Abstract
Molybdenum disulfide has broad applications in catalysis, optoelectronics, and solid lubrication, where lanthanide (Ln) doping can be used to tune its physicochemical properties. The reduction of oxygen is an electrochemical process important in determining fuel cell efficiency, or a possible environmentaldegradation mechanism for nanodevices and coatings consisting of Lndoped MoS_{2}. Here, by combining densityfunctional theory calculations and currentpotential polarization curve simulations, we show that the dopantinduced high oxygen reduction activity at LnMoS_{2}/water interfaces scales as a biperiodic function of Ln type. A defectstate pairing mechanism, which selectively stabilizes the hydroxyl and hydroperoxyl adsorbates on LnMoS_{2}, is proposed for the activity enhancement, and the biperiodic chemical trend in activity is found originating from the similar trends in intraatomic 4f–5d6s orbital hybridization and interatomic Ln–S bonding. A generic orbitalchemistry mechanism is described for explaining the simultaneous biperiodic trends observed in many electronic, thermodynamic, and kinetic properties.
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Introduction
Oxygen reduction reaction (ORR) is an electrochemical process reducing O_{2} into H_{2}O, which plays significant roles in the fields of clean energy and corrosion^{1}. As the cathode reaction in fuel cells, active enough ORR is required for efficient energy conversion^{2}, and one contemporary urgent task is replacing the noblemetal catalysts (e.g., Pt) with less expensive, sufficiently active, and durable candidate alternatives^{3}. On the other hand, as a cathodic reaction readily occurring in regular oxic humid/aqueous conditions^{4}, the activated ORR on a surface spot will cause the electron loss and potential rise of surrounding materials (e.g., metal substrates), which tends to induce the galvaniccorrosion phenomena^{1,5}. Thus, accurately understanding the ORR behaviors and relevant mechanisms is not only desired by the design of advanced electrocatalysts but also by the appropriate protection and longlasting working of many functional nanodevices and coatings in realistic environments.
Earthabundant molybdenum disulfide (MoS_{2}) is a typical twodimensional material with great application potential in catalysis, optoelectronic devices, and solid lubrication due to its preferred structural stability, suitable band gap, and easy shearing^{6,7}. Lanthanidedoped MoS_{2} (LnMoS_{2}) recently has emerged as an important group of materials with the electronic and optical properties profoundly tuned by the Ln dopants^{8,9}, and many kinds of LnMoS_{2} systems (e.g., Ln = Sm, Eu, Dy, Ho, Er, and Yb) have been successfully synthesized in experiments^{10,11,12,13,14,15}. Ln dopants can introduce many defect states in the band gap of MoS_{2}, and the degenerate 4f multiplet orbitals of Ln dopants are split by the highly anisotropic local crystal field in MoS_{2} matrix. These two electronicstructure mechanisms will lead to the photoluminescence emission of MoS_{2} from the visible range to the nearinfrared spectrum, including the telecommunication range at 1.55 μm^{10,12}, as well as to the improved electrical property of LnMoS_{2}^{11,15}, making LnMoS_{2} promising for optoelectronic materials and nanodevices.
Pristine MoS_{2} has a quite inert basal plane for ORR catalysis, and only small MoS_{2} nanoflakes with a considerably increased ratio of active edge sites can exhibit observable ORR activity^{16,17,18}. However, MoS_{2} edges have low chemical stability and may incur degrading corrosion and oxidization of nanoflakes when exposed to realistic environments^{19,20}, thus largescale MoS_{2} flakes should still be preferred for longlasting performance. Due to the significant tuning effect on the electronic structure of MoS_{2}, Ln doping may be a promising way to stimulate the ORR activity on its surface for catalysis purposes. However, for the nanodevices and lubricating films made of LnMoS_{2}, the activated ORR processes tend to bring unexpected galvaniccorrosion phenomena to many surrounding component materials (e.g., metal substrates and connecting wires)^{1,19,21}. Therefore, it is meaningful and urgent to clearly understand and accurately predict the ORR behaviors on LnMoS_{2} surfaces, which can not only motivate their future electrocatalytic applications but also guide the appropriate protection against galvanic corrosion for the longlasting service of advanced nanodevices and coatings.
In this work, by considering all the 15 Ln dopants in MoS_{2} and combining densityfunctional theory (DFT) calculations and currentpotential polarization curve simulations, we discover the considerably enhanced ORR activity on LnMoS_{2} surfaces with an intriguing modulating biperiodic chemical trend. We first use DFT to calculate the stability of Ln dopants in MoS_{2}, the adsorption stability of various ORR intermediates, and their reaction behaviors at the LnMoS_{2}/water interfaces, where the water effect is strictly modeled by statistically sampling the H_{2}Ofilm configurations. Many closely correlated biperiodic chemical trends are observed in various thermodynamic and kinetic properties, and the unifying electronicstructure mechanisms are revealed by analyzing the intraatomic orbital hybridizations and interatomic bondings of Ln dopants. A defectstate pairing mechanism is proposed for the selectively and largely (moderately) enhanced hydroxyl (hydroperoxyl) adsorption by Ln doping, which leads to the considerably enhanced ORR activity on LnMoS_{2}. We finally simulate the currentpotential polarization curves for ORR processes on LnMoS_{2} surfaces, where the individual roles of involved microkinetic steps are also clearly revealed.
Results and discussion
Biperiodic chemical trend in dopant stability
The screening of different Lndopant configurations in MoS_{2} using DFT calculations (see section A in Supplementary Information, SI) reveals the most stable doping site located at the Mo site (Fig. 1a), which is consistent with the experimental observation using scanning transmission electron microscopy (STEM) (Fig. 1b)^{10,15}. Furthermore, the calculated Raman spectra for such LnMoS_{2} configuration also exhibit the same mode redshifts as the experimental measurements^{10,22,23} (see section B in SI). These systematically close theoryexperiment agreements strongly validate the atomicstructure model for LnMoS_{2} constructed here, which will be used in the following calculations. The way of a material interacts with external environmental agents always largely depends on its intrinsic stability, and the stability of an Ln dopant in MoS_{2} can be quantitatively described by its formation energy (E_{f}), which is defined as the energy change associated with the filling of a Mo vacancy in MoS_{2} by a free Ln atom (see Eq. (1) in the “Methods” section) and then can directly reflect the atomicbonding strength therein. The E_{f}s for all the 15 Ln dopants calculated using the standard Ln pseudopotentials (i.e., with valence 4f electrons) are shown in Fig. 1c, and the largely negative values (−6 ~ −11 eV) obviously indicate the high thermodynamic stability of LnMoS_{2}. In addition, the calculated phonon densities of states further prove the favorable dynamical stability of all the fifteen LnMoS_{2} systems (see section A in SI).
In the variation of E_{f} with respect to Ln type, we can observe a remarkable biperiodic chemical trend with a large modulating amplitude of 4.5 eV, which fully disappears if the Ln pseudopotentials with 4f electrons included in the ionic part are used in calculations (see the ionic4f E_{f}s in Fig. 1c), i.e., neglecting the participation of 4f orbitals in any interatomic bonding. From this dramatic difference between the valence4f and ionic4f E_{f}s, we can derive that although the 4f orbitals are highly localized (see section C in SI for atomicorbital wavefunctions), the hybridization between 4f electrons with delocalized 5d and 6s electrons should play a significant role in many physicochemical properties of LnMoS_{2}. In addition to the above E_{f}s for Ln dopant in MoS_{2}, the Lndopant charge state (\({q}_{{{{{{{{\rm{Ln}}}}}}}}}\), Fig. 1c) also exhibits a simultaneous biperiodic chemical trend. After a broader literature investigation, we further find more similar biperiodic trends in the Lnmetal sublimation heats, Lnatom ionization potentials (IP), and homolytic bond energies of LnF_{3} molecules (see section C in SI)^{24,25}. The weighted summation of the 4frelevant third and fourth ionization potentials (IP_{3} + 0.2IP_{4}) is also shown in Fig. 1c for comparison. Such generic biperiodic chemical trends in various properties of Ln elements in different states (e.g., atom, elemental metal, compound molecule, and solid dopant) can well validate our finding on the E_{f}s here and should be governed by a common intrinsic electronicstructure mechanism, which will be uncovered by analyzing the characters of valence 4f, 5d, and 6s orbitals in the following.
The electronic wavefunctions and energy levels of Ln atoms in the \(4{f}^{{n}_{{\rm {v}}}3}5{d}^{1}6{s}^{2}\) configuration (n_{v} is the valenceelectron number) are calculated using the allelectron fullpotential method^{26}, where highly localized (delocalized) character of the lower 4f orbitals (upper 5d and 6s orbitals) clearly shows up (see Fig. S7a and S7b). The variation of magnetic moment in LnMoS_{2} (see Fig. S7c) clearly proves such atomic configuration for Ln dopants, where the Hund’s rule for magnetic 4f electrons results in the monotonic increase (decrease) of the magnetic moment before (after) the half filling of 4f orbitals, i.e., at Gd dopant with 4f^{7}5d^{1}6s^{2}. The ground state of most free Ln atoms is in the \(4{f}^{{n}_{{\rm {v}}}2}6{s}^{2}\) configuration, with the 4f orbitals half filled at Eu atom (4f^{7}6s^{2}), and the energy required for the \(4{f}^{{n}_{{\rm {v}}}2}6{s}^{2}\to 4{f}^{{n}_{{\rm {v}}}3}5{d}^{1}6{s}^{2}\) transition on free Ln atoms also exhibits a biperiodic chemical trend as measured by experiments (see Fig. S7d)^{27,28}: The transition energy increases in both the underhalffilled (from La to Eu) and overhalffilled branches (from Gd to Yb), which is bisected by an abrupt drop at Eu ~ Gd. Such biperiodic trend in electronic transition energy originates from a similar trend in the attractive exchange potential (origin for Hund’s rule) felt by the 4f electrons transiting up to 5d6s orbitals. This also explains the biperiodic trends in ionization potentials of Ln atoms mentioned above. From the viewpoint of orbital chemistry^{29}, a lower 4f–5d6s transition energy will lead to an easier 4f–5d6s hybridization on an Ln atom, which can facilitate the stronger interatomic bonding of delocalized Ln5d6s orbitals with surrounding atoms, e.g., the Ln–Ln bonding in Ln metals, Ln–F bonding in LnF_{3}, and Ln–S bonding in LnMoS_{2}. Therefore, the biperiodic trends in intraatomic orbital hybridization and interatomic bonding can give out a unifying explanation for all the biperiodic trends in dopant stability of LnMoS_{2} (Fig. 1c), sublimation heat of Ln metals (Fig. S5a), and homolytic Ln–F bond energy of LnF_{3} (Fig. S6). For both La and Lu residing at the periodictablerow ends, there exists a reverse 5d6s–4f electron transfer in LaMoS_{2}, resulting in the decreased bonding 5d6s electrons and then the upshifted E_{f} (i.e., weakened dopant stability), while the increased number of 5d6s electrons in LuMoS_{2} leads to the lowered E_{f} (i.e., strengthened dopant stability).
The Ln–S bonding strength as reflected by E_{f} will closely correlate with many thermodynamic and kinetic quantities for the surface reactivity of LnMoS_{2}, because the bonding between an exterior adsorbate with an active S site is preceded by the endothermic partial breaking of the nearby Ln–S bonds. To clearly understand such interatomic bonding mechanism, the differential electron densities (Δρ) induced by interatomic bonding are calculated for pristine MoS_{2} and LnMoS_{2}, from which the radial distributions (Δρ_{r}, by Eq. (2) in the “Methods” section) around the dopant site are further derived. The calculated Δρ_{r} curves for all the 15 LnMoS_{2} systems are individually shown in Fig. S8 and summarized in Fig. 1d, where two common characters are prominent: (1) the accumulation of 4f electrons at r ~ 0.7 Å (i.e., Δρ_{r} > 0) implying the 4f–5d6s orbital hybridization and (2) the accumulated interatomicbonding electrons at r ~ 2.0 Å originating from the bonding between delocalized Ln5d6s orbitals and neighboring S3sp orbitals. The bonding electrons in the Ln–S bond of LnMoS_{2} are closer to the S atom (by ~0.2 Å) than those in the Mo–S bond of pristine MoS_{2}, indicating the higher ionicity of Ln–S bond, and more electrons transferred out of the cation site after Ln doping. This can also be proved by the charge state of S atom (Fig. S9) and will be favored by the adsorption of ORR intermediates on S atom. It can be derived that an easier 4f–5d6s orbital hybridization on a Ln dopant will lead to more sufficient interatomic 5d6s–3sp bonding and then more Ln–S electron transfer, which explains the simultaneous biperiodic chemical trends in both E_{f} and \({q}_{{{{{{{{\rm{Ln}}}}}}}}}\) (Fig. 1c). The above indepth orbital analysis is consistent with the qualitative expectation from electronegativity values (Ln 1.00 ~ 1.25, Mo 2.15, and S 2.58)^{24}, and the dopant–matrix electron transfer decreases the surface potential from 1.58 V down to 1.25–1.39 V with respect to the standard hydrogen electrode (SHE, see more details in the “Methods” section) after Ln doping, closer to the ORR equilibrium potential of 1.23 V (Fig. 1e). It is also the similarity in Ln–S bonding character for all of the LnMoS_{2} systems that allows us to select Ce and SmMoS_{2} as representatives in the following to analyze many calculated properties and mechanisms.
Water effects for adsorbate stability
An ORR process mainly consists of the adsorptions and transitions of O_{2}, O, OH, and OOH intermediates (see section D in SI for more details), which can be understood by calculating their adsorption free energies (ΔG_{ads}, see sections E and F in SI for detailed formula). Since ORR occurs at the solid/liquid interface, it is desired to accurately understand the effect of the water environment, and the dynamically accessible structures of H_{2}O molecules on MoS_{2} should require sufficient statistical samplings (see the “Methods” section). This is especially necessary for the relatively weak (loose) MoS_{2}/water interface, as shown by a representative LnMoS_{2}/water interface in Figs. 2a and S10 (section G in SI), and the distance between water film and LnMoS_{2} surface is around 2.1 Å (see Fig. S11 for detailed statistical analysis). Eighteen water structures are sampled from the moleculardynamics simulations of 45,000 steps (0.5 fs/step), and many sampled atomic structures for LnMoS_{2}/water interfaces with and without adsorbates are shown in Figs. S12 and S13. Generally speaking, the water effect mainly includes three aspects: (1) setting up an electric field by forming the electrical double layer, (2) forming hydrogen bonds with the polar adsorbate and surface, and (3) bringing the endothermic reorientation process during a reaction. According to the classical doublelayer theory^{30}, the electric field at a solid/water interface is about 10^{9} V/m, which changes the ΔG_{ads}s only by ≲ 0.02 eV here (Fig. S14). On the representative CeMoS_{2} surface, it can be seen that the statistical fluctuations in ΔG_{ads}s (Figs. 2b and S15) have been well captured by the samplings here, which allows us to implement the Weibulldistribution analyses on the ΔG_{ads} data (Figs. 2c and S16). Then, the maximumprobability ΔG_{ads} for each kind of adsorbate is located and used as the statistically average ΔG_{ads}, and the effect of interfacial hydrogen bonds can be revealed by comparing the average ΔG_{ads}s with and without water film.
On CeMoS_{2} surface, the ΔG_{ads}s of OH and OOH (Figs. 2b and S15) are decreased by 0.29 and 0.14 eV, respectively, due to the existence of water film, where the stabilizing interfacial hydrogen bonding should have competed over the endothermic water reorientation. However, the ΔG_{ads}s of less polar O and nonpolar O_{2} are increased by 0.1 and 0.2 eV, respectively, due to the dominating effect of water reorientation. The changes in ΔG_{ads} (ΔΔG_{ads}) caused by the water effect for O, OH, and OOH under different water structures are plotted against the corresponding hydrogenbond length (d_{Hbond}) in Fig. 2d, where a nearlogarithmic relationship shows up. The strong interfacial hydrogen bonds on adsorbed OH and OOH (labeled as OH^{*} and OOH^{*}) result in the short d_{Hbond}s and the sharp decrease of ΔΔG_{ads} with decreasing d_{Hbond}, while the weak hydrogen bonds on O^{*} in the longer d_{H−bond}s and a flat variation of ΔΔG_{ads}. The contribution of water reorientation can be uncovered by comparing the ΔG_{ads} values with a water film and a single H_{2}O molecule (Figs. 2b and S15), where the waterreorientation effect is absent in the later situation. The waterreorientation effect for O^{*}, OH^{*}, O\({}_{2}^{*}\), and OOH^{*} on CeMoS_{2} are calculated to be 0.17, 0.16, 0.17, and 0.25 eV, respectively, which are the same for other similar LnMoS_{2}/water interfaces but are lower than those (0.22 ~ 0.28 eV) for Pt(111) surface with a stronger binding with water^{31,32}.
Enhancement and biperiodic trends in surface adsorption
The ΔG_{ads}s of O, OH, OOH, and O_{2} on all the 15 kinds of LnMoS_{2} surfaces underwater film are shown in Fig. 2e, f, where the simultaneous biperiodic chemical trends can be observed in the ΔG_{ads}s for O, OH, and OOH that form covalent bonds with the substrate S atom. These biperiodic chemical trends in ΔG_{ads} are almost opposite to that in E_{f} (Fig. 1c) because a weaker Ln–S bond (higher in E_{f}) is always easier to be perturbed by an exterior adsorbate (lower in ΔG_{ads}). There are also welldefined linear relationships between the ΔG_{ads}s of O, OH, and OOH (Fig. S17) because their adsorption stabilities rely on the S–O covalent bonding and then are tuned by the Ln dopant at the same pace. The biperiodic trend is absent in ΔG_{ads}(O_{2}) that is determined by a weak electrostatic attraction between the adsorbate and surface, but such weak adsorption is still stronger than that on pristine MoS_{2} by 0.03–0.13 eV (see section H in SI, Fig. S18).
The individual effects of Ln doping and water environment on the stability of any ORR intermediate can be sequentially disentangled by comparing the ΔG_{ads}s at different surface states, i.e., pristine MoS_{2} in a vacuum, LnMoS_{2} in a vacuum, and LnMoS_{2} with water (Fig. 2g). All the 15 LnMoS_{2} surfaces are averaged for each data point in Fig. 2g to reveal the general effects of Ln doping and water environment, and these two effects for different adsorbates on all kinds of LnMoS_{2} surfaces are shown in Fig. S19. The ΔG_{ads}s of O_{2} and O is only decreased by 0.07 and 0.12 eV after Ln doping, respectively, and OOH^{*} by a moderate magnitude of 0.35 eV. However, an exceptionally large decrease of 1.31 eV is observed in ΔG_{ads}(OH), associated with an obvious shortening in S–O bond by 0.16 Å (Fig. S20). It is regularly expected that different ORR intermediates may be stabilized by a similar energy magnitude, due to their common dependence on the surface reactivity^{33}. Thus, it is somewhat counterintuitive to observe such large stabilizing effect of Ln doping selectively on OH^{*}, for which the electronicstructure analysis below will reveal a special defectstate pairing mechanism. It is the weak OH^{*} on pristine MoS_{2} that usually acts as the ORRrate bottleneck^{16}, and Nørskov et al.^{33,34} have also proposed that an ideal ORR catalyst can be realized when ΔG_{ads}(OH) is higher than that of Pt(111) by 0–0.2 eV. The ΔG_{ads}(OH)s for many LnMoS_{2} surfaces (Ln = La, Pm, Sm, Eu, Gd, Er, Tm, Yb, Lu) exactly reside within this favored energy region (see Fig. S21).
To understand the selective and large enhancement on ΔG_{ads}(OH) by Ln dopant, the projected density of states (pDOS) of S atom before and after adsorption, as well as the crystal orbital Hamilton population (pCOHP) spectra^{35,36} for the S–O bonds on adsorbed surfaces, are calculated. The pDOS and pCOHP spectra for both pristine MoS_{2} and SmMoS_{2} surfaces (clean or adsorbed with O^{*}/OH^{*}) are compared in Fig. 2h and i to reveal the underlying electronicstructure mechanism, and the spectra of other LnMoS_{2} surfaces have the same characters as those of SmMoS_{2} surfaces (see Figs. S22 and S23). It can be seen that the adsorbate–S bonding increases the bonding states (–pCOHP > 0) at the valenceband edges (−7.5 ~ −5.0 eV), and the electronic states will progressively convert into the antibonding type (–pCOHP < 0) around −5.0 and −2.3 eV for OH^{*} and O^{*}, respectively. Comparing the pDOS and –pCOHP spectra for MoS_{2}, LnMoS_{2}, and OH@MoS_{2}, it can be seen that both Ln doping and OH adsorption will create localized antibonding defect states around the Fermi level. The selectively and largely enhanced adsorption of OH (with a single dangling bond) can be ascribed to the effective pairing between these two kinds of defect states. For the surfaces with chemically adsorbed OOH (with a single dangling bond), the pDOS spectra present the same characters as those of OH (Fig. S22) due to the same defectstate pairing mechanism. It should be noted that the decrease in ΔG_{ads} by Ln doping is less for OOH than OH (Fig. 2g) because the physical adsorption state of OOH (see Fig. S20) is more stable than its chemical state on pristine MoS_{2}, and then instead is used here to yield a dopant effect smaller than that of OH. In contrast, the adsorption of O (with double dangling bonds) does not create such an unpaired defect state on pristine MoS_{2}, thus the defectstate pairing mechanism is absent here. The adsorption strength can be also reflected by the integrated –pCOHP for the occupied valence states, and the obtained values for the S–O bonds in OH@MoS_{2} and OH@LnMoS_{2} are 5.0 and 7.1–7.3 eV, respectively, but both ~10.7 eV in O@MoS_{2} and O@LnMoS_{2}. This quantitatively proves the defectstate pairing mechanism for the selective and large enhancement of OH^{*} above, which can provide a precise chemical approach for the atomistic design of electrocatalysts in the future.
Thermodynamic rationale for ORR activity
ORR mainly has two possible pathways, i.e., the O_{2}dissociative and the OOHassociative ones (see section D in SI for a detailed description). On LnMoS_{2}, the dissociation of O\({}_{2}^{*}\) requires a quite high activation energy of ~1.4 eV and is difficult to overcome at room temperature. However, the associative transition of O\({}_{2}^{*}\) into OOH^{*} only needs an activation energy of ~0.2 eV, because there exists the preferred attraction between a hydronium ion and the negatively charged O\({}_{2}^{*}\) (see Fig. S24). Similar mechanism has been also found on Ndoped graphene, an excellent ORR catalyst realized in experiment^{37}. It is indispensable to have a conductive surface to freely exchange electrons during an ORR process. As seen from the pDOSs of LnMoS_{2} (Figs. 2h and S22), the defect states at the Fermi level brought by Ln doping indeed will result in the ptype conductivity of MoS_{2}, which is consistent with a recent experimental result from fieldeffect measurement on SmMoS_{2}^{11}. In addition, the electron transfer from Ln dopant onto MoS_{2} matrix and the lowered surface potential as revealed above (Fig. 1e) can promote more electrons transferred onto O\({}_{2}^{*}\) and then contribute to the enhanced ORR.
The ORR reactivity along the preferred association pathway can be well indicated by the corresponding free energy diagram (FED) at the ORR equilibrium potential of 1.23 V (see section E in SI for calculation formula)^{38}. The reversible hydrogen electrode (RHE) is used as the default potential reference in this work unless otherwise specified. In a FED at 1.23 V, the freeenergy change associated with each step is defined as ΔG, and the electroninvolved step with the maximumΔG is the potentiallimiting step for the whole ORR process. Below the corresponding limiting potential (\({U}_{{{{{{{{\rm{limit}}}}}}}}}=1.23\frac{\Delta {{{{G}}}}_{\max }}{e}\)), all ORR steps are exothermic. The FEDs for both pristine MoS_{2} and SmMoS_{2} are shown in Fig. 3a, and the FED profiles and potentiallimiting steps for other LnMoS_{2} surfaces are all the same as those of the representative SmMoS_{2} surface (see section I in SI, Fig. S25). For the ORR on pristine MoS_{2} in vacuum (i.e., neglecting water effect), the potentiallimiting step is the protonation of O^{*} into OH^{*} with a very high ΔG of 1.99 eV. After Sm doping, the largely stabilized OH^{*} leads to the considerably lowered ΔG down to 0.75 eV for this O^{*} → OH^{*} step. Then, the \({{{{{{{{\rm{O}}}}}}}}}_{2}^{*}\to {{{{{{{{\rm{OOH}}}}}}}}}^{*}\) step with a higher ΔG of 0.98 eV becomes the potentiallimiting step. When the water effect is considered, the ΔGs of these two steps on SmMoS_{2} will further drop down to 0.39 and 0.70 eV, respectively, due to the stabilizing effect of interfacial hydrogen bondings on OH^{*} and OOH^{*}. The U_{limit}s for all the 15 LnMoS_{2} surfaces underwater are shown in Fig. 3b, where it can be seen that the magnitude is modulated between 0.31 and 0.54 V by a biperiodic chemical trend, and is almost inverse to the trend in ΔG_{ads}(OOH) (Fig. 2f). These U_{limit}s are a little lower than that of Pt (0.78 V)^{38} and close to those of MoS_{2} edges (~0.57 V)^{16,17}. In addition, although the possible byproduct H_{2}O_{2} often has a negative impact on ORR performance, we find it difficult to be produced on LnMoS_{2}, because the endothermic OOH^{*} → H_{2}O_{2} step (ΔG ~ 0.56 eV) cannot compete with the exothermic OOH^{*} → O^{*} step (ΔG ~ −1.69 eV).
The surface Pourbaix diagram (see section J in SI for calculation formula)^{4,39} can be used to reveal the electrochemical stability of LnMoS_{2} surface state. The diagram and associated chemical potentials (μ) for the representative SmMoS_{2} surface are shown in Fig. 3c, d, and the similar electrochemical results for all the 15 LnMoS_{2} surfaces are summarized in Figs. S26–S28. In addition, the possible release of H_{2}S from defective sites of MoS_{2}^{40} is also considered in our electrochemical simulation here, where an active S atom (bonding with the Ln dopant) is extracted out to form an H_{2}S molecule, leaving an S vacancy (V_{S}) behind. From the persistent large positive μ(H_{2}S + V_{S})s for all LnMoS_{2} surfaces at 0 ~ 1.23 V_{RHE} (Figs. 3d and S27), it is clear that the active S atoms are very stable against the formation of H_{2}S. It is interesting to observe that μ(H_{2}S + V_{S}) also has a biperiodic chemical trend (Fig. S29) reverse to that of E_{f} (Fig. 1c) because the weaker an Ln–S bond is (higher in E_{f}), the less energy cost to form H_{2}S. According to the surface Pourbaix diagrams, any adsorbate is metastable at a potential around U_{limit} and then will not remain for too long time on the surface during an ORR process, and O^{*} will only become stable at potential >0.88 V (RHE). If two of the three active S sites are occupied by O^{*}, there will be an interadsorbate repulsion of 0.07 eV, making the doubleO^{*} configuration less stable than single O^{*}. Therefore, the LnMoS_{2} surfaces will be stably preserved during the ORR process, and it is valid to consider the single adsorbate as the ORR reactant here.
Polarizationcurve simulations for ORR
A thermodynamic model may underestimate the ORR activity, because it only yields the active condition with all the involved steps being exothermic. However, some endothermic reaction steps can be kinetically overcome in realistic conditions (e.g., at room temperature), and it actually is the kinetic activity that is directly associated with many experimental measurements, e.g., current–potential polarization curves. For example, the singleFeatom catalyst on Ndoped graphene may be predicted to be ORR inactive according to its low U_{limit} (0.25–0.43 V), however, the measured/simulated polarization curves clearly reveal its high ORR activity comparable with the standard Pt(111) surface possessing a high U_{limit} at 0.79 V^{41,42}. Furthermore, in many previous theoretical simulations of different material surfaces, certain simplified water configurations are frequently used^{41} or the kinetic barriers for ORR steps on Pt(111) are simply borrowed^{42}. However, the above analysis of water effects and the following kinetic results can show that it is highly desired to use the appropriate watermolecular structure for the LnMoS_{2}/water interface (with a loose morphology and a specific chemical character) into the simulation of kinetic processes. To accurately understand the ORR activity and guide future related experiments, microkinetic simulations for the multiplestep ORR processes on LnMoS_{2} surfaces are carried out here to obtain the potentialdependent current densities ( j)^{34,41}. The activation energy (E_{a}) of each ORR step is first calculated to derive its reaction rate constant, and then the obtained rate constants of all the steps are used to solve the simultaneous reaction equations for the ORR on a rotating disk electrode (RDE)^{31}. More theoretical details are given in the METHODS section below and the section K in SI.
The E_{a}s for various ORR steps on representative SmMoS_{2} surface with three different water configurations (labeled as R25, H20, and R45) are shown in Fig. 4a, and the corresponding atomicstructure evolutions for these steps are shown in Fig. S30. The adsorption process of a O_{2} molecule in the double layer, i.e., O_{2}(dl) → O\({}_{2}^{*}\), is proved to be not the ratelimiting step (see Fig. S31 and the description above it) and its atomicstructure evolution is not shown here. It can be seen from Fig. 4a that the two dissociative steps of O\({}_{2}^{*}\to\) 2O^{*} and OOH^{*} → O^{*} + OH^{*} have E_{a}s (about 1.4 and 0.5 eV) much higher than those of the competing associative steps of O\({}_{2}^{*}\to\) OOH^{*} and OOH^{*} → O^{*} + H_{2}O (about 0.2 and 0.03 eV), respectively. Then, the reaction rates of the former two dissociative steps at room temperature will be lower than their counterpart associative steps by ≳ 10^{7} times and can be excluded from the possible ORR pathway. The H20 water configuration is chosen to carry out the kinetic calculations for six more LnMoS_{2} systems (Ln = La, Ce, Pr, Dy, Yb, Lu) due to the medium E_{a} values yielded for SmMoS_{2} (Fig. 4a). As shown in Figs. 4b and S32, S33, on these LnMoS_{2} surfaces, the obtained E_{a}s for the O^{*} → OH^{*} step almost keep constant (~0.12 eV); the OOH^{*} → O^{*} + H_{2}O step has very low E_{a}s of ~ 0.03 eV; for the \({{{{{{{{\rm{O}}}}}}}}}_{2}^{*}\to {{{{{{{{\rm{OOH}}}}}}}}}^{*}\) and OH^{*} → H_{2}O steps, their E_{a}s have the linear Brønsted–Evans–Polanyi relationships^{31} with their reaction energies (ΔE). These observed data tendencies are used to estimate the E_{a}s for the remaining eight LnMoS_{2} systems, which can speed up the kinetic simulations here with the numerical accuracy safely guaranteed.
The simulated j–U polarization curves for different LnMoS_{2} surfaces at 25 °C and a typical RDE rotation speed (1600 rpm) are shown in Fig. 4c, where the curves indistinguishable from each other are merged together. More details for each j–U curve, the derived onset potentials (U_{onset}), adsorbate coverages, the effect of RDE rotation speed (from 900 to 3200 rpm), and thermal effect (from 25 to 60 °C) can be found in Figs. S34–S38. The available experimental j–U curves for porous MoS_{2}, OMoS_{2}, and PMoS_{2}^{43,44} are also shown in Fig. 4c, and their similar potential dependence as those for LnMoS_{2} surfaces can validate the microkinetic simulations here. As an effective kinetic indicator for ORR activity, the halfwave potential (U_{half}) tells the potential at which j reaches half of its maximum value (i.e., the diffusionlimited value). The calculated U_{half}s for LnMoS_{2} surfaces (Fig. 4d) exhibit a similar biperiodic chemical trend as that in U_{limit} (Fig. 3b) and are close to or even higher than those of Pt(111), OMoS_{2}, and PMoS_{2}^{31,43,44}, indicating the superior ORR activity of LnMoS_{2} surfaces. Furthermore, as another similar kinetic indicator, the derived U_{onset}s (Fig. S35) exhibit the same biperiodic trend and can also effectively reveal high ORR activity. The U_{onset}s are higher than the U_{limit}s by ~0.45 V, quantitatively indicating how far the kinetic activity is away from the thermodynamic threshold.
To fully understand the microkinetic mechanisms underlying the polarization curves, the degree of kinetic rate control (X_{RC}, see Eq. (6) in the “Methods” section)^{45} is used to reveal the sensitivity of total ORR rate (r_{tot}) to the rateconstant change of each step. The X_{RC} curves for the representative SmMoS_{2} surface are shown in Fig. 4e, where the dominating role of O_{2} diffusion is replaced by the \({{{{{{{{\rm{O}}}}}}}}}_{2}^{*}\to {{{{{{{{\rm{OOH}}}}}}}}}^{*}\) and OOH^{*} → O^{*} steps at U > 0.9 V. Therefore, it is the fast forward transition through OOH^{*} (a product in the potentiallimiting step, Fig. 3a) that determines the ORR rate here. The OOH^{*} → O^{*} step (E_{a} ≲ 0.03 eV) is almost spontaneous at room temperature, thus it actually is the \({{{{{{{{\rm{O}}}}}}}}}_{2}^{*}\to {{{{{{{{\rm{OOH}}}}}}}}}^{*}\) step with a secondary X_{RC} value at U = U_{half} that brings the biperiodic Lntype dependence of ORR activity, and then it is the biperiodic chemical trend in ΔG_{ads}(OOH) (Fig. 2f) that leads to the opposite trends in U_{half} and U_{onset}. The simulated curves for surfacestate coverages (θ, in Figs. 4f and S36), are consistent with the aforementioned surface Pourbaix diagram (Fig. 3c), e.g., O^{*} only becomes stable on the surface above 0.88 V and other metastable (kinetically important) intermediates have very low θs (<0.1).
Volcano plot for ORR activity
Electrochemical reactivity is often understood and predicted by using the volcano plot^{33}, which well indicates that both too strong and too weak surface adsorptions will make ORR difficult to happen. Using the linear relationships between ΔG_{ads}s of different ORR intermediates and the E_{a}–ΔE relationships discussed above, the analytical variation of j within a given range of ΔG_{ads}(OH) can be simulated, yielding the volcano curve as shown in Fig. 5a (red curve). The prototypical Pt(111) is considered as the reference surface in the volcano plot for setting the electrode potential (0.9 V, the U_{onset} of Pt(111)), positioning the reference ΔG_{ads}(OH) at 0.8 eV, and normalizing the j values (j_{Pt} = 1.2 mA/cm^{2})^{31,34}. The j–ΔG_{ads}(OH) data for various noblemetal surfaces are also collected from literature for comparison in Fig. 5a, and their numerical data are listed in Table S3. According to the volcanotype curve, the highest j can be obtained on a surface having a ΔG_{ads}(OH) higher than that of Pt(111) by 0.0–0.2 eV, quantitatively consistent with the previous claim for metal surfaces^{31,33,34}. Nine kinds of LnMoS_{2} surfaces (Ln = La, Pm, Sm, Eu, Gd, Er, Tm, Yb, Lu) indeed reside in this optimal region with high js (1.2–2.7 mA/cm^{2}), and the other six kinds of surfaces (Ln = Ce, Pr, Nd, Tb, Dy, Ho) in the nearby region (relative ΔG_{ads}(OH) at 0.2–0.3 eV) have moderate js (0.03–0.6 mA/cm^{2}). The biperiodic chemical trend in j can show up when plotted in terms of Ln type (Fig. 5b), which is in accordance with the biperiodic trends in other ORRactivity indicators, e.g., U_{limit} (Fig. 3b), U_{half} (Fig. 4d), and U_{onset} (Fig. S35), but opposite to the biperiodic trends in ΔG_{ads}s (Fig. 2e and f).
To reveal the microkinetic mechanisms underlying the volcano plot, we calculate the X_{RC} curves in terms of ΔG_{ads}(OH) (Fig. 5c), as well as the curves for thermodynamic rate control (X_{TRC}, Eq. (7) in the “Methods” section)^{46} to measure the sensitivity of r_{tot} to the freeenergy change of any surface state (Fig. 5d). A positive (negative) X_{TRC} indicates that the increase in r_{tot} needs to further stabilize (destabilize) the corresponding surface state. On the strongadsorption side of the volcano plot (relative ΔG_{ads}(OH) < 0.0 eV), the negative X_{TRC}s of OH^{*} and O^{*} indicate that their destabilization can lead to the increase in r_{tot}, while X_{RC} is mainly dominated by the O_{2} adsorption, because the more O atoms the surface captures, the faster a forward ORR reaction proceeds through the strong adsorbates (OH^{*} and O^{*}). On the weakadsorption side (relative ΔG_{ads}(OH) > 0.2 eV), the largely positive X_{TRC} of OOH^{*} indicates that it still needs to be stabilized for the increase in r_{tot}. This is the reason why the six LnMoS_{2} surfaces (Ln = Ce, Pr, Nd, Tb, Dy, Ho) with the highest ΔG_{ads}s have the lowest js. In the optimal region (relative ΔG_{ads}(OH) at 0.0–0.2 eV), r_{tot} is mainly determined by the O_{2} diffusion in water and becomes almost surfacechemistry independent. This is the reason why various materials (e.g., doped MoS_{2} and noble metals) with dramatically different chemical characters have very close j values at the volcano top.
Summary remarks for this study
In summary, we have carried out DFT calculations and polarization curve simulations for the ORR process on all the 15 LnMoS_{2} surfaces. We not only have found the considerably enhanced ORR activity of MoS_{2} surface induced by Ln doping, but also have identified a modulating biperiodic chemical trend in ORR activity with respect to Ln type. Many simultaneous biperiodic chemical trends have also been observed in various electronic structures, thermodynamic, and kinetic quantities, e.g., dopant stability, dopant charge state, ORRintermediate adsorption strength, free energies of reaction for ORR intermediates (and U_{limit}), characteristic potentials for polarization curve (U_{half} and U_{onset}), and current density. Based on the electronicstructure analysis, we find that the high ORR activity on LnMoS_{2} originates from a defectstate pairing mechanism that selectively strengthens the hydroxyl and hydroperoxyl adsorptions, and the simultaneous biperiodic chemical trends originate from the similar biperiodic trends in intraatomic 4f–5d6s orbital hybridization on Ln dopant and interatomic Ln–S bonding. These analysis results also allow us to establish a generic orbitalchemistry mechanism that can closely correlate those simultaneous biperiodic trends in different properties. The ORR behaviors and key fundamental mechanisms revealed on LnMoS_{2} can well guide more investigation and design of related material systems for many technologically important applications, e.g., electrocatalysts, optoelectronic nanodevices, and lubricating coatings.
Methods
DFT parameters and formula
DFT calculations are carried out using the VASP code package^{47}, where the ionic potential is described by the projector augmentedwave method^{48}. The electronic exchangecorrelation potential is expressed by the spinpolarized PBE functional in the generalizedgradient approximation (GGA)^{49}, and the dispersive van de Waals force is described using the zerodamping DFTD3 functional^{50}. The valence configurations in the used Mo, S, O, and H pseudopotentials are 4d^{5}5s^{1}5p^{0}4f^{0}, 3s^{2}3p^{4}3d^{0}, 2s^{2}2p^{4}3d^{0}, and 1s^{1}2p^{0}, respectively, and those in the Ln pseudopotentials include 5s, 6s, 5p, 5d, and 4f orbitals. The planewave cutoff energy is set to 450 eV, and the convergence thresholds for atomic force and electronic energy are 0.01 eV/Å and 10^{−5} eV, respectively. A periodic \(4\times 2\sqrt{3}\) rectangular supercell of MoS_{2} layer (12.61 × 10.92 Å^{2}) with an interlayer vacuum spacing of 20 Å is constructed as the structural model, and its Brillouin zone is spanned by a reciprocalpoint grid of 2 × 2 × 1.
Reaction paths and activation energies are calculated using the climbingimage nudged elastic band (CINEB) method^{51} with a force convergence threshold of 0.05 eV/Å. The protonation rate of a surface adsorbate is limited by the reaction at water/MoS_{2} interface because a proton can quickly reach the electrical double layer due to its very low diffusion barrier in water (0.07–0.11 eV^{52}). To model this ratelimiting interfacial step, an H atom is placed on a water molecule nearby the adsorbate to form an H_{3}O unit, and the relaxed structural model is used as the initial state for the CINEB path (see Fig. S30). Crystal orbital Hamilton population analysis as implemented in the LOBSTER code package^{35,36} is used to study the bonding and antibonding characters of atomic bonds, and atomic charges are calculated using Bader charge analysis^{53}. The effect of electronic selfinteraction problem intrinsic in the GGA functional for Ln atoms is tested by using the GGA plus HubbardU_{eff} method^{54}, and found negligible for surface adsorption on S atom (see Table S4 in SI for details). More testing calculations on the spin–orbit coupling effect, cutoff energy, reciprocalpoint mesh, supercell size, and magnetic configurations are also comprehensively carried out (see section L of SI), which further stringently validate the structural model and computational parameters considered in this work.
The formation energy (E_{f}) of an Ln dopant in MoS_{2} is defined as the energy change associated with the filling of a Mo vacancy by a free Ln atom, which is expressed as
where ε_{d} and ε_{0} are the total electronic energies of LnMoS_{2} and MoS_{2} with a Mo vacancy, respectively, and \({\mu }_{{{{{{{{\rm{Ln}}}}}}}}}\) is the electronic energy of an isolated Ln atom. With such a definition, the obtained magnitude in E_{f} will have a direct correlation with the interatomic bonding strength in LnMoS_{2}, which is highly useful for exploring the orbitalchemistry mechanism in both dopant stability and surface reactivity here.
The radial electron density distribution (Δρ_{r})^{55} is calculated by
where Δρ_{r}(r) is the average electron density on a spherical surface with radius of r; \(\tilde{{{{{{{{\bf{r}}}}}}}}}\) is the position vector with length of r, and \(\Delta \rho (\tilde{{{{{{{{\bf{r}}}}}}}}})\) is the bulk electron density at \(\tilde{{{{{{{{\bf{r}}}}}}}}}\) point; σ is the sphericalsurface area.
The surface potential shown in Fig. 1e is calculated by referring the surface work function (Φ) to that of the SHE (Φ_{SHE}), which is expressed as
where Φ_{SHE} is measured to be 4.44 eV in experiment^{56}.
Waterstructure statistical sampling
MoS_{2} will form a relatively weak interface with water, thus the interfacial H_{2}O structure should have a high degree of dynamical disorder, which requires sufficient statistical samplings to accurately obtain the average water effect. This is different from some metals (e.g., Pt) that can form quite strong metalwater interfaces, leading to some stable ordered interfacial water configurations^{57}. We exploit the abinitio molecular dynamics (AIMD) method to simulate such a dynamically disordered H_{2}O environment on LnMoS_{2}, where a thick enough water film with 32 H_{2}O molecules (thickness ~ 7 Å) is considered. It is thicker than that of the electrical double layer at the solidwater interface (~3 Å^{38}). Two kinds of seed water structures are provided to initialize two threads of MD simulations: (1) the H atoms in H_{2}O molecules at the interface pointing to the surface S atom (labeled as “H water”), and (2) the interfacial H_{2}O molecules randomly oriented (labeled as “R water”). The weak interfacial interaction can be well proved by the relatively large interface distance (about 2.1 Å) in the simulated structures (Fig. S11). The Nosé–Hoover thermostat^{58} is used in the AIMD simulations at 300 K for 45,000 steps (0.5 fs/step). There is no structural damage on the LnMoS_{2} substrates during the AIMD simulations, indicating the preferred dynamical stability of doped structures. We sample the simulated LnMoS_{2}/water structures every 5000 steps and label them as H05, H10, …, and H45 (R05, R10, …, and R45) for the Hwater (Rwater) group, for which the atomic structures are shown in Fig. S12. The calculated electrostatic potentials along the normal direction of the LnMoS_{2}/water structures also clearly exhibit a twolayered morphology (Fig. S10) that is wellknown as a typical solvent character on solid surfaces^{59}.
Microkinetic modeling
The simultaneous rate equations for an ORR process can be briefly summarized as
where n indexes the species, and r_{i} is the reaction rate of an elementary ORR step (i) involving the species n; ν_{ni} is the stoichiometric coefficient of species n in step i, where ν_{ni} is positive (negative) if the species n is a product (reactant); θ_{R} and θ_{P} represent the coverages of involved reactants and products in step i, respectively; and k_{i} and k_{−i} are the forward and reverse rate constants of step i, respectively. Together with some necessary constraints (e.g., the conservation of total state number), the set of simultaneous rate equations can be solved at the steady state, which is described in detail in SI (section K). The turnover frequency of O_{2} (\({{{{{{{{\rm{TOF}}}}}}}}}_{{{{{{{{{\rm{O}}}}}}}}}_{2}}\)) equals the total net reaction rate (r_{tot}), and is used to derive the current density (j) by
where 4 is the number of transferred electrons, and ρ is the surface density of active sites.
The sensitivities of r_{tot} to the rateconstant change of each step (e.g., k_{i}) and the freeenergy change of each species (e.g., \({G}_{n}^{0}\)) can be revealed by the degree of kinetic rate control (X_{RC}) and thermodynamic rate control (X_{TRC}), respectively, defined as^{45,46}
and
where K_{i} is the equilibrium constant of step i; k_{B} is the Boltzmann constant; and a small variation of 1.0% in both k_{i} and \({G}_{n}^{0}\) is used for the calculations of partial derivatives.
Data availability
The data supporting all the conclusions of this study are available in the paper and Supplementary Information. Source data are provided with this paper. Additional data related to this study may be requested from the corresponding authors. Source data are provided with this paper.
Code availability
The VASP code package used in this work to carry out the DFT calculations can be accessible after a user license is authorized by the VASP company (https://www.vasp.at).
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Acknowledgements
The authors are sponsored by the National Natural Science Foundation of China (Grant No. U21A20127 and 22272192, L.W. and L.F.H.), the Fund of Science and Technology on Surface Physics and Chemistry Laboratory (Grant No. XKFZ202101, L.F.H.), the National Key Research and Development Project (Grant No. 2022YFB3402803, L.F.H.), and the Natural Science Foundation of Ningbo City (Grant No. 2021J229, L.F.H.). The Supercomputing Center at Ningbo Institute of Materials Technology and Engineering is also acknowledged for providing the computing resources.
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Y.H. and L.F.H. designed and performed the DFT calculations and wrote the draft. All authors analyzed the results and revised the manuscript. L.W. and L.F.H. acquired the research funds and were responsible for supervision.
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Hao, Y., Wang, L. & Huang, LF. Lanthanidedoped MoS_{2} with enhanced oxygen reduction activity and biperiodic chemical trends. Nat Commun 14, 3256 (2023). https://doi.org/10.1038/s41467023391005
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DOI: https://doi.org/10.1038/s41467023391005
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