Cooperativity of Halogen, Chalcogen, and Pnictogen Bonds in

Article pubs.acs.org/JPCA

Cooperativity of Halogen, Chalcogen, and Pnictogen Bonds in Infinite Molecular Chains by Electronic Structure Theory Janine George,† Volker L. Deringer,† and Richard Dronskowski*,†,‡ †

Institute of Inorganic Chemistry, Chair of Solid-State and Quantum Chemistry, RWTH Aachen University, Landoltweg 1, 52056 Aachen, Germany ‡ Jülich-Aachen Research Alliance (JARA-HPC), RWTH Aachen University, 52056 Aachen, Germany S Supporting Information *

ABSTRACT: Halogen bonds (XBs) are intriguing noncovalent interactions that are frequently being exploited for crystal engineering. Recently, similar bonding mechanisms have been proposed for adjacent main-group elements, and noncovalent “chalcogen bonds” and “pnictogen bonds” have been identified in crystal structures. A fundamental question, largely unresolved thus far, is how XBs and related contacts interact with each other in crystals; similar to hydrogen bonding, one might expect “cooperativity” (bonds amplifying each other), but evidence has been sparse. Here, we explore the crucial step from gas-phase oligomers to truly infinite chains by means of quantum chemical computations. A periodic density functional theory (DFT) framework allows us to address polymeric chains of molecules avoiding the dreaded “cluster effects” as well as the arbitrariness of defining a “large enough” cluster. We focus on three types of molecular chains that we cut from crystal structures; furthermore, we explore reasonable substitutional variants in silico. We find evidence of cooperativity in chains of halogen cyanides and also in similar chalcogen- and pnictogen-bonded systems; the bonds, in the most extreme cases, are amplified through cooperative effects by 79% (I···N), 90% (Te···N), and 103% (Sb···N). Two experimentally known organic crystals, albeit with similar atomic connectivity and XB characteristics, show signs of cooperativity in one case but not in another. Finally, no cooperativity is observed in alternating halogen/acetone and halogen/1,4-dioxane chains; in fact, these XBs weaken each other by up to 26% compared to the respective gas-phase dimers.

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INTRODUCTION Within molecular crystal chemistry, the term “halogen bond” (XB) is used to group those relatively weak bonding interactions of a halogen atom that is otherwise covalently bonded and whose local electronic structure corresponds to an already filled noble gas shell, as depicted in Scheme 1. Such XBs

and pnictogen bonds all are sigma-hole interactions, in which the halogen, chalcogen, or pnictogen atoms, respectively, possess the sigma-hole, a region of positive electrostatic potential (ESP) on these atoms to which a suitable partner with an outer negative ESP may be electrostatically attracted along the X−CN axis. The matter is gaining attention fast,5−8 and it has been aptly reviewed in ref 9. In addition, the corresponding interactions of electronegative elements of main group IV (that is, carbon bonds) have been investigated.10 Not only are isolated interactions important for the design of crystals but also the mechanism by which these interactions influence each other. A typical effect of such mutual influence is the enhancement of interaction strengths (the bond cooperativity), most widely studied for the ubiquitous hydrogen bond.11,12 Not surprisingly, several groups have quantum chemically investigated the cooperativity of XBs and have come to important insights from molecular cluster computations.13−21 Such a “molecular” approach to crystals with threedimensionally extended structures, however, will naturally arrive at a molecular picture because of being linked to isolated gas-phase fragments. As an alternative, a computational

Scheme 1. Cartoon of an XB Interaction, with a Halogen Cyanide (X = Cl, Br, I) Molecule and an Acceptor R Involved

are not only known from biological molecules such as thyroid hormones,1 but they have also been well-established as crucial interactions that govern molecular recognition.1 Meanwhile, the term is widely recognized both in supramolecular chemistry and in crystal engineering, too.2 More recently, so-called pnictogen and chalcogen bonds were explored in which the above definition is boldly extended to electronegative elements of main groups V and VI;3,4 again, their importance is mainly in crystal engineering. The above-mentioned halogen, chalcogen, © 2014 American Chemical Society

Received: February 12, 2014 Revised: April 8, 2014 Published: April 8, 2014 3193

dx.doi.org/10.1021/jp5015302 | J. Phys. Chem. A 2014, 118, 3193−3200

The Journal of Physical Chemistry A

Article

optimized structure, and all energy values given pertain to such single-point calculations. The interaction energies ΔEint are referenced to the monomers cut from the chain or fragment examined (i.e., monomers are frozen in the previously relaxed geometry):

treatment of truly infinite networks might be attempted. Indeed, studies of this kind have been carried out by us and others to study hydrogen bond cooperativity.22−24 In these contributions, crystalline and infinite fragments were derived from three-dimensionally infinite networks, leading to characteristic fragments such as one-dimensional chains or twodimensional sheets. In this work, the cooperativity of the halogen, the chalcogen, and the pnictogen bond are investigated using one-dimensionally infinite chain models. These investigations are an interim stage toward the examination of cooperativity in the whole crystal structure and its understanding, but these infinite chains with only one type of interaction are notably easier to rationalize than crystals with possibly multiple cooperative and anticooperative interactions. In fact, it is often impossible to “isolate” interactions in a 3D network except for serendipitous cases where the interactions are clearly aligned with the crystallographic directions.24 We argue in the following that 1D chains provide much insight here as they have traditionally done for the understanding of more “classical” chemical-bonding phenomena; indeed, we have been inspired by many of the latter.25−28

ΔE int = Echain/fragment −

∑ Emonomer

(1)

The chains are more stable if ΔEint is more negative.

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RESULTS AND DISCUSSION Infinite Chains of Cyanides. We start by looking at chains of the type XCN, where X denotes a halogen atom (F−I). Our focus will be on the cooperativity of the chemical bonding (and energies) between these molecules. In other words, does the strength of the intermolecular interaction depend on the number of the molecules in an n-mer and, if so, will it increase (cooperative behavior) or decrease (anticooperative) while the n-mer grows to a one-dimensionally infinite chain? As it happens, Politzer et al. have already studied the cooperativity of linear clusters of these XCN (X = F, Cl, Br) molecules;15 one such linear molecular cluster is sketched in Scheme 2. We also note that whether or not XBs exist with fluorine is a controversial subject.42 Nevertheless, we will evaluate them here.

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THEORY Electronic structure calculations based on density functional theory (DFT) were performed with the Vienna ab initio simulation package (VASP).29−32 The GGA functional of Perdew, Burke, and Ernzerhof (PBE)33 and the projector augmented wave method34,35 were used. The kinetic energy cutoff for the plane wave expansion was 500 eV. Moreover, the “D2” dispersion correction36 as implemented in VASP37 was applied, which is necessary because the XB is mainly electrostatic and dispersive in character.38,39 The D2 method has been benchmarked in the successful prediction of several until then “unpredictable” experimentally known molecular crystal structures.40,41 Zero-dimensional fragments such as molecules, dimers, and trimers, as well as the one-dimensional chain models were treated using a supercell approach, as applied before.23 This procedure is illustrated in Figure 1. In each direction without translational symmetry, a region of at least 19 Å of vacuum was inserted. Chain models were structurally optimized under the constraint of constant volume; the lattice parameters were allowed to relax. Afterward, a final single-point energy calculation was performed for each

Scheme 2. Cartoon of a Linear Halogen Cyanide Dimer (X = Cl, Br, I)

There are two crystal structures for the halogen cyanides. One, the [ICN] structure, is adopted by ICN only,43 and the other one, the [BrCN] structure, is taken by BrCN and ClCN.44,45 The [ICN] and [BrCN] structure types exhibit a similar linear arrangement of molecules and differ only in how the chains are aligned (see Figure 2). Their X···N bond lengths are notably short, as presented in the following paragraph. To our knowledge, there is no FCN crystal structure; liquid FCN polymerizes at room temperature.46 Table 1 displays the X···N bond lengths, and it includes experimental and theoretical data for the [ICN] (left) and

Figure 1. Computational treatment of structurally optimized onedimensional chains and zero-dimensional fragments in supercells. The fragments are cut from the structurally optimized one-dimensional chain.

Figure 2. Alignment of the one-dimensionally infinite chains in the [ICN] and the [BrCN] crystal structures. The arrows indicate the chain direction. 3194



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Table 1. Comparison of X···N Bond Lengths (Å) in Crystals, Chains, Trimers, and Dimersa [ICN] structure molecule FCN ClCN BrCN ICN

expt.

[BrCN] structure

DFT

expt.

a

2.74d

2.97 2.91a 2.74a 2.64

chain

trimer

dimer

DFT

DFT

DFT

DFT

a

2.97 2.92 2.76 2.65

2.97/2.97 3.01/2.99 2.90/2.89 2.84/2.83

3.01 3.04 2.95 2.92

2.94 2.95 2.79 2.67a

3.01b 2.87c

Each of the systems in columns labeled “DFT” have been structurally optimized. Hypothetical structures were derived by computational substitution of halogen atoms in the [ICN] and [BrCN] structures with the particular halogen and a structural optimization. bTaken from ref 45. c Taken from ref 44. dTaken from ref 43. a

thereof increases from FCN to ICN, which seems plausible due to the increasing polarizability of the heavier halogens. To shed more light on this phenomenon of cooperativity, let us look at the most extreme case, ICN, in more detail. We note that the XB has been described as being mostly electrostatic in character,9 and therefore, Figure 4 compares the computed

[BrCN] (middle) structures. The experimental bond lengths in the crystal structures are considerably shorter than the sum of the van der Waals radii47 (Cl···N: 3.01 Å < 3.30 Å; Br···N: 2.87 Å < 3.40 Å; I···N: 2.74 Å < 3.53 Å). The covalent X−C and CN bond lengths are not influenced by which particular structure type is taken, which seems reasonable. Furthermore, the table contains our computed data for hypothetical onedimensional chains, trimers, and dimers of XCN (right). We note that the X···N bond lengths in the infinite onedimensional chains are nearly identical to the respective bond lengths in the two crystal structures gained from DFT calculations. Therefore, the alignment of the chains, which differs between [ICN] and [BrCN], does not influence the bond length heavily. The X···N distances in the optimized dimers and trimers (except for FCN) are significantly larger. These bond length results suggest that only clusters of a specific critical size should be able to approximate bond lengths and other properties in a crystal structure when cooperativity is involved. Still, a cluster even of a critical size is an approximation of an infinite chain.22 On the contrary, a truly periodic calculation of an infinite chain is arguably more accurate in approximating the crystal. A connection between these short intermolecular X···N distances in the crystal and the chain and a possible bond strength cooperativity seems obvious. Hence, we show the halogen bond energies within the infinite one-dimensional chains (expressed as stabilization per bond) and compare them to their counterparts in the dimer and trimer fragments cut from those chains in Figure 3. The interaction energy as defined in eq 1 grows when going from the dimer to the trimer fragment and even more so when moving on to the infinite chain; clearly, the behavior is cooperative, and the extent

Figure 4. Charge density isosurface (0.05 electrons/Å3) plots for a structure-optimized infinite chain of ICN molecules and also for isolated dimer and trimer fragments cut from this infinite chain. The isosurfaces have been colored according to the ESP (red: most negative regions; blue: most positive regions). The interaction energies ΔEint are normalized per XB. The isosurfaces were visualized with VESTA.71

ESPs of dimeric, trimeric, and infinite polymeric ICN. This way of looking at XBs is very popular for sigma-hole interactions in general.9 The dimer and trimer have been cut from the optimized infinite chain. In Figure 4, the regions of most positive electrostatic potential are represented by the color blue, and the most negative regions are in red. In the dimer fragment, the bonding atoms are orange (N) and blue−green (I). In going from the dimer to the trimer, these colors change, which reflects the change in ESPs. The color on the left bonding nitrogen is more yellowish, and hence, its ESP is less negative; that on the left bonding iodine is bluer, and its ESP is more positive than that in the dimer. The right bonding nitrogen’s ESP and the left bonding iodine’s ESP are more negative than those in the dimer. In conclusion, the bonds within the trimer differ from each other and also from that in the dimer bond as seen from their ESPs. All molecules within the infinite chain show identical ESPs, naturally so. The color of the nitrogen atom is redder; the color of the iodine atom is bluer than that in the dimer and trimer fragment. This increasing difference in the ESP (represented by the color change) indicates that all XBs within the infinite chain are identical and stronger than those in the dimer and trimer fragment. We add that the depicted ESPs strongly differ from those of isolated molecules. The bonding

Figure 3. Interaction energy per bond (ΔEint) of the structurally optimized infinite chains XCN compared to trimer and dimer fragments as cut from the infinite chain. 3195



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molecules, but the correct inclusion of periodicity via boundary conditions seems the more natural choice. The interaction energy of the chain depends also on the atomic polarizability; a larger polarizability leads to stronger halogen, chalcogen, and pnictogen bonds. This is in good agreement with previous molecular approaches.3,9,15 Not only the interaction strength alone but also the cooperativity increases with greater polarizability. A New Mechanism of Cooperativity? We move on to more complex molecules whose cooperative behavior has already been the subject of experimental research. Bilewicz et al.58 investigated the cooperativity of XBs in 1-methylpryrrol-2yl-trichloromethyl ketone (PTK), and they assumed a new halogen bond cooperativity mechanism with the involvement of π-electrons. No calculation on cooperativity was performed, understandably so because, as stated in the Introduction, a calculation of one single interaction strength within the lattice is difficult, to say the least. A computational study on the chlorine XB and various other interactions in the PTK crystal has already been carried out.59 To investigate the influence of the C−Cl···OC XBs on each other, we compared the interaction energies in structurally optimized chains and dimers (see Figure 6 for a drawing of the 1D chain). This comparison is displayed

atoms and their ESP mutually interact, and therefore, the ESP is partially neutralized in the bonding region. Here, the weaker colors simply reflect this neutralization. What about chalcogen and pnictogen bonds? In analogy to the chain structures of halogen cyanides, we next created infinite chains from cyanides of main groups V and VI, that is, of X(CN)n molecules (n = 2−3); see Scheme 3. Again, this Scheme 3. Arrangement of X(CN)3 Molecules in the OneDimensionally Infinite Chaina

a The brackets illustrate the repeat unit. The X−CN bonds are nearly perpendicular to one another.

chain model consists of only one molecule per repeat unit. Indeed, the crystal structures of the pnictogen cyanides P(CN)348 and As(CN)349 and also of the chalcogen cyanides S(CN)2,50−54 Se(CN)2,53,55,56 and Te(CN)257 are experimentally known; these, like the halogen cyanides, are built up of molecular chains. The chains in the experimentally known structures, however, are built up from at least two inequivalent molecules per repeat unit other than those in our model calculations; hence, a direct comparison of bond lengths would be misleading and is, therefore, not performed. Notably, As(CN)3, S(CN)2 and Se(CN)2 molecules have already been investigated with regard to σ-bonding3,9 but not yet concerning cooperativity. As seen for the halogen cyanides, adducts are again more stable with increasing period within groups V and VI (see Figure 5). Moreover, the cyanides are more strongly bonded

Figure 6. (a) Lewis structure of the PTK molecule. (b) Onedimensionally infinite chain of PTK molecules as derived from the crystal structure but subsequently fully relaxed. Figure 5. Interaction energy per bond (ΔEint) of the structurally optimized infinite chains X(CN)n, compared to trimer and dimer fragments as cut from the infinite chain.

in Figure 7. It shows the gained interaction energy within the chain plotted against the gained interaction energy of the dimer fragment. This allows for a facile grouping of data points according to their cooperative behavior. Cooperative bonds would appear in the green region and anticooperative bonds in the red one; a bond that is neither cooperative nor anticooperative will be represented by a data point on the diagonal identity. Such is the case for the PTK XBs, which are not cooperative. One might speculate that substituting Cl with Br or I in this structure should increase the interaction strength and could evoke cooperativity as XBs of bromine and iodine are usually stronger than those of chlorine.9 Therefore, substitution of chlorine with bromine or iodine and a subsequent structural

going from main group VII to VI to V. Each of the chains is cooperative, and in particular, the difference between the chain cooperativity and the trimer fragment cooperativity is remarkable, in the most extreme case about −24 kJ/mol per bond (Sb(CN)3; 67% of the chain cooperativity). As this exercise underlines, trimer fragments are insufficient approximants for infinite chains (and, therefore, also for the crystal). In the most extreme case, the Sb(CN)3 chain, the trimer reaches only 66% of the interaction energy in the infinite chain. One might choose larger oligomers of four, five, or six 3196



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iodine, as expected, leads both to a larger absolute interaction energy and also to a larger cooperativity. To conclude, a new XB cooperativity mechanism that has been suggested involving π electrons58 may be present in SAMDAL, but there is no energetic evidence for it in PTK; such a distinction could not be expected or made from structural criteria alone. From Co-crystals to Co-chains. Politzer et al.15 assumed that cooperativity of XBs is only possible when the negative site and the σ-hole are in the same molecule. Therefore, co-crystals such as 1,4-dioxane with bromine62 or acetone with bromine,63 first investigated by Hassel et al. in the 1950s, should not show cooperativity. These structures offer themselves as fitting examples because they have been central for the early understanding of XBs.64 Structurally optimized dimers of these systems have already been studied by molecular orbital calculations.65 Here, again, we derive periodic models that represent what we dub “co-chains”. The chains were cut from these co-crystals and structurally optimized as before, to give the structures shown in Schemes 4 and 5.

Figure 7. Scatter plot of interaction energies for structurally optimized chains (−ΔEchain) compared to dimer fragments (−ΔEdimer) cut from this chain. The interaction energy is normalized per bond, so that the bond enhancement is clearly visible. PTK is represented by squares and SAMDAL by circles.

Scheme 4. Co-chain of Acetone and Bromine Moleculesa optimization has been performed. A likewise hypothetical computational substitution (Br → H) was recently performed on the bromomalonic aldehyde crystal.24 Here, changing of Cl to Br or I enlarges the overall absolute interaction energy but does not significantly change the cooperativity. On a side note, a chain of weak C−H···O hydrogen bonds cut from the PTK crystal does show cooperativity (nearest-neighbor dimer interaction per bond: −17.7 kJ/mol; chain interaction per bond: −20.8 kJ/mol). The H···O distance accounts for 2.26 Å in the optimized structure. This is a notably short contact compared to the same contacts in amino acid structures characterized by neutron diffraction.60 Bilewicz et al.58 mention other structures that show an alignment of XBs similar to that of PTK and, therefore, possibly cooperativity. We structurally optimized an infinite chain from the example with the smallest and, therefore, most tractable unit cell, the ditrichloroacetimide (SAMDAL) crystal.61 The chain is displayed in Figure 8, and its interaction energy has also been plotted in Figure 7. The overall absolute interaction energy in the chain is more pronounced than that in PTK. Moreover, this interaction is indeed slightly cooperative. Computational substitution of chlorine with bromine and

a

The bracket symbolizes the repeat unit.

Scheme 5. As in Scheme 4 but for a Co-chain of 1,4-Dioxane and Bromine Molecules

As before, bromine in the chains was also substituted with chlorine and iodine for a more complete picture. 1,4-Dioxane with chlorine and 1,4-dioxane with iodine experimentally crystallize in the 1,4-dioxane/bromine structure type.66,67 The computational substitution leads to chains that do not seem far, structurally, from the experimental structures. The results are illustrated in Figure 9. As in Figure 7, the gained interaction energy within the chain is plotted against the gained interaction energy of the dimer. The overall interaction energy rises due to the substitution of chlorine with bromine. Unexpectedly, the absolute chain interaction energies of the chains with iodine are only slightly higher than of those with bromine. As expected, these co-chains do display anticooperativity. In the most extreme case, only 74% of the dimer fragment interaction energy is reached in the chain. Moreover, the absolute interaction energies of the chains with acetone (red circles) are lower than these of 1,4-dioxane (red triangles). This is consistent with the calculations on the structurally optimized dimers with bromine by Lo et al.65 Their BSSE-corrected interaction energies at the MP2/6-311+G* level of theory amount to −18.8 (1,4-dioxane) and −15.5 kJ/mol (acetone). They recalculated these energies at the CBS-QB3 level of theory and arrived at −21.8 (1,4-dioxane) and −19.4 kJ/mol (acetone). The interaction energies at the PBE+D2/PAW level of theory of the XB within the chains are even more negative;

Figure 8. (a) Lewis structure of the SAMDAL molecule. (b) Onedimensionally infinite chain of SAMDAL molecules. 3197



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but the tendencies are more distinct, and we believe that the methodology better reflects the “real life” situation of a periodic network, as said before. Moreover, cooperativities of one type of interaction are easier to evaluate than those in a complex crystalline network. In the case of largely cooperative XBs in XCN chains, the chain model reproduces the intermolecular bond lengths in a crystal almost exactly (Δd ≤ 0.03 Å). The gas-phase trimer calculation fails to reproduce these lengths (Δd ≤ 0.21 Å). Searching for a critical cluster length may result in better bond lengths than a trimer calculation but is only an approximation of the truly periodic calculation.22 Additionally, a new mechanism of XB cooperativity could be confirmed with this chain model. The evaluation of cooperativity of synthons in one-dimensionally infinite chains can lead to a better understanding of crystal structures and even their rational design.

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ASSOCIATED CONTENT

* Supporting Information S

Optimized positions of all calculated molecular species in POSCAR format, a comparison of the calculated interaction energies with and without D2 correction, and local densities-ofstates for the ICN chain. This material is available free of charge via the Internet at http://pubs.acs.org.

Figure 9. Scatter plot similar to that in Figure 7 but this time including all systems investigated in this work. One of the displayed cooperative systems is X(CN)n, whereas X represents the halogen atoms (triangle), the chalcogen atoms (circle), and the pnictogen atoms (square). As already shown in Figure 5, the chain energy increases with the principal quantum number of the halogen/chalcogen/pnictogen atom. The chains from the PTK crystal (with chlorine as the halogen) and the substituted chains (with bromine and iodine) are shown with gray squares. The SAMDAL chain (with chlorine as the halogen) and the substituted chains (with bromine and iodine) are represented by gray circles. The co-chains are built from acetone plus a halogen molecule (red circle) and 1,4-dioxane plus a halogen molecule (red triangle).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +49 (0)241 80-92642. Phone: +49 (0)241 80-93642. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the high-performance computing cluster at Rechenzentrum RWTH Aachen for large amounts of CPU time on the JARA-HPC partition. J.G. thanks the Fonds der Chemischen Industrie (Chemical Industry Fund), and V.L.D. thanks the Studienstiftung des deutschen Volkes (German National Academic Foundation) for dissertation scholarships.

we obtain −29.6 (1,4-dioxane) and −27.5 kJ/mol (acetone). The MP2 method shows a large basis set dependency when it comes to the calculation of noncovalent interaction energies.68 Several basis sets show an underbinding, especially the small basis sets (e.g., the 6-311++G** basis set). On the contrary, the D2 correction has previously shown overbinding of dispersion interactions.69,70 This combination of over- and underbinding could explain the relatively large interaction energy difference between the two methods. In this study, only bond enhancement and weakening (not absolute interaction energies) are important. Nonetheless, the trends obtained by all methods are similar. In order to elucidate the influence of the D2 correction on the cooperativity, a comparison at the PBE/PAW level of theory with and without D2 correction was made; see the Supporting Information. It turns out that the different levels of theory do not influence the cooperativity trends. In any case, the above-mentioned co-chains exhibit an unexpectedly large anticooperativity within the halogen-bonded chains.

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CONCLUSIONS Chains of XBs can be largely cooperative or notably anticooperative, and cooperativity may play an important role for pnictogen and chalcogen bonds, too. This is the result of our computational survey, in which we have analyzed the interplay of interactions in molecular one-dimensionally infinite chains. The overall results are summarized in Figure 9; they are qualitatively in agreement with previous gas-phase calculations, 3198



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