Introduction

V2O5-based catalysts are of great importance in the catalytic reactions used to care for and protect the environment, such as de-NOx processes. These reactions are mainly responsible for the removal of the waste gases that are the products of liquid or gaseous fuel combustion [1]. The interest in using vanadium-based catalysts in industry is also a result of their resistance to SO2 poisoning. One useful process is the selective catalytic reduction (SCR) of nitrogen oxides (NOx) in the presence of ammonia, which can proceed either in the absence or in the presence of oxygen. Both processes are called “standard SCR” [2–20] and proceed according to the following equations:

$$ \begin{array}{l}6\mathrm{NO}+{4\mathrm{N}\mathrm{H}}_3\to {5\mathrm{N}}_2+{6\mathrm{H}}_2\mathrm{O}\hfill \\ {}4\mathrm{N}\mathrm{O}+{4\mathrm{N}\mathrm{H}}_3+{\mathrm{O}}_2\to {4\mathrm{N}}_2+{6\mathrm{H}}_2\mathrm{O}.\hfill \end{array} $$

In 2002, the reaction mechanism of so-called fast SCR was proposed by Koebel et al. [21, 22] and by Madia et al.: [23]:

$$ 2\mathrm{NO}+{2\mathrm{NO}}_2+{4\mathrm{N}\mathrm{H}}_3={4\mathrm{N}}_2+{6\mathrm{H}}_2\mathrm{O}. $$

In the fast SCR process, the catalyst is re-oxidized by nitrogen dioxide instead of by the oxygen molecule, and the rate of this reaction is ten times higher than that for the standard SCR process. However, such acceleration occurs only for the equimolecular NO and NO2 mixture, and the reaction rate decreases dramatically if the fraction of NO2 is larger than 50 %. In all SCR processes, side reactions such as NH3 oxidation to NO, NO2, or N2O (competition with SCR at high temperature) or the formation of ammonium nitrate (catalyst poisoning) occur.

The mechanism of the standard SCR reaction, in which nitrogen oxide is reduced to pure nitrogen and water, is still not fully clear; therefore, this mechanism has been investigated extensively by both experimentalists and theoreticians. Many attempts to understand this process have been made in the last few years, and two mechanisms are postulated, namely the Eley–Rideal and Langmuir–Hinshelwood mechanisms. According to the Eley–Rideal mechanism [24–42], ammonia is adsorbed and activated at Brønsted centers. Next, an NH3 species reacts with the gas-phase or weakly adsorbed NO molecule to yield a dinitrogen molecule and water, whereas the reduced surface (i.e., V–OH groups) is re-oxidized to V=O by O2 from the gas phase or O from the bulk. The Langmuir–Hinshelwood mechanism [43–46] also postulates ammonia adsorption. However, NO is first oxidized by gaseous O2 to NO2, and then the reaction between the adsorbed ammonia and the adsorbed NO2 species occurs. The reduced Brønsted centers are regenerated by a water molecule. Although these two mechanisms agree with the results of an experiment suggested by Topsøe et al. [2, 5], the SCR reaction proceeds according to both the Eley–Rideal and the Langmuir–Hinshelwood mechanisms. This conclusion is supported by the fact that NO molecules can be adsorbed at the coordinatively unsaturated metallic centers at the catalyst surface, thus reacting easily as weakly adsorbed species.

The main discussion in the literature concerns the forms of both the NH3 and NO molecules. Table 1 lists the postulated active forms of both substrates in the SCR reaction for different catalysts. In the case of the reactions catalyzed by pure V2O5, the NH3 molecule is adsorbed at the Brønsted acid centers in the form of NH4 + cations, whereas NO is in the gaseous phase; the reaction occurs via the Eley–Rideal mechanism. However, the detailed mechanism of the simple activation of the ammonia molecule is still a matter of controversy, especially regarding the localization of the active sites responsible for this elementary step. Miyamoto and Inomata et al. [24–27] suggested that the active Brønsted centers are localized at the (010) surface of V2O5, whereas Gasior and Haber [42] indicated planes that host the surface OH groups. The existence of Brønsted acid sites at the unsaturated (001) and (100) faces of the V2O5 crystals was also confirmed by Andersson [51], who postulated that these net planes are responsible for the adsorption and dissociation of a water molecule, which consequently leads to surface hydroxylation. Moreover, Ozkan et al. [39–41] also demonstrated that the hypocoordinated (001) and (100) net planes of V2O5 serve as active faces in the SCR mechanism, and the (010) face is mainly responsible for the ammonia oxidation reactions. It has also been suggested that ammonia can be coordinatively adsorbed on the surface vanadium cations, which act as the Lewis acidic centers in the form of V–NH3 or V–NH2 species.

Table 1 Forms of the activated NH3 and NO species postulated to be involved in the SCR mechanism as a function of the catalyst used. Additionally, the table includes a list of postulated active centers thought to be responsible for the stabilization of ammonia
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In this study, the first step in the selective catalytic reduction of NOx by ammonia is discussed, mainly involving NH3 adsorption on the surface OH groups (Brønsted acid centers) that are present at three low-index V2O5 surfaces. There have been a number of theoretical studies of the ammonia adsorption on Brønsted acid sites using both cluster [26, 49, 50, 52–58] and periodic [59, 60] approaches at different levels of theory, including the semiempirical level [26], post-Hartree methods [61], and the density functional theory level [49, 50, 52, 53, 55–61]. The conclusions from these investigations are similar and indicate that, in almost all cases, ammonia is stabilized at surface OH groups in the form of NH4 + cations, as postulated on the basis of experimental results. However, the above studies are focused only on the (010) V2O5 net plane, but it is known that vanadium crystals can expose other low-index surfaces, such as coordinatively unsaturated (100) and (001) surfaces. The fact that approximately 15 % of the overall contribution to the crystallite structure comes from these surfaces [62] indicates that unsaturated surfaces might play an important role in the catalytic process, as was postulated by Haber [42] and Ozkan [39–41]. The present paper discusses ammonia adsorption on OH centers of all three low-index V2O5 surfaces. Two different modes of ammonia stabilization are reported: (i) an NH4 + moiety hydrogen bonded to surface oxygen atoms and (ii) an NH3 moiety hydrogen bonded to the surface OH group. The mode and strength of the ammonia stabilization over various adsorption sites are discussed in terms of the local electrostatic potential of the surface binding sites and the strength of the hydrogen bonds formed between the ammonia molecule and the surface oxygen atoms.

Models and computational details

Model setup

The crystal lattice of vanadium pentoxide has an orthorhombic symmetry and is assigned to the space group D2h-Pmmn, with unit cell parameters defined as a = 11.51 Å, b = 4.37 Å, c = 3.56 Å [63, 64]. The building unit forms a distorted octahedron with V–O bond distances varying between very short (1.58 Å, vanadyl groups) and very long (2.79 Å, van der Waals type bonding). Three possible low-index surfaces exist: the saturated (010) and unsaturated (001 and 100) surfaces are shown in Fig. 1.

Fig. 1a–c
figure 1

Three possible low-index surfaces: a saturated (010) and b unsaturated (001) and (100). The annotation describes the type of atoms involved, with their coordination number shown in parentheses. The superscript e indicates “edge” localization of the Oe(2) oxygen atom

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The most thermodynamically stable (010) surface [62] (Fig. 1a) is characterized by three structurally different oxygen sites: (i) terminal vanadyl oxygen atoms O(1), which are singly coordinated to vanadium atoms and protrude from the surface in rows, and two bridging oxygen sites that are (ii) doubly, i.e., O(2), or (iii) triply, i.e., O(3), coordinated to vanadium centers. The unsaturated (001) surface (Fig. 1b), which is described by the existence of “valley”- and “hill”-like regions, exhibits coordinatively unsaturated vanadium atoms and three structurally different oxygen sites that lie in the plane (Fig. 1b): vanadyl oxygen O(1) and bridging O(2) or Oe(2) oxygen atoms coordinated to two vanadium atoms (the Oe(2) atom is connected to two vanadium atoms from different atomic layers and positioned on the surface edges). The unsaturated (100) surface may have a different termination [62]; the most thermodynamically stable structure is shown in Fig. 1c and contains unsaturated V centers and in-plane singly (O(1)) and doubly O(2)) coordinated sites.

The V10O31H12 cluster (Fig. 2) was selected as a model of the (010) surface, as described in our previous studies [65], in order to discuss electronic/adsorption properties of the (010) net plane. To mimic the (001) V2O5 surface, the V21O65H25 cluster was used to describe both the “hill” and “valley” regions (Fig. 2). The V16O52H24 cluster (Fig. 2) was chosen as the most appropriate model to characterize the (100) V2O5 net plane [65]. For all clusters, the dangling bonds of the peripheral O atoms were saturated with H atoms, forming OH groups and neutralizing the clusters [66, 67]. All initial clusters selected as surface models were closed shell. To prepare sites for ammonia adsorption, an additional H atom was added to the selected surface oxygen sites, thus forming surface OH groups and leading to the doublet systems [56, 68]. This procedure simulated the mechanism of surface OH formation under the reaction conditions (e.g., by dissociative adsorption of H2O [69] or the reaction of NH3 and NO on the V5+=O sites [70]).

Fig. 2
figure 2

Structural models of the clusters used in this study

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Calculation procedure

The program StoBe, the local version of DeMon, was applied to perform the calculations [71]. This used an ab initio density functional theory (DFT) method in which the Kohn–Sham orbitals were represented by a linear combination of atomic orbitals (LCAOs). For constrained geometry optimization of all cluster models, we applied the revised version of the gradient corrected functional of Perdew–Burke–Ernzerhof (RPBE) [72, 73] with all-electron DZVP basis sets of contracted Gaussians [74, 75]. This functional proved suitable for studying the interactions of small molecules with a broad range of adsorption sites, ranging from metal oxides to transition metal complexes [69, 76–81]. Models were subjected to partial geometry optimization using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm according to the procedure described in [65]. In short, only the local environment near to each oxygen adsorption site was allowed to relax for both H and NH3 absorption. The local environment of a particular oxygen was defined by its nearest V neighbors together with the oxygen atoms linked to these metal atoms and the adsorbate molecule. The rest of the atoms were kept frozen at their crystallographic positions. The vibration analysis for the final V2O5–H–NH3 complexes was performed only for the geometry-relaxed sections, and no imaginary frequencies indicating local energy minima were observed.

The structure of the model with an OH group was obtained by adding the hydrogen atom to a particular oxygen site and then performing geometry relaxation, as described in [82]. Hydrogen becomes stabilized at all oxygen sites present on three low-index V2O5 surfaces, with this process being spontaneous, as shown by periodic calculations [83]. The figures presenting the structures of clusters with adsorbed hydrogen atoms are provided in the “Electronic supplementary material” (ESM; Figs. S1–S3).

A detailed analysis of the electronic structure of each cluster was performed using the charge density distribution (Mulliken populations) [84], the Mayer bond orders [85, 86], and an analysis of electrostatic potentials. The electrostatic potentials were calculated 2 Å above each adsorbed hydrogen atom (i.e., x,y coordinates of the hydrogen atom). Such an approach provided a uniform and objective method for estimating the electrostatic interaction of the local surface with an NH3 molecule before a hydrogen bond is formed, which can result in the potential transfer of the H+ from the surface OH to the adsorbate. On the other hand, in order to estimate the electrostatic interaction of the surface with the already adsorbed NH4 +/NH3 moiety, the electrostatic potential was calculated for the respective surface (i.e., “bare” or with an OH group) at the coordinates of the N atom of the adsorbate.

The ammonia adsorption energies were calculated according to the following equation:

$$ {E}_{\mathrm{ads}}={E}_{\mathrm{tot}}\left(\mathrm{cluster}+N{H}_3\right)-\left[{E}_{\mathrm{tot}}\left(\mathrm{cluster}\right)-{E}_{\mathrm{tot}}\left(N{H}_3\right)\right], $$
(1)

where E tot(cluster) denotes a cluster with a Brønsted acid OH group.

These adsorption energies were corrected for London dispersion forces that are not included in RPBE with the DFT + D2 procedure using empirical damped dispersion correction [87]. A global scaling factor of 1.25 (s6) was used for RPBE calculations and 0.75 for geometries optimized with the PBE functional [81, 88].

Model validation

The influence of the basis set on the adsorption energies calculated with the RPBE functional was investigated by performing RPBE/TZVP single point calculations for the (010) net plane.

In order to cross-validate the performance of the RPBE functional, we conducted test calculations for NH3 adsorption on O sites of the (010) net plane in Turbomole v.6.3 [89] with the gradient-corrected Perdew–Burke–Ernzerhof (PBE) functional [90–93] and the def-TZVP all-electron basis set [94]. The resolution of identity (RI) approach was applied to compute the electronic Coulomb interactions [95, 96]. Complete geometry optimization was performed for the (010) models with the exception of terminal oxygen atoms terminated with hydrogen atoms. The positions of terminal O and H atoms were frozen in order to preserve the structural constraints imposed by the surface structure. The locations of energetic minima were confirmed by vibration analysis and by checking for a lack of imaginary frequencies. The structures of the respective models with adsorbed hydrogen and ammonium ion are presented in the ESM (Figs. S4 and S6).

Similar optimizations of unsaturated (001) and (100) model surfaces were not possible, as they led to significant surface reconstruction and yielded an artificial geometry for the V2O5 surface. Comparison of the obtained reconstructed surface structures with model net planes obtained with periodic calculations [83, 97] showed that the partially constrained cluster models described the surface more accurately than the relaxed models in which boundary constraints were imposed. The reconstructed geometries obtained for the (001) and (100) net planes are provided in the ESM.

Results and discussion

The ammonia is stabilized via O–H–N hydrogen bonds with surface hydroxyl groups present at each low-index V2O5 surface. However, the adsorption mechanism and adsorption geometry depend on both the type of center and the type of net plane involved (see Tables 2, S2, and 5).

Table 2 DFT (RPBE/DZVP) and DFT + D2 corrected energies of ammonia adsorption and NH3/NH4 + charges. The Mulliken charge on the adsorbed ammonia was calculated both with and without the H atom from the OH group as Q(NH4) and Q(NH3), respectively
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Table 2 summarizes the data obtained for the process of ammonia adsorption at the three discussed low-index V2O5 surfaces. It contains the adsorption energies (E ads(NH3)) and Mulliken atomic charges (Q), while Table S2 in the ESM contains the Mayer bond orders (BO) and the distances (R) and angles (α) of the N···H···O hydrogen bonds.

NH3 adsorption at a (010) V2O5 surface

At the (010) V2O5 surface, ammonia is adsorbed as an NH4 + cation and stabilized by single or double hydrogen bonds (see Fig. 3 and Figure S4 of the ESM). In all of the studied cases, ammonia is spontaneously adsorbed at each of the adsorption sites (Table 2). The adsorption energies E ads(NH3) attain negative values: −0.98 eV, −1.07 eV, and −1.31 eV (−30.2, −22.6, and −24.7 kcal/mol-1, respectively) for stabilization at the O(2), O(3)–O(2), and O(1)–O(1) centers, respectively. The largest adsorption energy (−1.31 eV) is observed for the stabilization of two O(1) oxygen sites. The introduction of the correction for London dispersion forces does not change the qualitative results, i.e., the largest adsorption energy is observed for two O(1) oxygen sites (−1.44 eV) followed by O(3)–O(2) (−1.39 eV) and O(2) (−1.40 eV). Moreover, the calculation of adsorption energies at the RPBE/TZVP level also does not change the qualitative description of the adsorption, yielding −0.66 eV, −0.88 eV, and −1.02 eV eV at the O(2), O(3)–O(2), and O(1)–O(1) centers, respectively.

Fig. 3
figure 3

Geometries of ammonia adsorption on the (010) V2O5 model surface. The NH4 + cations are stabilized by either a single hydrogen bond with an O(2) atom or double hydrogen bonds with O(3) and O(2) or two O(1) oxygen atoms. The geometries obtained for V10O31H12 are translated to the model (010) surface for visualization purposes. The adsorption geometries on the V10O31H12 are presented in Fig. S1 of the ESM

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When NH3 approaches the V-O(1)H Brønsted acidic group it becomes tilted and is stabilized in the bi-dentate form by two hydrogen bonds with hydrogen donor-acceptor distances (O(1)–N) of 2.55 Å and 2.78 Å and N–H–O angles equal to 170° and 155°, respectively (Fig. 3). The proton of the surface O–H group is shifted toward NH3 (the O–H distance is elongated from 0.98 to 1.55 Å, and the BO is weakened from 1 to 0.18) and an H bond is formed with NH4 + acting as a donor and the surface O atom as the H-bond acceptor. A second hydrogen bond is formed between a hydrogen atom of ammonia and the other vanadyl O(1) oxygen atom (d(H―O )= 1.7 Å, BO = 0.15).

A similar type of bidentate stabilization is observed when ammonia approaches an O(3) site. The hydrogen-bonding interactions with O(3)–H and O(2)–H lead to the formation of two bonds (Fig. 3) with O···N distances of 2.63 and 2.84 Å and NHO angles equal to 165° and 133°, respectively. The O–H and N–H bond distances/bond orders are 1.55/0.15 and 1.10/0.71 for the first hydrogen bond and 2.03/0.06 and 1.04/0.87 for the second hydrogen bond, again indicating the transfer of the proton from the O(3)–H group to the ammonia and its stabilization in the cationic form. Finally, for the adsorption site above the surface O(2)H group, only one single hydrogen bond is created, with an O···N distance of 2.60 Å and an NHO angle of 175°. The O–H and N–H bond distances/bond orders are 1.48/0.18 and 1.12/0.66, which suggests the formation of an NH4 + species.

The formation of ammonium cations (NH4 +) is further supported by the results of a Mulliken population analysis (see Table 2). The charge on the NH4 + species when it is stabilized at an O(1)–O(1), O(2), or O(3)–O(2) site is +0.81, +0.87, or +0.87, respectively. This result demonstrates that, in each case, the proton is abstracted from the surface OH group and shifted toward the nitrogen atom. As a result, NH4 + groups are formed and act as proton donors in the newly created H3N–H→O hydrogen bonds.

The introduction of corrections for dispersion forces lowers the adsorption energy of each site by 0.13–0.34 eV (3.1–7.8 kcal/mol-1). The dispersion attraction appears to be higher for an ammonia ion adsorbed in between double rows of V=O ligands (around 0.3 eV), i.e., for O(2) and O(3), O(2) sites, than for an ammonia ion adsorbed on two O(1) oxygen atoms (0.13 eV). As a result, all three adsorption sites exhibit similar ammonia adsorption energies of 1.32–1.44 eV, although the overall preference for the O(1) site is still maintained. These calculations indicate that, in the case of ammonia ions adsorbed on O(2) and (O3) sites, dispersion accounts for ∼25 % of the stabilization, while dispersion accounts only for 10 % of the stabilization of ions adsorbed on the tops of O(1) rows.

The above results demonstrate that, at the (010) surface, ammonia is activated according to the same mechanism at Brønsted acid centers. NH4 + cations act as proton-donating groups in the hydrogen bonds. The formation of hydrogen bonds plays a vital role in ammonia stabilization. Our results are consistent with the recent DFT calculations of Sun et al. [50] and Yuan et al. [49], which showed energetically favorable stabilization of NH4 + cations by two hydrogen-bonding interactions with O(1) atoms. However, because the clusters used in those studies were very small (V2O9H8 and V6O20H11, respectively), the authors could not study adsorption at the O(2) or O(3) sites.

NH3 adsorption at the (100) V2O5 surface

At the (100) surface, NH3 is stabilized at the surface hydroxyl groups O(1)H and O(2)H (Fig. 4). In analogy to the (010) V2O5 surface, ammonia undergoes spontaneous adsorption with E ads(NH3) values of −0.86 and −0.70 eV (−19.8 and −16.1 kcal/mol-1) for stabilization at the O(1) and O(2) centers, respectively, while the dispersion-corrected adsorption energies are −1.07 and −1.03 eV (−24.6 and −23.8 kcal/mol-1) for stabilization at the O(1) and O(2) centers, respectively.

Fig. 4
figure 4

Geometries of the ammonia adsorption sites on the (100) V2O5 model surface. The NH4 + cations are stabilized by a single hydrogen bond with O(1) and by two hydrogen bonds with two O(2) oxygen atoms. The geometries were obtained for the V16O52H24 cluster, and the position of the NH4 + at O(1) was moved to the edge of the cluster for visualization purposes

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Adsorption at Brønsted acidic vanadyl sites (V–O(1)H) leads to the creation of a single hydrogen bond with a hydrogen donor–acceptor distance (O(1)···N) of 2.54 Å and an NHO bond angle of 179°. At the second adsorption center localized above the surface O(2)H site, ammonia is stabilized by two hydrogen bonds formed between two bridging O(2) oxygen atoms. One strong hydrogen bond is formed between O(2) and an ammonium cation with an O(2)···N distance of 2.67 Å and an NHO angle of 175°, and the other—weaker—hydrogen bond is formed with O(2) from a parallel atomic row and has an O(2)···N distance of 2.95 Å and an NHO angle of 178°.

The mechanism of stabilization is similar for both sites, namely the protons shift from the O sites to the ammonia molecule and the formation of NH4 + is observed.

The cationic form is substantiated by the Mulliken population and a geometry analysis. The total charge on the NH4 + species is +0.82 for O(1) and +0.83 for the O(2) site.

In the hydrogen bond formed at O(1), the N–H distance is fairly long (d(N–H) = 1.17 Å, BO = 0.56), whereas the interaction between the hydrogen and oxygen occurs at a short distance and is strongly covalent (d(H–O) 1.38 Å, BO = 0.29).

In the case of the O(2) site, the stronger hydrogen bond is characterized by an N–H distance of 1.11 Å (BO = 0.70) and an H–O distance of 1.56 Å (BO = 0.20). The weaker hydrogen bond has a shorter N–H distance (1.05 Å, BO = 0.82) and a longer H–O distance (d(H–O) 1.90 Å, BO = 0.08). The stronger H-bonding at O(2) results in closer contact of the ammonium ion with the V2O5 surface than in the case of the O(1) binding site. As a result, the dispersion forces contribute more to stabilizing the adsorption, lowering the overall energy by −0.33 eV (−7.7 kcal/mol-1) for the O(2) binding site, as compared to −0.21 eV (−4.8 kcal/mol-1) for the O(1) site.

NH3 adsorption at the (001) V2O5 surface

At unsaturated (001) V2O5 surfaces, the net plane process of ammonia adsorption is more complex because NH3 is stabilized by single and triple hydrogen-bonding interactions that can also be trifurcated toward different donors. As was the case for the two other low-index faces of V2O5, the E ads(NH3) energies indicate that the adsorption of ammonia on Brønsted acid centers at the (001) surface is spontaneous. The adsorption energies E ads(NH3) (Table 2) are −0.49 eV (−11.3 kcal/mol-1) and −1.97 eV (−45.4 kcal/mol-1) for the ammonia stabilization at the “hill”-like O(2) and the valley-like Oe(2), Oe(2),Oe(2)–O(1)–O(1) oxygen sites. The dispersion correction lowers the adsorption energy by −0.21 and −0.31 eV (−5.2 and −7.3 kcal/mol-1) for the hill and the valley regions, respectively. The London attraction force for the hill-like O(2) site is comparable with the dispersion stabilization observed for the (100) O(1) site and twice as big as that calculated for O(1),O(1) sites on the (010) net plane. Interestingly, for valley-like adsorption sites, where ammonia ions seem to have the highest degree of van der Waals contact, the overall stabilization is only −0.32 eV, which is in the range of dispersion stabilization observed for O(2) sites on the (010) or O(2),O(2) sites on the (100) net plane.

Tables 2 and 5 list the stabilization energies and characteristics of the hydrogen bonds, and the geometries of the adsorbed NH3 molecules are plotted in Fig. 5. Two different mechanisms of stabilization are observed on this surface: H3N–H→O and O–H→NH3. The former mechanism occurs for the adsorption sites localized above the surface valley-like region. These adsorption minima are populated independently of the starting geometries, i.e. when NH3 approaches O(1)H or O(2)eH, there is a proton shift from the surface OH groups to the ammonia molecule. After formation, the NH4 + cation migrates from the former OH site toward the valley region, where it is stabilized by multiple hydrogen-bonding interactions and favorable attractive electrostatic interactions (vide infra).

Fig. 5
figure 5

Geometries of the ammonia adsorption sites of the (001) V2O5 model surface. The NH4 + cation is stabilized by multiple hydrogen bonds involving three Oe(2) and two O(1) atoms, whereas the NH3 molecule is stabilized by a single hydrogen bond with an O(2) oxygen atom. The geometries were obtained from the V21O65H24 cluster

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The ammonium ion (charge +0.87) forms two single hydrogen bonds with the O(2)e atoms from two opposite hill regions with N···O distances of 2.70 Å and 2.72 Å and NHO angles of 173.2° and 174.3°. In addition, a weak trifurcated hydrogen-bonding interaction with one O(2)e atom and two O(1) atoms from the bottom of the valley occurs. The N···O distances are 3.72 Å, 3.34 Å, and 3.30 Å and the NHO angles are 135.5°, 106°, and 105°, respectively. Moreover, the Mayer bond indices suggest that the N–H bonds (0.76–0.89) have higher covalences than the H–O bonds (0.1 for strong bonds, 0.01 for weak trifurcated bonds) do. Finally, small contributions to the adsorption energies also seem to be introduced by the interactions of NH4 + with surrounding V atoms. Although each of these interactions is characterized by a very small Mayer index (in the range of 0.007–0.016), the overall sum of the bond orders calculated for all three H atoms pointing into the valley equals 0.13, a value which is comparable with the strength of one hydrogen bond.

The latter O–H→NH3 mechanism is present only for the stable position localized in the “mountain”-like region of the (001) net plane, i.e., over the surface O(2)H group. Such a mode leads to the formation of a monodentate hydrogen bond (d(N···O) 2.71 Å, NHO angle 165.8°). The surface O–H acts as a proton donor (d(O–H) = 1.04 Å, BO = 0.69), forming a long hydrogen bond of moderate strength (d(H–N) = 1.69, BO = 0.15). The NH3 species remains almost neutral (+0.14), indicating an O–H → NH3 mechanism of hydrogen-bond formation. An inspection of the adsorption geometry at the O(2) site suggests that, in this case, the hydroxyl group is a proton donor; the H atom remains closer to the surface O atom than to the nitrogen atom from the ammonia molecule.

NH3 adsorption at the fully relaxed (010) V2O5 surface

The optimization of NH3 adsorption at the PBE/TZVP level of theory yielded qualitatively the same results as those obtained for RPBE/DZVP calculations, i.e., adsorption in the form of the NH4 + ion after proton transfer from the surface OH group to NH3 (see Table 3 and Table S3 in the ESM). As in previous (010) models, the most energetically favorable adsorption site was localized over O(1), the next most favorable was over O(3), O(2), and the least favorable was over O(2) (−1.58, −1.02, and −0.89 eV, respectively). The introduction of dispersion corrections did not change that trend (−1.72, −1.25, −1.16 eV, respectively). Similarly to RPBE models, the smallest D2 correction was observed for NH4 + adsorbed over V=O(1) ligands due to its relatively long distance from the V2O5 surface.

Table 3 DFT (PBE/TZVP) and DFT + D2 corrected energies of ammonia adsorption over the (010) net plane and NH3/NH4 + charges calculated without and with H atoms adsorbed on the surface
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However, the application of a different optimization algorithm implemented in Turbomole, as well as a more diffuse basis set, led to some minor changes in the geometry of the NH4 ions that resulted in greater H-bond interaction (Fig. 6).

Fig. 6
figure 6

Geometries of ammonia adsorption on the (010) V2O5 model surface, calculated at the PBE/TZVP level of theory with full optimization of the surface. The NH4 + cations are either stabilized by hydrogen bonds with an O(2) atom and two O(3) atoms, hydrogen bonds with one O(3) and two O(2) atoms, or two strong H-bond interactions with O(1) oxygen atoms and one weak bifurcated H-bond with two O(1) atoms. The geometries obtained for V10O31H12 are translated to the model (010) surface for visualization purposes. The adsorption geometries on the V10O31H12 are presented in Fig. S2 of the ESM

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The tilt of the ammonia ion for the O(1),O(1) adsorption site becomes bigger than in RPBE model, which results in the presence of an additional bifurcated H-bond interaction of the third H atom with two O(1) atoms. This bifurcated bond is relatively weak, with H–O Mayer bond orders of 0.041 and 0.044 and H–O bond distances of 2.2 Å. Similarly, the ammonia is tilted over O(2) sites, which enables the formation of two weak H-bond contacts with O(3) oxygen atoms (BO = 0.036, d(H–O) = 2.33 Å). Finally, also in the case of NH4 + adsorption over O(3) sites, aside from two strong H-bonds with O(2) and O(3) oxygen atoms (H–O BO = 0.14 and 0.1, d(H–O) = 1.74 and 1.78 Å, respectively), it was possible to detect the formation of one weak H-bond between a third hydrogen atom and an O(2) oxygen atom (BO = 0.047, d(H–O) = 2.1 Å).

Summing up, the calculations performed with almost full optimization of cluster geometry and with the application of the TZVP basis set led to similar results to those seen for models with only local geometry optimization and in which the DZVP basis set was applied. It seems that the main reason for the observed geometry differences stem from the different geometry optimization algorithms implemented in the Stobe and Turbomole codes.

NH3 binding mechanism

There has been a long ongoing discussion in the literature concerning a form of adsorbed ammonia (see Table 1) [18]. Our results indicate that at low-index V2O5 surfaces, two types of adsorption over Brønsted acid (surface OH) centers may occur: (i) ammonia as a positively charged NH4 + cation with a surface O site acting as a hydrogen acceptor, or (ii) ammonia as a neutral NH3 molecule with a surface OH group acting as a hydrogen donor. Although hydrogen bonds are clearly the main force stabilizing the adsorbed ammonia, the local electrostatic characteristics of the surface where NH3 contacts the OH group seem to determine the final form of the stabilized ammonia (i.e., either neutral or cationic).

This effect is especially visible in the case of a (001) low-index surface, which has varied electrostatic characteristics (i.e., some regions of positive and negative electrostatic potential are present) [65]. If the neutral NH3 approaches Brønsted sites, it can accept a proton from the OH group to attain a positive charge. As a result, a decrease in the electrostatic potential of the adsorption sites is observed due to the local accumulation of a negative charge at the deprotonated Brønsted site (Table 4). Naturally, the electrostatic interaction becomes significant between the positively charged ammonium cation (Mulliken charge ca. 0.8) and the local negatively charged surface. As a result, the adsorption energy decreases further due to the attractive electrostatic interaction of the positive charge of the ammonium cation with the negative electrostatic potential produced by the surface.

Table 4 The electrostatic characteristics of ammonia adsorption over the Brønsted sites of the (010), (100), and (001) V2O5 model surfaces
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For surface sites with a very stable or strong positive electrostatic potential that is insensitive to the OH protonation state, such a proton shift would result in an increase of the system energy due to the repulsive electrostatic interaction (i.e., an interaction of a positively charged surface with an NH4 + cation). Therefore, in such cases, ammonia remains in an almost neutral form (i.e., an NH3 molecule with a small charge of ca. +0.2, which results from NH3 acting as a hydrogen-bond acceptor), minimizing the increase in the total energy due to the unfavorable, repulsive electrostatic interactions. Similar conclusions have been drawn by Calatayud et al. [98], who have used electrostatic potential as a reactivity index for V2O5 gas-phase clusters as well as unsupported and TiO2-supported (010) V2O5 surfaces. This approach allowed spatial mapping of the regions that are most susceptible to electrophilic attack and, in accordance with our results, pointed to the region between terminal (O1) oxygen atoms.

This observation can be studied in a more quantitative manner if one considers the change in the potential electrostatic energy upon shifting the proton from the OH site toward the approaching NH3. Table 4 contains electrostatic potentials calculated at a distance of 2 Å above the hydrogen atom of each OH group for the studied surface. These potentials approximate the electrostatic environment affecting the NH3 molecule approaching the surface (i.e., before the hydrogen bond is formed). The electrostatic potentials are determined for surfaces with an adsorbed hydrogen atom (V OH) and a “bare” V2O5 surface (V bare) without an adsorbed hydrogen atom. The change in potential energy ΔPE upon shifting the proton from the surface OH group to NH3 is approximated as the difference between the electrostatic potential energy (PE) of NH4 + over a bare V2O5 surface and the PE of NH3 over the OH group from the surface with an adsorbed hydrogen atom.

$$ \Delta \mathrm{PE}=\mathrm{PE}\kern0.5em {\mathrm{NH}}_4^{+}-\mathrm{PE}\kern0.5em {\mathrm{NH}}_3={ V}^{\mathrm{bare}}{\mathrm{q}}^{\mathrm{NH}4+}-{ V}^{\mathrm{OH}}{\mathrm{q}}^{\mathrm{NH}3}, $$

where q NH4+ represents the average charge on the adsorbed ammonium cations (+0.86) and q NH3 represents the charge on the adsorbed ammonia (+0.14) over the O(2) site at the (001) net plane. Thus, ΔPE describes the gain (or loss) in the electrostatic energy due to the transfer of a hydrogen from a surface OH group to an NH3 molecule.

The transfer of a hydrogen in the form of a proton occurs when ΔPE is negative, ensuring strong electrostatic stabilization of the positively charged ammonium cation. In most of the cases studied, the change in electrostatic energy following the hydrogen shift is highly negative (from approximately −0.4 to −0.9 eV), which results in a thermodynamic preference for NH4 +. However, for O(2) sites at a (001) surface, there is no energy gain connected with the hydrogen shift because the ΔPE attains a positive value (+0.03 eV). As a result, the ammonia is stabilized in its neutral form. Notably, at a (001) surface, the site of the proton shift is distant from the final, most favorable adsorption site. Regardless of the initial starting place of the NH3 molecule (i.e., over O(1) or Oe(2)), the proton is shifted from the surface OH group. To probe the electrostatic influence of the surface on the proton shift process, the electrostatic potentials were calculated at distance of 2 Å above the H atoms adsorbed at the Oe(2) and O(1) sites. The results are collected in Table 4.

As observed from Table 4, the positive potential of the surface with the adsorbed H atom becomes negative (changing from 0.16 eV to −0.47 eV for the O(1) site and from 0.55 eV to −0.57 eV for the Oe(2) site). This result explains why ammonia becomes an ammonium cation at those sites. However, the vicinity of the deep negative potential well at the center of the valley (−1.58 eV for the NH4 + absorption site) attracts the cations to the most energetically favorable position.

Thus, the surface electrostatics influence the form of the stabilized ammonia. The local surface electrostatics of the spot at which ammonia contacts the surface determines whether the proton transfer will occur. If the proton is shifted, the ammonium cation can migrate further across the surface to maximize the electrostatic and hydrogen-bond interaction energies, as exemplified by a model of the adsorption over the O(1) and Oe(2) over (001) surface.

Quantitative modeling of adsorption energies

As shown above, the stabilization of ammonia over the Brønsted acid sites originates from the hydrogen bonds and is sensitive to the surface electrostatics. An interesting question arises as to whether it is possible to predict the strength of each adsorption site (i.e., the adsorption energy) based on a knowledge of the hydrogen-bond strength (derived only from geometry parameters) and on the local electrostatic potential. Theoretically, such a model would allow for the estimation of the relative importance of the forces (i.e., hydrogen bonds versus electrostatic) involved in the stabilization of ammonia over the V2O5 surface. Moreover, such a model would allow estimation of the adsorption site strength based solely on the geometry of the final structure of the V2O5-OH–NH3 complex without the need to calculate the geometry and energy of the V2O5–OH reference model (thus shortening the calculation procedure). The usefulness of the electrostatic potential for predicting adsorption phenomena (such as interaction energies) has already been demonstrated by Tielens and Geerlings [99].

To build such a semiquantitative structure–property relationship (QSPR) model, each hydrogen-bond strength was described according to the methodology of the hydrogen bond analysis proposed by Jeffrey [100, 101], who studied a large number of hydrogen bonds and demonstrated that the energy of the particular bond varies between 0.2 and 40 kcal/mol-1 (which is up to ∼1.7 eV). He then classified the hydrogen bonds into “strong,” “moderate,” and “weak” bonds based on several bond geometric parameters, such as

  • The distance (H–A, in Å) between the proton (H) and the proton-acceptor group (A)

  • An increased distance (Δ(D–H), in Å) between the proton (H) and the proton-donor group (D)

  • The distance (D–A, in Å) between the proton-donor (D) and the proton-acceptor (A) groups

  • The angle (α) of the N–H–O bond.

According to Jeffrey’s criteria, all of the necessary parameters were divided into “weak” (w), “moderate” (m), and “strong” (s) class contributions. Based on this concept, we selected a set of four parameters to describe the strength of each hydrogen bond responsible for the stabilization of ammonia at the V2O5 surfaces according to the scheme illustrated in Table S1 of the ESM and Table 5. Based on the categorization of these four parameters, we assigned a numerical value to each bond representing its strength, with 1 representing a weak, 2 a moderately strong, and 3 a strong hydrogen bond. Moreover, for hydrogen bonds of intermediate strength, we allocated intermediate values (for example, two moderate and two strong features results in a value of 2.5). Finally, for each site, the strengths of all identified hydrogen bonds were added together and this sum was used as a site hydrogen bond strength descriptor (SHBS).

Table 5 Parameters used in the hydrogen-bond analysis. E ads: ammonia adsorption energy, D: proton donor species, H···A: distance between the hydrogen atom and the hydrogen bond acceptor, D···A: distance between the donor and acceptor, Δ(D–H): change in donor-hydrogen atom bond length upon hydrogen-bond formation, α: D···H···A angle. The strength of a particular Jeffrey hydrogen bonding criterion is shown using color: black for strong, gray for moderately strong, and white for weak hydrogen bonds. The number representing the hydrogen-bond strength is provided in the hydrogen-bond strength column, whereas the site hydrogen bond strength (SHBS) provides the sum of the strengths of all hydrogen-bond interactions in a particular binding site. Elect. energy: electrostatic energy calculated at the atomic coordinates of the N atom of the adsorbed ammonia over the respective surface
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The electrostatic energy was calculated as the product of the charge on the adsorbed species (NH3 or NH4 +) and the electrostatic potential of the respective surface (V OH or V bare, respectively) at the atomic coordinates of the N atom of the adsorbed ammonia. The energy values obtained ranged from positive values (0.18 eV) for the (001) O(2) site to highly negative values for the valley adsorption site at the (001) surface (−1.54 eV). These extreme cases exemplify the effect of the electrostatic interaction on the overall energy (a decrease of E ads in the case of the positive electrostatic energy for the O(2) site at the (001) net plane and an increase of E ads in the case of the 4×Oe(2)O(2) site at the (001) net plane).

The results of the correlation analysis show a very high linear correlation of the adsorption energy E ads with the SHBS (R = −0.93) and a moderate correlation with the electrostatic energy (R = 0.79). Theoretically, both variables could be used to predict E ads. However, these variables are nonorthogonal, i.e., they are linearly intercorrelated with R = −0.82. The collinearity indicates that multiple strong hydrogen-bonding interactions are present for sites with favorable (i.e., negative) electrostatic interactions. As a result, it is not possible to construct a QSPR model with these two variables; because of the collinearity problem, the electrostatic energy is statistically insignificant when used in one equation together with SHBS.

Therefore, it is not possible to independently estimate the influence of both variables on the adsorption energy. Because more of the variance of the E ads value can be explained by SHBS (R 2 = 0.87), this descriptor can be used to approximate the energy using the following simple QSPR model:

$$ \begin{array}{l}{ E}^{\mathrm{ads}}=-0.21\left(\pm 0.037\right)\mathrm{SHBS}-0.20\left(\pm 0.17\right)\hfill \\ {} n=7\kern0.5em { R}^2=0.8609,\mathrm{corr}.\kern0.5em { R}^2=0.8331,\kern0.5em F=30.996,\kern0.5em p=0.00258.\hfill \end{array} $$

The same model is obtained for DFT + D2 corrected adsorption energies (R 2 = 0.87, corr. R 2 = 0.84404, F = 33.472, p < 0. 00217), where London dispersion forces are accounted for with a more negative constant (−0.44 instead of −0.2).

$$ { E}^{\mathrm{ads}\left(\mathrm{DFT}+\mathrm{D}2\right)}=-0.21\left(\pm 0.036\right)\mathrm{SHBS}-0.44\left(\pm 0.17.\right) $$

This result indicates that introducing DFT + D2 corrections on average does not cause any significant change to the observed trend.

The QSPR model demonstrates that higher hydrogen-bond strengths at the particular site result in lower adsorption energies. The quality of the model’s predictions is graphically presented on a scatter plot (see Fig. 7).

Fig. 7
figure 7

Correlation scatter plot showing the predicted and DFT-calculated values for the ammonia adsorption energy (n = 7, R 2 = 0.8609, corr. R 2 = 0.8331, F = 30.996, p = 0.00258)

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The apparent success of the applied hydrogen-bond strength index in predicting the adsorption energy clearly indicates two points: (i) the importance of these interactions in the stabilization of ammonia over V2O5 surfaces and (ii) the additivity of the hydrogen bonds at the particular adsorption site. However, as was demonstrated by statistical analysis, it is also important to take into account the fact that hydrogen bonds and surface electrostatic interactions are not separable, independent phenomena. If a nondirectional positive electrostatic interaction exists, it allows for the formation of stronger, shorter hydrogen bonds. In contrast, when a repulsive interaction with the surface adsorbate occurs, the hydrogen bonds should be elongated, weakening the overall interaction. This relationship explains the high negative linear correlation that was observed between SHBS and the electrostatic energy at the adsorption site.

Conclusions

Based on the theoretical results, we can conclude that not only the saturated (010) but also the two unsaturated (001) and (100) surfaces are able to stabilize ammonia by adsorbing it at Brønsted acid sites, i.e., at OH surface groups. In all cases, the hydrogen bonds play a major role in this process.

Hydrogen bonds are formed via two different adsorption mechanisms. In the dominant scheme, a surface proton from the OH group is abstracted during ammonia adsorption and shifted toward the ammonia to become an NH4 + cation that serves as a “proton-donor” group in the newly created hydrogen bond. In the second scheme, no proton transfer is observed during the NH3 adsorption; consequently, a surface hydroxyl species serves as the proton-donor group.

The local electrostatic interaction and the change in this interaction following proton transfer from the surface to the ammonia (when approaching the Brønsted site) appear to determine the adsorption mechanism. The electrostatic interactions between the catalyst surface and the adsorbing species also contribute to the overall stabilization, although it was not possible to evaluate the influence of these interactions on the adsorption energy independently of the input introduced by hydrogen bonding. The magnitude of this contribution strongly depends on the surface and is the largest for the negatively charged “valley” region of the (001) net plane (−1.97 eV). The adsorption energies of ammonia correlate very well with the hydrogen-bond strengths of the site. The strength of the hydrogen-bond stabilization can be derived only from geometrical features such as angles and atomic distances.

Finally, the results of our calculations fully confirm the previous predictions that the active sites for ammonia activation in the SCR mechanism are localized not only at saturated (010) sites but also at the unsaturated (001) and (100) V2O5 surfaces.