The Influence of Support Basicity on the Adsorption of Lead on the (100) Surface of Alkaline Earth Metal Oxide Crystals

Abstract

Supports used in heterogeneous metallic catalysts serve as a structural skeleton across which metallic nanoparticles are dispersed, but specific properties of the supports may also determine the behavior of these nanoparticles in catalytic processes. For example, it is known that among various properties of crystalline alkaline earth metal oxides serving as supports, the ability of their surface sites to donate electrons, that is their basicity, has an influence on the characteristics of the adsorbed metal. In the present work, the influence of MeO (Me = Mg, Ca, and Sr) basicity on the adsorption of Pb on the (100) surface of MeO crystals is studied by means of a dispersion-corrected density functional theory (DFT-D) computational method. The DFT-D calculations have characterized essential structural parameters, energetics, and the distribution of the electron charge for the Pb atoms and Pb dimers adsorbed at the regular O²⁻ and defective F_s centers of MeO(100). It has been observed that an increase in the basicity of MeO(100) in the sequence MgO < CaO < SrO results in a more energetically favorable effect of Pb adsorption, a stronger interaction between Pb and the surface, and a greater amount of electron charge acquired by the adsorbed Pb atoms and dimers. These findings contribute to a better understanding of how support basicity may modulate certain characteristics of MeO-supported metallic catalysts containing Pb as an additive. From a computational viewpoint, this work shows that the inclusion of spin–orbit relativistic correction in the DFT-D calculations leads to a significant reduction in the strength of the interaction between Pb and MeO(100), but it does not change the aforementioned trend in the strength of this interaction as a function of support basicity.

1. Introduction

In the field of heterogeneous catalysis, monometallic catalysts are frequently modified by adding a second metallic element to improve their catalytic properties and open up possibilities for industrial applications [1]. In particular, such additivities should tune the activity of catalysts and their selectivity toward a desired reaction, reactant, or product [2]. Typical heavy p-block post-transition metal elements such as Tl, Pb, or Bi are usually introduced as additives into catalysts based on noble metals [1]. For example, lead is utilized as an additive to various supported palladium-based catalysts. The current industrial standard for performing the hydrogenation of carbon–carbon triple bonds to double bonds without any over-hydrogenation is the Lindlar catalyst [3] in which the ability of Pd active sites to form palladium hydrides is partially modulated by the presence of Pb [4]. Moreover, there are other important industrial and laboratory applications of Pd-Pb catalysts in the aerobic oxidation of amines to imines [5] and oxidative esterification of methacrolein with methanol [6,7]. In these applications, the Pd-Pb catalysts consist of intermetallic nanoparticles deposited on a support containing MgO, and consequently, both the Pb additive and the support are able to modify the properties of the catalysts. In the case of amine oxidation over Pd-Pb/MgO, a combination of the effects of Pb and support basicity constitutes a well-concerted bifunctional catalyst in which Pb promotes the desorption of imine while basic sites on the support accelerate the adsorption of amine [5]. Unfortunately, the use of lead as an additive creates environmental and health risks, and cleaner alternatives for the industrial catalysts of selective hydrogenation processes are currently under investigation, e.g., lead-free Pd-based catalysts with such additives as boron, carbon, iron, or zinc [8,9].

The above-mentioned application of Pd-Pb/MgO to amine oxidation proves that the choice of support for metallic catalysts is of high relevance to the final catalytic properties of metallic active sites [10,11]. In the case of supported bimetallic catalysts, the support influences the nucleation and growth of metal nanoparticles and controls their alloying. Crystalline metal oxides are widely used as substrates for mono- and bimetallic catalysts based on noble metals [10,11]. Among a variety of such oxides, magnesium oxide is regarded as a prototypical substrate for finely dispersed metal nanoparticles, including single metal atoms and their small clusters [11]. This is due to its strong ionicity, wide electronic gap, simple cubic crystalline structure, and easy synthesis of various samples (from powders to ultrathin films and single crystals) [12]. The single-crystal (100) surface of MgO has received particular attention because this surface has a well-defined structure and stoichiometry [13] and is more stable in terms of its surface energy than other crystal faces of MgO [14,15]. Additionally, it is relatively easy to generate point defects on this surface [16]. The presence of point defects on the (100) surface of an MgO support may modify the catalytic properties of both the surface and adsorbed metal nanoparticles [17]. Point defects also act as trapping sites and nucleation centers for metal atoms [18,19]. The most important point defects on MgO(100) are those created by oxygen vacancies, in particular the surface vacancy corresponding to the removal of a neutral oxygen atom, while two electrons are still trapped in the vacancy [20]. The resulting F_s defect is also termed ‘color center’ because of the two trapped electrons, which give rise to electronic transitions in the visible region of the electromagnetic spectrum, thus changing the color of MgO samples.

In comparison to MgO, other members of the family of alkaline earth metal oxides have attracted less interest in the experimental studies of model supported catalysts [21,22,23]. This contrasts with a wealth of theoretical studies on the interaction between various metals and the (100) surface of MeO (Me = Mg, Ca, Sr, Ba), e.g., [24,25,26,27]. The family of alkaline earth metal oxides shows the same crystal structure but different ionicity and basicity, and therefore, is suitable for examining how the properties of MeO(100) affect the deposited metallic nanoparticles and their interaction with the surface. In the family of alkaline earth metal oxides, their ionicity decreases gradually yet rather slowly with the increasing atomic number of Me [28], while the inverse trend corresponds to the basicity of MeO [29]. The trend in the basicity is associated with the variation in the Madelung potential along the series of MeO rather than with a large change in the ionicity of MeO.

Here, the adsorption of Pb atoms and Pb dimers (Pb₂) at the regular anionic O²⁻ and defective F_s centers on the (100) surface of a series of three alkaline earth metal oxides MeO (Me = Mg, Ca, and Sr) is studied using computational quantum–chemical methods to establish the influence of support basicity on various parameters characterizing the deposited atoms and dimers. The adsorption of Pb atoms and dimers has become the focus of this study because such species are present on the surface of supported metallic catalysts containing Pb as an additive. For example, it is known that single Pb atoms and larger forms of zero-valent metallic lead appear on the surface of the Lindlar catalyst in the process of its preparation [30,31].

The present study is a continuation of our previous theoretical work on atomic Pb adsorption on MgO(100) with defects [32]. To our knowledge, there are no other theoretical studies on the adsorption of small Pb clusters on the surfaces of alkaline earth metal oxides. Therefore, providing the missing theoretical description of Pb adsorption on these surfaces has been a strong motivation for the present study. Experimental studies of Pb adsorption on crystalline MeO substrates have so far been limited to the (100) surface of MgO [33,34,35,36,37].

2. Methods

Quantum–chemical calculations are carried out at a dispersion-corrected density functional theory (DFT-D) level of theory. The generalized gradient approximation density functional proposed by Perdew, Burke, and Ernzerhof (PBE) [38] is combined with the Grimme D3 correction [39] for long-range dispersion effects with rational damping according to Becke and Johnson [40]. The dispersion-corrected PBE-D functional was previously used to predict various properties of alkaline earth metal oxides [41,42,43] and to investigate the adsorption of molecules and metal clusters on the surfaces of such oxides [44,45,46,47,48].

The regular O²⁻ and defective F_s adsorption centers on the (100) surface of MeO crystals are modeled within the framework of an embedded cluster method. The O²⁻ center on MeO(100) is represented by an Me₁₃O₁₃ cluster treated quantum–chemically and embedded in a large array of point charges. The Me₁₃O₁₃ cluster is composed of the surface Me₄O₉ and subsurface Me₉O₄ layers cut out from ideal MeO crystals with their Me–O distances amounting to 2.106 Å, 2.405 Å, and 2.580 Å for MgO, CaO, and SrO, respectively. The cluster is embedded in a 15 × 15 × 8 array of point charges that follow the Evjen embedding scheme [49] to minimize unphysical effects of cluster borders and to approximate the Madelung field of the extended surface at the adsorption center on the cluster. This embedding scheme assumes that the point charges adopt values of ±2e, ±1e, ±0.5e, and ±0.25e for the interior, face, edge, and corner points of the grid, respectively. The point charges are at the positions of ions in the ideal crystal lattices of MeO. Sixteen positive point charges in the immediate vicinity of the cluster are replaced by effective core potentials (ECPs) corresponding to Me²⁺ to provide a representation of the finite size of the cations and to avoid the over-polarization of the O atoms at the cluster borders. The defective F_s adsorption center on MeO(100) is represented by the embedded cluster described above with one modification: the central oxygen atom is removed from the surface layer of Me₁₃O₁₃ to generate the Me₁₃O₁₂ cluster modeling the F_s center on MeO(100). In several previous studies of metal adsorption on MgO, the embedded Mg₁₃O₁₃ and Mg₁₃O₁₂ clusters were successfully used to represent the O²⁻ and F_s centers of MgO(100) [19,32,48,50]. Moreover, the results yielded for these clusters were fairly close to those obtained for much larger clusters [50].

In the surface layer of the Me₁₃O₁₃ and Me₁₃O₁₂ clusters, the central Me and O atoms are described by the LFK basis set [51], whereas four corner oxygen atoms are described by the SBKJC basis set [52,53]. The LFK basis set relies on the SBKJC basis set augmented with a (p,2d) set of basis functions. The SBKJC basis set, which is an ECP basis set with its valence part of double-ζ quality, is assigned to all atoms belonging to the subsurface layer. The SBKJC-ECPs are used for 16 cations surrounding the Me₁₃O₁₃ and Me₁₃O₁₂ clusters. The Pb atoms and dimers are described by the def2-SVP basis set [54]. It was reported that this basis set is capable of predicting fundamental properties of an isolated Pb₂ molecule with reasonable accuracy [55], so it is likely that this basis set also performs well for Pb atoms and dimers investigated here.

Geometry optimizations of Pb atoms and dimers on the embedded Me₁₃O₁₃ and Me₁₃O₁₂ clusters are carried out to examine the adsorption of Pb on MeO(100). Both Pb atoms and the atoms belonging to each adsorption center are allowed to relax in the geometry optimizations, while more distant Me and O atoms, the Me²⁺ ions treated with ECPs, as well as the array of point charges are kept fixed. Two electronic spin states are considered for each center with the Pb atom or dimer adsorbed. One is a low-spin (LS) state that corresponds to a singlet configuration, while another is a high-spin (HS) state exhibiting a triplet multiplicity.

The energetic effects associated with Pb adsorption on the O²⁻ and F_s centers of MeO(100) are characterized in terms of adsorption energy (E_ads) and adhesion energy (E_adh). For the adsorbed Pb atoms and dimers in any electronic spin state, their E_ads energies are defined by the following formulas:

E_ads = E_tot(Pb/MeO) − E_tot(Pb)_isolated − E_tot(MeO)_isolated

(1)

E_ads = E_tot(Pb₂/MeO) − E_tot(Pb₂)_isolated − E_tot(MeO)_isolated

(2)

where the E_tot quantities signify the total energies of the whole system containing Pb at a given adsorption center and of the isolated constituents in their ground states and relaxed geometries. The E_adh energy in turn is formulated as follows:

E_adh = E_tot(Pb/MeO) − E_tot(Pb)_interacting − E_tot(MeO)_interacting

(3)

E_adh = E_tot(Pb₂/MeO) − E_tot(Pb₂)_interacting − E_tot(MeO)_interacting

(4)

where the total energies of interacting fragments correspond to their geometries taken from the Pb/MeO(100) and Pb₂/MeO(100) systems. The interacting Pb and Pb₂ fragments are considered in their spin states inherited from Pb/MeO(100) and Pb₂/MeO(100), respectively, while the embedded MeO cluster shows the lowest possible spin multiplicity. The basis set superposition error in E_adh is eliminated by the counterpoise method [56].

A tendency of single Pb atoms to form Pb₂ on MeO(100) is assessed in terms of two dimerization energies ($E_{\dim }^{\mathrm{gas}}$ and $E_{\dim }^{\mathrm{ads}}$) [57].

$$E_{\dim }^{\mathrm{gas}}=E_{\mathrm{tot}}({\mathrm{Pb}}_2/\mathrm{MeO})-E_{\mathrm{tot}}(\mathrm{Pb}/\mathrm{MeO})-E_{\mathrm{tot}}{\left(\mathrm{Pb}\right)}_{\mathrm{isolated}}$$

(5)

$$E_{\dim }^{\mathrm{ads}}=E_{\mathrm{tot}}({\mathrm{Pb}}_2/\mathrm{MeO})+E_{\mathrm{tot}}{\left(\mathrm{MeO}\right)}_{\mathrm{regular}}-E_{\mathrm{tot}}(\mathrm{Pb}/\mathrm{MeO})-E_{\mathrm{tot}}{(\mathrm{Pb}/\mathrm{MeO})}_{\mathrm{regular}}$$

(6)

Part of the terms on the right-hand sides of Equations (5) and (6) has been explained above, while E_tot(MeO)_regular denotes the total energy of the optimized embedded Me₁₃O₁₃ cluster and E_tot(Pb/MeO)_regular is the total energy of the defect-free MeO(100) surface with the Pb atom adsorbed.

The effect of spin–orbit (SO) relativistic correction on E_adh is estimated in a series of single-point energy calculations carried out using the PBE-D density functional combined with the dhf-SVP-2c basis set [58]. This basis set is assigned to the Pb atoms and all atoms of Me₁₃O₁₃ and Me₁₃O₁₂. Scalar relativistic corrections are taken into account in one-component PBE-D/dhf-SVP-2c calculations, while both scalar and SO relativistic corrections are covered in two-component PBE-D/dhf-SVP-2c calculations. In the one- and two-component calculations, the periodic electrostatic embedded cluster method (PEECM) [59] is employed as the embedding scheme operating on the Me₁₃O₁₃ and Me₁₃O₁₂ clusters with the adsorbed metal. The PEECM can be considered to be equivalent to the embedding scheme described earlier in this section.

The distribution of the electron charge in Pb/MeO(100) and Pb₂/MeO(100) is probed by means of the Mulliken population analysis [60] and the Bader charge analysis [61]. Fuzzy bond order (FBO) analysis [62] is employed to estimate the bond order between the atoms of adsorbed Pb dimers.

Geometry optimizations and single-point energy calculations were carried out using the Gaussian 16 C.01 program [63]. SO relativistic effects were estimated with the aid of the TURBOMOLE 7.9 program [64,65]. A grid-based implementation of Bader charge analysis [66] was conducted with the Bader 1.04 program [67]. The latest development version of Multiwfn 3.8 [68,69] was used to calculate the FBO.

3. Results and Discussion

The first stage of this study explores the adsorption of single Pb atoms at the regular O²⁻ and defective F_s centers of MeO(100). The calculated lowest-energy structures of Pb/MeO(100) are illustrated schematically in Figure 1, and the essential geometrical and energetic parameters describing Pb-atom adsorption in both LS and HS states are reported in

Table 1. Geometrical and energetic parameters for Pb-atom adsorption at the O²⁻ and F_s centers of MeO(100). Distances are given in Å; energies are in eV.

MeO	Center	Spin State	d1 a	ΔE	Eads	Eadh
MgO	O2−	LS	2.429	0.25	−1.32	−2.35
		HS	2.431	0.00	−1.57	−1.58
	Fs	LS	2.368	0.18	−2.66	−3.64
		HS	2.383	0.00	−2.84	−2.79
CaO	O2−	LS	2.376	0.20	−1.78	−2.85
		HS	2.386	0.00	−1.98	−2.03
	Fs	LS	2.448	0.19	−2.96	−3.86
		HS	2.461	0.00	−3.15	−3.02
SrO	O2−	LS	2.323	0.20	−2.23	−3.22
		HS	2.328	0.00	−2.43	−2.37
	Fs	LS	2.043	0.19	−3.08	−3.70
		HS	2.046	0.00	−3.27	−2.86

^a This distance is calculated between Pb and O for the regular adsorption center, while a height above the surface layer of MeO is taken for the defective center (Figure 1).

.

As shown in Figure 1, the Pb atom adsorbed at the O²⁻ center sits on top of an oxygen anion, while the F_s defect binds the Pb atom above the central point of the oxygen vacancy of MeO(100). The negative values of E_ads in Table 1 indicate that the adsorption of a free Pb atom on MeO(100) is energetically favorable at both considered surface centers of all three alkaline earth metal oxides. The ground state of a free Pb atom is characterized by a triplet spin multiplicity, and the adsorbed Pb atoms tend to preserve their HS state. In comparison with the adsorbed Pb atoms in the HS state, their LS state lies higher in energy by 0.18 eV to 0.25 eV, as evidenced by the difference in E_tot between the LS and HS states (ΔE). The distance between the Pb atom and the oxygen anion of the O²⁻ center (d₁) for the LS state is somewhat shorter than this distance for the HS state. The same is observed for the d₁ distance between the Pb atom and the surface layer containing the F_s center. The calculated values of E_ads prove that the adsorption of the Pb atom at the F_s center is more energetically favorable than binding to the O²⁻ center on the (100) surface of all three MeO crystals. This is accompanied by a stronger interaction between the adsorbed Pb atom and the F_s center. The strength of this interaction is expressed by E_adh; the more negative the yielded value of E_adh is, the greater strength this interaction demonstrates. For the adsorbed Pb atom in the HS state, its E_adh and E_ads energies differ due to the structural relaxation of surface centers upon Pb-atom adsorption. With the exception of Pb at the F_s center of SrO(100), the Pb atoms adsorbed at the remaining studied centers show relatively small differences between E_adh and E_ads, which implies a rather minor relaxation of these centers upon the formation of Pb/MeO(100) structures in the HS state. However, E_adh differs significantly from the corresponding E_ads energy for the Pb/MeO(100) structures in their LS state. In this case, the difference between E_adh and E_ads is attributed not only to the structural relaxation of the adsorption centers but also to spin pairing (for a free Pb atom, its transition from a triplet to a singlet requires 1.06 eV at the PBE-D/def2-SVP level of theory).

Experimental measurements of the energetics of Pb adsorption on alkaline earth metal oxides are available only for Pb/MgO(100). An initial heat of adsorption of 1.07 eV was measured for a Pb film on MgO(100) at 300 K using single-crystal adsorption microcalorimetry [33]. The strength of the bond between Pb and MgO(100) was estimated to be of 0.33 eV. In another experimental study, a range from 0.72 eV to 0.81 eV was deduced for the heat of adsorption of Pb/MgO(100) from the atomic beam/surface scattering measurements of Pb lifetime on the (100) terrace of MgO at low coverage [37]. Although the calculated E_ads energy of Pb at the O²⁻ center of MgO(100) cannot be compared directly with the experimental estimates of the heat of adsorption for Pb/MgO(100), the absolute values of E_ads are relatively close to these experimental estimates.

From the results presented in Table 1, it can be deduced that an increase in the basicity of MeO in the sequence MgO < CaO < SrO is associated with a more and more energetically favorable effect of Pb-atom adsorption, as well as with the growing strength of the interaction between the adsorbed Pb atom and the surface center. This trend is observed for each adsorption center and spin state. Additionally, the distance of the adsorbed Pb atom from the surface oxygen anion becomes shorter (that is, the values of d₁ decrease gradually) as the basicity of MeO(100) grows. The same effect of MeO-support basicity on the strength of atomic adsorption was previously reported for transition and noble metal atoms [25,27].

As was mentioned in the introduction, the trend in the basicity of MeO is associated with the variation in the Madelung potential (V_Madelung). To be precise, the growing basicity in the sequence MgO < CaO < SrO corresponds to the gradual decrease in V_Madelung along this sequence [70]. The values of V_Madelung at the O²⁻ centers of MeO(100) amount to 23.01 eV, 20.15 eV, and 18.78 eV for MgO(100), CaO(100), and SrO(100), respectively. These values were calculated using the Madelung constant of 1.68155 [71] and the Me–O distances given in the previous section. The geometrical and energetic parameters of Pb/MeO(100) in the most stable adsorption configurations are plotted against V_Madelung in Figure 2. Based on V_Madelung as the measure of MeO(100) basicity, the plots in Figure 2 confirm visually the findings made in the previous paragraph. Moreover, the dependencies of d₁, E_ads, and E_adh on V_Madelung yield reasonable correlations, as manifested by the corresponding coefficients of determination (R²).

Next, the most stable adsorption configurations of Pb₂ at the O²⁻ and F_s centers of MeO(100) have been identified, and these are presented schematically in Figure 3. The calculated values of several geometrical and energetic parameters describing the lowest-energy structures of Pb₂/MeO(100) in both spin states are listed in

Table 2. Geometrical and energetic parameters for Pb₂ adsorption at the O²⁻ and F_s centers of MeO(100). Distances are given in Å, energies are in eV.

MeO	Center	Spin State	d1 a	d2 b	d3	ΔE	Eads	Eadh
MgO	O2−	LS	2.456	2.536	2.940	0.00	−2.17	−2.66
		HS	2.584	2.911	2.967	0.68	−1.49	−1.35
	Fs	LS	2.360	2.680	2.854	0.00	−3.69	−4.24
		HS	2.373	2.667	3.114	0.94	−2.75	−2.70
CaO	O2−	LS	2.418	2.436	2.969	0.00	−3.07	−3.62
		HS	2.414	2.440	3.263	0.76	−2.31	−2.48
	Fs	LS	2.379	2.568	2.889	0.00	−4.37	−4.79
		HS	2.357	2.522	3.159	0.84	−3.53	−3.43
SrO	O2−	LS	2.355	2.355	2.989	0.00	−3.89	−4.25
		HS	2.350	2.366	3.294	0.71	−3.18	−3.18
	Fs	LS	2.035	2.421	2.912	0.00	−4.91	−4.90
		HS	1.844	2.371	3.013	0.60	−4.31	−3.74

^a This distance is defined as Pb¹-O for the O²⁻ center, while a height above the surface layer of MeO is taken for the F_s center (Figure 3). ^b This distance is defined as Pb²-O for all centers.

. The most stable adsorption configuration of Pb₂ on the regular surface of MeO(100) is always found for the LS state. In this case, the d₁ and d₂ distances between the atoms of the dimer (Pb¹ and Pb² in Figure 3) differ from one another only slightly, and therefore, the bond axis of Pb₂ is positioned practically parallel to the surface. The difference between d₁ and d₂ results from the finite size of the Me₁₃O₁₃ cluster treated quantum–chemically. The Pb¹ and Pb² atoms of the adsorbed dimer sit on top of two neighboring oxygen anions on MeO(100), which is essentially expected from the preference of single Pb atoms for their adsorption at the O²⁻ centers on the defect-free MeO(100) surfaces. For the HS state, the Pb¹ and Pb² atoms still bind to two neighboring oxygen anions on the regular MeO(100) surface and the bond axis of Pb₂ runs practically parallel to CaO(100) and SrO(100). By contrast, the bond axis of the Pb dimer adsorbed on MgO(100) in the HS state is tilted toward the surface, with the Pb² atom being significantly more distant from the surface. The adsorption of Pb₂ at the F_s center on MeO(100) leads to the most stable configuration in which the Pb¹ atom sits on top of the oxygen vacancy, while the Pb² atom binds to one of the oxygen anions surrounding this vacancy. The bond axis of the adsorbed dimer is always tilted toward the cavity of the F_s defect, while the Pb atom bound to one of the surrounding oxygen anions is moved upward, above the surface. This most stable configuration is found for the LS state. The negative values of E_ads indicate that the adsorption of Pb₂ on the regular and defective MeO(100) surfaces is an energetically favorable process, regardless of the spin state assumed. The adsorption of Pb₂ at the F_s center of MeO(100) is associated with a more favorable energetic effect than the Pb₂ adsorption at the O²⁻ center. In that regard, the preference of the F_s defect for capturing Pb atoms determines the behavior of Pb₂ on the defective MeO(100) surface. The preferred spin state of the Pb dimer adsorbed on MeO(100) without and with F_s defects is the LS state, although the ground state of a free Pb₂ molecule corresponds to a triplet multiplicity (³Σ) [72]. The values of ∆E prove that the adsorption configurations of Pb₂/MeO(100) in the HS state are destabilized by 0.60 eV to 0.94 eV relative to the corresponding configurations in the LS state. This is accompanied by a weaker interaction of Pb₂ with the MeO(100) surface in the HS state than in the LS state, as evidenced by the less negative values of E_adh for the former state. The energetic parameters describing Pb₂/MeO(100) present the same dependence on the support basicity as that observed for the Pb-atom adsorption (Figure 2). For example, the strength of the interaction between Pb₂ and the MeO(100) surface increases gradually with the growing basicity of MeO.

The adsorption of Pb₂ on the MeO(100) surface affects the bond length of the dimer. The bond length in the adsorbed dimer is described by the corresponding geometrical parameter (d₃) appended to Table 2. The adsorbed dimer shows a longer bond in the HS state than in the LS state. The bond length in a free Pb₂ molecule in its ground state (³Σ) amounts to 2.942 Å (at the PBE-D/def2-SVP level of theory), and this bond becomes longer upon adsorption on MeO(100) with the triplet spin multiplicity preserved. However, the most stable adsorption configuration of Pb₂/MeO(100) contains no unpaired electrons, and therefore, the adsorbed dimer in the LS state usually has a slightly shorter bond than the bond length of a free Pb₂ molecule in its ground state. The bond of the dimer adsorbed at the O²⁻ center demonstrates a gradual elongation as the lattice constant of MeO grows (MgO < CaO < SrO). The adsorption of the dimer and changes in its bond length also affect the bond order between Pb¹ and Pb². The order of this bond in the adsorbed dimers in the LS state has been estimated by means of the FBO, and the resulting values are collected in

Table 3. Fuzzy bond order (FBO) between the atoms of the Pb dimers adsorbed at the O²⁻ and F_s centers of MeO(100) in their LS state. For comparison, the FBO value for an isolated Pb₂ molecule in its ground state is also given.

Pb2/MeO or Pb2	Center	FBO
MgO	O2−	1.68
	Fs	1.71
CaO	O2−	1.65
	Fs	1.68
SrO	O2−	1.49
	Fs	1.62
Pb2		2.33

. It is clearly evident that the adsorbed dimers feature a reduced bond order in comparison with the bond order of a free Pb₂ molecule. It suggests that the bond of Pb₂ becomes weaker when the dimer has been adsorbed on MeO(100). The increase in MeO basicity results in a larger reduction in the Pb¹-Pb² bond order.

The distribution of the electron charge in Pb/MeO(100) and Pb₂/MeO(100) is assessed using the Mulliken and Bader partial charges calculated for individual atoms in the lowest-energy structures in their LS and HS states. The results are summarized in

Table 4. Charge and spin distributions for the Pb atoms and dimers adsorbed at the O²⁻ and F_s centers of MeO(100). Results yielded by the Mulliken and Bader analyses are shown without and in parentheses, respectively. All values are given in au.

MeO	Center	Spin State	Pb/MeO		Pb2/MeO
			q(Pb)	Nspin(Pb)	q(Pb2)	Nspin(Pb1)	Nspin(Pb2)
MgO	O2−	LS	−0.020 (−0.156)	0.000	−0.266 (−0.328)	0.000	0.000
		HS	−0.057 (−0.156)	1.806	−0.107 (−0.248)	0.745	1.033
	Fs	LS	−0.377 (−1.698)	0.000	−0.507 (−1.811)	0.000	0.000
		HS	−0.427 (−1.693)	1.627	−0.601 (−1.807)	0.786	0.908
CaO	O2−	LS	−0.097 (−0.375)	0.000	−0.393 (−0.642)	0.000	0.000
		HS	−0.137 (−0.357)	1.767	−0.508 (−0.635)	0.880	0.927
	Fs	LS	−0.483 (−1.926)	0.000	−0.711 (−2.131)	0.000	0.000
		HS	−0.539 (−1.920)	1.707	−0.840 (−2.156)	0.821	0.916
SrO	O2−	LS	−0.420 (−0.540)	0.000	−0.869 (−0.805)	0.000	0.000
		HS	−0.438 (−0.523)	1.787	−0.947 (−0.799)	0.910	0.930
	Fs	LS	−1.240 (−2.045)	0.000	−1.588 (−2.281)	0.000	0.000
		HS	−1.234 (−1.980)	1.873	−1.582 (−1.992)	1.088	0.132

. The amount of the electron charge (q) on the adsorbed Pb atoms has a negative sign, implying an ancillary electron charge acquired by these atoms upon adsorbing on MeO(100). This finding is valid for the electron charge distributions produced by both Mulliken and Bader analyses. The electron charge carried by the adsorbed Pb dimers is evaluated as a sum of partial charges accumulated on the Pb¹ and Pb² atoms of the adsorbed dimers. The amount of the electron charge calculated in this manner for the adsorbed dimers is denoted as q(Pb₂) in Table 4. The q(Pb₂) values indicate that the dimers adsorbed on the MeO(100) surfaces acquire an ancillary electron charge. Specifically, the Pb atoms and dimers adsorbed at the F_s center behave as strong electron acceptors. As could be expected, the growing basicity of MeO in the sequence MgO < CaO < SrO results in a gradual increase in the electron charge transferred to the adsorbed Pb atoms and dimers (Figure 2d). The values of atomic spin density (N_spin) in Table 4 prove that significant spin populations reside on the Pb atoms upon their adsorption on MeO(100) in the HS state.

It is also examined whether MeO-support basicity has an influence on the highest occupied molecular orbital (HOMO) for the most stable adsorption configurations of Pb₂ on MeO(100). The contours of the HOMO for these configurations are plotted in Figure 4. An isovalue of 0.04 au was used to plot these contours. The phases of the HOMO are colored in two different colors (blue and pink). For the dimers adsorbed on the regular MeO(100) surfaces, the shapes of the HOMO look almost identical, and they reveal the presence of leading contributions from p-type atomic orbitals of both Pb atoms. While the shape of the HOMO for Pb₂ at the F_s center of MgO(100) resembles that plotted for Pb₂ at the O²⁻ center of MgO(100), the HOMO shapes of Pb₂ at the F_s centers of CaO(100) and SrO(100) demonstrate the leading contribution from the atomic orbitals of the Pb¹ atom only.

Next, a tendency of Pb atoms to dimerize on the regular and defective MeO(100) surfaces is inspected. Quantifying this tendency is crucial in the context of cluster growth. The calculated values of $E_{\dim }^{\mathrm{gas}}$ and $E_{\dim }^{\mathrm{ads}}$ are shown in

Table 5. Dimerization energies of the Pb atoms adsorbed at the O²⁻ and F_s centers of MeO(100). All values are given in eV.

MeO	Center	Spin State	${\mathit{E}}_{\mathbf{dim}}^{\mathbf{gas}}$	${\mathit{E}}_{\mathbf{dim}}^{\mathbf{ads}}$
MgO	O2−	LS	−3.07	−1.49
		HS	−2.39	−0.82
	Fs	LS	−3.32	−1.75
		HS	−2.38	−0.81
CaO	O2−	LS	−3.56	−1.58
		HS	−2.80	−0.83
	Fs	LS	−3.69	−1.72
		HS	−2.85	−0.88
SrO	O2−	LS	−3.93	−1.50
		HS	−3.22	−0.78
	Fs	LS	−4.11	−1.68
		HS	−3.51	−1.07

. The $E_{\dim }^{\mathrm{gas}}$ energy signifies the dimerization energy of a Pb atom bound by a given adsorption center with another Pb atom from the gas phase, that is, an isolated Pb atom is captured by Pb/MeO(100). The $E_{\dim }^{\mathrm{ads}}$ energy in turn estimates the dimerization energy between two already adsorbed Pb atoms, one of which has always been bound at the regular O²⁻ center of MeO(100). The growing tendency of single Pb atoms to dimerize is signaled by more and more negative values of $E_{\dim }^{\mathrm{gas}}$ and $E_{\dim }^{\mathrm{ads}}$. The tabulated $E_{\dim }^{\mathrm{gas}}$ values indicate that the Pb dimer can be easily formed through the binding of a free Pb atom to another Pb atom already adsorbed at either O²⁻ or F_s center on the (100) surfaces of all three alkaline earth metal oxides. With the exception of the dimerization at the O²⁻ and F_s centers of MgO(100) in the HS state, the formation of Pb₂ at all remaining MeO(100) centers yields more negative values of $E_{\dim }^{\mathrm{gas}}$ than the binding energy of a free Pb₂ molecule (−2.47 eV at the PBE-D/def2-SVP level of theory). This points towards an additional energy gain due to the binding of the free Pb atom to MeO(100). Like the capture of a free Pb atom by Pb/MeO(100), the dimerization of two already adsorbed Pb atoms, one of which is adsorbed at the O²⁻ center by definition, also produces an energetically favorable effect ($E_{\dim }^{\mathrm{ads}}$ < 0). However, the dimerization of two already adsorbed Pb atoms leads to a smaller gain of energy than the dimerization through the capture of a free Pb atom by another already adsorbed Pb atom. The calculated $E_{\dim }^{\mathrm{ads}}$ energies are less negative than the binding energy of a free Pb₂ molecule, which is another evidence for the weakening of the Pb¹-Pb² bond in the dimer adsorbed on MeO(100). While the increasing basicity of MeO support clearly enhances the tendency of dimerization via the capture of a free Pb atom on Pb/MeO(100), the effect of MeO basicity on $E_{\dim }^{\mathrm{ads}}$ turns out to be small and irregular.

Lead is a heavy element, and therefore, it is essential to estimate the impact of relativistic effects on the Pb atoms and dimers adsorbed on MeO(100). The estimation of relativistic effects makes use of the LS-state Pb/MeO(100) and Pb₂/MeO(100) structures in their optimized geometries characterized in Table 1 and Table 2. Thus, these structures and their energetics take account of scalar relativistic corrections such as the leading mass-velocity and Darwin corrections via the ECPs incorporated into the LFK, SBKJC, and def2-SVP basis sets. However, the SO relativistic effect, arising from the splitting of inner atomic shells by SO coupling, is not handled by these basis sets. To estimate the importance of SO relativistic effect, one- and two-component PBE-D single-point energy calculations were carried out using the dhf-SVP-2c basis set; this ECP basis set was designed to account for SO coupling. The E_adh energies calculated without and with the SO relativistic correction are shown in

Table 6. Adhesion energies for the Pb atoms and dimers adsorbed at the O²⁻ and F_s centers of MeO(100) in their LS state. All values are given in eV.

MeO	Center	Pb/MeO		Pb2/MeO
		Scalar	Scalar + SO	Scalar	Scalar + SO
MgO	O2−	−1.70	−1.07	−3.09	−2.03
	Fs	−3.02	−2.08	−4.71	−3.46
CaO	O2−	−2.21	−1.44	−4.12	−2.86
	Fs	−3.62	−2.44	−5.30	−4.00
SrO	O2−	−3.03	−1.92	−4.94	−3.52
	Fs	−3.74	−3.02	−5.45	−4.40

. From this table, it can be deduced that the effect of SO correction on the E_adh energy is significant. The inclusion of SO correction in the calculations reduces the values of E_adh by 19% to 37%. Despite the significant reduction in E_adh, the inclusion of SO correction in the calculations does not disturb the dependence of E_adh on the basicity of MeO—the interaction between the adsorbed metal and MeO(100) still becomes stronger with the growing basicity of MeO.

Finally, another aspect of the computational methodology employed here needs to be raised. The results presented above were obtained using a combination of ECP basis sets, demonstrating an approximately double-ζ quality of their valence parts. Obviously, the reason behind using such basis sets was to reduce the computational cost of all calculations. It is, however, unclear to what extent the presented results depend on the quality of the basis sets employed. To check this basis set dependence, three basis sets, denoted here as BS1, BS2, and BS3, are used to optimize the structures of Pb/MeO(100) and calculate their energetic parameters. BS1 is composed of the basis sets used to produce all the results presented above, that is, a combination of LFK, SBKJC, and def2-SVP. BS2 consists of def2-SVP and def2-SVPD [73], while BS3 is composed of def2-TZVP [54] and def2-TZVPD [73], which are triple-ζ quality ECP basis sets. Results obtained from the PBE-D functional combined with each of BS1–BS3 are summarized in

Table 7. Geometrical and energetic parameters for Pb-atom adsorption at the O²⁻ center of MeO(100). Results calculated using the basis sets BS1, BS2, and BS3 are shown without parentheses, in parentheses, and in square brackets, respectively. Results for BS1 are repeated after Table 1. Distances are given in Å; energies are in eV.

MeO	Spin State	d1	ΔE	Eads	Eadh
MgO	LS	2.429 (2.403) [2.395]	0.25 (0.21) [0.19]	−1.32 (−1.39) [−1.36]	−2.35 (−2.41) [−2.37]
	HS	2.431 (2.412) [2.403]	0.00 (0.00) [0.00]	−1.57 (−1.60) [−1.55]	−1.58 (−1.58) [−1.57]
CaO	LS	2.376 (2.336) [2.313]	0.20 (0.20) [0.19]	−1.78 (−1.81) [−1.78]	−2.85 (−2.90) [−2.84]
	HS	2.386 (2.345) [2.321]	0.00 (0.00) [0.00]	−1.98 (−2.01) [−1.96]	−2.03 (−2.06) [−2.04]
SrO	LS	2.323 (2.166) [2.146]	0.20 (0.40) [0.17]	−2.23 (−2.29) [−2.20]	−3.22 (−3.55) [−3.90]
	HS	2.328 (2.166) [2.147]	0.00 (0.00) [0.00]	−2.43 (−2.69) [−2.67]	−2.37 (−3.20) [−3.39]

. In comparison with BS3, BS1 leads to the structures of Pb/MgO(100) and Pb/CaO(100) in which the d₁ distance is overestimated slightly but the energetic parameters deviate only marginally. Unfortunately, the differences between the parameters obtained from BS1 and BS3 are much larger for Pb/SrO(100). These differences stem from a mismatch between BS1 and BS3 in the size of the ECPs describing the atomic cores of Sr₁₃O₁₃ and Sr₁₃O₁₂. For BS1, the ECPs of the LFK and SBKJC basis sets replace 2 and 36 core electrons of oxygen and strontium, respectively, whereas BS3 exclusively replaces 28 core electrons of strontium with the corresponding ‘small core’ ECP.

4. Conclusions

The present work is one of the very first theoretical studies on the adsorption of lead on the crystals of alkaline earth metal oxides. A variety of parameters describing single Pb atoms and Pb dimers deposited on the regular and defective (100) surfaces of three MeO crystals were calculated at a DFT-D level of theory to discern how the basicity of MeO affects the adsorption of lead on MeO(100). The calculations revealed that the basicity of MeO has a direct influence on the characteristics of the adsorbed Pb atoms and dimers. Specifically, the increasing basicity of MeO in the sequence MgO < CaO < SrO leads to a more and more energetically favorable effect of Pb adsorption on MeO(100). This is associated with the greater strength of the interaction between the adsorbed metal and the surface, demonstrating a higher basicity. Furthermore, the increasing basicity of MeO facilitates the charge transfer to the adsorbed metal, and therefore, the amount of the ancillary electron charge acquired by the adsorbed Pb atoms and dimers grows gradually while going from MgO to SrO. In the case of Pb₂ adsorption, the increase in MeO basicity is accompanied by the elongation of the Pb-Pb bond and the reduction in its order. The tendency to form Pb₂ via capturing a free Pb atom by another already adsorbed is enhanced by the increasing basicity of the MeO support.

The aforementioned conclusions contribute to a better understanding of support effects on metal adsorption. In particular, the presented theoretical characterization of Pb atoms and dimers on MeO(100) may be helpful for elucidating the relationships between the supports and deposited metals in MeO-supported metallic catalysts containing Pb as an additive. By choosing a specific MeO support, the strength of its interaction with Pb can be modulated, which influences the growth of Pb nanoparticles and ultrathin films on the MeO support in catalysts. Describing the diffusion of Pb atoms on MeO(100) and formation of larger Pb clusters will be the next stage in the theoretical exploration of the behavior of Pb on MeO surfaces.