1. Introduction
Interactions through σ- and π-holes are responsible for the formation of a wide group of noncovalently bound complexes [
1,
2,
3,
4,
5]. Both of these sorts of hole originate in the anisotropic distribution of electron density, as for example in a depletion arising along extensions of covalent bonds to electron-withdrawing substituents, or in regions lying above a molecular plane. Depending upon the identity of the atom which has acquired such a positive region, the ensuing bonds are typically labeled as halogen [
6,
7,
8,
9], chalcogen [
10,
11,
12], pnicogen [
13,
14,
15,
16], tetrel [
17,
18,
19,
20], triel [
21,
22,
23], or aerogen bonds [
24,
25,
26,
27]. The underlying nature of these interactions have been the subject of considerable theoretical research, and have applications in fields such as crystal engineering [
28,
29,
30,
31,
32,
33], supramolecular chemistry [
34,
35,
36,
37], materials chemistry [
38,
39], and biochemistry [
40,
41,
42,
43]. A number of experimental works have generated an impressive database of crystalline structures which inspire detailed theoretical analyses. These same ideas have been extended to the nominally unreactive inert gas atoms, which Bauza and Frontera [
27] dubbed the aerogen bond. While the aforementioned noncovalent bonds are generally associated with atoms commonly found on earth, often important components of biological structures, or participating in chemical reactions, the noble gases are characterized by their rare occurrence and low reactivity, so their participation in these noncovalent bonds was not entirely expected.
There has not been a great deal of past study of the aerogen bond (AeB). Most previous works have been devoted to complexes of noble gas oxides [
44,
45,
46,
47,
48,
49]. For example, Miao et al. examined geometries and spectral properties of several small molecular clusters containing XeO
3 [
47]. A series of DFT computation found binding energies of the more stable conformations of dimers are larger than in excess of 10 kcal/mol, and twice that for trimers. Another study [
48] combined XeO
3 with benzene, again yielding complexation energies on the order of 10 kcal/mol, either with various DFT functionals or with CCSD(T)/CBS. The binding is considerably weaker, however, less than 3 kcal/mol, for heterocyclic derivatives of benzene [
50]. Our own group has previously considered AeBs between AeOF
2 and diazines. AeOF
2 contained both σ and π-holes; the former engaged in AeBs of up to 18 kcal/mol, as compared to the weaker bonds of the π-holes in the 6–8 kcal/mol range [
46]. Similar energies were obtained by Gomila and Frontera for various complexes which appeared in the ICSD database [
51] of xenon fluorides with a number of electron donors. Like their related noncovalent bond counterparts, AeBs are also subject to cooperative effects [
45,
49]. Chain elongation of the (KrOF
2)
n=2–6 and (XeOF
2)
n=2–6 clusters strengthened the individual bonds, more for the latter than for the former [
45]. Likewise, the presence of an AeB strengthens a neighboring halogen bond [
49]. With respect to individual Ae atoms, Carvalho and co-workers [
52] provided an experimental benchmark to their computations of Ae···methanol complexes in the gas phase, finding that the binding strengthened along with increasing Ae atom size, from −0.4 to −3.9 kJ/mol. Their energy decomposition documented the importance of dispersion to this bonding. Similar conclusions were drawn by de Araujo Oliviera et al., for complexes between H
2S and noble gases [
53].
The forgoing papers, along with others, suggest that aerogen bonding follows the same patterns as the more extensively studied pnicogen or halogen bonds. However, surprisingly little is known about the impact of solvent on noncovalent bonds. In 2011 Lu et al., compared the interaction energies of iodo-perfluoroalkenes and -arenes, with halide ions, ammonia, and water in the gas phase and three different solvents [
54]. Their results indicated that the bond strengths significantly weaken in solution, and is accompanied by elongation of the intermolecular distances. For example, the interaction energy of C
2F
3I···Cl
− in the gas phase is −26.2 kcal/mol, while placing this complex in chloroform results in almost a four-fold drop. In another set of systems, solvent caused a slight shortening of halogen bonds in neutral systems and relatively small changes in their energetics [
54]. On the other hand, Bania et al. found that the change from vacuum to polar solvent reverses the negative interaction energies of cation–π complexes formed between light metal cations and substituted benzenes and borazines to positive values [
55]. There has also been some study of the effects of solvents on cooperativity [
25,
56,
57]. Esrafili’s group described the tuning of pnicogen and chalcogen bonds by aerogen-bonding in the presence of solvent [
57], finding that the immersion in solvent reduces the interaction energies of binary and ternary complexes. Additionally, the increase of the solvent’s dielectric constant elongated the Ae···N distances, indicative of a weaker bond. These results are consistent with the weakening of pnicogen and chalcogen bonds in the presence of solvent [
25].
While a primary effect of immersion in solvent appears to be a general weakening of the pertinent noncovalent bond, there have been a number of recent reports of a more drastic change when the two species involved are ions of like charge. Despite the Coulombic repulsions that keep these ions apart in the gas phase, charge dispersal effects accompanying solvation can allow them to approach close enough together so as to overcome the electrostatic repulsion and engage in a stable complex. After initial findings of this effect in the case of H-bonds [
58,
59,
60,
61,
62,
63,
64,
65,
66,
67,
68,
69], more recent work has shown these ideas can be extended to halogen [
70,
71,
72,
73,
74,
75,
76,
77], triel [
78], pnicogen [
79], and related types of noncovalent bonds [
80,
81,
82,
83,
84]. There is an important question as to whether aerogen bonds, which are generally much weaker than most of the other related interactions, can likewise occur between pairs of anions, and if so, how strongly polarizing a solvent is needed.
The present work attempts to address this question via quantum chemical calculations. Potential AeB donors place Kr and Xe within the context of a AeX
5− anion where X refers to either F or Cl. The planar D
5h geometry of these anions has the potential to induce a relatively positive π-hole directly above the Ae atom which might attract a nucleophile. Anionic nucleophiles chosen to interact in this way are F
−, Cl
−, and CN
−, all of which are compact so avoid dispersal of their charge over an extended system, and to avoid secondary interactions which might blur the results. In order to directly assess the effect of the solvent in a measured manner, three different solvents were chosen. Tetrahydrofuran (THF) is the least polar with a dielectric constant ε = 7.4. Dimethylformamide (DMF) is considerably more polar, with ε = 37.2, and water is strongest in this regard with a dielectric constant of 78.4. The possibility of each of the Ae-containing Lewis acids binding to each of the three anions is considered in each of these solvents, monitoring the strength of any bonding in each case. An inspiration for the choice of model system is derived from an important X-ray structure [
84] of the pentafluoroxenate(IV) anion (XeF
5−) [
85] which represents the first reported example of a pentagonal planar specimen including an aerogen atom.
2. Computational Methods
Geometries of all monomers and their complexes were optimized at the MP2/aug-cc-pVDZ level [
86,
87] of theory. The pseudopotential aug-cc-pVDZ-PP basis was used for Xe atoms in order to incorporate relativistic effects [
88]. This basis set has proven its accuracy and reliability for systems of this type in numerous comparisons with larger basis sets and with various levels of treatment of electron correlation [
89,
90,
91,
92,
93,
94,
95,
96,
97,
98,
99]. To take into account solvent effects (solvents tetrahydrofuran THF, water, and
N,
N-dimethylformamide DMF), calculations utilized the Polarizable Continuum Model (PCM) in its linear response (LR-PCM) variant [
100]. Harmonic frequency analysis verified that all optimized structures were in fact true local minima, with no imaginary frequencies. In the next step the interaction energy (E
int) and the binding energy (E
b) were calculated as the difference in energy between the complex and the sum of the two monomers. E
int placed the constituent monomers in their geometry within the complex, whereas E
b takes as its reference the monomers in their fully optimized isolated geometries. These two quantities thus differ by the deformation energy E
def induced by the complexation process on the geometries of the two subunits. Both quantities were corrected for the basis set superposition error (BSSE) via the counterpoise protocol defined by Boys and Bernardi [
101].
Calculations were carried out within the framework of the latest version of the Gaussian 16 (C.01) program package [
102]. QTAIM methodology was used to identify bond paths and their quantitative features through analysis of the electron density topology embedded in the AIMAll program [
103]. The decomposition of the interaction energies was carried out by the LMO-EDA method based on the original Kitaura and Morokuma scheme [
104] at the M06-2X/aug-cc-pVDZ level using MP2 optimized geometries (implemented in the GAMESS-US 2014 software) [
105]. In this method, the total interaction energy is decomposed into electrostatic, exchange, repulsion, polarization and dispersion components [
106]. The molecular electrostatic potential (MEP) and its extrema on the 0.001 au electronic isodensity surface, or at other particular points, were evaluated via the MultiWFN [
107,
108] and visualized by VMD [
109] programs.
4. Discussion
While it may be notable that a pair of anions can form a complex, even a metastable one, the very weak binding in the aerogen bonds is a point of particular interest. The binding energies do not exceed 2 kcal/mol, even in the strongly polar water solvent. This behavior contrasts with binding energies of various other anion pairs. Taking aqueous solution for the sake of consistency, the binding energy of CN
− with the various ACl
3− anions, where A is a member of Group 2A of the periodic table can be quite a bit larger, ranging all the way up to 20 kcal/mol [
82] for A=Be. Similarly large binding energies occur when A is a 2B element Zn, Cd, or Hg [
83]. Pnicogen bonds between anions are even larger in magnitude, more than 20 kcal/mol for the ZCl
4− series, with Z=P, As or Sb [
79].
It is perhaps not surprising that the electrostatic component of the interaction energies in these anion-anion complexes is a large positive value, strongly repulsive. It is only because of larger attractive components, chiefly polarization, that these dimers are able to form at all. Here again, these AeBs differ from the other anion-anion complexes discussed above. The electrostatic component is very small for the Group 2A complexes, and its sign depends on the specific central A atom [
82]. The electrostatic energy is rather attractive for the Group 2B analogues between 40 and 100 kcal/mol [
83] and ramps up to even larger negative amounts even as much as 111 kcal/mol for the pnicogen-bonded anion pairs [
79].
One may not have anticipated that a π-hole might develop directly above the AeX
5− anion, albeit one of negative sign. A simple VSEPR analysis of this anion suggests the central Ae atom ought to contain two lone electron pairs. Given the D
5h geometry of this unit, these pairs should be disposed directly above and below the central Ae, coinciding with the π-hole. The two NBO lone pair orbitals of KrF
5− are illustrated in
Figure 3a,b. The
p-orbital of Kr in
Figure 3a lies above and below the molecular plane and the
s-orbital is of course symmetric. Both of these orbitals will contribute electron density to the regions directly above and below the Kr atom. An alternate view combines these two atomic orbitals into a pair of
sp orbitals, one lying above and one below the molecular plane. This disposition of these two electron pairs is reinforced by the ELF diagram in
Figure 3c. Despite the positioning of these two electron pairs, there is indeed a maximum in the MEP that occurs directly along the C
5 axis which seems capable of attracting the anion. It is not only on the ρ = 0.001 au isosurface that these maxima are so positioned; the same is true of a range of densities. This maximum is likely due to the ability of the five X substituents to draw electron density toward themselves, and out of the region perpendicular to the molecular plane. Nonetheless, the coincidence of the positions of the π-holes and the two Ae lone pairs represents a major factor in the very weak nature of the aerogen bonding in these complexes.
Again drawing a comparison to the other anions mentioned above, the Group 2A and 2B ACl
3− anions are planar, as is AeX
5− here [
82,
83]. However, the central A atom does not have any lone pairs that point directly along their C
3 axis that would inhibit the approach of an anion from this direction. The central Z pnicogen atom of planar ZCl
4− contains only a single lone pair [
83], whose NBO orbital shape resembles an isotropic
s-orbital, as in
Figure 3b, so is not directed toward the π-hole. It is thus partly for this reason that the binding energies of these various Lewis acid anions with another anion are so much larger than those of the AeBs here.
As noted above, there are a number of complexes which represent metastable minima in the sense that the energy of the complex is higher than that of the separated monomers, and that the dissociation of the complex is impeded by an energy barrier. The data in
Table 4 indicate that this barrier is rather shallow, on the order of 2 kcal/mol or less. The idea of a metastable complex between a pair of anions is reminiscent of what has been seen earlier in a number of cases. Previous computations have estimated the dissociation barriers to be considerably higher than those observed here [
111]. These barriers are roughly 20 kcal/mol when CN
− is added to ACl
3− where A represents Group IIA atoms Be-Ba [
82], and somewhat higher, around 25 kcal/mol, when it is a Group IIB atom Zn, Cd, or Hg that lies at the center [
83]. The same magnitude barrier to dissociation occurs for ZCl
4− anions where Z is a 5A pnicogen atom [
79].