Chemical bonding of HF, HCl, and H 2 O onto YF 3 surfaces: Quantification by first principles

The surfaces of waimirite β‐ YF3 have been studied for their fluorine and chlorine versus water affinity. Bonding patterns of HF, HCl, and H2O chemically adsorbed onto surfaces of (010), (100), (011), and (101) have been quantified by density functional theory applying energy decomposition analysis. We found that the adsorption of H2O is dominated by about 65% of electrostatics, which causes a low surface sensitivity and weak interactions. On the contrary, the adsorptions of HF and HCl are driven by strong hydrogen bonds resulting in a highly surface‐dependent ratio of 30–60% electrostatic versus orbital contribution. Among the stoichiometric surfaces, the shortest and strongest hydrogen bonds and consequently most covalent bonding patterns are found within YF3· HCl. However, when including the preparation energy, each surface favors the adsorption of HF over HCl, which reproduces the higher affinity of yttrium towards fluoride over chloride, previously known for solutions, also for the solid state.

However, above that threshold, YF 3 has been predicted the most dominant Y-species, despite the still 100 times higher availability of chloride. 5 The difference in affinity for chloride and fluoride shown by the HFSE can already be qualitatively predicted by electrostatics, only, or the simple concept of hard and soft Lewis acids and bases (HSAB). However, electrostatics alone cannot predict that two cations of equivalent charge to radius ratio show a different affinity for the same anion. However, such fluoro-specific interactions have been found within dissolving measurements of solid β-YF 3  By this simplistic model system, we aim to quantify the difference in affinity between chloride and fluoride in reference to water, explore how large the ratios of electrostatics versus orbital contributions vary, which bonding patterns are inherent to these, and to which degree they depend on the chosen surface.
Within a previous study, the surface formation energies (E surf ) have been calculated from the difference in total energies of the slab supercell (E n ) and the bulk unit cell (E bulk ) multiplied by the number of unit cells within the slab (n). 29 This difference has been divided by double the surface area (A) as symmetric slabs have been used.
For the substoichiometric surface of (101), the F potential (μ F ) is added to the numerator for each missing F. μ F itself has been derived from the unit cells of YF 3  Together, these three surfaces constitute 68% of the overall crystalline surface. Additionally, we also include the lesser abundant stoichiometric surface (100) to compare to future studies on HoF 3 surface, as in contrast to YF 3 , it is with 25% the second most available surface in HoF 3 . All four surfaces cover 75% of the YF 3 crystal. Within the bare relaxed surface supercells, (010) only contains eight-fold coordinated Y surf (see Figure 2). (100) and (011) show six-and ninefold coordinations, in which the six-fold coordination of (100) leaves the Y surf more exposed. The substoichiometric (101) contains Y surf in six-, seven-, and eight-fold coordination. These six-fold coordination polyhedra leave the Y surf much more accessible, than in the other surfaces. Thus, the accessibility of Y surf increases as (010) < (011) < (100) < (101).  Table 2). For substoichiometric (101), the difference grows to ≤ 5 kJ mol À1 , however, given the much larger absolute values, these are just ≤ 1:6%.

| Quantifying adsorption by pEDA with NOCV extension
Within this paper, we quantified the electronic adsorption energies of different adsorbates (Ads) onto different surfaces of YF 3 Therefore both adsorption energies differ by the relaxation (or preparation) of the reactants (ΔE prep ).
Using a PBE+D3 approach, 33 The first two terms of Equation (4) may be combined to the attractive interaction (ΔE attr ).
Finally, ΔE orb is split into pairwise orbital interactions of natural orbitals for chemical valence (NOCV) between the surface and the adsorbate. 37,38 The NOCVs are the eigenvectors of the deformation density matrix, which is the density difference between the intermediate and the final state in the EDA procedure. The corresponding eigenvalues are a qualitative measure of the amount of charge transferred.

| Computational details
All atomic structures within this study have been partially (adsorbates and top two YF 3 -layers) relaxed. These originate from our preceding potentials showed a better description using the latter, especially for HF. 32 Around the isolated molecules and perpendicular to the surface plane, 25 Å vacuum has been applied as converged in our previous YF 3 study. 29 A neglectable adsorbate-adsorbate interaction using the Γ-point only was found at supercell sizes of (4 Â 3 Â 4) YF 3 -layers for  Figure S1 and Table S1 ). The effects of basis set, k-grid and numerical quality were tested (see SI Section 1). These tests yielded TZ2P at the Γ-point only with a very good numerical quality as the best setup. The letter corresponds to a SCF criterion of at least 1:6 Â 10 À7 eV. Scalar relativistic effects were treated by the zeroth order regular approximation (ZORA). 45,46 All systems that converged F I G U R E 3 Atomic structures of the respective strongest adsorptions of YF 3 ÁHF (1-4a), T A B L E 1 Comparison of studied surfaces ordered according to their Y surf accessibility listing their surface energies (E surf ; PBE) and ratios (% surf ) 29 with the respective strongest bound YF 3 ÁAds (see Figure 3; PBE+D3(BJ)) yielding the strongest interaction (ΔE int ), as well as bonding energy (ΔE bond ); for (100)ÁHCl, these are obtained by two different structures giving the one with the strongest ΔE int (2b') in parenthesis; the coordination numbers (CN Y surf ) correspond to the empty adsorption site Y surf of the bare surface.      is formed within the same polyhedron, which goes along with a much stronger H-Cl bond elongation.
In Table 1, their respective adsorption energies are related with the properties of the bare surface as Y surf accessibility, surface energy (E surf ), and ratio of that surface within a perfect nanocrystal at 0 K (% surf ). It also gives the Y surf coordination numbers (CN Y surf ) referring to the empty adsorption sites of the bare surfaces. While (010) and (011) hardly differ in E surf , the latter binds any adsorbate much stronger. On the contrary, the bare surface of (100) is significantly less stable but regardless of reactant relaxation, HF and HCl adsorb only slightly stronger onto (100) than (011). The opposite is even found for H 2 O. Within YF 3 Á H 2 O, the four surfaces seem to form two groups of slightly weaker (010) and (100) versus slightly stronger (011) and (101) interacting surfaces. However, these differences are much less pronounced than those found for YF 3 ÁHF/HCl. A more detailed comparison of the strongest single adsorptions is given in Table 2 listing the different energy contributions to ΔE int and ΔE bond .  (100) and (011), ΔE prep is found to be larger than ΔE bond itself. The largest ratio of ΔE prep to ΔE bond is found in (100)ÁHCl 2b' with more than three times the latter.  Table S2.

| Structural features
According to Jeffrey's classification, 50  find that the H-bond angle and more importantly its distance correlate with a stronger interaction for adsorptions of HF and HCl onto any surface (see Figure 5A-B). At comparable H-bond distances, YF 3 ÁHF and YF 3 ÁHCl, both give comparable ΔE int . However, as HCl is a much better H-donor than HF, the stronger bound YF 3 ÁHCl form H-bonds of ClÁÁÁH-F surf yielding the shortest R HÁÁÁFsurf (see Figure 9 3a). Accordingly, these also come at the strongest ΔE int giving a slightly (15 pm) lower weighted mean for HCl than HF adsorptions. On the contrary, the YF 3 Á H 2 O adsorptions show little variation and correlation. Only within (010), the dependence of ΔE int onto the H-bond distance is clearly given. This already indicates, that the H-bond contributes less to the adsorption compared to those of HF and HCl.
In contrast to the H-bond distance, a shorter R X -Ysurf correlates to a stronger interaction for all three adsorbates (see Figure 5C). At similar distances, similar ΔE int for YF 3 ÁHF and YF 3 Á H 2 O are found, while the respective YF 3 ÁHCl adsorptions show an about 50 pm larger distance due to the equally larger ionic radius. 21 As the hydride-forming adsorptions onto the electron-rich, substoichiometric (101) possess no H-bond, these are also not given in Figure 5A-B. The formed negatively charged hydride (q CM5 (H)¼ À0:2 e) bridges two Y surf atoms with R H -Ysurf ¼ 208-220 pm. Moreover, by their large ΔE int (see Figure 7D),

| Dispersion energy
The strength of dispersion is linked to the polarizability, which is especially low for fluorine. Therefore, the energy attributed to dispersion interaction is low but increases as YF 3 Á HF < YF 3 Á H 2 O < YF 3 ÁHCl (see Figure 6A). It only contributes < 10% to the sum of attractive interactions and ΔE disp (see Equation 5 and Figure 6B). Even for very weak ΔE int and thus also weak electrostatics and orbital interactions, dispersion accounts for only a fifth of the adsorption. The relation of ΔE disp versus ΔE int is plotted in Figure S20.

| Electrostatic and orbital contributions in single adsorptions
As discussed above, ΔE int is only little effected by dispersion. The significant contributions originate from electrostatics and orbital interactions. Their ranges within each surface are plotted together with the adsorption energies in Figure 7. As this study did not sample the conformational space in its entirety, but focused on the adsorption sites of strongest interactions, the plotted ranges rather visualize the limit of strongest energy contributions. We expect that a more complete scan of the conformational space would include very weak adsorptions with near zero energies for any of these ranges. structures, the latter is by about 40 kJ mol À1 weaker in ΔE int , but stronger by the same magnitude in each of ΔE elstat and ΔE orb . This goes along with a considerable shift in electron density at Y surf only found in the latter structure (Δq Bader (Y)¼ þ0:4 e). 32 However, by the significant shift in electronic density, the repulsive ΔE Pauli is also considerably larger and overcompensates the gains in electrostatic and orbital interactions. The ratio of ΔE elstat within ΔE attr , the sum of ΔE elstat and ΔE orb (see Equation 5) is visualized in Figure 8. Depending on which term dominates within this ratio, an adsorption may classify as ionic or covalent. For YF 3 ÁHF and YF 3 ÁHCl adsorptions of at least jΔE int j ≥ 60 kJ mol À1 , for which the weak contribution of ΔE disp becomes negligible, ΔE int grows stronger with the degree of covalency. This correlation is not found for YF 3  Within the nonhydride-forming adsorptions, the increase in covalent bonding character correlates with the formation of strong Hbonds to F surf introduced above (see Figure 5). For YF 3 ÁHF, it is the formation of rather symmetric [FHF] moieties (see Figure 3 2-3a). For YF 3 ÁHCl, it is the partial dissociation of H-Cl to form a H-bond of ClÁÁÁH -F surf (see Figure 3 2b'+3b and Figure 9 3a). Alike, structural features that come with dominating electrostatics are weak or even absent H-bonds. Instead, the adsorption is dominated by a direct coordinated via X-Y surf with X = {O, F, Cl}. This supports that the direct coordination to Y surf is electrostatic dominated, while the Hbond to F surf is orbital dominated.

| Pairwise electron interactions
The orbital energy is further divided into pairwise NOCV interactions between surface and adsorbate. All corresponding deformation densities are considered, which show an electronic charge displacement  upon adsorption of ν n ≥ 0:1 e. This relatively low cutoff is chosen as the overall ΔE orb within many YF 3 ÁAds, and thus, also their ν n , are rather small. All ν n versus their corresponding contribution to the orbital energy (ΔE n orb ) are plotted in Figure S21. The flatter slope of Δν n =ΔE n orb shown by the stronger adsorbed HF or HCl onto (100), (011) or (101) also supports that their bonding character is less ionic than within the weaker adsorbed (hkl)ÁAds. The NOCV deformation densities are grouped into different interactions of σ-like or π-like interactions of three-centered H-bonds of X-HÁÁÁF surf (or XÁÁÁH -F surf ) in contrast to two-centered direct coordinations of X-Y surf with X = {O, F, Cl} or H -F surf . However, only the σ-like X-HÁÁÁF surf and σ-like X-Y surf are found within most YF 3 ÁAds. These two interactions also give the largest ν n for all nonhydride-forming adsorptions. Their ΔE n orb are plotted in Figure 9 versus the overall ΔE orb or ΔE int (for the corresponding ν n see Figure S23). Note that within the former (1a-b), the strongest bound (100)ÁHCl by ΔE int (2b') is outside the zoom because of its very large ΔE orb (see Table 2). Its deformation densities are discussed versus the strongest bound (100)ÁHCl by ΔE bond (2b) in the SI (see Figure S24). The same applies to the hydride-forming adsorptions of (101)ÁH 3Å F/Cl (see Figure S25). On the opposite, weak end of the ΔE int range, several H-bonds and direct coordinations found by atomic positions (see Figure 5) are too weak in their pairwise electron interaction to meet the applied threshold. This is most prominently the case within the weak, nonhydride-forming adsorptions onto (101), for which no H-bond, but only the direct coordinations of (101)ÁH 2 O show. For these, the sum of α and β-components are plotted.
Moderate H-bonds are defined to be bound by 17-63 kJ mol À1 (see gray area in Figure 9 1-3a). 50  above. We therefore conclude that the formation of strong H-bonds sets the interaction of YF 3 towards HF and HCl apart from H 2 O.
Coming to the electrostatic-driven direct coordinations, we find that the total ranges of ΔE direct orb are much smaller than the corresponding H-bond terms (see Figure 9 2a-b). Accordingly, the direct coordination strength is less decisive for the bonding than the H-bond strength for the moderately and strongly bound YF 3 ÁHF/HCl. On the contrary, it is more decisive than the H-bond strength for YF 3 Á H 2 O. For a detailed look at the bonding patterns, it should be noted that several weakly, but also moderately (jΔE int j < 95 kJ mol À1 ) bound adsorbates coordinate via the direct X-Y surf only, whereas a few weakly (jΔE int j < 35 kJ mol À1 ) coordinations coordinate by the H-bond only.
Furthermore, within some weakly and moderately bound (hkl)ÁHF/ HCl, NOCV deformation densities are found that show a combination of X-HÁÁÁF surf and X-Y surf . Therefore, the corresponding energy contributions were chosen to be halved to enter each of the categories.
From these, only within one (010)ÁHCl, both ν n remain above the threshold and are thus also present as two entries at the same overall Because the H-F interaction is much stronger than the respective H-Cl one, or in other words, because HF is the worse H-bond donor, the strongest H-bonds within YF 3 ÁHCl are of ClÁÁÁH -F surf type, in which the hydrogen is much closer to F surf (see Figure 10 1b). Within (011)Á HCl, the H-bond is about 120 kJ mol À1 stronger than within the respective HF structure (see Figure 10 2a-b).
At the same time, the direct coordinations of Cl-Y surf and F-Y surf are very similar in ΔE direct orb (see Figure 10 3a-b). However, the NOCV deformation density predominantly attributed to F -Y surf also accumulates electron density along H -F surf . Noteworthy is also the third main contribution of the two adsorptions, which favors ClÁÁÁH -F surf by another 20 kJ mol À1 over F -H -F surf (see Figure 10 4a-b). A very similar energy difference reproduces itself also in ΔE elstat . On the other hand, the H-bond-driven much larger ΔE orb of (011)ÁHCl is counter-balanced by ΔE Pauli leaving an overall difference of merely about 10 kJ mol À1 within ΔE int (see Table 2). Finally, due to the large ΔE prep required for the partial H-Cl dissociation, the (011)Á HCl adsorption is even about 30 kJ mol À1 weaker judged by ΔE bond .
Among all studied adsorptions, the largest ΔE orb , as well as overall ΔE int is shown by (101)ÁH 3Å F/Cl, which spontaneously dissociated in a hydride-forming possess. This is accompanied by a reduction in magnetic moment from eight to six. At the bare substoichiometric surface, all formal 8 Y(II) centers orientate ferromagnetically. However, within (101)ÁH 3Å F/Cl, the Y-centers coordinated by the anions lost their magnetic moment. Something that is not observed for weakly bound (101)ÁHF/Cl or the (101)ÁH 2 O. The classification as charge transfer is backed up by the change in electron density topography leading to the change in partial Bader charges. 32 The Löwdin-based CM5 partial charges are smaller in magnitude but qualitatively agree.
These show a reduction from AE0:2 e in free HF or AE0:1 e in free HCl to q H ¼ À0:2 e, q F ¼ À0:5 e or q Cl ¼ À0:4 e for (101)ÁH 3Å F/Cl. The dissociated atoms coordinate to the same polyhedron (see Figure 3 4a-4b). Nonetheless, in contrast to the H-bond partially dissociated adsorbates (see negative distance differences of (100)/(011)ÁHCl in  The deformation densities of both adsorptions are equivalent in shape. However, due to the smaller electronegativity of Cl and therefore less ionic character of the (101)ÁH 3Å Cl adsorption (see Figure 8), the respective ΔE n orb are smaller than those of (101)ÁH 3Å F. This is especially pronounced (23%) for the strongest ΔE α orb (2a, IIa). It corresponds to one transferred α-electron previously rather localized at Y surf towards H and F or Cl spanning a larger volume as typical for anions. By the second strongest interaction (2b, IIb), β-electron F I G U R E 1 0 Strongest adsorbed structures within (011)ÁHF (1a) and (011)ÁHCl (1b), with respective NOCV deformation densities (red = reduction / blue = accumulation of electron density) of jΔE n orb j > 20 kJ mol À1 visualized with isosurface values of 0.006 (2ab), 0.0015 (3a-b), and 0.0003 (4a-4b). Within the inserts, the first row gives the eigenvalues (ν n ) in e and the each second row the ΔE n orb in kJ mol À1 . density of 0.5 e further accumulates at H, while along the same directions 0.3 e of α-electron density depletes from H (3a, IIIa). The next weaker interactions show the same σ-like direct coordination of F -Y surf (4a-b) and Cl-Y surf (IVa-b) with a comparable ν direct and ΔE orb;direct as within the nonhydride-forming YF 3 ÁAds (see Figure 10 3a-b). The weaker contributions are π-like direct coordinations of F -Y surf (4b, 5a-b) or Cl -Y surf (IVb, Va-b). In accordance to the negative polarization of H, no deformation density indicates an H-bond.