Some interesting features of the rich chemistry around electron-deficient systems

Introduction

The International Union of Pure and Applied Chemistry (IUPAC) in its Compendium of Chemical Terminology, usually known as Golden Book (https://goldbook.iupac.org/index.html) defines as electron deficient the “molecules or ions that contain too few electrons to allow their bonding to be described exclusively in terms of two-center, two-electron, i.e. covalent, bonds. Such molecules or certain fragments in these are often held together by the multicenter bonds.” Indeed, for many years the term electron deficient was frequently used to designate molecules stabilized through the formation of multicenter bonds. In this respect the boron hydride is a paradigmatic example, because its structure does not correspond, as it could be expected from the three valence electrons of B, to a BH₃ unit but to its dimeric B₂H₆ form, as already pointed out by Stock back in 1933 [1]. Indeed, in a review on this book published a year later [2] it is written: “It is also interesting to learn that BH₃ has never been prepared and probably does not exist.” However, the existence of diborane was a challenge from the bonding viewpoint. As nicely explained by Longuet-Higgins back in 1957 [3], “a molecule composed by eight atoms requires at least seven “two-centre bonds” to hold it together; seven covalent bonds demand fourteen valency electrons and in diborane the number of valency electrons is only twelve. In this sense, therefore, B₂H₆ is an “electron-deficient” molecule”. Indeed, there were many proposals on the possible structure of diborane, even suggesting that it could be a paramagnetic system [4], until the experimental paper of Farkas and Sachsse [4], suggested that its normal state should be diamagnetic. In a new paper published by Mulliken [5], it was suggested that the structure of diborane involved two-electron pair bonds and one one-electron bond. New attempts to built-up a suitable bonding model were proposed [6], [7], [8] suggesting that two of the H atoms were bridging between two BH₂ groups. This interpretation will be further analyzed and ratified by Pitzer [9]. Later on, the existence of a three-center two-electron bonds would be ratified through a valence bond (VB) viewpoint [10], and found also in other boron derivatives, such as the B₃H₈⁻ anion [11], methyleneboranes [12], as well as in carbon dications [13]. Nowadays many are the systems that as diborane are stabilized through either one- or two-electron three-center bonds. A particular interesting family being the so called carboranes, clusters that in many cases obey the general formula C₂B_nH_n+2, but which can contain other metal elements as well [14], [15], [16], [17], [18], [19], [20], [21]. Three-center bonds are also responsible for the stability of many species other than carboranes, for instance CH₅⁺ cation [22], many other cations [23], [24], cyano derivatives of diborane [25], onium-boronium dications [26], non-classical carbocations [27], disilyl cations [28], boron oxide clusters [29], covalent inorganic compounds [30], organosilver complexes [31], ternary CBe₄Au₄ clusters [32], gold bonding [33], and many more.

In general the electron-deficient systems, and in particular boron derivatives, behave, as expected, as good Lewis acids. There are hundreds of papers showing this property for boron compounds, and a good compilation can be found in a book containing the Proceedings of 10^th International Conference on the Chemistry of Boron [34]. One specific aspect of the Lewis acidity of boron compounds and of electron-deficient systems in general, is the perturbation they cause on the electron density distribution of both interacting systems, the Lewis base and the Lewis acid. These effects are particularly visible when dealing with another interesting set of electron-deficient derivatives, such as the beryllium derivatives. We have shown that the interaction of BeX₂ (X=H, F, Cl, OH) with different Lewis bases [35], leads to very stable adducts, which are the result of the charge transfer from the lone pairs of the Lewis base into the empty p orbitals of Be and into the σ_BeX* antibonding orbitals of the BeX₂ molecule. The obvious consequence of the first charge transfer is a change in Be hybridization and accordingly a significant bending of the X–Be–X moiety initially linear, whereas the second charge transfer results in a sizable lengthening of the Be–X bond. Unavoidably then, the intrinsic properties of the two interacting systems, the electron-deficient compound and the Lewis base, change significantly when the adduct is formed. To this specific question we have paid a particular attention within my research group in close collaboration with different experimental groups in an effort at providing an analysis of this phenomenon as complete as possible. The aim of this short review is to show how the aforementioned electron density redistributions triggered by electron-deficient systems may result in huge acidity enhancements, in very strong cooperative effects, in generating ion-pairs in the gas phase and many other phenomena.

Computational details

Even though this paper is essentially a review some interesting peculiarities of the chemistry of electron-deficient compounds, in some specific cases we have decided to include new systems not explored before that permit to have a more complete view of the questions that are being analyzed. To ensure that the theoretical methods used are reliable all these new calculations have been carried using the G4 theory [36]. The G4 formalism is an ab initio composite method in which the molecular structures and thermal corrections to the final energy are evaluated at the B3LYP/6-31G(2df,p) level of theory. The total final energy is obtained as a combination of different components obtained at different levels (MP2 and MP4) of the Møller–Plesset perturbation theory [37], [38] and the CCSD(T) approach [39]. To these contributions an estimate the Hartree–Fock limit is added, with the final result that the G4 enthalpies deviate, in average, 3.5 kJ·mol⁻¹ from the experimental values.

In order to visualize the effects that the electron densities distortions undergone by the systems when they become protonated or deprotonated or when they are interacting among them, we will use the atoms in molecules theory (QTAIM) [40]. This formalism is based on the analysis of the topology of the electron density, by locating the so-called bond critical points, whose electron density is a measurement of the intensity and nature of the different linkages within a molecular aggregate. The NBO [41] is an efficient method to estimate the charge transfer that usually takes place when a Lewis base interacts with a Lewis acid, and to obtain reliable net atomic charges. The strength of these interactions can be estimated either by means of a second-order perturbation analysis [42], or through the calculation of the corresponding Wiberg bond orders [43]. The QTAIM and NBO calculations were carried out with the AIMAll [44] and the NBO-3.1 [45] packages, respectively.

Acidity and acidity-enhancements triggered by electron-deficient systems

To start with it is important to highlight that electron-deficient systems exhibit some peculiarities as far as their intrinsic acidity is concerned. Back in 2005 Bartmess and Hinde [46] found, through the use of high-level ab initio calculations, that similarly to what was known for the hydrides of the groups 14, 15 and 16 of the periodic table [47] borane was less acidic than AlH₃ and GaH₃ in the gas-phase. However, quite unexpectedly, the intrinsic acidity of borane was slightly greater than that of methane [46]. The other peculiarity is that in alkylboranes, such as methyl-, ethyl, vinyl- and ethynylborane, the most acidic center is not the BH₂ group, but the alkyl moiety, i.e. these alkylboranes are all carbon acids in the gas phase [48]. In this paper we have decided to complete this review, by examining what should be the behavior of the analogous Be- containing systems. The intrinsic acidity within this group, follows a similar trend as the other groups of the periodic table just mentioned [47], i.e. BeH₂<MgH₂<CaH₂, trend that is well reproduced at the G4 level of theory (see Table S1 of the Supporting information); but again, BeH₂ is predicted to be a stronger acid than borane and methane in agreement with the experiment (see Table S1 of the Supporting information).

The important finding however is that our G4 high-level ab initio calculations predict (see Fig. 1) that the HBeCH₃ derivative behaves, similarly to the boron containing analogue [48], as a carbon acid rather than as Be acid. When the methyl group is replaced by a vinyl one (HMC₂H₃ (M=Be and Mg)) besides the deprotonation of the –MH group, the deprotonations of C_αH or the C_βH groups are also possible. The C_αH deprotonation (see Fig. S1) results in a slight reinforcement of the C=C, C–M bonds, and a weakening of the M–H one, whereas C_βH deprotonation facilitates the cyclization of the anionic species, with the formation of two rather stable C–M bonds, this process being the most favorable from the energetic viewpoint.

Fig. 1:

G4 calculated intrinsic acidities (kJ·mol⁻¹) of methyl and vinylberylium hydrides as compared with the corresponding magnesium analogues. The Be derivatives behave as C acids (red values), whereas the Mg analogues behave as Mg acids (red values). Bond lengths are given in Å.

Figure 1 also shows that, as it is the case for the corresponding hydrides [47], the HMgCH₃ and the HMgC₂H₃ compounds are stronger acids than the Be-containing analogues. Note however that whereas the Be derivatives behave as C-acids, the Mg derivatives are Mg-acids in the gas phase. This different behavior just reflects subtle differences between the Be- and the Mg-containing systems, since the bonding changes upon deprotonation are qualitatively the same in both cases. If we consider the methyl derivatives the deprotonation of the MH (M=Be, Mg) group in both cases leads to a weakening of the C–M bond, whereas the deprotonation of the methyl group in both cases reinforces de C–M bond whereas a concomitant weakening of the M–H is also observed in both cases. However, quantitatively the balance is not the same and for Be derivatives the strong stabilization of the C–Be bonds overcomes the weakening of the Be–H one, rendering the anion deprotated at C_β the global minimum, whereas this is not the case in the Mg-containing systems.

Perhaps the most relevant role of electron-deficient compounds in gas-phase reactivity is their capacity to dramatically enlarge the acidity of the Lewis bases interacting with them. One perfect example is that of the association of borane to phosphines, because the resulting phosphine-boranes are not only much less volatile than the free phosphines, and not pyrophoric at all, but exhibit a huge increase in acidity, up to 18 orders of magnitude, in terms of the ionization constants [49]. These acidity enhancements are even stronger when Be derivatives are used as Lewis acids instead of boron derivatives [50], to the point that conventional N-bases, such as 1H-tetrazole become N-acids stronger than the strongest oxyacids by association with Be-derivatives, whereas other typical bases, such as pyridine, becomes a C acid slightly stronger ( ΔHacid0=1527.4 kJ · mol−1 ) than acetic acid ( ΔHacid0=1540±13 kJ · mol−1 ) [47].

In this paper, again for the sake of completeness, we are going to explore what would be the effects of replacing the N atom of pyridine by a P atom to yield phosphinine. The G4 calculations we have carried out show that, as in the case of pyridine, for phosphinine the most acidic site is the CH group at the orto position, situation that does not change upon complexation of phosphinine with BeCl₂ (see Table S2 of the Supporting Information). Although the experimental gas-phase acidity of phosphinine is not known, our results predict it to be slightly more acidic ( ΔHacid0=1624 kJ · mol−1 ) than pyridine ( ΔHacid0=1637 kJ · mol−1 ) [50]. Also, as it was the case for many other systems [50], the association of phosphinine with BeCl₂ enhances its acidity by 118 kJ·mol⁻¹. This huge increase can be rationalized through the scheme shown in Fig. 2, which indicates that the origin of such an increase is the extra-stabilization of the deprotonated form, that behaves as a much better electron donor towards the BeCl₂ molecule than the neutral compound.

Fig. 2:

Thermodynamic cycle connecting the neutral and deprotonated forms of phosphinine and its adduct with BeCl₂. Horizontal arrows correspond to the stabilization of neutral and deprotonated phosphinine by their association with BeCl₂, whereas de vertical ones measure the intrinsic acidity of phosphinine and its BeCl₂ adduct. All values in kJ·mol⁻¹.

This enhanced stabilization of the anion with respect to the neutral upon its association with BeCl₂ is a consequence mainly of the increase in the strength of the P–Be bond upon the deprotonation of the system. Indeed, the molecular graphs of both adducts (see Fig. S2 of the Supporting Information) show that the electron density at the P–Be bond critical point is larger in the anion than in the neutral system, as well as at the ring critical point of the aromatic ring. Concomitantly, the Wiberg bond order of the bond is also larger for the anion (0.36) than for the neutral (0.25). Energetically speaking, the NBO analysis shows that whereas the second order interaction between the P-lone pairs and the empty p orbitals of Be increases from 267 to 397 kJ·mol⁻¹ on going from the neutral to the deprotonated species.

Cooperativity with non-covalent interactions

For long time the mutual reinforcement of non-covalent interactions has been known as cooperativity [51], [52], [53], [54]. Most intermolecular interactions, perhaps only excluding those involving exclusively dispersion interactions, can be analyzed in terms of the behavior of interacting systems as Lewis acids and Lewis bases. The signature of cooperativity is non-additivity due to the electron density changes undergone by the two interacting moieties, the electron-deficient systems acting as very good Lewis acids, and the cluster stabilized by non-covalent interactions acting as a Lewis base. This situation can be nicely illustrated with a very simple system, the result of the interaction of a water dimer, stabilized by an intermolecular hydrogen bond with a beryllium derivative as electron deficient system. The characteristics of water dimer are known, both theoretically and experimentally, since long time ago [55], [56], and its complexes with BeH₂ and BeF₂ were described by Albretch et al. [57], together with those of the water trimer. In what follows we are going to include the clusters of the dimer with BeCl₂ to compare them with those involving BeF₂ as Lewis acid.

The molecular graphs of the isolated molecules, BeF₂, H₂O and BeCl₂, those of the corresponding binary complexes, F₂Be···OH₂, (H₂O)₂ and Cl₂Be···OH₂ and ternary complexes F₂Be···(H₂O)₂ and Cl₂Be···(H₂O)₂ are presented in Fig. 3 with the goal of having a clear overview of the evolution of the different electron densities, and of cooperativity between hydrogen and beryllium bonds. As it has been already mentioned the binary F₂Be···OH₂ and Cl₂Be···OH₂ complexes are stabilized by the formation of an O···Be bond, which leads to the bending of the BeX₂ (X=F, Cl) moiety and the weakening of their Be–X bonds [35]; but the most distinctive characteristic of the ternary complexes containing either BeCl₂ or BeF₂ is the obvious reinforcement of both the beryllium bond and the OH···O hydrogen bond. A third factor, the intramolecular hydrogen bond between the F or the Cl atom with the terminal OH group of the water dimer, also contributes in both cases to enhance the stability of the ternary complex.

Fig. 3:

Molecular graphs of the BeF₂, H₂O and BeCl₂ molecules and the binary and ternary complexes formed by their mutual interaction. Green and red dots denote bond and ring critical points, respectively. Electron densities are given in a.u.

The formation of the X₂Be···OH₂ binary complex entitles a significant increase of the proton donor capacity of the water molecule, because its oxygen atom has transferred a significant amount of charge towards the empty orbitals of Be, and recovers part of this charge by depopulating the OH bonds. This results in a noticeable reinforcement of the OH···OH₂ bond in the ternary complex, reinforcement that is still stronger, because the second water molecule acts simultaneously as a proton donor toward the X substituent of the X₂Be molecule. Similarly, the formation of the water dimer complex implies an enhancement of the electron donor capacity of the oxygen atom acting as a proton donor, what necessarily results in a reinforcement of the O···BeX₂ on going from the binary to the ternary complexes.

To analyze the process of the formation of the ternary complexes from an energetic viewpoint it is convenient to consider the two alternative ways, the formation of the beryllium bond followed by the formation of the hydrogen bond [reaction (1)] or the reverse order [reaction (2)],

The results obtained are presented in the two schemes of Fig. 4, which show that for both BeF₂ and BeCl₂ complexes the enhancement of both non-covalent interactions is almost the same. It is also obvious that, since the enthalpy is a state function, the total energy balance is the same whether the first step is the formation of the beryllium or the hydrogen bond and therefore the energetic enhancements undergone by the hydrogen bond and the beryllium bond are identical in absolute terms (42 kJ·mol⁻¹ for BeF₂ complexes and 42.4 kJ·mol⁻¹ for BeCl₂ complexes), but not in relative terms. Indeed, whereas the interaction energy of the beryllium bond increases ca. 47% (from 90.3 and 97.4 to 132.3 and 139.8 kJ·mol⁻¹ for BeF₂ and BeCl₂, respectively) that of the hydrogen bond increases 280% (from 15 to 57 or 57.4 for BeF₂ and BeCl₂, respectively). This confirms previous findings that, also in the cooperativity between hydrogen and halogen bonds and alkaline-earth bonds [58], and between tetrel and alkaline-earth bonds [59], the weaker the interaction the greater the energetic effect arising from cooperativity.

Fig. 4:

Energetic schemes (enthalpies in kJ mol⁻¹) of the formation of ternary complexes by association of water dimer with BeF₂ (a) and BeCl₂ (b), following two alternative pathways: the first step is the formation of the water dimer followed by the formation of the beryllium bond (blue), the first step is the formation of the beryllium bond followed by the attachment of the second water molecule (green).

Cooperativity was first evident in clusters stabilized through hydrogen bonds [60], [61], being responsible, for instance, of the enhanced stability and structure of the water trimer [62], being also behind spontaneous proton transfer in some triads [63], or in the enhanced interactions with π-systems [64], and also present in the interactions between H-bonds and both anion-π and lone-pair-π interactions [65]. Similar cooperativity effects were found in clusters stabilized by halogen bonds [66], [67], or by tetrel bonds [68], and also between anion-π and halogen bonds [69]. More recently, special attention was paid to cooperativity between different kinds of non-covalent interactions stabilizing the same molecular aggregate. A very interesting review on cooperativity involving hydrogen, hydric, dihydrogen, and halogen bonds, as well as ion-π interactions was reported by Alkorta et al. [70]. Although it is impossible to mention all the studies published in the last decade on this topic we can highlight a few on different topics: the studies on the cooperativity between halogen, chalcogen, and pnictogen bonds[71], the role of cooperativity in supramolecular chemistry [72], or in the spontaneous formation of ion-pairs in the gas phase [73], [74], the cooperativity between halogen and beryllium bonds [75], hydrogen and halogen bonds [76], hydrogen, lithium and halogen bods [77], or its role in the stabilization of ammonia-borane clusters [78].

Spontaneous formation of ion pairs

One of the interesting consequences of cooperativity between non-covalent interactions is the possibility of observing the spontaneous formation of ion pairs in the gas phase. Ions are common in condensed phases, either solids or solutions, but it is not so easy to find them in the gas phase, because in general ionization potentials are much larger than electron affinities. The first experimental evidences of a spontaneous proton transfer leading to the formation of an ion-pair in the gas phase, based on rotational spectroscopy of supersonically expanded jets were reported by Legon et al. [79], [80], [81], [82]. In these studies it was clear that only when the proton acceptor has a sufficiently high basicity, as it is the case of trimethylamine, and the proton donor a high intrinsic acidity, such as HI, the characteristics of the system correspond to an ion-pair involving I⁻ and the protonated amine [81], however, this is not the case when confronting trimethylphosphine with HBr, where the heterodimer cannot be described as (CH₃)₃PH⁺…Br⁻, but as (CH₃)₃P…HBr hydrogen bonded adduct [80]. For these reasons is not possible to find in the gas-phase ion-pairs derived from the direct interaction between hydrogen fluoride and ammonia, unless the corresponding heterodimer interacts with BeX₂ derivatives [73]. Similarly, it has been shown that is possible to change halogen bonds from traditional to ion-pair bonds by the intervention of beryllium bonds [74].

Let us analyze here a simple but interesting example, which is the hydrogen bond complexes between water and ammonia, methylamine and dimethylamine, and the effects that a further interaction of these heterodimers with BeCl₂ have on their structure an bonding. As illustrated in Fig. 5, the heterodimers are stabilized by hydrogen bonds (HBs) whose strength increases slightly by increasing the number of the methyl substituents. The reinforcement of the HB is reflected in the increase of the density at the corresponding BCP (from 0.028 a.u. to 0.031 a.u.) and the concomitant decrease (from 0.352 a.u. to 0.349 a.u.) at the OH group acting as proton donor. Consistently, the corresponding OH stretching frequency is red shifted by 200, 231 and 239 cm⁻¹ with respect to the isolated water molecule. The changes are much more significant when BeCl₂ interacts with the corresponding heterodimers. The HB becomes significantly stronger and shorter in the complexes with ammonia and methylamine; but in the case of the dimethylamine a proton transfer takes place, and the system cannot be described a as the Cl₂BeOH₂···NHMe₂ adduct, but as a Cl₂BeOH⁻···NH₂Me₂⁺ ion pair, as confirmed by the population obtained in the framework of the NBO method, which shows that the NH₂Me₂ group has a positive charge close to unity (+0.83).

Fig. 5:

Optimized structures and molecular graphs of the complexes between water and ammonia, methylamine and dimethyl amine (first two rows) and of the ternary complexes when they interact with BeCl₂ (last two rows). Bond lengths are in Å and the electron densities in a.u. For the molecular graphs the conventions are the same as in Fig. 3.

As expected in the first two ternary complexes the stretching frequency of the OH donor group appears strongly red-shifted with respect to the binary complexes, 1342 cm⁻¹ for the complex with ammonia and 1734 cm⁻¹ for the complex with methylamine. For the complex with dimethylamine the OH stretching frequency appears replaced by a NH stretching one (at 2189 cm⁻¹) due to the aforementioned spontaneous proton transfer.

It should also be noted that the reinforcement of the OH···N interaction is accompanied by a concomitant reinforcement of the HB between one of the Cl atoms of BeCl₂ and the NH group of the base, reflected in a shortening of the NH···Cl distance and in the increase of the electron density at the corresponding BCP (see Fig. 5). This reinforcement is particularly strong for the dimethylamine complex, because the proton transfer from the water molecule towards the amine results necessarily in a strong enhancement of the proton donor ability of the resulting NH₂Me₂⁺ moiety. All the aforementioned features are also consistent with the NBO results. The reinforcement of the OH···N hydrogen bond on going from the Cl₂BeOH₂···NH₃ to the Cl₂BeOH₂···NH₂Me complex is a consequence of a stronger second order perturbation interaction between the N lone pair of the amine and the σ_OH* antibonding orbital (310 vs. 394 kJ·mol⁻¹), which for the Cl₂BeOH₂···NHMe₂ complex is replaced by the interaction of the lone pair of the O atom of the OH group and the σ_NH* antibonding orbital of the NH₂Me₂⁺ moiety because of the proton transfer mentioned above. Similarly, the reinforcement of the NH···Cl HB is also reflected in an increase of the second order perturbation energy for the interaction between the lone pair of the Cl atom and the σ_NH* antibonding orbital of the amine (15, 18 and 71 kJ·mol⁻¹ for the complexes containing NH₃, NH₂Me and NHMe₂, respectively).

Electron and anion sponges

The fact that –BeX groups are excellent electron acceptors moved us to consider the possibility of having some kind of electron sponges, mimicking some of the well known proton sponges [83], such as in 1,8-bis(dimethylamino)naphthalene, in which the close proximity between the two basic sites results in an exceptionally high basicity constants of the system. The idea was then to explore if by replacing the amino groups by –BeX groups to yield 1,8-diBeX-naphthalene derivatives we could have excellent electron capturers [84].

A very large set of X substituents (X=H, F, Cl, Br, CH₃ NH₂, OH, CF₃, C(CF₃)₃, NF₂, OF, CN, NO₂, SOH, t-Bu, Ph) were explored using different CCSD(T) [39] and G4 [36] high-level ab initio calculations, and it was systematically found that the electron attachment to any of the 1,8-diBeX-naphthalene derivatives included in the aforementioned series was accompanied by a drastic shortening, from 0.538 Å when X=OH to 1.243 Å when X=C(CF₃)₃. This shortening indicated the appearance of a Be–Be attractive interaction in the anion not existent in the neutral. Indeed, as illustrated in Fig. 6, the AIM theory predicts the existence of a bond critical point between the two Be atoms of the anion, indicating that a new Be–Be bond is formed after the electron attachment process. This AIM description is coherent with the existence of a Be–Be one-electron bond (the calculated population is 0.922) when the NBO approach is used. This allowed us to conclude that, similarly to 1,8-bis(dialkylamino)naphthalene derivatives that behave as proton sponges in the gas-phase, the 1,8-bis(diBeX)naphthalene derivatives should behave as electron sponges.

Fig. 6:

Changes in the electron density distribution of 1,8-diBeX-naphthalene after capturing one electron reflected in the corresponding molecular graphs that show that in the anion a Be–Be one-electron bond is formed, fact that is ratified by the NBO analysis showing the existence of Be–Be bonding localized orbital with a population close to unity. In the molecular graphs green and red dots denote bond and ring critical points, respectively. Electron densities are given in a.u.

More recently, the one-electron nature of the Be–Be interaction in the anion of 1,8-diBeX-naphthalene was ratified by using the interacting quantum atoms (IQA) approach, the electron distribution functions (EDF) and the natural adaptive orbitals (NAdOs) [85]. In this analysis it was found that although both Be atoms are positively charged leading to an electrostatic destabilization, the C1BeH and C8BeH groups are negatively charged, so according to the IQA approach the total attractive interaction energy between both groups overcome the Be···Be electrostatic destabilization. Consistently, the NAdOs shows the existence of an in-phase combination of sp²-like orbitals, very similar to the NBO singly occupied molecular orbital (SOMO) shown in Fig. 6, as responsible of the Be–Be bonding.

It is important to emphasize that the ability of forming this kind of one-electron bonding interactions has been also found for electron-deficient analogues containing boron instead of beryllium [86]. Indeed, for [X₃B·BX₃]⁻¹ (X=H, Me, OMe, OH, F, Cl, CN) radical anions, the two BX₃ groups are bound, as in the 1,8-diBeX-naphthalene derivatives discussed above, through a covalent one-electron sigma bond, its strength being the larger the greater the electronegativity of the X group.

Also interestingly, the existence of three BeX geometrically close to each other in a certain molecular environment, as it is the case of the 1,3,5-trisubstituted cyclohexanes, strongly favors the formation of three-centered one-electron bonds when the system becomes anionic [87]. Indeed, a detailed examination of the corresponding potential energy surface for the anionic form of the 1,3,5-trisubstituted BeH derivative, shows that the global minimum corresponds to the structure shown in Fig. 7, stabilized by the formation of a three-center one-electron Be–Be–Be bond. In the same analysis is also found that the structure shown in Fig. 6 is still the global minimum of the anion when the BeH groups are replaced by BeF, BeCl or BeCN. In this context it is also necessary to mentioned that the isolated Be₃²⁻ cluster, has been shown to be stabilized by a three-center two-electron bond of σ character [88].

Fig. 7:

NBO SOMO orbital of the [1,3,5-(HBe)₃-C₆H₉]⁻ anion. The population shown confirms that it is a three-center one-electron bonding orbital.

The good behavior of these derivatives in electron capturing processes should likely be reflected in high anion affinities, so they should also behave as good anion traps. This was actually explored for a variety singly charged and doubly charged conventional anions, namely F⁻, Cl⁻, Br⁻, CN⁻, NO₂⁻, NO₃⁻, SO₄²⁻ when interacting with 1,8-diBeX-naphthalene (X=H, F, Cl, CN, CF₃, C(CF₃)₃) derivatives [89].

As suitable examples we compare in Fig. 8 the behavior of 1,8-diBeX-naphthalene (X=F, CN, Cl) compounds (see Fig. 8a) when they interact with NO₃⁻, Cl⁻ and SO₄⁼, respectively (see Fig. 8b). It is apparent that in all cases the anion interacts with both Be atoms as reflected in the appearance of the corresponding BCPs.

Fig. 8:

G4MP2 optimized geometries of: (a) 1,8-diBeX-naphthalene (X=F, CN, Cl) neutral compounds; (b) [1,8-diBeF-naphthalene]-NO₃⁻, [1,8-diBeCN-naphthalene]-Cl⁻ and [1,8-diBeCl-naphthalene]-SO₄⁼ complexes. Only the interatomic distances directly related with the interaction between the Be atoms and the anions are reported in Å. The corresponding G4MP2 estimated anion affinities in kJ·mol⁻¹ are given in bold.

The anion attachment leads also to a notorious electron density redistribution of both the anion and the Be-containing Lewis acid. Indeed, it can be observed in the first complex that the N–O bond of the O interacting with the two Be atoms lengthens significantly (0.2 Å) as well as the Be–F bond. Similar changes are observed for the last complex where again the two S–O bonds interacting with Be lengthen by almost 0.1 Å, as well as the Be–Cl linkage (0.19 Å). These effects reflect the charge donation from the lone-pairs of the oxygen atoms of the anions into the empty orbitals of Be, leading to a bending of the C–Be–X (X=F, CN, Cl) and into the σ_BeX* antibonding orbitals, that is observed in the NBO analysis. This charge transfer enhances the electronegativity of the participating oxygen atoms, which recover part of this charge by depopulating the other bonds in which they participate, leading to the observed length increase. The relevant finding however is the values of the corresponding anion affinities. Unfortunately, there are not many anion affinities reported in the literature to compare with, and most of them correspond to F⁻ affinities. However, an indication that these systems behave as real anion sponges is that all these 1,8-diBeX-naphthalene derivatives have F⁻ affinities larger than the largest one previously reported in the literature [89]. For instance, the calculated F⁻ affinities for 1,8-diBeX-naphthalene (X=H, F, Cl, CF₃, CN) are 532, 550, 584, 634, 660 kJ·mol⁻¹, respectively, all of them larger than the largest F⁻ affinity reported so far for SbF₅ (503 kJ·mol⁻¹) [90] or for AsF₅ (464 kJ·mol⁻¹) [91]. The same trends were found for the other monoanions, Cl⁻, CN⁻, NO₂⁻, NO₃⁻, the largest one being 771 kJ· mol⁻¹ for SO₄⁼ [89]. Fluorene beryllium derivatives [92], as well as some magnesium containing compounds [93] were also found to be rather efficient anion traps.

Be–Be interactions

There are still many other interesting questions related with electron-deficient systems and, in particular with Be-containing compounds, but I would like not to finish this mini-review without mentioning the very interesting peculiarities of the Be–Be bond, starting from beryllium dimer. A rather complete compilation of our knowledge about Be clusters and its chemistry has been recently published [94], so here we will discuss a little the questions around beryllium dimer. In a previous section we have already discuss the possibility to find two- and three-center one-electron bonds stabilizing certain anions, but just the bonding of the beryllium dimer has constituted for a long time a very interesting and complicated question.

The problems with Be₂ start at the basic molecular orbital level which predicts the system to be unbound; but even limited configuration interaction calculations predicted its ground state to be repulsive [95], though the electron correlation effect through the participation of triple and quadruple excitations play a role in correctly describing Be₂ dimer as a weakly bound species [96]. Today it seems rather well established that the bonding in Be₂ belongs to a new type based on non-dynamical correlation [97].

It is quite unexpectedly however, to find that although the link in Be₂ is rather weak (with a dissociation energy around 935 cm⁻¹) the Be–Be bonding becomes very strong in rather simple systems formed by the interaction of Be₂ with radical ligands, L:Be−Be:L [98]. In this short survey, for the sake of conciseness, we will focus our attention in the system formed when Be₂ dimer interacts with two CN^• radicals, the most stable adduct being that in which the CN moiety attaches to Be through the N atom [98]. The first important point found in Brea and Corral study [98] is that although the bonding in beryllium dimer comes from non-dynamical correlation effects, all of the L:Be−Be:L complexes considered in that work are single-reference systems. As a matter of fact the formation of CN:Be−Be:NC complex implies a charge transfer from the Be₂ moiety towards the radical. This results in the formation of a Be₂²⁺ unit with a rather reinforced Be−Be bond, because the aforementioned electron transfer empties the σ*_BeBe antibonding orbital. The obvious consequence is a significant shortening of the Be−Be distance (0.4 Å) with respect to the neutral dimer. The effects on the overall electron density are evident by comparing the electron localization function (ELF) [99] of Be₂ and CNBeBeCN complex (see Fig. 9).

Fig. 9:

Three-dimensional ELF plots (ELF=0.85) of Be₂ and CNBeBeCN complex. Green and red lobes correspond to disynaptic and monosynaptic basins, respectively. The population of the basins in e.

For the neutral Be₂ dimer the calculations were carried out at the CASSCF(4,16)/cc-pVTZ [98] since a good description of this system cannot be achieved forma single-determinant wavefunction. The electron population is accumulated in monosynaptic basins, compatible with a weak interaction that originates in non-dynamical electron correlation effects. Conversely in the CNBeBeCN complex, the only monosynaptic basins correspond to the N-lone pairs, whereas a donut-like disynaptic basin between the two Be atoms has a population of practically two electrons, compatible with its Be₂²⁺ nature. Obviously, the two ligands become formally anions. The ELF shows the delocalization between the CN bond and the newly formed NBe bond, whose disynaptic basins have a rather similar population (see Fig. 9).

Finally, it should be mentioned that other systems, like Be₂F₂, have been also found to be characterized by rather short Be–Be distances [100], as in the L:Be−Be:L cases mentioned above [98]. In that study, it is also shown how the occupied MOs provide a clear picture of its bonding, leading to a high Be−Be dissociation energy (272 kJ·mol⁻¹) [100], its dissociation into BeF₂+Be being also endergonic [100]. Very interesting, however, in the same paper it is also shown that not always a very short Be−Be distance implies the existence of a Be−Be bond. That situation appears in (D_8h) Be₂B₈ clusters, whose CCSD(T)/cc-pVTZ optimized geometry [100] is shown in Fig. 10.

Fig. 10:

CCSD(T)/cc-pVTZ optimized geometry for Be₂B₈ taken from ref. [100]. Bond lengths in Å. The net atomic charge at the Be atoms is given in red.

In this system the Be−Be distance is even shorter than in Be₂F₂ molecule, but the AIM theory shows that there is no bond-path or bond critical point between both Be atoms. A similar situation is found in the Be₂B₇⁻ anion [100]. Though the non-existence of a bond critical point cannot be taken necessarily as a proof on absence of Be–Be bond, both cyclic compounds exhibit double aromaticity with 6s and 6p electrons, which bind the Be₂ fragment to the boron atoms, maintaining both Be atoms very close each other, in spite of bearing a rather high net positive charge (see Fig. 10), which would be consistent with the non-existence of a Be–Be BCP.

More recently, a similar situation was reported [101] for Ng−Be₂O₂−Ng′ complexes involving the cyclic diberyllium dioxide and noble gas atoms (Ng, Ng′=Ne, Ar, Kr, Xe). Such complexes have been isolated and spectroscopically identified in low temperature matrices, and again, although they are characterized by very short Be−Be distances, the analysis of their electronic structure indicates that no Be−Be stabilizing interaction is present.

Concluding remarks

In this short review I tried to emphasize how rich can be the chemistry of electron-deficient systems, and in particular of beryllium and boron compounds. Of course there are many other applications and properties that have not been discussed here, such as the capacity to produce radicals in exergonic and spontaneous processes [102], or the possibility of designing new materials for an efficient H₂ storage [103], but I hope that I was able to transmit that some of this new chemistry is closely related with the behavior of these systems as very efficient Lewis acids, so they can be used not only to modify the acidity or the basicity of other compounds, but also, through cooperative effects, to enhance the strength of weak non-covalent interactions when some of the components involved in these non-covalent interactions can act as Lewis bases with respect to these electron-deficient systems.