side 1− point charge at 4.0 Å (induced dipole); (b) fully optimized I3− anion without any evident residual I2 dipole. The selected MEP range is −0.6/+0.5 hartree.

Indeed, the polarization determines a σ hole, which enhances the possibility of nucleophilic attack. However, the σ hole disappears at the 3.0 Å distance found in the ultimate I3− adduct (Figure 3b). To interpret better the result, in solvent optimizations 1764



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were carried out by fixing progressively shorter separations between I2 and the attacking iodide. A clear effect starts appearing at ∼6.50 Å, since the I2 elongates from 2.73 Å to 2.86 Å and the bonding energy of the I2 + I− adduct is computed −7.1 kcal mol−1. At 3.5 Å, the energy gain is as large as −19.9 kcal mol−1 (I2 is stretched to 2.94 Å), while from this point to the fully optimized D∞h structure (I−I = 3.04 Å), the additional stabilization is only −4.7 kcal mol−1. The quasi plateau seems to justify the occasionally observed asymmetric I3− species. Importantly, a NBO analysis42 shows increasing transfer of electrons from the entering I− into I2, with larger population of the I atom at the opposite end. In fact, the charge of the latter increases from −0.28 at 6.5 Å to −0.46 at 3.04 Å, while the central atom remains almost uncharged (−0.08). Such an electron flow from the entering nucleophile corresponds to an increased electron sharing, which implies covalency (hypervalency) of the adduct. Perturbation theory rules will be used below to explain how the wave functions adapt to the overall σ delocalization depending on the donor power of the approaching nucleophile. A consistent picture is applicable also to the classic HalB of I···I−R− systems, which are normally attributed a largely prevailing electrostatic character. Role of Positive Charges in Determining Symmetric or Asymmetric I3− Structures. Nature and location of the counterions in a crystal may control the I3− features. For instance, the phenyl rings in the structure of [Ph4P][I3]43 can efficiently screen the positive charge at the P atom, with a solid state effect similar to that of the solvent (refer to the energy data in Table 1). In contrast, an alkaline cation such Cs+ in CsI339a is quite effective for the I3−asymmetrization and indeed the I−I distances are as different as 2.83 and 3.04 Å.44 Some authors have already tried to simulate I3− asymmetries39 by inserting the unit in a cage of 14 fractional point charges with no major I−I differentiation. Also, the definition of a trigonal prism with +0.167 point charges at the vertexes has a small effect (2.959 vs 2.981 Å). Recently, the I3− deformation energy has been evaluated in the presence/absence of the appropriate point charge to conclude that “cation-coordination” favors asymmetrization.39b To gain convincing evidence for the relation between I3− geometry and counterions, we constructed Hirshfeld surfaces45 from selected sets of crystal data. The package Crystal Explorer of Spackman and Byrom,21 used for the purpose, provides insights into crystal packing. The procedure partitions the crystal in the promolecule to be examined (I3− in our case) and the protocrystal formed by the remaining crystal contents within a threshold distance. The surface corresponds to the region where the electron distribution at the atoms of the promolecule dominates over that of the protocrystal, so that shapes, contours, and colors highlight environmental perturbations such as electrostatic potential, dipole moments, and more. Atoms falling within a critical short-range, but without the mentioned critical properties, do not affect the surface. Figure 4 presents two different Hirshfeld surfaces about I3−. Case (a) corresponds to the crystalline salt [1-methyl cytosinium][I3−],18 with asymmetric I−I distances of 3.124 and 2.794 Å. Here, four positive pyridinium centers form short contacts of about 4.0 Å with the more loosely bound terminal I atom, as reflected by the red dots on the surface around it. Conversely, the [Et4][I3] salt46 with symmetric I−I distances of 2.94 Å (case b) presents a homogeneous surface without peculiar discontinuity points; hence no major effective perturbation is at work. To mimic the above deformational trends, systematic in solvent optimizations were carried out. Initially, a +1 point

Figure 4. Hirshfeld surfaces and chemical surroundings in the crystal structures of (a) [1-methyl cytosinium][I3] (CCDC refcode = MCYTRI); (b) [NEt][I3] (refcode = TETAMI). The red dots in the (a) surface indicate a larger electrostatic interaction between the underlying I atom and the cations.

charge was located perpendicularly to triiodide at 4.0 Å from the lateral I1 atom. The loss of basicity in a direction perpendicular to the dipole is too large since the I1−I2 linkage is as long as 4.07 Å and the adjacent I2−I3 one is almost unaffected (2.73 Å). Because the model unrealistically biases the entire I 3 − unit toward the positive charge, a perpendicular square of positive fractional charges (+0.25 each) was centered at I1 with separations of 4.0 Å. No I3− tilting occurs while the unit shifts through the square for about a half I−I linkage, as shown in Scheme 3a. The triatomic Scheme 3. Optimized I3− Anion in Presence of (a) Four Fixed +0.25 Point Charges at the Apexes of a Single Square; (b) Eight +0.125 Point Charges Fixed at the Apexes of Two Lateral Squares

is clearly asymmetric (2.97 and 3.07 Å), as in some known crystal structures. Instead, two orthogonal squares, through the external atoms and formed by +0.125 point charges, allow maintenance of symmetric I-I linkages (Scheme 3b). The isomer of Scheme 3a is more stable by −5.4 kcal mol−1, whereas in the absence of charges, the symmetric minimum is favored (less than 1.0 kcal mol−1). Electronic Control of the Bonding in Trihalides. The charge-induced higher electronegativity of one lateral atom of I3− mimics I2X− heteromolecules (X = Cl or Br), with only the I−I distance being directly comparable. It must also be underlined that a I−X−I− isomer with the most electronegative atom in the central position has ever been reported;47 hence an accumulation of the positive charges around the central atom of I3− is improbable. Validation is provided by DFT calculations, which indicate that I−Br−I− is about +6 kcal mol−1 more destabilized than I−I−Br−, while the central bromine atom would be absurdly +0.35 more positive than the lateral more electropositive iodines (NBO42 values). A preferential position of a more electronegative substituent is not uncommon for main group hypervalent molecules. For instance, a fluorine in place of a chlorine atom of the PCl5 trigonal bipyramid invariably is 1765



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as I−I is ∼0.05 Å shorter in I2Br−. Also, a NBO analysis shows that the electron transfer into I2 is 0.55e− in charge unperturbed I3− but 0.49e− in I2Br−, whereas in the charge perturbed I3− of Scheme 3a, the amount is only 0.46e−, validating the proposed electronegativity effect. Trihalides and Classic I···I−R− HalB Systems (R = alkyl, aryl). The interaction between the two iodines in I···I−R− systems (R = alkyl, aryl) is much weaker than in any I2X− trihalide, due to the high energy of the carbon σ hybrid and its magnified donor power. With reference to the MO Scheme 4, the right side orbital lies much closer to I2 σ*, which also dynamically lowers with I−I elongation, hence their interaction is stronger. Moreover, a large gap reduces repulsion with the lower I2 σ level. The transfer of electron density into I2 is enhanced and the increased population of the σ* induces cleavage of the I−I bond and even a 4e− repulsion. For this reason, the residual HalB is attributed only to an electrostatic attraction. In this case, one would expect to see in the MEP an external σ hole at the iodine atom of the R−I linkage.5 This is not featured in the MEP of CH3−I···I− at the equilibrium (Figure 6a), similarly to the case of I3− (Figure 3b). The feature is not observed in the isolated precursor CH3I to support a possible HalB interaction (see Figure 6b). On the other hand, the NBO charge of the remote iodide atom in CH3−I···I− is lowered to −0.8 from −1.0 and such an electron transfer confirms a partial covalent interaction between the R−I and I− fragments, which are largely separated by 3.61 Å. The σ hybrid of an aryl group normally lies lower in energy than that of an alkyl one, and such a difference is further enhanced by good electron withdrawing substituents at the aromatic ring. Consequently, the Ar−I unit can behave as a better halogen donor toward an approaching iodide base. In particular, the (NO2)3H2C6 group significantly enhances HalB in the corresponding Ar−I···I− adducts, since the experimental I···I separation is as short as 3.33 Å.50 An optimized DFT model of the corresponding structure gives an even shorter I...I separation of 3.16 Å, close to the values observed in some I2X− triatomics. The MEP surface of the isolated (NO2)3H2C6I precursor (Figure 6d) features a clear σ hole at iodine, which vanishes in the equilibrium adduct (NO2)3H2C6I···I− (Figure 6c). In this case, the −1 charge of the remote iodide is lowered by 40% (see Table 2 of the Supporting Information), not far from that reported for I2X− species. In conclusion, the electron flow compensates for the evident polarization in the precursor and confirms a good degree of covalency of the HalB. To generalize, the features of Y−X···D− halogen bonding, when X=D=I, depend on the electronegativity of the Y group (different energy positions of the right side orbital in the MO Scheme 4). Scheme 5 highlights the different I−I distances in optimized models having a Y group of increasing electronegativity. The I−I elongation diminishes from alkyl, to aryl, iodide, charge-perturbed iodide, bromide and chloride, also in agreement with available experimental data.50,47,51 I42− Dianion. The largest I−I distances (in Scheme 5), between 3.2−3.6 Å, are similar to the side ones in linear I42− dianions.20 Most often the latter have D∞h symmetry, an example being the salt [Me3N(CH2)6NMe3][I4],20g (CCDC refcode19 NUTSOL) with central and lateral I−I distances of 2.83 Å and 3.44 Å, respectively. Conversely, the salts with [(CNCH3)6V]2+20h or a tripositive triazonium macrocycle20c as counterions (refcodes YIRLOA and NABWOD, respectively) have a similar asymmetric sequence of I−I distances (3.19, 2.82,

located at one apex, which only permits a larger electron accumulation (hence, the term apicophilicity48). Simple perturbation theory arguments correlate I3− and I2X− species, by indicating the evolution of frontier wave functions (consider as reference the D∞h model in Scheme 1). Scheme 4 Scheme 4. Bonding Scheme for an Asymmetric Halogen Triatomic of the Type I2X− (X = Higher Electronegativity Element, either Natural or Induced by Asymmetric Distribution of the Positive Charges)

shows the frontier MO2, MO3, and MO4 levels of I2X− which arise from the interactions of I2 σ and σ* (left side) with the px lone pair of the right side X atom. The latter is assumed to have variable electronegativity; hence the gap with the uniquely vacant I2 σ* level is progressively larger for a charge-perturbed I−, Br−, and Cl−. While the uniquely possible donation is reduced, the repulsion with the populated I2 σ level increases, also because the latter, although bonding, is characterized by outpointing s/p hybrids, which enhance antibonding toward X. To mitigate the MO2 destabilization, the I2 σ* level mixes in it with a phase, which reduces the weight of the central px orbital as shown in the box of Scheme 4. The higher is the energy of the right side lone pair, the larger is the effect. In this respect, only an iodide not perturbed by charges has maximum strength to cancel the s/p hybridization at the central atom and restore the symmetric MO picture of Scheme 1. Conversely, the lower in energy the right side lone pair lies, the more reduced is the strength of I-X linkage and the stronger is the adjacent I−I one, with some similarity to the trans-influence typical of transition metal complexes.49 The qualitative MO picture is confirmed by the MO2 drawings derived from DFT calculations for I3− and I2Br− in the absence of positive counterions (see Figure 5, panels a and

Figure 5. Comparative pictures of the critical MO2 of Scheme 4, as obtained from the DFT wave functions of the anions I3− (a) and I2Br− (b).

b, respectively). In the latter case the central I atom has evident s/px hybridization, which enhances I−Br antibonding and favors I−I bonding. This is consistent with the experimental I− I distances, of 2.90 Å vs. 2.78 Å for I3− 30 and I2Br−,47 respectively. The trend is also confirmed by DFT optimizations 1766



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Figure 6. Molecular electrostatic potential surfaces (at 0.04 electrons Bohr−3 isodensity) for (a) CH3I···I−; (b) CH3I; (c) (NO2)3H2C6I···I−; (d) (NO2)3H2C6I. At the limiting red and blue colors the MEP values are −0.6 and +0.35 hartree, respectively.

Scheme 5. Variations of the I···I Distance in Collinear Anionic Adducts with the Common I2 Unit and a Left Side Group of Increasing Electronegativity (Lower Donor Power)

destroy centrosymmetry. Instead, the distribution of the dots in Figure 8b confirms that I42− is more perturbed at one side by the closer contacts with one triazonium trication; hence the corresponding I−I distance is elongated (3.53 Å). Again, DFT strategies reproduce asymmetrization trends and their associated energies. Calculations on the I42− Dianion. An optimization in the gas phase and without symmetry constraints leads to a D∞h species with central and terminal I−I distances of 2.95 Å and 3.62 Å, respectively. These values are ∼0.15−0.20 Å overestimated possibly due to the used basis set.32 On the other hand, previous MP2/LANL2DZ calculations lead to comparable side linkages (3.61 Å) and an even longer central bond (3.09 Å).20f Usage of the CHCl3 solvent (PCM model40) affords a better geometry with two reasonably shorter lateral bonds (3.44 Å). Then, various distributions of positive point charges were introduced, as already done for I3− (see Scheme 3). Two equal squares of +0.25 point charges (Scheme 6a), across the terminal atoms, maintain D∞h symmetry and better reproduce the experimental structures (I−I distances of 2.93 and 3.47 Å). Conversely, by accumulating the entire 2+ charge at one square across one lateral I atom (Scheme 6b) causes the definite separation of the latter (4.32 Å), while the adjacent I3− unit behaves as it was isolated (symmetric distances of 3.03 Å). Therefore, a more realistic redistribution of the charges was attempted with two lateral squares of δ1 = +0.23 and δ2 = +0.27 point charges (see Scheme 6c). The sequence of I−I distances is 3.38, 2.93, and 3.57 Å, which is close enough to that of the asymmetric NUTSOL20g and NABWOD20c structures. Finally, as anticipated, an attempt was made also to mimic the quasi symmetric I42− core in Tl6PbI10 (Figure 4). The minimal model was limited to a single tetratomic surrounded by triangles of positive point charges across each I−I vector (and beyond) at the positions of the Tl+ cations. As shown in Scheme 6d, the difference between the I−I distances is reduced, although those at the sides (3.40 Å) still largely exceed the central one (3.07 Å). Band structure calculations are evidently necessary, but the above trends confirm the qualitative dependence of the geometry on the distribution of the positive charges. Energy Profiles for I42− Formation. A concerted nucleophilic attack of two iodides to one I2 molecule is an improbable termolecular reaction, so that formation of I3− must preliminarly occur. The ΔE and ΔG values in Scheme 7 confirm the exothermic and exoergonic stability of the triatomic (see also Table 1). Conversely, the addition of iodide seems disfavored both in vacuo and in CHCl3 solvent, although in the latter the energy cost is reduced by a factor of ∼4. A ΔE > 40 kcal mol−1, found from previous MP2 calculations,20f induced the authors to exclude any I−I lateral bonds in I42− and justify the adduct with a rather vague charge transfer model.22 In contrast, AIM bond critical points52 have been detected for the lateral

and 3.53 Å, on the average). Finally, the I42− moiety is unique in the solid state compound Tl6PbI10,20e for having almost three equal I−I linkages of ∼3.16 Å (ave.). These units extend over an infinite line (a crystallographic 3-fold axis), with 4.03 Å gaps, which do not exclude residual interactions between them. Figure 7 shows

Figure 7. A portion of the Tl6PbI10 crystal structure.20e

that across each I−I vector there is a triplet of Tl+ cations, while more external PbI64− octahedra are not reported. Most likely, unique features of I42− depend on the compactness of the arrangement in the solid state structure. Below, we will briefly illustrate an attempt of modeling the situation. As for I3−, Hirshfeld surfaces have been constructed from the available crystal data of two I42− prototypes, namely, the symmetric NUTSOL20g and the asymmetric NABWOD.20c In the former case (Figure 8a), small red circles appear at both

Figure 8. Hirshfeld surfaces and chemical surroundings for the crystal structures of (a) [Me3N(CH2)6NMe3][I4], NUTSOL20g and (b) [3,10,17-triazonia-1(1,3)-benzenacyclo-octa decaphane] [I4]I, NABWOD.20c

lateral atoms (some are hidden in the backside), confirming equivalent lateral perturbations of the charges, which do not 1767



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Scheme 6. Effects on the I42− Geometry for Various Distributions of the Total 2+ Charge: (a) Two Symmetric Squares (δ+ = 0.25); (b) a Single Square (δ+ = 0.5); (c) Two Nonequivalent Squares (δ1 = +0.23 and δ2 = +0.27); (d) Five Reciprocally Staggered Triangles at the Position of the Tl+ Cations in Tl6PbI10 (δ1 = +0.167, δ2 = +0.083)

Scheme 8. ΔE’s (kcal mol−1) of the Transition States and Product for the Addition of Separated I− + I3− Species in Vacuo and in CHCl3 Solvent, Respectivelya

Scheme 7. Comparisons of ΔE (Upper) and ΔG (Lower) Values (in kcal mol−1) for Various Steps of Iodide Additions to an I2 Molecule (a) in Vacuo; (b) in CHCl3 Solvent

linkages,53 and bonding is also supported by positive Wiberg and Bader54 indexes (∼0.12), although smaller than the central one (0.57). Lower Scheme 7b shows that the energy for an overall termolecular 2I− + I2 association, disfavored in vacuo (left side), is exothermic (−9.18 kcal mol−1) or barely endoergonic (+1.94 kcal mol−1) in solvent (right side). The results are important for validating for the first time I42− as a stable adduct. Optimized transition states (TS) help outlining addition profiles (Scheme 8), the in solvent one being much lower in energy due to a less effective repulsion between the approaching negative charges. Consider that, in any case, the TS barrier is overestimated because the asymmetric I3− is not assisted by positive charges. The TS lies close in energy to the symmetric I42− product (ΔE < 1 kcal mol−1), in spite of the still large geometric differences between the two points (at TS the atom I4 is still at a nonbonding distance > 4 Å). Therefore, it has been assumed that the approaching negative charge can induce important polarization effects on I3−. To prove this point, a series of I42− optimizations was performed in solvent by fixing different lateral separations. At 7.0 Å (see Figure 9), the I1−I2 and I2−I3 vectors are already asymmetric (2.99 and 3.06 Å, respectively), but the NBO charge of the remote I4 atom is still −1.0, while 0.05 electrons are shifted from the adjacent I3 atom to the most remote I1 one (I2 is unaffected). However, the MEP of Figure 9 does not confirm with an incipient σ hole the reduced electron density at the I3 atom, also because this is still highly negative (−0.40). By further shortening the I4−I3 distance, as the in

a

At each point, the corresponding I−I distances and NBO atomic charges (italics) are also reported above and below the I42− unit.

Figure 9. MEP surface (at 0.04 e−/Bohr3, with the red and blue colors corresponding to potentials −0.15 and +0.1 hartree) for an incipient I42− adduct with one lateral 7.0 Å separation. Distances and atom charges (in italics) are shown.

solvent TS structure (see Scheme 8), the increased I3− polarization is accompanied by the transfer of 0.15 electrons from I4, which eventually becomes 0.22 at the I42− product. At this point, the inner electron redistribution conveys a −0.44 charge to central I2 unit, which would be instead uncharged if no lateral bonding existed, as previously supported.20f We think that such a major electron redistribution corresponds to significant delocalization of the σ bonding over the entire adduct, hence a good degree of covalency (or again hypervalency) ensues. Orbital Modeling of I42−. The tetraatomic consists of 30 valence electrons, 16 of them totally occupying the π set (8 pπ 1768



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adjacent I2 or I3− unit. Solvent is important to reduce the electrostatic repulsions and, in particular. lowers the barrier toward I42−. At TS, the originally symmetric I3− component is already much distorted while the incoming iodide is still remote. In the absence of surrounding positive charges, which favor deformation, the 1− charge of the approaching iodide must induce polarization at I3−. Evidence for the latter effect has been searched through MEP surfaces. The induced electrostatic interaction can be initially important to anchor together the I− and I3− units, but very soon an electron transfer from the incoming nucleophile determines delocalization throughout the entire σ systems. A similar effect also occurs for the I2 + I− addition, implying some orbital overlap already at still large distances. This implies an increasing degree of covalency or, better to say, hypervalency due to the electron richness of the central atom(s). Similar aspects also apply to classic I···I−R− HalB systems, where the high energy of the carbon hybrid conveys a large electron density shift towards the remote iodide and induces 4e- repulsion. In any case, a fraction of the σ electrons continues to be shared by the system, the long I···I linkage being comparable to those of I42− systems. The delocalization is best highlighted by R groups, which carry good electron withdrawing substituents; hence HalB is not purely electrostatic as it is frequently assumed.

orbitals) and 14 in the σ system (four pairs of s and px orbitals). In first approximation, two low lying combinations may be considered external σ lone pairs, hence formally excluded from the inner σ bonding. The latter consists of six MO combinations containing 10 electrons (6c/10e− model, where c are orbitals rather than atoms), so that the degree of hypervalency is higher than in I3−. The corresponding levels of the D∞h I42− dianion (Scheme 9) have an increasing number of nodes, with Scheme 9. Qualitative MO Picture of the Six Inner σ Levels for a D∞h I42− Species

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the two highest populated ones (2Σu+ and 3Σg+) being clearly antibonding at the central and lateral I−I linkages, respectively. Under these circumstances, the overall number of single bonds for the three I−I connections can only be one, and it is ensured by the uniquely vacant 3Σu+ level, which is overall antibonding. Therefore, the delocalized three linkages can span from 0.33 bond order each to a single and two null ones, the latter picture having being invoked by some authors.20f Recall that the symmetric I3−, also featuring a unique antibonding MO (2Σu+ in Scheme 1), was attributed two 0.5 bond orders, because the populated 2Σg+ level is also antibonding and cancels out one of the two possible I−I linkages (6e−/4c model). I42− is also subject to variable s/px rehybridizations at the central atoms depending on the donor power of the lateral ones, with variable effects on the σ* populated 2Σu+ and 3Σg+ levels. A I3− + I− interaction MO diagram highlights in some details the mentioned aspects, which for the sake of brevity, are only illustrated in the Supporting Information. An important point to be made is that the lower the I− lone pair lies, the weaker is the formed linkage. In turn, also the linkages of the adjacent I3− unit are affected, consistently with the trends of the asymmetric I42− structures YIRLOA20h and NABWOD.20c

COMPUTATIONAL DETAILS DFT optimizations were carried out with the Gaussian09 package.33 The conductor-like polarizable continuum model (CPCM) was used for in solvent calculations (CH3Cl).40 Standard effective Stuttgart/Dresden core potential (SDD) was used for I atoms55 with polarizing d functions. Different DFT functionals, such as B3LYP,36 the M05-2X,37 and B2PLYP-D,38 were tested, the latter two in order to evaluate the dispersion forces considered important for halogen bonding. Given the consistency of the results, much work was based on the B3LYP approach. Frequency calculations confirmed the nature of all the optimized stationary points, as either minima or transition states. For the latter, intrinsic reaction coordinate (IRC) analysis was carried out.56 Atomic charges were calculated using NBO charge analysis.42 Qualitative MO arguments also were developed with the help of numeric or graphic packages, such as Molekel,57 AOMIX,53 and CACAO.26 The surroundings of I3− and I42− anions in selected crystal structures were analyzed from Hirshfeld surfaces obtained with the Crystal Explorer package.21 MEP plots22 were generated from the optimized geometries using the GaussView package.

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CONCLUSIONS Basic geometric and electronic aspects of the building blocks of larger polyiodides (I−, I2, I3−, I4−) have been addressed. The occasional asymmetry of the linear anions has been attributed to a solid state effect such as an unbalanced distribution of the cations in some crystals, as confirmed by Hirshfeld surfaces.21 The accumulation of positive charges influences the orbitals of the closest iodide and directionally reduces its electronegativity, hence the interaction with adjacent I2 or I3− units. The experimental asymmetry trends have been satisfactorily mimicked by DFT methods by imposing variable surroundings of external positive point charges. The behavior is ascribed to some critical wave functions of the tri- and tetraatomics, having different s/p mixings at the central atom(s), which increase repulsion toward the lateral atom(s). Energy profiles allow monitoring the addition of one iodide to an

ASSOCIATED CONTENT

S Supporting Information *

Perturbation theory effects in I42−; computed coordinates of all the optimized I2, I3−, and I42− units. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel: +39 05552525884. Fax: +39 05552525203. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Ministero dell’Istruzione, Università e Ricerca (MIUR), Project PRIN2008 No. 2008RFEB3X. 1769



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(18) Rosssi, M.; Marzilli, L. G.; Kistenmacher, T. J. Acta Crystallogr., Sect. B 1978, 34, 2030 . (19) Cambridge Structural Database System, Cambridge Crystallographic Data Centre, Cambridge, UK Version 5.32. (20) (a) Herbstein, F. H.; Kapon, M.; Schwotzer, W. Helv. Chim. Acta 1983, 35. (b) Herbstein, F. H.; Schwotzer, W. J. Am. Chem. Soc. 1984, 106, 2367. (c) Illioudis, C. A.; Steed, J. W. CrystEngComm 2004, 6, 239. (d) Long, De-L.; Hu, H.-M.; Chen, J.-T.; Huang, J.-S. Acta Crystallogr., Sect C 1999, 55, 339. (e) Rabenau, A.; Schulz, H.; Stoeger, W. Naturwissen. 1976, 63, 245. (f) Muller, M.; Albrecht, M.; Gossen, V.; Peters, T.; Hoffmann, A.; Raabe, G.; Valkonen, A.; Rissanen., K. Chem.Eur. J. 2010, 16, 12446. (g) Abate, A.; Brischetto, M.; Cavallo, G.; Lahtinen, M.; Metrangolo, P.; Pilati, T.; Radice, S.; Resnati, G.; Rissanen, K.; Terraneo, G. Chem. Commun. 2010, 46, 2724. (h) Hitchcock, P. B.; Hughes, D. L.; Leigh, G. J.; Sanders, J. R.; de Souza, J.; McGarry, C. J.; Larkworthy, L. F. J. Chem. Soc., Dalton Trans. 1984, 3683. (i) Redel, E.; Rohr, C.; Janiak, C. Chem. Commun. 2009, 2103. (j) Dubler, E.; Linowsky, L. Helv. Chim. Acta 1975, 58, 283. (21) (a) McKinnon, J. J.; Jayatilaka, D.; Spackman, M. A. Chem. Commun. 2007, 3814. (b) Spackman, M. A.; Byrom, P. G. Chem. Phys. Lett. 1997, 267, 215. (c) McKinnon, J. J.; Mitchell, A. S.; Spackman, M. A. Chem.Eur. J. 1998, 4, 2136. (22) Hassel, O. Mol. Phys. 1958, 1, 241. (23) (a) Stewart, R. F. J. Chem. Phys. 1972, 57−1664. (b) Politzer, P.; Truhlar, D. G., Eds.; Chemical Applications of Atomic and Molecular Electrostatic Potentials; Plenum: New York, 1981. The definition of electrostatic potential created by a molecule’s nuclei and electron is given where ZA is the charge on nucleus A, located at RA and ρ(r) is the molecular electronic density.

Computations were allowed by the ISCRA-CINECA HP Grant HP10BNL89W. CNR-DPM and MATTM supported this research through Project “PIRODE”.

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V ( r )⃗ =

∑

ZA − |RA − r|

∫

ρ(r′) dr′ |r′ − r|

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Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, O.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 0.9, Revision B.01 ed.; Gaussian, Inc.: Wallingford CT, 2010. (34) (a) Cízek, J. J. Chem. Phys. 1966, 45, 4256. (b) Cízek, J. Adv. Chem. Phys. 1969, 14, 35. (c) Cízek, J.; Paldus, J. Int. J. Quantum Chem. 1971, 5, 359. (35) Møller, C.; Plesset, M. S. Phys. Rev. 1934, 46, 618. (36) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (37) (a) Zhao, Y.; Schultz, N. E.; Truhlar, D. G. J. Chem. Phys. 2005, 123, 194101: 1. (b) Zhao, Y.; Schultz, N. E.; Truhlar, D. G. J. Chem. Theor. Comput. 2006, 2, 364. (38) Grimme, S. J. Chem. Phys. 2006, 124, 34108. (39) (a) Datta, S. N.; Ewig, C. S.; Wazer, J. R. V. J. Mol. Struct. 1978, 48, 407. (b) Svensson, P. H.; Kloo, L. J. Chem. Soc., Dalton Trans. 2000, 2449. (40) (a) Barone, V.; Cossi, M. J. Phys. Chem. 1998, A102, 1995. (b) Cossi, M.; Rega, N.; Scalmani, G.; Barone, V. J. Comput. Chem. 2003, 24, 669. (41) In general the reported MEP plots were derived from calculation with the 3-21G(*) basis set for iodine, but the usage of the SDD pseudo-potential does not significantly alter the picture (42) Glendening, E. D.; Badenhoop, J. K.; Reed, A. E.; Carpenter, J. E.; Bohmann, J. A.; Morales, C. M.; Weinhold, F. NBO 5.0; Theoretical Chemistry Institute, University of Wisconsin: Madison, WI, 2001. (43) Parvez, M.; Wang, M.; Boorman, P. M. Acta Crystallogr., Sect. C 1996, 52, 377 . (44) (a) Tasman, H. A.; Boswijk, K. H. Acta Crystallogr. 1957, 10, 596. (b) Mooney-Slater, R. C. L. Acta Crystallogr. 1959, 12, 187. (45) Hirshfeld, F. L. Theor. Chim. Acta 1977, 44, 129. (46) Migchelsen, T.; Vos, A. Acta Crystallogr. 1967, 23, 796 . (47) The sequence I-Br-I has been reported for the anion I2Br− in the structure with refcode PILDOD. (see Naito, T.; Tateno, A.; Udagawa, T.; Kobayashi, H.; Kato, R.; Kobayashi, A.; Nogami, T. J. Chem. Soc., Faraday Trans. 1994, 90, 763). In another structure the same compound (Refcode: YIWTUT) more correctly carries the atom Br at one lateral position. (see Tateno, A.; Udagawa, T.; Naito, T.; Kobayashi, H.; Kobayashi, A.; Nogami, T. J. Mater. Chem. 1994, 4, 1559). (48) Muetterties, E. L.; Mahler, W.; Schmutzler, R. Inorg. Chem. 1963, 2, 613. (49) (a) Coe, B. J.; Glenwright, S. J. Coord. Chem. Rev. 2000, 203, 5. (b) Crabtree, R. H. The Organometallic Chemistry of the Transition Metals, 4th ed.; Wiley-Interscience: New York, 2005. (c) Hartley, F. R. Chem. Soc. Rev. 1973, 2, 163. (50) Weiss, R.; Schwab, O.; Hampel, F. Chem.Eur. J. 1999, 5, 968 . (51) Wang, Y.-Q.; Wang, Z.-M.; Liao, C.-S.; Yan, C.-H. Acta Crystallogr., Sect. C 1999, 55, 1503 . (52) Bader, R. F. W. Atoms in Molecules. A Quantum Theory; Clarendon Press: Oxford, 1990. (53) Nelyubina, Y. V.; Antipin, M. Yu.; Dunin, D. S.; Kotov, V. Yu.; Lyssenko, K. A. Chem. Commun. 2010, 46, 5325. (54) (a) Gorelsky, S. I. AOMix: Program for Molecular Orbital Analysis, version 6.5, 2011; University of Ottawa, http://www.sgchem.net/. (b) Gorelsky, S. I.; Lever, A. B. P. J. Organomet. Chem. 2001, 635, 187. (55) (a) Dolg, M.; Wedig, U.; Stoll, H.; Preuss, H. J. Chem. Phys. 1987, 86, 866. (b) Andrae, D.; Haussermann, U.; Dolg, M.; Stoll, H.; Preuss, H. Theor. Chim. Acta 1990, 77, 123. (56) Fukui, K. Acc. Chem. Res. 1981, 14, 363. (57) MOLEKEL 4.0; Flükiger, P.; Lüthi, H. P.; Portmann, S.; Weber, J. Swiss Center for Scientific Computing: Manno, Switzerland, 2000.

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