On the asymmetry in molybdenum–oxygen bonding in the MoO3 structure: ETS–NOCV analysis

In the present study, the analysis of natural orbitals for chemical valence (NOCV) combined with the extended-transition-state (ETS) bond-energy decomposition method (ETS–NOCV) was applied to characterize an asymmetry in Mo–O bonding in MoO3 crystal. Considered were three non-equivalent oxygen sites (O1, O2, O3) in the Mo7O30H18 cluster model of (010) surface of MoO3. The ETS–NOCV method leads to the conclusion that an increase in the Mo–O distances, from 1.68 Å (for Mo–O1), through 1.73 Å (for Mo–O2), up to 1.94 Å (for Mo–O3), is directly related to decrease in strength of both σ- and π-contributions of Mo–O bond. Further, Mo–O connection appeared to exhibit both ionic (the charge transfer from 2p orbital of oxygen to molybdenum) and the covalent (charge accumulation in the region of Mo–O) components. Finally, the trend in the orbital energy stabilization (ΔEorb) originating from the dominant σ- and π-bond contributions appeared to correlate very well with the oxygen-vacancy formation energies published earlier by Tokarz-Sobieraj et al. (Surf Sci 489:107, 2001).


Introduction
Since the pioneering applications of theoretical methods of quantum-chemistry in heterogeneous catalysis, [1][2][3][4][5][6] the computational approaches based on both, cluster models and periodic approaches, provide nowadays standard tools for investigating the properties of the active sites of catalysts and the mechanisms of catalytic reaction. Among many examples in catalysis, the theoretical investigations on the structural and electronic surface properties and the catalytic reactions of transition-metal oxides, in particular based on vanadium and molybdenum, [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] are especially important as they provided a deep insight into the structure-activity relationship of these compounds, used in a variety of applications.
Besides its importance in catalysis, [22,23] the molybdenum oxide MoO 3 provides an interesting example of chemical bonding, because of the existence in its crystal structure [24] of three non-equivalent oxygen atoms, leading to molybdenum-oxygen bonds of different character. Namely, the ionic, layer type orthorhombic structure of MoO 3 is built of the distorted MoO 3 octahedra sharing the oxygen atoms, and the (010) surface represents the easy cleavage plane of the crystal. The features of the MoO 3 structure are visualized in Fig. 1 using the example of the Mo 7 O 30 H 18 cluster modeling of the (010) surface. The O1 oxygen atom is bound to molybdenum atom by the shortest bond (1.67 Å ). The O2 site (and the equivalent O2 0 ) is linked to one molybdenum atom by the relatively short bond (1.73 Å ), and is substantially more distant from another metal atom (2.25 Å ). The third oxygen type O3 (and O3 0 , O3 00 ) is bound symmetrically to two molybdenum atoms (1.94 Å ) and weakly interacting with the third one of another layer (2.33 Å ). The Mo-O bonding was characterized previously by the electron density-difference maps (deformation density), [10] as well as by the quantumchemical bond-order indices originating from various approaches; [7][8][9][10]25] the electronic properties of the three oxygen sites on the (010) and (100) surfaces were characterized, and the oxygen-vacancy formation energies were determined [7][8][9][10].
The asymmetry in Mo-O bonds in the MoO 3 structure can serve as testing example for new theoretical methods for characterizing chemical bonding. In the present account we will describe the Mo-O bonding in the Mo 7 O 30 H 18 cluster using the recently developed extended transition state-natural orbitals for chemical valence (ETS-NOCV) approach [26] based on NOCV [27,28] and the Ziegler-Rauk bond-energy partitioning (ETS) [29]. This approach was successfully applied in characterizing various types of chemical bonds in inorganic and organic compounds, involving donor-acceptor, ionic and covalent bonds as well as relatively weak interactions (hydrogen bonds, agostic bonds) [26,[30][31][32]. The main advantage of the NOCVbased approach is that it allows one to separate the contributions to the deformation density originating from different components of the bond (r-, p-, d-), providing the corresponding charge-flow and energy estimates [26][27][28]. In this article, the ETS-NOCV method is used for the first time to characterize bonding in transition-metal oxide systems, for which the rand p-components of the metaloxygen bond has not been explicitly discussed yet.

Computational details and models
All the DFT calculations presented here were based on the Amsterdam density functional (ADF 2009.01) program [33][34][35][36][37] in which ETS-NOCV scheme was implemented [26]. The Becke-Perdew exchange-correlation functional [33,34] was applied (BP86). A standard triple-zeta STO basis containing one set of polarization functions (TZP) was adopted for molybdenum, whereas for hydrogen and oxygen, standard double-zeta STO with one set of polarization functions (DZP) were considered. The 1s electrons of oxygen as well as 1s-3d electrons of molybdenum were treated as a frozen core. Relativistic effects for Mo atom were included at ZORA level of approximation as implemented in ADF 2009.01 program. The contours of deformation densities were plotted based on ADF-GUI interface [38].
The bond-analysis performed here is based on the ETS-NOCV approach which is a combination of the ETS [29,39] bond-energy decomposition with the analysis of the NOCV scheme [26,27].
The NOCV have been derived from the Nalewajski-Mrozek valence theory [40][41][42][43][44][45] as eigenvectors that diagonalize the deformation density matrix. It was shown that the pairs of the natural orbitals for chemical valence (w -k , w k , corresponding to eigenvalues -v k and v k ) decompose the differential density Dq into NOCV-contributions (Dq k ): where M stands for the number of basis functions. Visual inspection of deformation density plots (Dq k ) helps to attribute symmetry and the direction of the charge-flow. In addition these pictures are enriched by providing charge (Dq k = |v k |) estimations for each charge-flow channel Dq k . The corresponding energy estimation (k-th channel orbital interaction energy) is given by: where F i,i TS are diagonal Kohn-Sham matrix elements defined over NOCV with respect to the transition state density (at the midpoint between density of the molecule and the sum of fragment densities); for further details see Ref. [26].
The ETS-NOCV analysis for Mo-O1, Mo-O2, and Mo-O3 bonds in the Mo 7 O 30 H 18 cluster modeling the (010) surface of MoO3 was performed by dividing the cluster into two closed-shell fragments: the first fragment containing corresponding oxygen ion [O1] 2-, [O2] 2or [O3] 2-, and the second comprising the rest of the cluster (with charge 2?). It should be emphasized here that the choice of the fragments is an arbitrary element of the ETS-NOCV approach. In principle, one could consider atomic (neutral) or ionic (charged) fragments.

Results and discussion
As it has been already mentioned in introduction [7,24] there exist three non-equivalent types of oxygen atoms (O1, O2, and O3) in MoO 3 crystal characterized by different Mo-O distances, see Fig. 1.
Let us first discuss leading deformation density contributions and the corresponding energies (see Eqs. 1 and 2) originating from ETS-NOCV scheme that characterize the interaction between terminal oxygen ion, [O1] 2and the rest  Fig. 2 that three components are of the vital importance for Mo-O1 bonding, one r-contribution, Dq r , with the corresponding stabilization DE orb r = -167.7 kcal/mol, and the two p-components, Dq p1 , Dq p2 , characterized by DE orb p1 = -146.4 kcal/mol and DE orb p2 = -121.5 kcal/mol, respectively. Total stabilization energy from both Mo-O1 p-terms dominates over r-bonding and p/r ratio is ca. 1.7. Similar trend was found using charge estimation of these bonding channels, see Table 1. It is noteworthy that r-contribution is not only based on the charge transfer from 2p orbital of oxygen to molybdenum and the neighboring oxygen atoms (ionic contribution) but as well as to the bonding region of Mo-O1 (covalent term). Similar conclusion on the presence of ionic and covalent terms is true for p-contributions, see Fig. 2. The existence of both components is in agreement with the previous studies [10,46,47].
Considering the bonding between asymmetric oxygen [O2] 2and the remaining part of the cluster one can see from B of Fig. 3 that three dominant deformation density channels are also important, one r-(Dq r ) and two p-bonds (Dq p1 , Dq p2 ). It is necessary to point out that they are localized in the Mo-O2 bonding region and nearly no electronic coupling with the adjacent molybdenum atom (Mo2; R Mo2-O2 = 2.25 A) is observed, see Fig. 3b. Qualitatively, they exhibit similar features as in the case of Mo-O1 connection. However, quantitatively these contributions appeared to be notably weaker, DE orb r is lower (in absolute term) by 31.7 kcal/mol, DE orb p1 by 20.8 and DE orb p2 by 40.7 kcal/mol. This is due to a weaker overlap between the orbitals participating in Mo-O2 bonding resulting from the Mo-O2 bond elongation, compared to Mo-O1.
Lengthening of the Mo-O2 bond can be in turn related to the electrostatic attraction between O2 and the neighboring Mo2 and/or to the fact that the same d p orbitals participate in the formation of the p-component of the Mo-O2 and Mo-O1 bonds or the Mo-O2 and Mo-O3 bonds. The ratio characterizing relative energetic strength of p/r components becomes lower (as compared to Mo-O1 connection) and is equal to 1.53. Similar trend on weaker electronic stabilization of Mo-O2 bond is true when analyzing the charge estimations of deformation density channels (Dq r , Dq p1 , Dq p2 ), see Table 1. As it can be seen the strengths of r(mDq r ) and total p-contribution (Dq p1 ? Dq p2 ) are lower in the case of Mo-O2 connection. It should be finally noticed that weaker strength of these components (obtained consistently on the basis of energetic and charge criterions) make the Mo-O2 bond longer as compared to Mo-O1, by 0.05 Å (see Fig. 1). Finally, let us characterize the interaction between oxygen, [O3] 2-, and the rest of the cluster. In this case three deformation density channels, presented in part B of Fig. 4, characterize symmetrical formation of both Mo-O3 and O3-Mo3 connections. Such charge transfer is   Fig. 4 and Table 1. The strengths of p-contributions are -28.05 kcal/mol and -30.95 kcal/mol, for each p-component, p1(O3-X) and p2(O3-X), respectively. Slightly stronger contribution characterized by Dq p2 (as compared to Dq p1 ) is related to the coupling of O3 with Mo4 site belonging to underlying sublayer-clearly, the lobe of oxygen 2p orbital overlaps with d z2 orbital of Mo4 leading to the charge transfer to O3-Mo4 bonding region, see Fig. 4. It is interesting to observe that such electronic coupling is evidently visible despite relatively large O3-Mo4 distance (2.33 Å ), whereas for O2-Mo2 with the distance 2.25 Å no such coupling was found (see Fig. 3). Finally, in the case of O3 bonding, p-component is of the same importance as r-connection (p/r ratio is 1.1).
It is worth commenting at this point on the possible influence of the basis set and the relativistic correction on the ETS-NOCV results presented here. In Table 2, we compare the results calculated with and without the ZORA relativistic correction and with TZP and TZ2P basis set for Mo-O1 bond. The results clearly show that the effect of both, the basis set as well as relativistic correction (\2 kcal/mol; i.e. 1-2 %) is not important for the qualitative conclusions from the present study; these effects are negligible comparing to the presented changes in the orbital interaction energy contributions for different Mo-O bonds (15-40 %).
Summarizing the ETS-NOCV results, we would like to emphasize that in this approach the bond between the  molecular fragments is characterized and the choice of the interacting fragments can be arbitrary. While in many cases of molecular systems the choice of fragments is very natural, in the case of the transition-metal oxides one can consider the atomic or ionic fragments (i.e., neutral O or the O 2anion), as the metal-oxygen bonds exhibit partly covalent and partly ionic character. As an obvious consequence, the energetic estimates of the i-th charge-flow channel, DE orb i , depend on the choice of the fragments, and can be used only as a qualitative measure of relative importance of the bond-components. In the present study we used ionic fragments. The results clearly show that increase in Mo-O distances, from 1.68 Å (for O1), through 1.73 Å (for O2), up to 1.94 Å (for O3) is directly related to decrease in the strength of both rand two p-contributions of Mo-O bond (see part A of Fig. 5). It should also be pointed out that the total strength of rand p-contributions (estimated by the sum DE orb r ? DE orb p1 ? DE orb p2 ) correlate very well (R 2 = 0.98) with the vacancy formation energies calculated by Tokarz-Sobieraj et al. [7], corresponding to the interaction of atomic oxygen with the rest of the cluster; this is illustrated in Fig. 5b. This very good correlation shows that both, ionic and atomic reference frames lead to a similar, qualitative picture of bonding. This a posteriori justifies use of ionic fragments in ETS-NOCV analysis presented here. ) and negative vacancy formation energies obtained by Tokarz-Sobieraj et al. [7] were presented in b

Concluding remarks
In the present study, we have verified applicability of ETS-NOCV scheme in a description of bonding of three inequivalent oxygen sites (O1, O2, O2) in the cluster modeling (010) surface of MoO 3 . We have considered oxygen atoms that are characterized by different Mo-O distances, 1.68 Å (for O1), 1.73 Å (for O2), and 1.94 Å (for O3).
We have found based on ETS-NOCV scheme that such systematic increase in the Mo-O distances is directly related to decrease in the strength of both rand two p-contributions of Mo-O bond. Qualitatively, these contributions appeared to show both ionic (the charge transfer from 2p orbital of oxygen to molybdenum) and the covalent components (charge accumulation in the Mo-O region). Moreover, it is gratifying to see that ETS-NOCV appeared to be useful not only in a description of strong molybdenum-oxygen connections, but also the weak coupling, for example between O2 and Mo4 could be detected (see Dq p2 in Fig. 4). It should be finally pointed out that the trend in total strength of rand two p-contributions (DE orb r?p ) correlate very well with the vacancy formation energies calculated by Tokarz-Sobieraj et al. [7].