Are beryllium-containing biphenyl derivatives efficient anion sponges?
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The structures and stabilities of 2,2′-diBeX-1,1′-biphenyl (X = H, F, Cl, CN) derivatives and their affinities for F−, Cl−, and CN− were theoretically investigated using a B3LYP/6–311 + G(3df,2p)//B3LYP/6–31 + G(d,p) model. The results obtained show that the 2,2′-diBeX-1,1′-biphenyl derivatives (X = H, F, Cl, CN) exhibit very high F−, Cl−, and CN− affinities, albeit lower than those reported before for their 1,8-diBeX-naphthalene analogs, in spite of the fact that the biphenyl derivatives are more flexible than their naphthalene counterparts. Nevertheless, some of the biphenyl derivatives investigated are predicted to have anion affinities larger than those measured for SbF5, which is considered one of the strongest anion capturers. Therefore, although weaker than their naphthalene analogs, the 2,2′-diBeX-1,1′-biphenyl derivatives can still be considered powerful anion sponges. This study supports the idea that compounds containing –BeX groups in chelating positions behave as anion sponges due to the electron-deficient nature and consequently high intrinsic Lewis acidity of these groups.
KeywordsAnion sponges Be-containing biphenyl derivatives Density functional theory
Noncovalent interactions play a crucial role in chemistry; indeed, the last decades of the twentieth century as well as the first decades of the present century have seen a significant increase in the number of noncovalent interactions described in the literature [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], and many of them have been fully characterized. The contributions of Peter Politzer and coworkers in this field of research are numerous and of great relevance . His pioneering work established the basis for obtaining quantitative information on the strength of these interactions from appropriate electronic densities, and it showed how the electrostatic and polarization energies associated with noncovalent interactions can be obtained from them. Also, new and interesting noncovalent interactions such as halogen bonds have been characterized [12, 13, 14]. Perhaps one of the most useful concepts to be introduced into this domain was that of the σ-hole [15, 16, 17], which allows the nature of some of these interactions, such as the halogen bonds mentioned above, to be rationalized . However, as stated above, the most fundamental finding was that noncovalent interactions control an enormous number of processes, including selective interactions between molecules and anions [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58]. As a matter of fact, the selective extraction of anions —a crucial process in many fields such as medicinal and biological chemistry, environmental science, and even basic chemistry—has received a great deal of attention, mainly from an experimental viewpoint , but also, more recently, from a theoretical perspective [32, 61, 62, 63, 64]. In particular, works aiming at the specific design of functionalized compounds for the capture and immobilization of toxic anions have been very popular over the last few years. Indeed, it was very recently shown that compounds containing electron-deficient elements, such as beryllium, behave as highly efficient anion sponges [63, 64], exhibiting anion binding energies that are estimated to be up to 30% higher than those of compounds such as SbF5 or AsF5, which are among the systems that had previously been considered to possess the highest anion affinities [19, 65]. This is the case for 1,8-diBeX-naphthalene (X = H, F, Cl, CN, CF3) derivatives  as well as for 4,5-bis(BeX)-fluorene (X = H, F, Cl, CN, NC, OCH3) derivatives .
The geometries of the 2,2′-diBeX-1,1′-biphenyl (X = H, F, Cl, CN) neutral derivatives and those of the complexes of these derivatives with a set of Y− anions (Y− = F−, Cl−,CN−) were optimized using the B3LYP hybrid functional [66, 67], which includes the three-parameter functional developed by Becke  and the correlation functional of Lee, Yang, and Parr , together with a 6–31 + G(d,p) basis set expansion. The final energies of these optimized structures were determined in single-point B3LYP/6–311 + G(3df,2p) calculations. This theoretical model was found to provide anion affinities that were only slightly larger than the values obtained through the use of high-level ab initio methods such as G4(MP2) , which typically provides thermodynamic magnitudes to an accuracy of ±4 kJ mol−1. The harmonic vibrational frequencies for both neutral and anion complexes were calculated at the B3LYP/6–31 + G(d,p) level of theory in order to check that the stationary points found were local minima of the potential energy surface, and to determine the vibrational corrections to the corresponding enthalpies.
To analyze the electronic characteristics of the anionic complexes under investigation, we used two different but complementary approaches: the quantum theory of atoms in molecules (QTAIM)  and the natural bond orbital (NBO) method . The first approach is based on an analysis of the topology of the electron density of the system, which usually exhibits different critical points, such as local maxima, associated with the position of the nuclei, and saddle points (usually called bond critical points, BCPs), the electron density of which reflects the strength of the bond. The sign of the so-called energy density at each BCP permits us to assess the covalent character of the bonding. Simultaneously, the existence of rings is evidenced by the presence of ring critical points (RCPs). The NBO approach allows us to detect and quantify the existence of charge donation and backdonation between the interacting moieties that stabilize the complex through the use of localized occupied and empty orbitals. All these calculations were carried out using the AIMAll v1.0  and NBO6G  programs.
Results and discussion
Structures and relative stabilities of the neutral compounds
It is interesting to note that the enhanced stability of the cis structures is very likely to be related to the fact that the two Be atoms in all of these structures appear to be tricoordinated rather than dicoordinated as in the trans isomers. In the C 2v cis1 structures, both Be atoms are bound to one X substituent and two C atoms, whereas in the nonsymmetric cis2 structures, only one of the Be atoms presents this coordination pattern; the other Be is bound to one C and two X substituents. This increased coordination of the Be atoms in the cis conformers seems to be the reason for the enhanced stability of these forms with respect to their trans analogs. Indeed, although the two C–Be bonds in the trans conformer are stronger than the four C–Be bonds in the cis1 isomer according to the corresponding electron densities (see the BeF derivatives in Fig. 2), the overall stabilizing effect is larger for the cis1 conformer, as there are four bonding interactions instead of two. In addition, an extra bonding interaction between these two C atoms further contributes to the stabilization of the cis1 conformer. This description is coherent with that obtained through NBO analysis. In this approach, the stabilization associated with the individual C–Be linkages is greater for the trans than for the cis1 forms (531 vs. 368 kJ mol−1), but according to the total number of interactions, the overall stabilizing effect is larger for cis1. The situation for the cis2 conformer is similar to that described for cis1 as far as the C–Be bonds are concerned. Again, these bonds are stronger in the trans conformer, but we replace two bonding interactions with three upon converting to the cis2 form, yielding a greater stabilizing effect overall. A new bonding interaction appears between the bridging F atom and one of the C atoms, contributing further to the stabilization of this cis2 form. Once more, the bonding picture obtained through the NBO analysis is coherent with that obtained using the QTAIM approach. In this case, the C–Be interactions involve similar energies for both conformers (ca. 1020 kJ mol−1 for the cis2 conformer vs. 1050 kJ mol−1 for the trans one), whereas the Be–F interactions are 110 kJ mol−1 stronger for the cis2 structure.
It should also be noted that the relative stabilities of the two cis isomers change depending on the nature of the X substituent. With –BeF and –BeH, the cis2 nonsymmetric minimum is the most stable, whereas –BeCl and –BeCN derivatives have the cis1 C 2v structure as their global minimum. This finding probably reflects the fact that, because the F and H atoms are relatively small, a F···C (H···C) stabilizing interaction occurs for the BeF (BeH) derivatives (see Fig. 2), which is not observed for the –BeCl and –BeCN derivatives.
Structures and relative stabilities of the anionic complexes
In order to obtain the anion affinities of our set of biphenyl derivatives (X = H, F, Cl, CN), we considered different anion binding patterns (Y− = F−, Cl−, CN−) for the two most stable isomers cis1 and cis2.
The C–Be bonds are also predicted to be slightly stronger in the global minimum, A3. However, the reduction in the number of the Be–Cl bonds overrides this, even though the Be–Cl bond is stronger in A3 than in A2, the electron density is not twice as strong. Accordingly, a destabilization of the system would be expected. The increase in the number of Be–F bonds upon switching from A2 to A3 stabilizes the system, because even though the two F–Be bonds involving the central F atom in A3 are weaker than each of the Be–F bonds in A2, the formation of two bonds results in an overall stabilizing effect. If this latter effect is the dominant one, we would expect the A3 structure to be more stable than A2. Unfortunately, the QTAIM approach does not provide information about the energetics of the aforementioned electron density redistributions, but this information can be deduced from the NBO analysis, which shows that the greater number of Be–F interactions in the A3 isomer stabilizes it by about 69 kJ mol−1, while the decreased number of Be–Cl interactions destabilizes it by around 52 kJ mol−1 with respect to A2. The NBO results also show that the C–Be interactions are slightly reinforced (by 20 kJ mol−1). Finally, because the Cl atom is larger than F, it forces a wider separation between the Be atoms (2.72 Å in A3 vs. 3.11 Å in A2) and therefore a greater distortion of the molecular skeleton, which has a corresponding energetic cost, estimated to be around 65 kJ mol−1. The small geometrical distortion of the aromatic system when the bridging atom is F is very likely the main factor that causes isomer A3 to be the most stable one for –BeF derivatives when they interact with Cl− and CN−. Instead, isomer A2 is the most stable one for –BeCl derivatives interacting with F− and CN−, as well as for –BeCN derivatives interacting with F−, although, in the latter case, the A3 form is found to be slightly more stable when the interaction takes place with CN− (see Fig. 4).
Comparison between the calculated anion affinities (in kJ mol−1) of the 2,2′-diBeX-1,1′-biphenyl derivatives (Biph) and those of the 1,8-BeX-naphthalene derivatives (Napht)
X = H
X = F
X = Cl
X = CN
The first conspicuous fact is that the anion affinities for the 2,2′-diBeX-1,1′-biphenyl derivatives are systematically lower than those for the corresponding naphthalene analogs. This result is rather unexpected, because we would expect the rigidity of naphthalene to enhance the anion affinity (AA) rather than decreasing it.
This correlation presents a residual RMS of 27.0 kJ mol−1. This value indicates that (with an error of about 27 kJ mol−1) biphenyls behave as anion sponges with anion affinities that are 85% of those of the naphthalene analogs. Indeed, the F− anion affinity for the 2,2′-diBeCN-1,1′-biphenyl derivative is estimated to be 18 kJ mol−1 higher than that of SbF5, which is considered one of the strongest F− capturers in the literature .
Our high-level DFT calculations show that 2,2′-diBeX-1,1′-biphenyl derivatives (X = H, F, Cl, CN), just like their 1,8-diBeX-naphthalene analogs, exhibit very high anion affinities when interacting with F−, Cl−, and CN−. However, rather unexpectedly, the biphenyl derivatives—although more flexible—are weaker Lewis acids than their naphthalene counterparts. In spite of this, it must be emphasized that some of the derivatives investigated are predicted to have larger anion affinities than those measured for SbF5, which is generally considered to be one of the strongest anion capturers. Therefore, although they have weaker anion affinities than the naphthalene analogs, the 2,2′-diBeX-1,1′-biphenyl derivatives can still be considered anion sponges. Thus, the main conclusion of this study is that compounds with BeX groups in positions which favor the chelation of anions behave as anion sponges due to the electron-deficient nature and therefore high intrinsic Lewis acidities of the BeX groups.
This work was supported by the projects CTQ2015-63997-C2 and CTQ2013-43698-P of the Ministerio de Economía y Competitividad of Spain, by the project FOTOCARBON-CM S2013/MIT-2841 of the Comunidad Autónoma de Madrid, and by the COST Action CM1204. Computational time at the Centro de Computación Científica (CCC) of Universidad Autónoma de Madrid is also gratefully acknowledged.
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