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. 2021 Jun 26;27(7):210. doi: 10.1007/s00894-021-04829-7

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

Dawid Faron 1, Piotr Skurski 1, Iwona Anusiewicz 1,✉
PMCID: PMC8233238  PMID: 34173072

Abstract

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.

Keywords: Mixed oxides, Gas-phase basicity, Gas-phase electrophilicity, Proton affinity, Hydride affinity

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[2–6], transesterification reactions [7–11], the Knoevenagel condensation[12, 13], the Michael addition[14–16], dehydrogenation reactions[17–19] 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 M2+ cation and the O2− 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 acid-base properties of MON2O 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 N2O 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 Co2+ 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” (1,8-bis(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 MON2O mixed oxides and their physicochemical properties with respect to chemical composition.

Methods

The equilibrium structures of the MO, (MO)2, MON2O, [MO]H+, [(MO)2]H+ and [MON2O]H+, [MO]H2, [(MO)2]H2 and [MON2O]H2 (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)[29–31] with the aug-cc-pVTZ basis set[32, 33]. The electronic energies of the systems studied were then refined by employing the coupled-cluster method with single, double and noniterative triple excitations (CCSD(T))[34–37] 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 and MON2O and electronic hydride affinity (HA, defined as the negative of the electronic energy change in the reaction BH++H–→BH2) of the MOH+, [(MO)2]H+, [MON2O]H+ were estimated at the CCSD(T)/aug-cc-pVTZ theory level. The corresponding gas-phase basicity (GPB, defined as the negative of the Gibbs free energy of protonation reaction) of MO, (MO)2 and MON2O and gas-phase electrophilicity (GPE, defined as the negative of the Gibbs free energy of hydride anion attachment) of the [MO]H+, [(MO)2]H+, [MON2O]H+ were evaluated using the CCSD(T)/aug-cc-pVTZ electronic energies and the zero-point energy corrections, thermal corrections (at T = 298.15K) and entropy contributions estimated with the MP2 method and the aug-cc-pVTZ basis set (in each case, the Gibbs free energy of a proton was also accounted for).

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

The [MO]H+, [(MO)2]H+, [MO]H2 and [(MO)2]H2 systems (M = Be, Mg, Ca)

The lowest energy structures of MO, [MO]H+, [MO]H2, (MO)2, [(MO)2]H+ and [(MO)2]H2 species (M = Be, Mg, Ca) are shown in Figs. 1 and 2, whereas the electronic proton affinity and gas-phase basicity of monomeric (MO) and dimeric ((MO)2) alkaline earth metal oxides as well as hydride affinity and gas-phase electrophilicity of the protonated forms of those oxides are gathered in Table 1. According to our findings, the lowest energy isomers of the [MO]H+ cations correspond to the linear C∞v-symmetry structures with the hydrogen atom bonded to the oxygen atom, while the analysis of the most stable structures obtained for [MO]H2 indicates that hydride anion attaches in all cases to the opposite side of [MO]H+ molecule (i.e. to the M atom, see Fig. 1). The H− attachment to [MgO]H+ or [CaO]H+ affects the structures only slightly as the resulting neutral [MgO]H2 and [CaO]H2 molecules are linear (C∞v-symmetry). In contrast, the addition of H− to the [BeO]H+ cation leads to the bent Cs-symmetry structure of [BeO]H2 (with the Be–O–H valence angle of 146.62°).

Fig. 1.

Fig. 1

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The equilibrium structures of the MO, [MO]H+ and [MO]H2 (where M = Be, Mg, Ca) obtained at the MP2/aug-cc-pVTZ level

Fig. 2.

Fig. 2

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The equilibrium structures of the (MO)2, [(MO)2]H+ and [(MO)2]H2 (where M = Be, Mg, Ca) obtained at the MP2/aug-cc-pVTZ level

Table 1.

The electronic proton affinities (PA in kcal/mol), gas-phase basicities (GPB in kcal/mol) of the MO, (MO)2 and MON2O as well as the electronic hydride affinity (HA in kcal/mol) and gas-phase electrophilicity (GPE in kcal/mol) of the corresponding protonated forms (i.e. MOH+, [(MO)2]H+ and [MON2O]H+; where M = Be, Mg, Ca; N = Li, Na, K ). The results are obtained at the CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ level

Species PA GPB Species HA GPE
BeO 236.3 220.5 [BeO]H+ 265.8 265.5
MgO 266.8 242.8 [MgO]H+ 226.8 218.1
CaO 302.5 278.2 [CaO]H+ 170.3 161.1
(BeO)2 220.4 207.9 [(BeO)2]H+ 253.6 245.3
(MgO)2 272.4 259.6 [(MgO)2]H+ 200.5 193.3
(CaO)2 300.8 288.2 [(CaO)2]H+ 153.8 143.1
BeOLi2O 272.0 259.9 [BeOLi2O]H+ 171.8 160.3
BeONa2O 297.1 287.5 [BeONa2O]H+ 154.5 140.5
BeOK2O 310.1 298.1 [BeOK2O]H+ 142.3 131.4
MgOLi2O 290.7 277.6 [MgOLi2O]H+ 166.7 156.9
MgONa2O 309.4 297.7 [MgONa2O]H+ 154.8 144.8
MgOK2O 321.7 308.9 [MgOK2O ]H+ 151.7 138.7
CaOLi2O 320.2 308.9 [CaOLi2O]H+ 147.6 138.3
CaONa2O 331.9 320.4 [CaONa2O]H+ 144.1 131.6
CaOK2O 333.1 322.2 [CaOK2O]H+ 134.9 122.0
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The calculated PAs and GPBs for alkaline earth metal oxides show a systematic growth with an increase of atomic number of M (i.e. the largest PA and GPB values correspond to CaO), see Table 1. The experimental PAs and GPBs are available only for MgO (PA = 236.14 kcal/mol; GPB = 229.30 kcal/mol) and CaO (PA = 284.56 kcal/mol; GPB = 277.80 kcal/mol)[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 [MO]H+ are concerned, our calculations indicate that the HA and GPE decrease in the [BeO]H+/[MgO]H+/[CaO]H+ series (i.e. the lowest HA and GPE correspond to [CaO]H+). Clearly, the basicity of MO is associated with the electrophilicity of [MO]H+, as the values gathered in Table 1 affirm (i.e. the larger the basicity of MO (CaO > MgO > BeO), the smaller the electrophilicity (with respect to H−) of the corresponding [MO]H+ ([CaO]H+ < [MgO]H+ < [BeO]H+)).

The most stable isomers of (MO)2 correspond to the rhombic D2h-symmetry structures, see Fig. 2. The M–O distances in the MO dimers are longer than those in the corresponding monomers by 0.141, 0.143 and 0.211 Å for M = Be, Mg and Ca, respectively. The lowest energy isomers of [(MO)2]H+ correspond to the kite-shaped C2v-symmetry structures with the proton attached to one of the oxygen atoms. As shown in Fig. 2, the M–O bonds involving the protonated oxygen atom are slightly longer (by ca. 0.08–0.16 Å) than those in the neutral (MO)2 systems, whereas the remaining M–O separations in [(MO)2]H+ are somewhat smaller (by ca. 0.05–0.07 Å) than the M–O distances in the corresponding dimeric oxides.

The attachment of H– to [(MO)2]H+ systems may lead to the formation of either Cs-symmetry chain-like H–O–M–O–M–H isomer or D2h-symmetry rhombic isomer of [(MO)2]H2. As we verified, the most stable isomer of [(BeO)2]H2 corresponds to the chain structure with the Be–O–H valence angle of 133.13° (while the rhombic structure is higher in energy by 67.7 kcal/mol), and the lowest energy isomers of [(MgO)2]H2 and [(CaO)2]H2 correspond to the rhombic structures (whereas the energies of the corresponding chain structures are larger by 4.3 and 16.6 kcal/mol, respectively), see Fig. 2.

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 are smaller by 12.6–15.9 kcal/mol and the HA and GPE of [(BeO)2]H+ are smaller by 12.2–20.2 kcal/mol than the corresponding values calculated for BeO and [BeO]H+), (ii) the dimerization of MgO increases the basicity as it leads to larger (by 5.6–16.8 kcal/mol) values of PA and GPB, while the HA and GPE values of the corresponding [(MgO)2]H+ are lower (by ca. 25 kcal/mol) than those predicted for [MgO]H+, (iii) the dimerization of CaO decreases the PA only slightly (by 2 kcal/mol) and increases the GPB by 10 kcal/mol, whereas the HA and GPE values decrease (by 17–18 kcal/mol) with respect to those calculated for [CaO]H+ (see 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]H2 and [(MO)2]H2 system by examining two dissociation channels, namely, the detachment of H2 and H2O (see Table 2). In fact, determining the susceptibility of these compounds to liberate molecular hydrogen or water molecule provides an insight not only into the thermodynamic stability of the [MO]H2 and [(MO)2]H2 systems but also on the recovery processes of the studied oxides (when serving as catalysts in dehydrogenation processes). The positive ΔGr298 values (spanning the 24–87 kcal/mol range and the 38–110 kcal/mol range for the reactions involving [MO]H2 and [(MO)2]H2, respectively; see Table 2) indicate that the [MO]H2 and [(MO)2]H2 systems are stable against the detachment of either H2 or H2O.

Table 2.

The Gibbs free energies (ΔGr298 in kcal/mol) of the fragmentation reactions (at T = 298.15 K) considered in this work. The results are obtained at the CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ level

Fragmentation path ΔGr298
[BeO]H2 → BeO + H2 87.4
[MgO]H2 → MgO + H2 79.3
[CaO]H2 → CaO + H2 58.8
[(BeO)2]H2 → [BeO]2 + H2 59.6
[(MgO)2]H2 → [MgO]2 + H2 59.4
[(CaO)2]H2 → [CaO]2 + H2 37.8
[BeOLi2O]H2 → BeOLi2O + H2 26.6
[BeONa2O]H2 → BeONa2O + H2 34.4
[BeOK2O]H2 → BeOK2O + H2 35.8
[MgOLi2O]H2 → MgOLi2O + H2 40.9
[MgONa2O]H2 → MgONa2O + H2 48.9
[MgOK2O]H2 → MgOK2O + H2 53.9
[CaOLi2O]H2→ CaOLi2O + H2 53.6
[CaONa2O]H2 → CaONa2O + H2 58.4
[CaOK2O]H2 → CaOK2O + H2 50.6
[BeO]H2 → Be + H2O 77.8
[MgO]H2 → Mg + H2O 23.8
[CaO]H2 → Ca + H2O 28.3
[(BeO)2]H2 → Be2O + H2O 110.0
[(MgO)2]H2 → Mg2O + H2O 79.1
[(CaO)2]H2 → Ca2O + H2O 60.1
[BeOLi2O]H2 → BeOLi2 + H2O 84.5
[BeONa2O]H2 → BeONa2 + H2O 73.8
[BeOK2O]H2 → BeOK2 + H2O 81.1
[MgOLi2O]H2 → MgOLi2 + H2O 55.2
[MgONa2O]H2 → MgONa2 + H2O 49.6
[MgOK2O]H2 → MgOK2 + H2O 57.1
[CaOLi2O]H2 → CaOLi2 + H2O 60.6
[CaONa2O]H2 → CaONa2 + H2O 52.3
[CaOK2O]H2 → CaOK2 + H2O 52.2
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The MON2O oxides and their protonated and hydrogenated forms (M = Be, Mg, Ca; N = Li, Na, K)

An extensive exploration of the ground-state MON2O potential energy surface of the neutral BeOLi2O, BeONa2O, BeOK2O, MgOLi2O, MgONa2O, MgOK2O, CaOLi2O, CaONa2O and CaOK2O systems matching the MON2O formula (where M and N stand for alkaline earth metal and alkali metal, respectively) led to four constitutional isomers for each compound considered, see Fig. 3. For each molecule, we verified the thermodynamic stability of its lowest energy isomer by confirming that the ΔGr298 values calculated for the most likely fragmentation path (i.e. MON2O→MO+N2O, M = Be, Mg, Ca; N = Li, Na, K) are positive (92–163 kcal/mol). Therefore, we conclude that the mixed MON2O oxides, once formed, should be stable in gas phase and not susceptible to decomposition yielding MO and N2O. While exploring the configuration space of the [MON2O]H+ and [MON2O]H2, we performed a random structure search using the previously obtained stationary-point geometries of the MON2O oxides with a proton or two hydrogen atoms attached as the initial structures. Namely, in order to determine the lowest energy isomeric structures of [MON2O]H+ and [MON2O]H2, various possibilities of attaching the proton or two hydrogen atoms to [MON2O] were examined by treating them as the starting structures during the independent geometry optimization procedure. Since our main goal was to predict the basicity of MON2O systems and electrophilicity of their protonated forms as well as to compare those features to the corresponding values predicted for the unmodified MO systems, only the lowest energy isomers of BeON2O, MgON2O and CaON2O and their protonated and hydrogenated forms are presented and discussed in the following sections.

Fig. 3.

Fig. 3

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The schematic structures of MON2O mixed oxides isomers (where M = Be, Mg, Ca; N = Li, Na, K)

BeON2O, [BeON2O]H+ and [BeON2O]H2 (N = Li, Na, K)

As revealed by our calculations, the most stable isomers of BeOLi2O and BeONa2O correspond to linear D∞h-symmetry structures (labelled 1 in Fig. 3), whereas the lowest energy isomer of BeOK2O corresponds to the non-planar compact C2v-symmetry structure resembling the system labelled 4 in Fig. 3 (see also Fig. 4 where these global minima are depicted). The second lowest energy isomers (i.e. the compact C2v-symmetry BeOLi2O and BeONa2O and linear D∞h-symmetry BeOK2O) are higher in energy than the corresponding global minima by ca. 21, 8 and 4 kcal/mol, respectively.

Fig. 4.

Fig. 4

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The equilibrium structures of the BeON2O, [BeON2O]H+, [BeON2O]H2 (where N = Li, Na, K) obtained at the MP2/aug-cc-pVTZ level

Proton attachment to one of the oxygen atoms of linear BeOLi2O and BeONa2O structures leads to the bending of the protonated fragment (the resulting Be–O–Li and Be–O–Na valence angles in [BeOLi2O]H+ and [BeONa2O]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 Cs-symmetry isomers containing a four-member MO2N ring with the remaining H and N atoms bonded to the oxygens (see Fig. 4). As it turned out, the lowest energy isomer of the [BeOK2O]H+ cation depicted in Fig. 4 corresponds to the similar Cs-symmetry structure as those of [BeOLi2O]H+ and [BeONa2O]H+.

As far as the hydrogenated forms of BeON2O are concerned, our calculations indicate that the lowest energy isomers of [BeON2O]H2 resemble the most stable Cs-symmetry structures of [BeON2O]H+ cations with the additional hydrogen atom attached to beryllium atom. The Be–H bond lengths in the [BeON2O]H2 systems span the 1.416–1.440 Å range and are slightly longer (by ca. 0.1 Å) than those in BeH2 (as predicted at the same theory level). As it can be seen from Fig. 4, the addition of H− to the [BeON2O]H+ systems shortens the N–O bonds (by 0.111–0.268 Å) in the four-membered ring and elongates the Be–O bonds (by 0.077–0.111 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 MON2O molecule as the alkaline earth metal oxide (MO) modified by the alkali metal oxide (N2O). Hence, the comparison of the PA and GPB of BeON2O species as well as the HA and GPE of [BeON2O]H+ cations to those of the corresponding BeO and [BeO]H+ systems allows us to establish the effects caused by this modification. According to our findings, the PA and GPB values increase significantly upon the attachment of the N2O to the beryllium oxide. In particular, the PAs and GPBs of the resulting BeOLi2O, BeONa2O and BeOK2O were found to be higher than those of the corresponding BeO by ca. 36–74 and 39–78 kcal/mol, respectively (see Table 1). Moreover, the resulting PAs (272–310 kcal/mol) and GPBs (260–298 kcal/mol) of BeON2O systems are larger than the corresponding values of 245 and 239 kcal/mol characterizing the PA and GPB of the “proton sponge”. Hence, we conclude that all BeON2O oxides considered might be classified as superbases. On the other hand, a basicity increase of BeO (when modified by the attachment of N2O) is associated with the electrophilicity decrease of [BeO]H+ (when modified with N2O). In particular, the calculated HAs and GPEs of [BeON2O]H+ span the 142–172 and 131–160 kcal/mol range, respectively, which means that the electrophilicity decreases by ca. 35–49% when the protonated beryllium oxide is mixed with an alkali metal oxide. It is also worth noting that the basicity increase (achieved by attaching N2O to BeO) and the electrophilicity decrease (attained by attaching N2O to [BeO]H+) change in the same direction (i.e. with an increase of the atomic number of N). As a result, we obtained the largest PA/GPB values and the lowest HA/GPE values for BeOK2O and its protonated form, respectively (see Table 1).

Finally, we verified the thermodynamic stability of each [BeON2O]H2 system by examining two possible dissociation channels: dehydration ([BeON2O]H2→BeON2+H2O) and dehydrogenation ([BeON2O]H2→ BeON2O+H2). Since the ΔGr298 values determined for these processes turned out to be large and positive (in the 27–84 kcal/mol range), we are confident that all the [BeON2O]H2 molecules studied are thermodynamically stable. Interestingly, the comparison of the ΔGr298 values obtained for the fragmentations yielding H2O are larger than those predicted for the fragmentations yielding H2 which indicates that the latter path should be considered more likely when the decomposition of [BeON2O]H2 systems is concerned, as the second column in Table 2 affirms.

The MgON2O, [MgON2O]H+ and [MgON2O]H2 systems (N = Li, Na, K)

The most stable structures of MgON2O, [MgON2O]H+ and [MgON2O]H2 involving various alkali metal atoms N are presented in Fig. 5. As predicted by our calculations, the lowest energy isomers of MgOLi2O, MgONa2O and MgOK2O mixed oxides correspond to the linear D∞h-symmetry NO–Mg–ON structures with the magnesium atom localized in the centre bridging two OLi, ONa or OK subunits. The attachment of H+ to these compounds leads to the formation of the [MgON2O]H+ cations whose most stable isomers depicted in Fig. 5 correspond to the structures containing a four-membered MgO2N ring with the remaining H and N atoms bonded to the oxygens. In fact, these global minima of the [MgON2O]H+ cations closely resemble those found for the [BeON2O]H+ systems (cf. Figs. 4 and 5). We also confirmed that the relative energies of other isomeric structures of the [MgON2O]H+ cations (which are not shown in Fig. 5) exceed 8 kcal/mol, thus rendering them uncompetitive near room temperatures.

Fig. 5.

Fig. 5

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The equilibrium structures of the MgON2O, [MgON2O]H+, [MgON2O]H2 (where N = Li, Na, K) obtained at the MP2/aug-cc-pVTZ level

The structures adopted by the lowest energy isomers of [MgOLi2O]H2 and [MgONa2O]H2 resemble those of the corresponding [MgOLi2O]H+ and [MgONa2O]H+ cations with the H− attached to the magnesium atom and thus involved in the formation of either Li–H or Na–H bond, see Fig. 5. The Mg–O, O–H, Li–O and Na–O distances in [MgON2O]H2 (N = Li, Na) differ from those in the [MgON2O]H+ systems only slightly as the predicted differences do not exceed 0.15 Å. The lengths of the N–H bonds (2.1–2.4 Å) involving terminal N atoms are substantially larger than those predicted (at the same theory level) for the corresponding isolated alkali metal hydrides (1.588 and 1.876 Å for the Li–H and Na–H, respectively) which indicates relatively weak N–H interactions. In contrast, the lowest energy isomer of [MgOK2O]H2 adopts the compact C2v-symmetry structure with two hydrogen atoms bonded to the oxygens (see Fig. 5). As far as the second lowest energy isomers of [MgON2O]H2 (N = Li, Na, K) are concerned, we found the C2v-symmetry structure of [MgONa2O]H2 and Cs-symmetry structure of [MgOK2O]H2 having their energies only slightly larger (by ca. 2 kcal/mol) than those of their corresponding global minima (thus rendering them competitive near room temperatures) and the C2v-symmetry structure of [MgOLi2O]H2 having its relative energy of ca. 12 kcal/mol.

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 MgON2O 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 MgON2O are larger by ca. 18–49 kcal/mol than those of (MgO)2. As far as the hydride affinity and gas-phase electrophilicity of [MgON2O]H+ are concerned, we confirmed that the more basic MgON2O the less electrophilic its corresponding protonated form. In the series of MgOLi2O/MgONa2O/MgOK2O, the MgOK2O molecule was identified as the most basic (having its PA = 321.7 kcal/mol and GPB = 308.9 kcal/mol), and thus its protonated [MgOK2O]H+ form exhibits the lowest (among the MgO-based mixed oxides considered) values of HA (151.7 kcal/mol) and GPE (138.7 kcal/mol), see Table 1. The corresponding [MgON2O]H2 compounds were all found stable with respect to the fragmentations yielding either H2 or H2O, as indicated by positive Gibbs free energies calculated for those processes (see ΔGr298 values gathered in Table 2).

The CaON2O, [CaON2O]H+ and [CaON2O]H2 systems (N = Li, Na, K)

Our calculations revealed that the lowest energy isomers of CaOLi2O, CaONa2O and CaOK2O correspond to the compact C2v-symmetry structures, see Fig. 6. We also found that the H+ attachment to these structures results in substantial geometry reorganization as the most stable isomers of the [CaON2O]H+ cations resemble their corresponding [BeON2O]H+ and [MgON2O]H+ systems (described in the preceding section, see Figs. 4–6 for comparison). Namely, each [CaON2O]H+ (N = Li, Na, K) structure is planar (Cs-symmetry) and contains a tetragonal CaO2N frame with the additional H and N bonded to the oxygen atoms, see Fig. 6.

Fig. 6.

Fig. 6

Open in a new tab

The equilibrium structures of the CaON2O, [CaON2O]H+, [CaON2O]H2 (where N = Li, Na, K) obtained at the MP2/aug-cc-pVTZ level

The lowest energy isomer of [CaOLi2O]H2 resembles the most stable structure of [CaOLi2O]H+ cation with the H− anion attached to calcium atom via the elongated (2.201 Å) Ca–H bond (as the Ca–H bond length of 2.048 Å was determined for the CaH2 molecule). On the other hand, the most stable isomers of [CaONa2O]H2 and [CaOK2O]H2 correspond to the C2v-symmetry compact structures with two hydrogen atoms bonded to oxygens (see Fig. 6). We should also mention that the energy of another isomer of [CaONa2O]H2 (adopting the Cs-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 [CaOK2O]H2 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 CaON2O (N = Li, Na, K) are higher by ca. 18–31 and 31–44 kcal/mol than those calculated for the isolated CaO molecule. Next, our calculations revealed that as the proton affinity and basicity of CaON2O systems increase (with an atomic number of N), the hydride affinity and the electrophilicity of the corresponding [CaON2O]H+ cations decrease (similar trends were observed for BeO- and MgO-based mixed oxides, see the preceding sections). In particular, the PA and GPB determined for the CaON2O mixed oxides increase with an increase of the atomic number of N (i.e. the highest PA and GPB values correspond to CaOK2O), whereas the HA and GPE values predicted for the [CaON2O]H+ cations decrease in the same direction (i.e. the lowest HA and GPE correspond to [CaOK2O]H+, see Table 1). It is also worth noting that the [CaOK2O]H+ is characterized by the lowest HA (134.9 kcal/mol) and the lowest GPE (122.0 kcal/mol) among all [MON2O]H+ cations studied.

Taking into account all the most stable isomers of the [MON2O]H2 (where M = Be, Mg, Ca; N = Li, Na, K) systems, it is worth emphasizing that the appearance of a structure with two hydrogen atoms attached to the oxygen atoms (see [MgOK2O]H2, [CaONa2O]H2 and [CaOK2O]H2 depicted in Figs. 5 and 6) does not exclude the catalytic activity (i.e. 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 of the structural differences, all calculated HA and GPE values estimated for [MON2O]H+ systems point to a decreasing binding strength of the anionic intermediate (resulting from the bond cleavage, e.g. C–H) with a basicity increase of the corresponding MON2O mixed oxide.

As far as the thermodynamic stability of the [CaON2O]H2 systems is concerned, we confirmed that all the hydrogenated CaO-based mixed oxides are stable with respect to fragmentation yielding either H2 or H2O. In particular, the ΔGr298 values predicted for the [CaON2O]H2→CaON2O+H2 and [CaON2O]H2→CaON2+H2O processes are positive (spanning the 51–58 kcal/mol and 52–61 kcal/mol range, respectively) which confirms that these fragmentation channels are practically closed, see Table 2. The CaON2O mixed oxide recovery by dehydrogenation is more probable in the case of [CaOLi2O]H2 and [CaOK2O]H2 (as the ΔGr298 values for the H2 detachment are less positive than those for the detachment of H2O), whereas in the case of [CaONa2O]H2 the detachment of water molecule turned out to be more achievable (as the ΔGr298 for H2O detachment is less positive (by ca. 6 kcal/mol) than that for the fragmentation yielding H2, see Table 2).

Conclusions

On the basis of our CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ calculations performed for (i) alkali earth metal oxides (MO) and their protonated and hydrogenated forms ([MO]H+ and [MO]H2), (ii) dimers of alkali earth metal oxides ((MO)2) and their protonated and hydrogenated forms ([(MO)2]H+ and [(MO)2]H2) and (iii) alkali earth metal oxides modified by the attachment of alkali metal oxides (MON2O) and their protonated and hydrogenated forms ([MON2O]H+ and [MON2O]H2) (where M = Be, Mg, Ca; N = Li, Na, K), we conclude the following:

  1. The MgO and CaO oxides can be classified as superbases as their electronic proton affinities (PA) and gas-phase basicities (GPB) are higher than the reference values of 245 and 239 kcal/mol (characterizing the “proton sponge”), whereas the BeO oxide is characterized by smaller PA and GPB values of 236.3 and 220.5 kcal/mol, respectively.

  2. The dimerization of MgO and CaO increases (by ca. 10–17 kcal/mol) the basicity of those oxides, whereas the PA and GPB values of BeO decrease (by 16 and 12 kcal/mol, respectively) upon dimerization.

  3. The electronic proton affinities (spanning the range of 272–333 kcal/mol) and gas-phase basicities (in the range of 260–322 kcal/mol) predicted for all MON2O considered are substantially higher than the PA and GPB characterizing the “proton sponge”, which justifies their classification as superbases.

  4. The basicity of BeON2O, MgON2O and CaON2O increases with an increase of the atomic number of N (i.e. the highest PA and GPB values correspond to BeOK2O, MgOK2O and CaOK2O).

  5. In the case of magnesium oxide and calcium oxide, the mixing with any alkali metal oxide (Li2O, Na2O or K2O) causes a larger PA and GPB increase than the dimerization process.

  6. The CaOK2O mixed oxide represents the strongest base described in this contribution (PA = 333.1 kcal/mol, GPB = 322.2 kcal/mol).

  7. The electronic hydride affinity (HA) and gas-phase electrophilicity (GPE) values of the [MO]H+ cations relate to the basicity of their corresponding MO molecules (the stronger the MO base the less electrophilic its protonated form).

  8. The protonated MO dimers ([(MO)2]H+) are characterized by even smaller (by ca. 12–26 kcal/mol) values of HA and GPE than their corresponding protonated monomeric forms ([MO]H+).

  9. The electrophilicity of [BeON2O]H+, [MgON2O]H+ and [CaON2O]H+ decreases with an increase of the atomic number of N (i.e. the lowest HA and GPE values correspond to [BeOK2O]H+, [MgOK2O]H+ and [CaOK2O]H+). The electrophilicity of the [BeON2O]H+, [MgON2O]H+ and [CaON2O]H+ strongly relates to the basicity of the corresponding non-protonated mixed oxides (MON2O). The MOK2O represents the strongest base in each MOLi2O/MONa2O/MOK2O series, and thus its protonated [MOK2O]H+ form is characterized by the lowest values of HA and GPE.

  10. The least electrophilic system (with respect to hydride anion) among all species studied is [CaOK2O]H+ cation (as its HA and GPE values are equal to 134.9 and 122.0 kcal/mol, respectively).

  11. All the [MON2O]H2 systems studied are thermodynamically stable species toward the detachment of either H2 or H2O. However, in most cases (except for [CaONa2O]H2), the dehydrogenation is less endergonic than the detachment of water molecule which indicates the potential reuse of such species as catalysts in dehydrogenation reactions.

Acknowledgements

The calculations have been carried out using resources provided by Wroclaw Centre for Networking and Supercomputing (http://wcss.pl) grant no. 435.

Code availability

Not applicable.

Author contribution

D.F.: investigation, methodology, funding acquisition, validation, visualization; P.S.: investigation, supervision, writing—original draft, funding acquisition. I.A.: conceptualization, investigation, project administration, supervision, writing—original draft.

Funding

This research was supported by the funding from the Polish Ministry of Science and Higher Education grant no. DS 531-T110-D844-21 and BMN 539-T110-B485-20 (to D.F.).

Data Availability

All data are available on request to the corresponding author.

Declarations

Conflict of interest

The authors declare no competing interests.

Footnotes

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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