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Tracing the acid-base catalytic properties of MON2O mixed oxides (M = Be, Mg, Ca; N = Li, Na, K) by theoretical calculations

The stability and acid-base properties of MON2O mixed oxides (where M = Be, Mg, Ca; N = Li, Na, K) are studied by using ab initio methods. It is demonstrated that (i) the basicity of such designed systems evaluated by estimation of electronic proton affinity and gas-phase basicity (defined as the electronic and Gibbs free energies of deprotonation processes for [MON2O]H+) were found significant (in the ranges of 272–333 and 260–322 kcal/mol, respectively); (ii) in each series of MOLi2O/MONa2O/MOK2O, the basicity increases with an increase of the atomic number of alkali metal involved; (ii) the Lewis acidity of the corresponding [MON2O]H+ determined with respect to hydride anion (assessed as the electronic and Gibbs free energies of H− detachment processes for [MON2O]H2) decreases as the basicity of the corresponding oxide increases. The thermodynamic stability of all [MON2O]H2 systems is confirmed by estimating the Gibbs free energies for the fragmentation processes yielding either H2 or H2O.


Introduction
The alkaline earth metal oxides are classical base catalysts where oxide ions behave as bases whereas the metal cations serve as Lewis acids. They catalyse a variety of organic reactions, e.g. isomerization of olefins [1], aldol condensation [2][3][4][5][6], transesterification reactions [7][8][9][10][11], the Knoevenagel condensation [12,13], the Michael addition [14][15][16], dehydrogenation reactions [17][18][19] and many other processes which require the cleavage of the C-H bond and the formation of carbanion intermediates [20,21]. For modern industrial applications, a good catalyst is the catalyst which is relatively inexpensive, easily accessible and, most importantly, environmental friendly. In many existing processes which use homogeneous catalysts, the removal of catalysts after the reaction is usually a difficult task and a large amount of liquid waste is produced. Among the different fields of catalysis, the heterogeneous catalysis utilizing metal oxides is very prominent in the context of improving industrial processes that fulfil the needs of sustainable technologies (regulated by environmental issues) [22]. In the case of solid catalysts, many important parameters or features act on catalytic properties, such as (i) atomic composition (i.e. the presence of transition metals or main group elements only), (ii) the structure of crystalline phase, (iii) the surface morphology (i.e. isotropic, anisotropic or amorphous) and (iv) structural defects [23]. As stated above, the solid alkaline earth metal oxides (MO) are bifunctional which means they possess two active sites (i.e. the M 2+ cation and the O 2− anion). Therefore, the catalytic activity may be also attributed to acid-base strength of MO. The acid-base strength is especially important in the organic reactions mentioned above. Namely, the stronger the basic site of the metal oxide catalyst, the faster the cleavage of the C-H bond, while the low Lewis acidity strength reduces the activation barrier related to the formation of carbanion-catalyst complex which in turn increases its reactivity. In this contribution, we present our theoretical study of the structure and acidbase properties of MON 2 O mixed oxides (where M = Be, Mg, Ca; N = Li, Na, K). Our goal was to investigate whether the potential catalytic properties (in terms of theoretically predicted acid-base properties) of alkaline earth metal oxides can be enhanced by combining with alkali metal oxides. The introduction of different metals (i.e. alkali or alkali earth metals) into the structure of solid transition metal catalyst (including transition metal oxides) is one of the ways to enhance either the selectivity or activity of the catalyst [24]. The promotion effect of dopants depends on the metal used and usually improves the active sites of a catalyst by changing its physicochemical properties. For instance, during the N 2 O decomposition reaction, strong promotion effects of alkali metals on cobalt-cerium composite oxide were observed [25]. The high catalytic activity was attributed to the redox ability of active Co 2+ site induced by alkali metal. This is consistent with our results reported for mixed nonstoichiometric MON oxides (where M = Be, Mg, Ca; N = Li, Na, K) [26]. We found that the introduction of alkali metal to alkaline earth metal oxide substantially affects the electron density distribution in the MO system (by reducing the partial charge on alkali earth metal atom) and rises the reductive ability (by ca. 2-3 eV with respect to the unmodified oxide).
In considering the potential applicability of base catalysts (pure or modified), it is convenient to be able to characterize their activity in terms of the number of sites and the strength thereof. It is being experimentally accomplished by the use of numerous technics, such as the usage of acid-base indicators, X-ray diffraction, photoelectron spectroscopy or thermal analysis [23]. On the other hand, the intrinsic basicity of any molecule can be estimated theoretically by performing ab initio calculations. The calculated values of proton affinity (PA) and the negative of the Gibbs free energy of protonation reaction (known as gas-phase basicity, GPB) have been determined for a large number of species and are available through the NIST chemistry webbook [27]. It is worth noting that among the neutral systems one of the strongest basis proposed thus far is the bidentate proton chelator "proton sponge" (1,8bis(dimethylamine)naphthalene) whose PA and GPB were estimated to be equal to ca. 245 and 239 kcal/mol, respectively [28]. In fact, many chemists adopt those values as the threshold values while classifying compounds as "superbases" (defined as compounds whose proton affinity and gas-phase basicity are both larger than that of the "proton sponge"). As far as the second (acidic) site is concerned, its strength might be estimated by its vulnerability to accept the electron pair (as this site is to promote the carbanion). Therefore, in our contribution, we decided to relate such property to hydride anion bounding strength. Namely, we calculated the hydride affinity (HA) and the Gibbs free energy of hydride anion detachment process (so-called gas-phase electrophilicity, GPE) by analogy with the PA and GPB values. To the best of our knowledge, this is the first report containing a systematic study of the acid-base properties of MON 2 O mixed oxides and their physicochemical properties with respect to chemical composition.

Methods
The equilibrium structures of the MO, (MO) 2 (where M = Be, Mg, Ca; N = Li, Na, K) molecules and the corresponding harmonic vibrational frequencies were calculated using the second-order Møller-Plesset perturbational method (MP2) [29][30][31] with the aug-cc-pVTZ basis set [32,33]. The electronic energies of the systems studied were then refined by employing the coupledcluster method with single, double and noniterative triple excitations (CCSD(T)) [34][35][36][37] and the same basis set. During the geometry optimizations followed by harmonic vibrational frequency calculations carried out by employing the MP2 method and while refining the electronic energies using the CCSD(T) method, all orbitals in the core and valence shells have been correlated.
The electronic proton affinity (PA, defined as the negative of the electronic energy change in the reaction B+H + → BH + ) of MO, (MO) 2  Thermodynamic stability related to the most likely fragmentations paths for all studied species was established accordingly, by using the CCSD(T) electronic energies and the MP2 zero-point energies, thermal corrections and entropy contributions (at T = 298.15K).
All calculations were performed with the GAUSSIAN16 program (Rev. C.01) [38], while the plots showing the molecular structures were generated with the CHEMCRAFT program [39] Results  [27]. The comparison of those values with our calculated PAs and GPBs may indicate that the CCSD(T)/ aug-cc-pVTZ theoretical treatment somewhat overestimates the proton affinity and gas-phase basicity of MgO and CaO by 17.9-30.7 and 0.4-13.5 kcal/mol, respectively. However, it is worth to mention that the experimental data available for magnesium and calcium oxides are based on a single report only (describing the measurements performed in 1962) and might be unreliable as such. Hence, we believe that our PA and GPB values are likely more accurate and represent the best estimates of these quantities available.
As far as the hydride affinities and gas-phase electrophilicities of [ The most stable isomers of (MO) 2 correspond to the rhombic D 2h -symmetry structures, see Similar to our predictions formulated for the MO monomers, our calculations performed for the (MO) 2 systems indicate that the larger the basicity of (MO) 2 the smaller the electrophilicity (with respect to H − ) of its corresponding protonated [(MO) 2 ]H + form. In particular, the calculated PA and GPB values for (MO) 2 increase (from 220 to 301 and from 208 to 288 kcal/mol, respectively) with an increase of the atomic number of M, whereas the calculated HAs and GPEs of [(MO) 2 ]H + decrease (from 254 to 154 and from 245 to 143 kcal/mol, respectively) with the M atomic number, see Table 1. In order to verify whether the dimerization affects the basicity and electrophilicity of MO systems, we compared the PA, GPB, HA and GPE values of (MO) 2 to those of their corresponding MO species. We found that (i) the dimerization of BeO decreases the basicity as well as the electrophilicity of its protonated form (as the PA and GPB of (BeO) 2 Table 1). Finally, it should also be mentioned that MgO, (MgO) 2 , CaO and (CaO) 2 can be classified as superbases, which means that their PAs (in the range of 267-302 kcal/mol) and GPBs (spanning the 243-288 kcal/mol range) are higher than those predicted for the "proton sponge" whose PA and GPB are equal to 245 and 239 kcal/mol, respectively. Since various metal oxides are used as catalysts in dehydrogenation reactions, we verified the thermodynamic stability of each neutral [MO]H 2 and [(MO) 2 ]H 2 system by examining two dissociation channels, namely, the detachment of H 2 and H 2 O (see Table 2). In fact, determining the susceptibility of these compounds to liberate molecular hydrogen or water   As revealed by our calculations, the most stable isomers of BeOLi 2 O and BeONa 2 O correspond to linear D ∞h -symmetry structures (labelled 1 in Fig. 3), whereas the lowest energy isomer of BeOK 2 O corresponds to the non-planar compact C 2v -symmetry structure resembling the system labelled 4 in H + are equal to 129°and 133°, respectively); however, we verified that these bent structures do not correspond to the global minima as their energies are larger by ca. 5 kcal/mol than those predicted for the C s -symmetry isomers containing a fourmember MO 2 N ring with the remaining H and N atoms bonded to the oxygens (see Fig. 4 .077-0.111 Å). Also, the terminal Li, Na and K atoms form the N-H bonds with the nearest H atoms, yet their lengths are larger by 0.316, 0.117 and 0.243 Å with respect to the Li-H, Na-H and K-H bond lengths in the corresponding alkali metal hydrides (as predicted at the same theory level).
As explained above, we view each MON 2 O molecule as the alkaline earth metal oxide (MO) modified by the alkali  Table 2  The data collected in Table 1 indicate that the proton affinity and gas-phase basicity increase when the magnesium oxide is modified by alkali metal oxides. In particular, the PA and GPB values predicted for MgON 2 O systems span the 291-322 and 278-309 kcal/mol range, respectively, whereas the PA of 266.8 kcal/mol and the GPB of 242.8 kcal/mol were calculated for the unmodified MgO. It is also worth to mention that the introduction of alkali metal oxide to magnesium oxide is more effective (with regard to the basicity increase) than the dimerization of MgO, as the PAs and GPBs of MgON 2 O are larger by ca. 18-49 kcal/mol than those of (MgO) 2 Fig. 6). We should also mention that the energy of another isomer of [CaONa 2 O]H 2 (adopting the C s -symmetry structure) is larger than the energy of the global minimum by only 0.8 kcal/mol; hence, both these isomers are likely co-existing near room temperatures. In contrast, the relative energy of the second most stable isomer of the [CaOK 2 O]H 2 compound is considerably larger (8.8 kcal/mol).
The results collected in Table 1 indicate that the introduction of an alkali metal oxide to calcium oxide causes the basicity increase of the latter system. Namely, the PA and GPB values predicted for CaON 2 O (N = Li, Na, K) are higher by ca. 18 Taking into account all the most stable isomers of the [MON 2 O]H 2 (where M = Be, Mg, Ca; N = Li, Na, K) systems, it is worth emphasizing that the appearance of a structure serving as a Lewis acid) of the alkali earth metal (M). In fact, the appearance of this isomeric structure (as the most stable configuration) is likely related to our approach of determining the Lewis acid strength by evaluating the affinity of a given system to hydride anion. As the H − is characterized by a relatively moderate value of the excess electron binding energy (0.754 eV [40]), its excess negative charge is expected to be effectively delocalized among other more electronegative fragments. Regardless Table 2).