Hydrogen Bonds with BF 4 − Anion as a Proton Acceptor

: The BF 4 − anion is characterised by weak Lewis base properties; it is usually classiﬁed as a “non-coordinating anion”. The searches through the Cambridge Structural Database (CSD) were performed and it was found that the BF 4 − anion often occurs in crystal structures and it is involved in numerous intermolecular interactions; hydrogen bonds are the majority of them. The hydrogen bonds involving the BF 4 − anion as a proton acceptor are closer to linearity with the increase of the strength of interaction that is in line with the tendency known for other hydrogen bonds. However, even for short contacts between the proton and the Lewis base centre, slight deviations from linearity occur. The MP2 / aug-cc-pVTZ calculations on the BF 4 − . . . HCN complex and on the BF 4 − . . . (HCN) 4 cluster were also carried out to characterise corresponding C-H . . . F hydrogen bonds; such interactions often occur in crystal structures.


Introduction
The term 'non-coordinating anion" was used in earlier [1][2][3][4] and in more recent studies [5] to characterise anions that do not interact with other species. However, it has been described that this term may be misleading since such anions known before as not able to be coordinated reveal properties to interact, at least weakly, with Lewis acid centres [1,4]. It was earlier explained that some ions matching this term were found to be coordinated in the water environment if water is rigorously excluded [6]. The BF 4 − species was often mentioned among the other so-called "non-coordinating" or "poorly-coordinating"anions [1]. However, it was mentioned that numerous crystal structures show the latter anion as a monodentate or bidentate bridging ligand [1]. It has been recognized early that the BF 4 − ion is not a completely non-nucleophilic species [7]; its reactivity was analysed recently [8], especially the reactions where the BF 4 − ion acts as a nucleophilic fluoride source were discussed in detail. It seems that the tetrahedral BF 4 − moiety possesses a stable electronic and consequently stable energetic structure. The boron centre in the planar trigonal BF 3 molecule is characterised by hypovalency [9] and the vacant p-orbital perpendicular to the plane of the molecule is responsible for the Lewis acid properties of BF 3 species and for its interactions with Lewis bases [10][11][12]. In a case of strong nucleophiles such as the F − anion, it leads to the formation of the stable tetrahedral structures [13].
It is worth mentioning that in the Cambridge Structural Database [14,15] mostly tetravalent BF 4 exists only in forms such as the H(H 2 O) n + BF 4 − or any another species where the proton is strongly coordinated by solvent molecules [16]. It has been described in various studies that the BF 4 − anion participates in hydrogen bond interactions since fluorine atoms may act as the Lewis base centres, especially as there are numerous examples of crystal structures where such interactions occur. One can mention the structure of S-amino thiodithiazyl salt, S 3 N 2 NH 2 + BF 4 − [17], where the hydrogen bonds are formed between the hydrogen atoms of the amine group and fluorine atoms of two related by symmetry BF 4 − anions; the F . . . H intermolecular distances are equal to 1.55(5) Å, and 2.14(6) Å. The crystal structure of the (CH 3 ) 3 NHBF 4 complex has been analysed by the X-ray diffraction methods in three phases [18]. For the room temperature phase III, the (CH 3 ) 3  In another study, interactions between imidazolium-based ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate and dimethyl sulfoxide were investigated by attenuated total reflection infrared spectroscopy (ATR-IR) and density functional theory calculations [19]. The similar experimental ATR-IR studies supported by the hydrogen nuclear magnetic resonance ( 1 H NMR) and density functional theory calculations were performed for interactions between 1-butyl-3-methylimidazolium tetrafluoroborate and acetonitrile [20]. In both cases of latter studies [19,20], the Lewis base properties of fluorine centres of BF 4 − anion were analysed.

Computational Methods
The calculations were performed on the BF 4 − . . . HCN complex and the BF 4 − . . . (HCN) 4 cluster with the Gaussian16 set of codes [22] using the second-order Møller-Plesset perturbation theory (MP2) [23], and the aug-cc-pVTZ basis set [24]. Frequency calculations have been carried out at the same computational level to confirm that the obtained structures correspond to energetic minima or to transition states. The Quantum Theory of 'Atoms in Molecules' (QTAIM) [25,26] was applied to analyse characteristics of bond critical points (BCPs). The QTAIM calculations were performed with the use of the AIMAll program [27]. The Natural Bond Orbital (NBO) method [28] was also applied to analyse electron charge density shifts being the result of complexation, particularly the orbital-orbital interactions. For example, the n B → σ AH * overlap is often considered as the characteristic interaction of the A-H . . . B hydrogen bond [9,28]. n B designates the lone electron pair of the B proton acceptor (the Lewis base) and σ AH * is an antibonding orbital of the proton donating bond (the Lewis acid).
The n B → σ AH * interaction is calculated as the second-order perturbation theory energy. For the complex and cluster considered here the hydrogen cyanide species play the role of the Lewis acid units and the BF 4 − anion acts as the Lewis base, hence for those species the n F → σ HC * orbital-orbital Crystals 2020, 10, 460 3 of 13 interactions occur. The NBO orbital-orbital energies were calculated at HF/aug-cc-pVTZ level for the previously optimised geometries at the MP2/aug-cc-pVTZ level. The BP86 functional [29,30] was applied and uncontracted Slater-type orbitals (STOs) with triple-ζ quality (ADF TZ2P basis set) as basis functions for all elements. The BP86/TZ2P decomposition energy calculations were performed with the ADF2017 program package [31] for two configurations of the BF 4 − . . . HCN complex using their geometries optimized previously at the MP2/aug-cc-pVTZ level.
The ADF decomposition [31] applied follows the energy partition of Morokuma [32] and it is based on the instantaneous interaction energy, ∆E int , within, for example, the AB complex between two fragments (A and B), in the particular electronic reference state and in the frozen geometry of AB. This interaction energy is divided into three main components and the additional dispersion term, ∆E disp , according to the equation given below.
The term ∆E elstat corresponds to the quasi-classical electrostatic interaction between the unperturbed charge distributions of the prepared atoms and it is usually attractive. The Pauli repulsion, ∆E Pauli , is the energy change associated with the transformation from the superposition of the unperturbed electron densities of the isolated fragments to the wave function that properly obeys the Pauli principle through explicit antisymmetrisation and renormalization of the product wave function. This term comprises the destabilizing interactions between electrons of the same spin on either fragment. The orbital interaction, ∆E orb , accounts for charge transfer and polarization effects.

Crystal Structures with BF 4 − Anion as Proton Acceptor in Hydrogen Bonds
It seems the BF 4 − anion is a very stable structure since its boron centre containing eight electrons in the valence shell obeys the octet rule.  The crystal structure of (R)-dideutero methyl N-benzoyl-3-(1H-imidazol-3-ium-5-yl)alaninate tetrafluoroborate (Figure 1b, SUXHID01 refcode) [36] is the only one neutron diffraction fulfilling the search criteria described above where the N-H…F(BF4 − ) hydrogen bonds exist. The corresponding H…F distance amounts 2.19 Å (Fig. 1b) that is shorter than the corresponding sum of van der Waals radii; two additional C-H…F contacts are observed for the same Lewis base unit (BF4 − ) with the H…F distances overwhelming the above sum. The fourth B-F bond of the proton acceptor is not involved in any close contact.
For the three samples of complexes found in CSD (X-ray and neutron diffraction results), that are characterised by the occurrence of the C-H…F, N-H…F and O-H…F hydrogen bonds, the histograms of the H…F distances are presented in Figure 2. One should consider them as the approximate distribution of such distances since the C-H, N-H and O-H proton-donating bonds for X-ray structures were normalized here; it is a rather crude estimation since it does not take into account the complexation and, in general, the influence of crystal environment on these bonds. The maximum number of H…F contacts for the C-H….F hydrogen bonds occurs for the distance amounting to approximately 2.45 Å . This corresponds to the sum of van der Waals radii of fluorine and hydrogen atoms being in contact and it indicates the weak dispersion forces mainly steering the C-H…F arrangements. For the N-H…F and O-H…F hydrogen bonds, the maximum number of H…F contacts occur for 1.95 Å and 1.75-1.80 Å distances, respectively, that are shorter than the distance corresponding to the van der Waals sum. It may indicate the other forces, not dispersion ones, are The fragment of the crystal structure of (a) bis(tetramethyl-tetraselenafulvalenium) tetrafluoroborate, BIXBIT03 refcode, reference [34], and (b) (R)-dideutero methyl N-benzoyl-3-(1H-imidazol-3-ium-5-yl)alaninate tetrafluoroborate, SUXHID01 refcode, reference [35], H . . . F distances are shown.
The crystal structure of (R)-dideutero methyl N-benzoyl-3-(1H-imidazol-3-ium-5-yl)alaninate tetrafluoroborate (Figure 1b, SUXHID01 refcode) [35] is the only one neutron diffraction fulfilling the search criteria described above where the N-H . . .  . . F arrangements. These may be electrostatic and charge transfer/polarization forces, which is to be discussed here. The histograms presented in Figure 2 show the increasing strength of the hydrogen bonds in the following order: . . F, since the maximum number of contacts in three samples considered here corresponds to the decreasing H . . . F distance, respectively. It corresponds also to the increase of the proton-donating properties of A-H bonds that follow the electronegativity increase of the A-centre.
Crystals 2020, 9, x FOR PEER REVIEW 5 of 13 more important to steer the N-H…F and O-H…F arrangements. These may be electrostatic and charge transfer/polarization forces, which is to be discussed here. The histograms presented in Figure  2 show the increasing strength of the hydrogen bonds in the following order: C-H…F < N-H…F < O-H…F, since the maximum number of contacts in three samples considered here corresponds to the decreasing H…F distance, respectively. It corresponds also to the increase of the proton-donating properties of A-H bonds that follow the electronegativity increase of the A-centre.   Figure 4 presents the scatter plots for the dependencies between H…F distance and the corresponding A-H…F angle for three samples of hydrogen bonds discussed here. One can see that for all samples the range of the A-H…F angle decreases with the decrease of the H…F distance being narrow and close to 180° for shorter H…F contacts. It is in line with the observations of the previous studies [21]. However, one can see (Figure 4) that this narrow range of angles is situated below the linearity, for 160°-170° angles rather, for C-H…F and N-H…F hydrogen bonds. This range is closer to 180° for the O-H…F systems but not exactly. It confirms the former conclusions concerning Figure 3.   linear systems and any additional factors may disturb the expected linear arrangement. Figure 4 presents the scatter plots for the dependencies between H…F distance and the corresponding A-H…F angle for three samples of hydrogen bonds discussed here. One can see that for all samples the range of the A-H…F angle decreases with the decrease of the H…F distance being narrow and close to 180° for shorter H…F contacts. It is in line with the observations of the previous studies [21]. However, one can see (Figure 4) that this narrow range of angles is situated below the linearity, for 160°-170° angles rather, for C-H…F and N-H…F hydrogen bonds. This range is closer to 180° for the O-H…F systems but not exactly. It confirms the former conclusions concerning Figure 3.

Theoretical Analysis of the Lewis Base Properties of the BF 4 − Anion
It was noted earlier here that the A-H . . . F hydrogen bonds are slightly disturbed from linearity even for short H . . . F distances. This may result from external factors, like the intermolecular forces in crystals and with the internal factors related to properties of the BF 4 − anion. There are numerous studies where it is pointed out that the electrostatic potential (EP) at molecular surfaces of interacting species is responsible for their mutual arrangement in the complex formed [36][37][38][39][40]. Consequently, contacts between the most positive EP areas and the most negative EP sites are often observed in numerous complexes and clusters. This is only the rough description and numerous exceptions are observed. Especially, significant changes in the geometries of interacting species are observed for strong interactions characterized by meaningful electron charge density shifts being a result of complexation as well as by the contribution of dispersion forces in the establishment of the geometry of a complex considered [39,40].
The σ-hole concept [39,40] explains the existence of areas of the positive EP for numerous atomic centres that consequently may act as Lewis acids interacting with nucleophiles. The BF 4 − anion as negatively charged species reveals the Lewis base properties. Figure

Theoretical Analysis of the Lewis Base Properties of the BF4 − Anion
It was noted earlier here that the A-H…F hydrogen bonds are slightly disturbed from linearity even for short H…F distances. This may result from external factors, like the intermolecular forces in crystals and with the internal factors related to properties of the BF4 − anion. There are numerous studies where it is pointed out that the electrostatic potential (EP) at molecular surfaces of interacting species is responsible for their mutual arrangement in the complex formed [37][38][39][40][41]. Consequently, contacts between the most positive EP areas and the most negative EP sites are often observed in numerous complexes and clusters. This is only the rough description and numerous exceptions are observed. Especially, significant changes in the geometries of interacting species are observed for strong interactions characterized by meaningful electron charge density shifts being a result of complexation as well as by the contribution of dispersion forces in the establishment of the geometry of a complex considered [40,41].
The -hole concept [40,41] explains the existence of areas of the positive EP for numerous atomic centres that consequently may act as Lewis acids interacting with nucleophiles. The BF4 − anion as negatively charged species reveals the Lewis base properties. Figure 5 presents the EP map for the BF4 − anion calculated at the 0.001 au electron density surface. The whole surface is characterized by the negative EP; the maximum EP values of −0.188 au are observed for F-atoms while the EP minima of −0.208 au occur at the boron centre in directions being bisectors of the F-B-F angles, four such EP minima are observed ( Figure 5). The EP map presented here results from the MP2/aug-c-pVTZ calculations that were also applied to optimise geometries of the BF4 − …HCN complex and the BF4 − …(HCN)4 cluster. The EP map of the BF4 − anion may suggest that in the BF4 − …HCN complex the C-H proton-donating bond of hydrogen cyanide is directed to B-centre that is characterised by the EP minimum. However, the B-centre is obscured by the fluorine atoms. The full optimization of the BF4 -…HCN complex led to the configuration presented in Figure 6a that corresponds to the energetic minimum (named hereafter a nonlinear configuration). On the other hand, the configuration with the fixed linear B-F…H-CN arrangement was optimized (C3v symmetry, Figure 6b); it corresponded to the transition state; it is the second order saddle point, since two imaginary frequencies are observed here. For the nonlinear configuration, the H…F intermolecular distance equal to 1.89 Å is observed with the corresponding C-H…F angle of 162. 8°. The H…B intermolecular distance is equal to 2.64 Å that corresponds to the C-H…B angle amounting 165. 5°. There is another intermolecular contact characterised by the H…F distance of 2.36 Å (Figure 6a). In the case of linear configuration, the H…F  nonlinear configuration is slightly more stable than the linear configuration since this energy is equal to −16.2 kcal/mol for the former species while it amounts −15.3 kcal/mol for the latter one. The BSSE correction amounts 0.6 and 0.4 kcal/mol, respectively.
Crystals 2020, 9, x FOR PEER REVIEW 8 of 13 distance of 1.75 Å is observed (Figure 6b). Table 1 presents energetic characteristics of both configurations as well as of the BF4 − …(HCN)4 cluster. The MP2 binding energy that includes the correction for basis set superposition error (BSSE) [42], designated as ΔEbin(MP2,BSSE), shows that the nonlinear configuration is slightly more stable than the linear configuration since this energy is equal to −16.2 kcal/mol for the former species while it amounts −15.3 kcal/mol for the latter one. The BSSE correction amounts 0.6 and 0.4 kcal/mol, respectively. Similarly, the interaction energy is "more negative' for the nonlinear configuration than for the linear one. The deformation energy, ΔEdef [43], is not important for both configurations; it amounts to 0.4 and 0.5 kcal/mol, indicating that complexation does not affect the geometry of interacting species (BF4 − and HCN) significantly. It is worth noting that the interaction energy does not take into account the deformation resulting from complexation but the binding energy does [43] (Equation (2)).
The Hartree-Fock interaction energies are presented in Table 1, ΔEint(HF); one may assume that correlation energy, ΔEcorr, may be calculated from the following equation (Equation (3)). Similarly, the interaction energy is "more negative' for the nonlinear configuration than for the linear one. The deformation energy, ∆E def [42], is not important for both configurations; it amounts to 0.4 and 0.5 kcal/mol, indicating that complexation does not affect the geometry of interacting species (BF 4 − and HCN) significantly. It is worth noting that the interaction energy does not take into account the deformation resulting from complexation but the binding energy does [42] (Equation (2)).
The Hartree-Fock interaction energies are presented in Table 1, ∆E int (HF); one may assume that correlation energy, ∆E corr , may be calculated from the following equation (Equation (3)).
However, it is an approximate evaluation since, according to the Löwdin definition [43] that is commonly accepted, "the correlation energy for a certain state with respect to a specified Hamiltonian Crystals 2020, 10, 460 9 of 13 is the difference between the exact eigenvalue of the Hamiltonian and its expectation value in the HF approximation for the state under consideration." The MP2 method takes into account correlation but it is still an approximate approach. Table 1 shows that the correlation energy is more important for the nonlinear configuration than for the linear one; the dispersion energy is the most important, attractive term of the correlation energy. One may speculate that the dispersion forces are those which cause the nonlinear configuration to be more stable than the linear one since the difference between the HF interaction energies for both configurations amounts only 0.3 kcal/mol while it is more than three times greater for MP2 results. The other important conclusion is that the more stable configuration is characterised by the C-H . . . It was pointed out in various studies that the electron density at BCP of the intermolecular bond path correlates with the interaction and/or binding energy [44]. It is not a case for configurations considered here where more negative ∆E in and ∆E bin values are observed for the smaller ρ BCP value related to the nonlinear configuration. However, in this case, ρ BCP corresponds to the single H . . . The energy corresponding to the n F → σ CH * orbital-orbital interaction (E NBO ) is presented in Figure 6. It corresponds to the shorter contact for the nonlinear configuration and it is equal to 8.8 (Table 1). Table 2 shows that for both configurations the electrostatic interaction is the most important attractive term, almost the same electrostatic energies are observed for these configurations. The orbital-orbital interactions are more important for linear configuration that is in line with the NBO results which show the interaction corresponding to n F → σ CH * overlap is more important for the linear configuration. However, for the latter configuration, the repulsive interaction, ∆E Pauli , is greater than for the nonlinear system. This is the reason the nonlinear configuration is more stable than the linear one, less important Pauli repulsion and¨more negative¨dispersion energy. It was pointed out earlier here, on the basis of the HF and MP2 results, that the dispersion forces are responsible the nonlinear configuration is more stable than the linear one.

Summary
In contrast to earlier studies stating that the tetrafluoroborate BF 4 − species is a non-coordinating