Effect of surface vacancies on the adsorption of Pd and Pb on MgO(100)

Abstract Theoretical quantum mechanical calculations have been carried out to establish the effect of surface vacancies on the adsorption of Pd and Pb atoms on the defective MgO(100) surface. The investigated defects included neutral, singly and doubly charged O and Mg vacancies on the (100) surface of MgO. These vacancies played the role of Fsn+ and Vsn− (n = 0, 1, 2) adsorption centers for a single Pd or Pb atom. From the results of calculations, it is clear that the Pd- and Pb-atom adsorption at the Fsn+ and Vsn− centers shows different characteristics than at the regular O2− and Mg2+ centers. Drastic changes in geometric, energetic, and electronic parameters are evident in Pd/Vsn− and Pb/Vsn−. The effect of Fs0 and Fs+, which in practice are the most important vacancies, is smaller, yet the adsorption of Pd and Pb at these centers is more energetically favorable than at the regular O2− center. Of the two metals studied, the atom of Pd is bound by the Fs0 and Fs+ centers with higher adsorption energies. Graphical abstract Electronic supplementary material The online version of this article (10.1007/s00706-018-2159-1) contains supplementary material, which is available to authorized users.


Introduction
Palladium supported on oxides has found numerous applications in heterogeneous catalysis [1][2][3]. The catalytic performance of Pd/oxide systems can be improved by coupling their Pd part with another metallic element [4,5]. In the resulting bimetallic Pd-M/oxide catalysts, Pd is usually combined with a typical metal or a half metal (M=Al, Si, Zn, Ga, Ge, In, Sn, Sb, Te, Tl, Pb, or Bi) [5]. Recently, it has been reported that bimetallic Pd-Pb/MgO catalysts are more effective than monometallic Pd/MgO catalysts in performing aerobic oxidations of amines [6] and oxidative esterification of methacrolein with methanol [7,8]. Understanding the enhanced catalytic performance of these bimetallic catalysts requires a detailed knowledge of several fundamental aspects of their metal-oxide interfaces. These aspects include, in particular, geometric and electronic features of interfaces and the strength of metal-oxide interaction. Ideally, the first step of such a characterization should concern small clusters of Pd and Pb, or even better single Pd and Pb atoms, at individual adsorption sites on a well-defined single-crystal MgO surface, such as the MgO(100) one. This surface is often regarded as a prototypical oxide surface in studies of metal adsorption, because it has a simple structure and well-defined stoichiometry [9]. Additionally, it is relatively easy to form defects on this surface [10].
This work is aimed at providing a theoretical quantum mechanical description for the adsorption of Pd and Pb on the MgO(100) surface with various point defects. Both oxygen (F s n? ) and magnesium (V s n-) vacancies in three charge states (n = 0, 1, 2) have been taken into account. From experimental studies [38,39], it is known that such defects may be formed on MgO(100), but with a significant differentiation in their concentrations. What is particularly important is that various defects occurring on the MgO(100) surface can act as anchoring sites for metal nanoparticles [38,40], and additionally, they can modify the properties of deposited metal nanoparticles [38,41]. Here, a set of essential geometric, energetic and electronic parameters for a single Pd or Pb atom adsorbed at the F s n?
and V s ncenters has been calculated to characterize the fundamental aspects of Pd-and Pb-atom adsorption on defective MgO(100). Due to the lack of any previous theoretical studies for Pb/MgO(100), it is vitally important to provide an insight into the effect of surface vacancies on Pb-atom adsorption at atomic level.

Results and discussion
The calculated values of three essential parameters (height from the surface h, adsorption energy E ads and electron charge q) characterizing a single Pd atom adsorbed at the F s n? and V s ncenters on the defective MgO(100) surface are listed in Table  Results obtained from calculations in which the Pd atom was described by the LANL08(f) basis set are listed without parentheses, whereas the results from calculations utilizing the def2-TZVP basis set for Pd are in parentheses an electron acceptor when it sits at the F s n? centers. The Pd/ F s 0 structure demonstrates the greatest charge transfer to the metal atom. This is because the isolated F s 0 center possesses two extra electrons that are largely localized in its cavity [42] and a significant amount of this electron charge can be easily transferred to an adsorbed atom [34]. Unlike Pd/F s n? , the Pd/V s nstructures show the opposite direction of charge transfer. Our calculations predict that the charge transfer from the Pd atom to the V s ncenters never exceeds 0.9 e even if the Pd atom is almost inserted into the V s ncavity. This charge transfer and the small h heights lead to a significant electrostatic stabilization between the ionized Pd atom and the V s ncenters. It is instructive to compare the Pd-atom adsorption at the vacancies with that occurring at non-defective sites. Results describing the adsorption of a single Pd atom at the regular anionic O 2and cationic Mg 2? centers of defectfree MgO(100) surface are appended to An inspection of the results in Table 1 also reveals that the kind of the basis set assigned to the Pd atom most often has a rather minor effect on the calculated values of h, E ads and q. A discrepancy in the interpretation of the results obtained from LANL08(f) and def2-TZVP appears for Pd/ V s 2and Pd/O 2-. The calculations employing the two basis sets designate different spin states as the energetically preferred state of Pd/V s 2-. In the case of Pd/O 2in the HS state, the calculations involving the LANL08(f) basis set predict an exothermic adsorption, in contrast to those carried out with def2-TZVP. However, the E ads HS value obtained from LANL08(f) is actually quite close to zero, and therefore, the significance of this discrepancy should not be overemphasized.
Our findings made for the Pd-atom adsorption are essentially in good agreement with conclusions reported in previous experimental [14][15][16] and theoretical [15, 24, 26-28, 33, 35, 36] studies of Pd/MgO(100). It is well-known that the defect-free MgO(100) surface is generally rather unreactive toward the adsorption of metal atoms [43]. The Mg 2? centers exhibit particularly low reactivity toward metal atoms [25]. In consequence, Pd atoms preferably occupy the O 2centers [28], with no significant charge transfer from or to the surface [27]. An experimental estimation of adsorption energy for Pd on MgO(100) is ca. 1.2 eV [14]. From an experimental measurement, a value of 2.22 Å was also deduced to be the height of an adsorbed Pd atom from the O 2center [26]. Our E ads LS and h LS values for Pd/O 2are very close to these experimental estimations. Similarly to metal adsorption on the defect-free MgO(100) surface, metal atoms on MgO(100) with defects also adsorb preferentially at centers where negative charge accumulates [33,44]. More specifically, the F s 0 centers play the key role in the adsorption of Pd atoms [15,16]. This is because these centers are the main part of vacancies formed on MgO(100), which was confirmed both experimentally [10] and theoretically [45,46]. Besides the F s 0 centers, the F s ? centers can also occur, but they are less likely due to their large formation energy [42]. Even larger formation energy was determined for the F s 2? center [42]. Previous computational studies have shown that the Pd/F s ? interaction is weaker than the Pd/F s 0 interaction but stronger than that of Pd/O 2- [15,33,36]. Apart from rendering this trend correctly, our h and E ads values also reproduce quantitatively other theoretical results [15,35,36]. It has also been reported that the interaction between Pd and V s ncenters is extremely strong [24]. According to an experimental study [10], the concentration of surface Mg vacancies seems, however, to be much lower than that of F s 0 and F s ? . Again, this is in line with large formation energies of V s nvacancies [42,47].
This review of existing results for Pd/MgO clearly indicates that the computational methodology applied in this work leads to the correct description of Pd-atom adsorption on MgO(100) with surface vacancies. Thus, one can expect that the parameters characterizing the adsorption of Pb atom at the F s n? and V s ncenters should also be predicted reliably.
Essential parameters for the Pb atom adsorbed at the F s n?
and V s ncenters are collected in Table 2. A careful inspection of these results reveals that there are several similarities between the Pd-atom adsorption and its Pb counterpart. The formation of Pb/V s nstructures is associated with extremely exothermic E ads values, many times greater than those calculated for the Pb/F s n? structures. For Pb/F s n? , their E ads energies decrease regularly with the growing formal charge of F s n? center. The adsorption of Pb at V s nleads to a significant charge transfer from Pb to the V s ncenters, while the reverse direction of charge transfer is observed for Pb/F s 0 and Pb/F s ? . A strong correlation between E ads and the magnitude of charge transfer can be found for both the Pd/F s n? and Pb/F s n? structures. On the other hand, the Pb-atom adsorption turns out to be different in certain aspects from the Pd-atom adsorption. First, the large atomic radius of Pb causes this atom not to replace the missing Mg atom at the V s ncavity. The h values of Pb/ V s nclearly indicate that the Pb atom sits higher above the V s ncenters than it has been detected for Pd/V s n-. Second, the Pb atom easily becomes ionized, if adsorbed at the V s ncenters, and the resulting charge transfer from Pb to these centers far exceeds one electron. The ionization potential of Pb is lower than that of Pd (7.42 eV [48] versus 8.34 eV [49]), thus the enhanced tendency of the former to donate electron charge to the V s ncenters. The same direction of charge transfer yet much smaller in magnitude occurs for Pb/F s 2? , whereas a negatively charged metal atom was found for Pd/F s 2? . Third, the HS state is preferred for the Pb/F s n? structures, which is a consequence of the triplet multiplicity of free Pb atom in its ground state. However, the extremely high E ads values of Pb/V s 0 and Pb/V s are sufficient for spin paring, and therefore, these structures favor the LS state. In the case of Pb/V s 2-, the difference between its E ads LS and E ads HS energies is too small for spin quenching.
The kind of basis set assigned to metal atom affects the parameters of Pb-atom adsorption to a greater extent than the results for the Pd-atom adsorption. The greater discrepancies in the parameters obtained using LANL08d and def2-TZVP result from an inherent difference in the treatment of Pb atom with the two basis sets. These basis sets differ not only in the number of basis functions in their valence parts, but also in the size of their core parts treated with pseudopotentials. LANL08d is expected to yield less accurate results because (1) its quality is formally inferior to that of def2-TZVP and (2) a previous benchmark study confirmed its poorer performance [50]. Notwithstanding this difference, the application of either basis sets provides a qualitatively consistent picture of Pb-atom adsorption at the F s n? and V s ncenters. To establish the effect of surface vacancies on the Pbatom adsorption, Table 2  An experimental study concerning the growth of Pb film on well-defined oxide surfaces [18] reported a calorimetrically measured initial heat of adsorption of 1.07 eV for Pb/MgO(100) at 300 K. This value was an average of the bonding of Pb atoms to MgO(100) and Pb-Pb bonding within small Pb nanoparticles formed on MgO(100). For such nanoparticles, their Pb-MgO(100) bond strength was roughly estimated to be either 0.33 or 0.16 eV, depending on the kind of Pb nanoparticles adsorbed (whether two-or three-dimensional Pb nanoparticles). In a more recent study based on atomic beam/surface scattering measurements [22], a range from 0.72 to 0.81 eV was proposed to be the heat of Pb adsorption at terrace sites on MgO(100). Our E ads HS energy of Pb/O 2exceeds by ca. 0.3 eV the upper limit of this range.
It is also interesting to examine how the surface vacancies affect the highest occupied molecular orbital

Conclusion
The results reported in this work point out that the presence of vacancies on the MgO(100) surface, such as F s n? and V s n-, has an important influence on the geometric, energetic, and electronic parameters characterizing the adsorption of Pd and Pb atoms. The F s 0 and F s ? vacancies, which are most likely among the F s n? and V s ndefects on MgO(100), constitute the centers at which the adsorption of single Pd or Pb atoms is more exothermic than at the regular O 2- and Pb/F s n? . In particular, the formation of Pb/V s 0 and Pb/ V s structures is associated with extremely high E ads energies, which turn out to be sufficient to stabilize the LS state of these structures.
The presented quantum mechanical study of the surface vacancy effect is a tentative step in elucidating the properties of Pd-Pb/MgO catalysts. The findings made for Pb/ F s n? and Pb/V s nmay be of particular importance, because the Pb-atom adsorption on the defective MgO(100) surface has not been investigated theoretically so far.

Methods
The structures of F s n? and V s ncenters with an adsorbed Pd or Pb atom were determined using a theoretical quantum mechanical approach based on the B3LYP computational method [51][52][53] and the embedded cluster model of surface [54]. These structures are denoted in this work by the abbreviation 'metal atom/adsorption center'. The aforementioned computational methodology was successfully used in many previous studies of adsorption on MgO(100), e.g., [41,55,56] O 13 ] nclusters were described by the 6-31G basis set [57,58]. Additional polarization and diffuse basis functions [58,59] were ascribed to several Mg and O atoms directly involved in the interaction with a Pd or Pb atom. Further details of the aforementioned cluster models are given in Section S1 in Electronic Supplementary Material.
The adsorption of a single Pd or Pb atom at each investigated center was simulated by optimizing the height (h) of the metal atom from the surface layer of the adsorption center. The effect of surface relaxation induced by metal adsorption was also included in these calculations. Two sets of calculations differing in the kind of basis set ascribed to the metal atoms were performed to estimate basis set effects in the results of calculations. The first kind was the LANL08 basis set [60] in its LANL08(f) version for Pd and LANL08d for Pb. The def2-TZVP basis set [61] was the second kind of basis set assigned to the metal atoms. Two low-lying electronic states with different spin multiplicities were studied for the Pd-and Pb-atom adsorption. The low-spin state (LS) was characterized by the singlet multiplicity of the center with a Pd or Pb atom adsorbed, whereas the high-spin state (HS) assumed a triplet for each adsorbed metal atom.
To calculate the adsorption energy (E ads ), the total energy of an adsorption center occupied with a metal atom was subtracted from a sum of the total energies of free metal atom in its ground state and the isolated surface center in its relaxed geometry. According to this definition, adsorption with a positive E ads value is an energetically favorable (exothermic) process. The electron charge (q) acquired by an adsorbed Pd or Pb atom was estimated by the partial charge of the atom. This partial charge was determined according to the Bader charge analysis [62].
All calculations except the Bader charge analysis were carried out using the GAUSSIAN 09 D.01 program [63]. The Bader charge analysis was done with the Multiwfn 3.4 program [64].