The clean α-Al2O3 (0001) surfaceThe (0001) surface of α-Al2O3 is well characterized and therefore often serves as a benchmark for developing theoretical models. The termination by a single layer of Al3+ cations has been predicted to be most stable in several atomistic[61,62], and first-principles[63,64] calculations and also confirmed experimentally.[8–10] Relaxation was shown to be crucial for the formation of this most stable surface of α-Al2O3. Both experiment[8,9] and calculations[13,64–71] demonstrated strong relaxation, by 50–90%, of the distance between the topmost aluminum and oxygen layers.
In both computational strategies, periodic slab and embedded cluster (EPE) modeling, we started by relaxing a clean surface terminated with a single Al-layer. In the EPE model, this was done by optimizing a periodic slab model with a shell model (atomistic) force field. In agreement with previous studies,[13,68–71], a significant relaxation of the surface layers was obtained (Table 1). Recent pseudopotential as well as all-electron slab calculations[68–71] on slabs with 12–15 atomic layers, using a variety of exchange–correlation approximations (including hybrid functionals), predicted a surface relaxation behavior that is especially large for the outermost Al layer, but comprises several subsurface layers. The interlayer distance between the first Al layer and the next O layer, Al1–O1, is substantially reduced compared to the bulk-terminated value, 0.84 Å.[72] Our result from atomistic calculations, 0.29 Å, compares favorably with experimental estimates of 0.3 ± 0.1 Å[8] and 0.41 ± 0.05 Å.[9] Our force-field based value is also close to results of other cluster or embedded cluster calculations,[14,15] which yielded 0.25 Å. Our PW91-slab calculations either with (2 × 2) or (3 × 3) supercell, similarly to the periodic CPMD study[13] where the BLYP[49,73] functional had been used, predicted an even stronger decrease of the Al1–O1 interlayer distance to 0.15 Å. Typical relaxation magnitudes obtained from periodic DFT-based calculations reported in the literature range from −79 to −94% (Table 1). The CPMD-BLYP result[13] of −82% agrees quantitatively with our PW91-slab results. Periodic DFT-based methods significantly overestimate the experimentally determined relaxation (Table 1). However, there is much uncertainty about these experimental values associated with difficulties in the preparation of a clean surface.
After the QM cluster was embedded and optimized in the next step of the EPE procedure, its equilibrium geometry changed somewhat compared to that optimized in periodic atomistic calculations. This is a consequence of the fact that the force-field and the QM descriptions do not match quite well enough.[18,37] Table 2 summarizes optimized interatomic distances from atomistic calculations, EPE embedded cluster model (which employed the PW91 DF for its QM part) and those from periodic slab calculations (also based on the PW91 DF). Not unexpectedly, the geometrical parameters of the QM cluster are closer to those rendered by PW91-slab calculations than to the geometry from atomistic calculations. The average Al1–O distance (1.72 Å) in our cluster model is 0.04 Å larger than that in the relaxed PW91-slab structure. The interlayer spacing of the “top” Al layer to the O layer underneath, 0.23 Å, lies in between the values from periodic atomistic and DFT-based calculations. This result corresponds to a smaller degree of surface relaxation, i.e. −72%, and is very close to other cluster model values (−70%)[14,15].
Water adsorption on α-Al2O3(0001)Adsorption of a single water molecule onto the α-Al2O3(0001) surface has previously been studied with several computational approaches.[13–15] Wittbrodt et al[14]. carried out HF and hybrid-DF (B3LYP) calculations on medium size cluster models; they used a 6-31+G(d) basis set in the central region of the cluster and a rather small 3-21G basis in the boundary region. These authors applied simple embedding in a field of rigid point charges to selected structures, mainly to examine the resulting changes in the energetics, which they found to be small. They concluded that the interaction energies for molecular and “1,2-dissociative” water adsorption should roughly be the same, whereas the interaction energy for “1,4-dissociative” adsorption was calculated 3–4 kcal mol−1 smaller. The notations “1,2-” and “1,4-” refer to different proton acceptor positions Os relative to the Al1 atom, which accepts the OH− moiety; see Fig. 1.
Subsequently, this conclusion was dismissed in periodic CPMD-BLYP calculations of Hass et al.,[13] who found dissociative adsorption to be favored by 10 kcal mol−1. The authors of the latter supercell study attributed the discrepancy to deficiencies of the cluster approach. To cast aside the differences in methods and basis sets, they repeated the non-embedded cluster calculations of [ref. 14] at their CPMD-BLYP level and found 1,2-dissociative adsorption to be only 3 kcal mol−1 more favorable. They also pointed to significant adsorption-induced long-range restructuring of the surface, which is not accounted for in small cluster models. Indeed, most atoms in those cluster models had been constrained to their bulk positions to avoid unphysical relaxation at the cluster boundaries.
The more recent cluster study of Shapovalov and Truong[15] employed the same Al8O12 model as Wittbrodt et al.,[14] but at a higher level of theory, namely a two-layer IMOMO methodology.[17] The “model system” treated at the coupled-cluster singles and doubles (CCSD) level was a non-embedded Al4O6 cluster with the adsorbate, whereas the “real system” treated at the MP2 level consisted of an Al8O12 cluster, surrounded by full ion pseudopotentials (without orbital basis functions) and embedded in an array of point charges. A basis set of double-ζ quality with effective core potentials on Al was employed for both “real” and “model” systems.[15] Also, a more elaborated embedding scheme, compared to the earlier cluster study,[14] was used, still with a rigid cluster environment. This improved model rendered binding energies for molecular and 1,2-dissociative adsorption in good agreement with those of the periodic CPMD study.[13] Shapovalov and Truong did not consider the 1,4-geometry,[15] although it constitutes the most interesting and controversial issue, in view of the discrepancy between the results of the cluster and the slab model, which have been attributed to long-range surface modifications not reflected by medium-size cluster models.[13]
In the present work, a somewhat different cluster model of the same size Al8O12 was chosen (Fig. 1). This cluster allowed us to consider both 1,2-and 1,4-dissociative water adsorption using the same model. The above mentioned cluster model of Wittbrodt et al. was criticized in [ref. 13] especially in reference to the 1,4-dissociative path, due to limitations of the model size, i.e. under-coordination of the proton acceptor (labeled as Os4 in Fig. 2) and lack of surface Al centers neighboring the Os4 center, which suggests edge artifacts.
Our cluster model overcomes these drawbacks and takes into account long-range electrostatic effects in a consistent manner. In addition, all degrees of freedom were allowed to relax in our model, whereas in the work of Shapovalov and Truong[15] only the position of the central Al atom of the substrate and the adsorbate were optimized and the rest of the QM cluster as well as its environment were kept frozen at the substrate geometry. As we will discuss below, energies for molecular and 1,2-dissociative adsorption obtained in both calculations are nevertheless in close agreement.
In their periodic CPMD-BLYP study, Hass et al[13]. considered molecular as well as 1,2-, 1,4-, and 1,6-dissociative adsorption of water. The 1,2-and 1,4-dissociative pathways were found to be most important; therefore, only these and molecular adsorption were considered in the present work.
Water adsorption noticeably affects the substrate geometry (Table 2). As a result of adsorption, the distance between the Al1 and O1 planes increased in the EPE calculation, as was also observed in previous theoretical studies.[13–15] The relaxation of the Al1–O1 interplanar distance relative to bulk geometry decreases from −69% for the bare cluster to −49% for molecular adsorption, to −15 to −26% for dissociative adsorption. Table 3 summarizes the corresponding relaxation (in percent) from the present as well as other periodic and cluster calculations. The relative upward displacement of the OH accepting Al atom is very similarly predicted by periodic as well as cluster methods.
For the bare surface, all periodic DFT-based calculations predict too large a relaxation compared to experiment. Embedded cluster models generally give a smaller relaxation of the outermost layer spacing; the percentage values range from 70 to 72%. For molecular adsorption, the calculated relaxation from periodic slab and embedded cluster models is −48 to −54%. For 1,2-dissociation, the cluster-model values scatter over a wider range, from −11 to −20%, than those from periodic calculations, from −13 to −15%, but all methods clearly predict a significant recovery of the Al1-O1 layer spacing in the direction of the bulk value. Of course, such comparisons of relaxation percentages have to be done with due caution, because the quoted value depends on the range around the “perturbation site” over which the interlayer spacing is averaged. Still, because the calculated relaxation of the O1-layer was found small (when considered), at least a qualitative comparison can be made. The present periodic and embedded cluster results yielded larger contraction values for 1,4-dissociative adsorption than for 1,2-dissociation, from −24 to −28%, whereas the periodic CPMD study[13] gave almost the same values for both dissociative modes (Table 3).
A closer look at the structures (compared in Table 2) reveals that 1,4-dissociation is indeed the only case, where the present work and the periodic CPMD study disagree notably;[13] below, we will discuss this disagreement in more detail. In Table 2, the optimized geometric parameters at the adsorption site are compared for the EPE-embedded cluster PW91 and periodic PW91 approaches employed in our study; the corresponding structures are shown in Fig. 2. The optimized geometries within these two very different computational methodologies, cluster and slab models, agree very well; slab model geometries for (2 × 2) and (3 × 3) supercells agree within 0.01 Å. In the EPE model, Al–Os bond lengths are predicted either 0.01–0.02 Å shorter or 0.01–0.04 Å longer. For molecular, 1,2-, and 1,4-dissociative adsorption, the Al–Oads bond lengths differ by 0.01, 0.02 and 0.04 Å, respectively.
Molecular adsorption results in slightly elongated Al–O distances only at the adsorption site, 1.71–1.77 Å; these distances are 0.02–0.03 Å longer than in the relaxed bare QM cluster. The periodic PW91 calculations gave significantly larger changes, from 1.68 Å for the relaxed surface to 1.73 Å in the chemisorbed complex. The Al–Oads distance (Fig. 2) is 1.98 and 1.96 Å in cluster and slab calculations, respectively. This is in close agreement with the value of 1.95 Å obtained in the periodic CPMD-BLYP study.[13] In our embedded-cluster model for 1,2-dissociative adsorption, we did not encounter artificially elongated Al–Os2 distances of 2–2.2 Å as obtained in previous cluster calculations.[14,15] Our cluster result, 1.91 Å, is identical to that from our periodic PW91 calculations, to be compared with the periodic CPMD value, 1.90 Å.
Overall, the EPE bond lengths for molecular and 1,2-dissociative adsorption agree quite well with the corresponding CPMD values.[13] The geometries from our periodic PW91 calculations are in almost quantitative agreement with that former slab model study, with the exception of 1,4-dissociative adsorption, where both our EPE and periodic models agree well, but predict a structure of the adsorption complex, which differs significantly from that of the CPMD study.[13] This may be a result of the different exchange–correlation functional used, PW91 here vs. BLYP.[74] Hass et al[13]. found significant and far extending restructuring of the substrate, in particular, the top-layer Al3 center bound to Os4 descended even below the top O layer and became six-fold coordinated. In our EPE and periodic results, we did not observe this type of restructuring, although Al3 moved 0.03 Å “down” compared to the clean substrate, i.e. the Al3-O1 spacing decreased at variance with the Al1–O1 spacing. However, we observed another type of restructuring: Os4 is no longer bound to Al2 and thus coordinated by only two Al atoms, both in the cluster and the slab model. This is likely a result of “bonding competition” between surface–adsorbate and intrasurface bonding. Breaking one of the Al–O bonds possibly accounts for the fact that we calculated the energy gain of 1,4-dissociative adsorption 12–14 kcal mol−1 smaller compared to 1,2-dissociative adsorption (see below).
We now turn to a discussion of the central results of our study, the interaction energies of a single water with the α-Al2O3(0001) surface for three selected adsorption modes: molecular, 1,2-dissociative, and 1,4-dissociative adsorption (Fig. 2).
The periodic CPMD slab model study of Hass et al.,[13] based on the BLYP functional,[49,73] found 1,2-dissociative adsorption 10 kcal mol−1 more favorable than molecular adsorption (Table 4). As one of the main conclusions, their work rejected simple cluster models, e.g. those of [ref. 14], as they failed to predict a significantly larger binding energy for dissociative than for molecular water adsorption (Table 4). In fact, Hass et al. repeated the bare cluster model calculations of [ref. 14] (i.e. without embedding) using their own CPMD-BLYP formalism. In this way, they obtained −25.7 kcal mol−1 binding energy for molecular adsorption and −28.9 kcal mol−1 for the dissociative adsorption. Thus, with the “free” cluster model, the preference for dissociative adsorption was notably reduced, from 10 to 3 kcal mol−1.
Similarly, without cluster embedding, close binding energies were obtained for molecular and 1,2-dissociative adsorption at the B3LYP[14] and the CCSD levels;[15] an MP2 cluster calculation, preferring molecular adsorption, even gave a qualitatively wrong picture.[15] For both MP2 and CCSD calculations, IMOMO cluster embedding was shown to stabilize dissociative adsorption and destabilize molecular adsorption.[15] When corrected for the basis set superposition error (BSSE) by the counterpoise method[75] (by 4–5 kcal mol−1), the CCSD results for the embedded cluster models on molecular and 1,2-dissociative adsorption agreed almost quantitatively with those of the earlier CPMD-BLYP slab model study.[13] The results for molecular adsorption, obtained in CPMD-BLYP slab model and CCSD embedded cluster calculations, were −23.3 kcal mol−1 and −23.4 kcal mol−1, respectively, and the results for 1,2-dissociative adsorption were −33.2 kcal mol−1 and −31.6 kcal mol−1, respectively. This rather close agreement indeed is most astonishing if one considers the markedly different procedures to account for electron correlation and the completely different approaches to account for environment effects (Table 4).
To compare periodic slab models and embedded cluster models in a strict sense, it is certainly desirable to have results at hand that were obtained for the same electronic structure approach. Thus far, this has not been the case. Therefore, we applied our advanced embedding strategy (EPE) and periodic first principle calculations for the PW91 functional, to obtain such a benchmark. To make this comparison more general, we also performed EPE embedded cluster calculations for two further gradient-corrected density functionals, BP and PBEN (see Computational Methods). We estimated basis set superposition errors using the counterpoise method.[75] Finally, in periodic PW91 calculations, we compared results for supercells of two sizes, (2 × 2) and (3 × 3).
As seen from Table 4, our EPE calculations give qualitatively correct energetics in all cases: molecular adsorption is 7.6–8.7 kcal mol−1 less favorable than 1,2-dissociative adsorption, depending on the functional. Also, the three functionals consistently render the interaction for 1,4-dissociative adsorption weakest, 5.2–5.6 kcal mol−1 less (in absolute value) than molecular adsorption. Of all density functionals, PW91 predicts the strongest interaction; BP interaction energies are 1.6–2.3 kcal mol−1 kcal mol−1 smaller (in absolute value) and PBEN energies are 4.4–5.5 kcal mol−1 smaller (Table 4). Overall, this agreement of the interaction energies as obtained from the EPE calculations is very satisfying and the order of interaction energies follows known trends: PW91 > BP > PBEN (in absolute value). Experience has shown that PBEN energetics are most reliable for metal–ligand interactions and such interaction energies are usually expected to be smaller than the corresponding PW91 results which tend to overestimate such interactions.[74,76]
The interaction energies from periodic calculations with a (3 × 3) surface unit cell and the PW91 functional are also very similar, both in trend and magnitude, to the energies from the corresponding PW91 EPE embedded cluster calculations; the cluster results are 3.5–5.7 kcal mol−1 smaller (by absolute value) than the analogous slab model results. In fact, the interaction energies obtained with the larger (3 × 3) and smaller (2 × 2) surface unit cells bracket the EPE cluster results (Table 4). It is remarkable that the differences between the two slab model calculations with different surface unit cells are rather substantial, 5.5–7.2 kcal mol−1, whereas the relative energetics of the three adsorption modes remain, nevertheless, essentially unaffected by the size of the surface unit cell. Indeed, the EPE interaction energies are rather close to those of periodic (2 × 2) calculations, with differences amounting to only 1.5–2.0 kcal mol−1 (Table 4). From this comparison it is evident that the substrate relaxation is large and extends far, as was also concluded in the CPMD-B3LYP study;[13] therefore, even larger surface unit cells may be required to recover that part of the interaction energy which is masked by the artificial periodicity of the slab models.
Qualitatively, the contributions of the substrate relaxation to the total binding energies can be deduced from the binding energies computed by optimizing only adsorbate-related degrees of freedom, i.e. with the positions of substrate atoms “frozen” at the clean surface geometry. The corresponding results, obtained for EPE embedded clusters and (2 × 2) slab models at the PW91 level, are also given in Table 4. Only for molecular adsorption is this latter interaction energy close to the total binding energy from EPE cluster calculations, −21.7 vs. −28.0 kcal mol−1, respectively; the corresponding energies from periodic (2 × 2) slab model calculations are very similar, −20.5 (“frozen”) and −26.5 kcal mol−1, respectively. For 1,2-dissociative adsorption, the EPE binding energy at the frozen substrate is only −1.8 kcal mol−1, and that for 1,4-dissociative adsorption is even positive, 28.2 kcal mol−1, i.e. the complex is unbound. The latter, surprising value is supported by the corresponding result of periodic calculations, 29.6 kcal mol−1. Unfortunately, it was not possible to converge the geometry of 1,2-dissociative adsorption with the substrate fixed at the structure without perturbation by the adsorbate; several calculations converged to the energetically favorable structure of molecular adsorption. From these calculations one concludes that the adsorbate-induced relaxation of the substrate is largest for 1,4-dissociative adsorption, ∼50 kcal mol−1, but only ∼34 kcal mol−1 for 1, 2-dissociative mode; for molecular adsorption it is only ∼6 kcal mol−1, i.e. almost negligible in comparison with the other two adsorption modes.
Our PBEN results for molecular and 1,2-dissociative adsorption from EPE-embedded cluster models agree almost quantitatively (up to 1–2 kcal mol−1) with the CCSD embedded-cluster results of [ref. 15] and the CPMD-BLYP periodic slab model results of .[ref. 13] However, this tight agreement does not extend to 1,4-dissociative adsorption. Recall that, for the PW91 functional, the current EPE and periodic slab model results for 1,4-dissociative adsorption agree equally well with each other, as do the results for the other two types of adsorption complexes, molecular adsorption and 1,2-adsorption (Table 4). Therefore, one cannot dismiss the large discrepancy between the PBEN EPE adsorption energy for 1,4-dissociative adsorption, −17.2 kcal mol−1, and the corresponding CPMD-BLYP slab model results, −32.5 kcal mol−1, as a cluster artifact (Table 4). Unfortunately, the structure of the latter adsorption complex was not available to us to crosscheck the energy for our two computational approaches.
Finally, we return to the IMOMO cluster calculations,[15] which are the cluster models that allow treatment by high-level post-HF correlation methods. In that sense, these IMOMO cluster results can also be taken as a set of benchmark data. In fact, they agree best of all with our PBEN energetics, corroborating the claimed higher quality of this density functional for the determination of binding energies. The fact that two rather diverse cluster-embedding strategies gave quite similar results, with energy differences of only 0.9 and 0.4 kcal mol−1 (Table 4), supports the reliability of these modeling approaches.