Introduction

Oxygen reduction reaction (ORR) is an electrochemical process reducing O2 into H2O, which plays significant roles in the fields of clean energy and corrosion1. As the cathode reaction in fuel cells, active enough ORR is required for efficient energy conversion2, and one contemporary urgent task is replacing the noble-metal catalysts (e.g., Pt) with less expensive, sufficiently active, and durable candidate alternatives3. On the other hand, as a cathodic reaction readily occurring in regular oxic humid/aqueous conditions4, 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 galvanic-corrosion phenomena1,5. 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 long-lasting working of many functional nanodevices and coatings in realistic environments.

Earth-abundant molybdenum disulfide (MoS2) is a typical two-dimensional material with great application potential in catalysis, optoelectronic devices, and solid lubrication due to its preferred structural stability, suitable band gap, and easy shearing6,7. Lanthanide-doped MoS2 (Ln-MoS2) recently has emerged as an important group of materials with the electronic and optical properties profoundly tuned by the Ln dopants8,9, and many kinds of Ln-MoS2 systems (e.g., Ln = Sm, Eu, Dy, Ho, Er, and Yb) have been successfully synthesized in experiments10,11,12,13,14,15. Ln dopants can introduce many defect states in the band gap of MoS2, and the degenerate 4f multiplet orbitals of Ln dopants are split by the highly anisotropic local crystal field in MoS2 matrix. These two electronic-structure mechanisms will lead to the photoluminescence emission of MoS2 from the visible range to the near-infrared spectrum, including the telecommunication range at 1.55 μm10,12, as well as to the improved electrical property of Ln-MoS211,15, making Ln-MoS2 promising for optoelectronic materials and nanodevices.

Pristine MoS2 has a quite inert basal plane for ORR catalysis, and only small MoS2 nanoflakes with a considerably increased ratio of active edge sites can exhibit observable ORR activity16,17,18. However, MoS2 edges have low chemical stability and may incur degrading corrosion and oxidization of nanoflakes when exposed to realistic environments19,20, thus large-scale MoS2 flakes should still be preferred for long-lasting performance. Due to the significant tuning effect on the electronic structure of MoS2, 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 Ln-MoS2, the activated ORR processes tend to bring unexpected galvanic-corrosion 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 Ln-MoS2 surfaces, which can not only motivate their future electrocatalytic applications but also guide the appropriate protection against galvanic corrosion for the long-lasting service of advanced nanodevices and coatings.

In this work, by considering all the 15 Ln dopants in MoS2 and combining density-functional theory (DFT) calculations and current-potential polarization curve simulations, we discover the considerably enhanced ORR activity on Ln-MoS2 surfaces with an intriguing modulating biperiodic chemical trend. We first use DFT to calculate the stability of Ln dopants in MoS2, the adsorption stability of various ORR intermediates, and their reaction behaviors at the Ln-MoS2/water interfaces, where the water effect is strictly modeled by statistically sampling the H2O-film configurations. Many closely correlated biperiodic chemical trends are observed in various thermodynamic and kinetic properties, and the unifying electronic-structure mechanisms are revealed by analyzing the intraatomic orbital hybridizations and interatomic bondings of Ln dopants. A defect-state 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 Ln-MoS2. We finally simulate the current-potential polarization curves for ORR processes on Ln-MoS2 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 Ln-dopant configurations in MoS2 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 Ln-MoS2 configuration also exhibit the same mode redshifts as the experimental measurements10,22,23 (see section B in SI). These systematically close theory-experiment agreements strongly validate the atomic-structure model for Ln-MoS2 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 MoS2 can be quantitatively described by its formation energy (Ef), which is defined as the energy change associated with the filling of a Mo vacancy in MoS2 by a free Ln atom (see Eq. (1) in the “Methods” section) and then can directly reflect the atomic-bonding strength therein. The Efs 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 Ln-MoS2. In addition, the calculated phonon densities of states further prove the favorable dynamical stability of all the fifteen Ln-MoS2 systems (see section A in SI).

Fig. 1: The atomic structure, dopant stability, and related electronic-structure analyses for Ln-MoS2.
figure 1

a The atomic-structure model for Ln-MoS2 used in this work and b the STEM image of Er-MoS2 observed in the experiment, as reproduced with permission from ref. 10 (Copyright 2016, John Wiley and Sons). c The Efs and \({q}_{{{{{{{{\rm{Ln}}}}}}}}}{{{{{{{\rm{s}}}}}}}}\) for Ln dopants (inset: the weighted summation of IP3 + 0.2IP4). d The Δρr curves around the doping site (r = 0) for both MoS2 and Ln-MoS2 (inset: the distribution of Δρ(r) in Ce-MoS2, side view), with the positions of S atoms labeled. e The surface potentials for both pristine MoS2 and Ln-MoS2 and the ORR equilibrium potential with respect to the standard hydrogen electrode (inset: the schematics for Ln–S electron transfer). Source data are provided as a Source Data file.

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In the variation of Ef 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 ionic-4f Efs in Fig. 1c), i.e., neglecting the participation of 4f orbitals in any interatomic bonding. From this dramatic difference between the valence-4f and ionic-4f Efs, we can derive that although the 4f orbitals are highly localized (see section C in SI for atomic-orbital wavefunctions), the hybridization between 4f electrons with delocalized 5d and 6s electrons should play a significant role in many physicochemical properties of Ln-MoS2. In addition to the above Efs for Ln dopant in MoS2, the Ln-dopant 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 Ln-metal sublimation heats, Ln-atom ionization potentials (IP), and homolytic bond energies of LnF3 molecules (see section C in SI)24,25. The weighted summation of the 4f-relevant third and fourth ionization potentials (IP3 + 0.2IP4) 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 Efs here and should be governed by a common intrinsic electronic-structure 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 (nv is the valence-electron number) are calculated using the all-electron full-potential method26, 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 Ln-MoS2 (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 4f75d16s2. 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 (4f76s2), 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 under-half-filled (from La to Eu) and over-half-filled 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 chemistry29, 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 Ln-5d6s orbitals with surrounding atoms, e.g., the Ln–Ln bonding in Ln metals, Ln–F bonding in LnF3, and Ln–S bonding in Ln-MoS2. 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 Ln-MoS2 (Fig. 1c), sublimation heat of Ln metals (Fig. S5a), and homolytic Ln–F bond energy of LnF3 (Fig. S6). For both La and Lu residing at the periodic-table-row ends, there exists a reverse 5d6s–4f electron transfer in La-MoS2, resulting in the decreased bonding 5d6s electrons and then the upshifted Ef (i.e., weakened dopant stability), while the increased number of 5d6s electrons in Lu-MoS2 leads to the lowered Ef (i.e., strengthened dopant stability).

The Ln–S bonding strength as reflected by Ef will closely correlate with many thermodynamic and kinetic quantities for the surface reactivity of Ln-MoS2, 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 MoS2 and Ln-MoS2, from which the radial distributions (Δρr, by Eq. (2) in the “Methods” section) around the dopant site are further derived. The calculated Δρr curves for all the 15 Ln-MoS2 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., Δρr > 0) implying the 4f–5d6s orbital hybridization and (2) the accumulated interatomic-bonding electrons at r ~ 2.0 Å originating from the bonding between delocalized Ln-5d6s orbitals and neighboring S-3sp orbitals. The bonding electrons in the Ln–S bond of Ln-MoS2 are closer to the S atom (by ~0.2 Å) than those in the Mo–S bond of pristine MoS2, 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 Ef and \({q}_{{{{{{{{\rm{Ln}}}}}}}}}\) (Fig. 1c). The above in-depth 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 Ln-MoS2 systems that allows us to select Ce- and Sm-MoS2 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 O2, O, OH, and OOH intermediates (see section D in SI for more details), which can be understood by calculating their adsorption free energies (ΔGads, 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 H2O molecules on MoS2 should require sufficient statistical samplings (see the “Methods” section). This is especially necessary for the relatively weak (loose) MoS2/water interface, as shown by a representative Ln-MoS2/water interface in Figs. 2a and S10 (section G in SI), and the distance between water film and Ln-MoS2 surface is around 2.1 Å (see Fig. S11 for detailed statistical analysis). Eighteen water structures are sampled from the molecular-dynamics simulations of 45,000 steps (0.5 fs/step), and many sampled atomic structures for Ln-MoS2/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 double-layer theory30, the electric field at a solid/water interface is about 109 V/m, which changes the ΔGadss only by ≲ 0.02 eV here (Fig. S14). On the representative Ce-MoS2 surface, it can be seen that the statistical fluctuations in ΔGadss (Figs. 2b and S15) have been well captured by the samplings here, which allows us to implement the Weibull-distribution analyses on the ΔGads data (Figs. 2c and S16). Then, the maximum-probability ΔGads for each kind of adsorbate is located and used as the statistically average ΔGads, and the effect of interfacial hydrogen bonds can be revealed by comparing the average ΔGadss with and without water film.

Fig. 2: The structural analysis of the Ln-MoS2/water interface, adsorption-free energies of ORR intermediates, and related electronic-structure analyses.
figure 2

a An example structure for the Ln-MoS2/water interface. b The calculated ΔGadss for OH and O2 on Ce-MoS2 with the statistically sampled water configurations, comparing with the results without water (dashed line) and with a single H2O molecule nearby (dotted line). c The Weibull-distribution analysis for ΔGads(OH) data. d The correlation between ΔΔGads and dH−bond data. e, f The ΔGadss for O, OH, O2, and OOH on Ln-MoS2 surfaces with water. g The average ΔGadss of ORR intermediates on different surfaces. h The pDOS spectra of the active S sites in pristine MoS2 and Sm-MoS2 (with/without O* and OH*) and i the –pCOHP spectra for the S–O bonds after O and OH adsorptions (0 eV: the highest occupied level). Source data are provided as a Source Data file.

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On Ce-MoS2 surface, the ΔGadss 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 ΔGadss of less polar O and nonpolar O2 are increased by 0.1 and 0.2 eV, respectively, due to the dominating effect of water reorientation. The changes in ΔGads (ΔΔGads) caused by the water effect for O, OH, and OOH under different water structures are plotted against the corresponding hydrogen-bond length (dH-bond) in Fig. 2d, where a near-logarithmic relationship shows up. The strong interfacial hydrogen bonds on adsorbed OH and OOH (labeled as OH* and OOH*) result in the short dH-bonds and the sharp decrease of ΔΔGads with decreasing dH-bond, while the weak hydrogen bonds on O* in the longer dH−bonds and a flat variation of ΔΔGads. The contribution of water reorientation can be uncovered by comparing the ΔGads values with a water film and a single H2O molecule (Figs. 2b and S15), where the water-reorientation effect is absent in the later situation. The water-reorientation effect for O*, OH*, O\({}_{2}^{*}\), and OOH* on Ce-MoS2 are calculated to be 0.17, 0.16, 0.17, and 0.25 eV, respectively, which are the same for other similar Ln-MoS2/water interfaces but are lower than those (0.22 ~ 0.28 eV) for Pt(111) surface with a stronger binding with water31,32.

Enhancement and biperiodic trends in surface adsorption

The ΔGadss of O, OH, OOH, and O2 on all the 15 kinds of Ln-MoS2 surfaces underwater film are shown in Fig. 2e, f, where the simultaneous biperiodic chemical trends can be observed in the ΔGadss for O, OH, and OOH that form covalent bonds with the substrate S atom. These biperiodic chemical trends in ΔGads are almost opposite to that in Ef (Fig. 1c) because a weaker Ln–S bond (higher in Ef) is always easier to be perturbed by an exterior adsorbate (lower in ΔGads). There are also well-defined linear relationships between the ΔGadss 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 ΔGads(O2) that is determined by a weak electrostatic attraction between the adsorbate and surface, but such weak adsorption is still stronger than that on pristine MoS2 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 ΔGadss at different surface states, i.e., pristine MoS2 in a vacuum, Ln-MoS2 in a vacuum, and Ln-MoS2 with water (Fig. 2g). All the 15 Ln-MoS2 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 Ln-MoS2 surfaces are shown in Fig. S19. The ΔGadss of O2 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 ΔGads(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 reactivity33. Thus, it is somewhat counterintuitive to observe such large stabilizing effect of Ln doping selectively on OH*, for which the electronic-structure analysis below will reveal a special defect-state pairing mechanism. It is the weak OH* on pristine MoS2 that usually acts as the ORR-rate bottleneck16, and Nørskov et al.33,34 have also proposed that an ideal ORR catalyst can be realized when ΔGads(OH) is higher than that of Pt(111) by 0–0.2 eV. The ΔGads(OH)s for many Ln-MoS2 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 ΔGads(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) spectra35,36 for the S–O bonds on adsorbed surfaces, are calculated. The pDOS and pCOHP spectra for both pristine MoS2 and Sm-MoS2 surfaces (clean or adsorbed with O*/OH*) are compared in Fig. 2h and i to reveal the underlying electronic-structure mechanism, and the spectra of other Ln-MoS2 surfaces have the same characters as those of Sm-MoS2 surfaces (see Figs. S22 and S23). It can be seen that the adsorbate–S bonding increases the bonding states (–pCOHP > 0) at the valence-band 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 MoS2, Ln-MoS2, and OH@MoS2, 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 defect-state pairing mechanism. It should be noted that the decrease in ΔGads 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 MoS2, 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 MoS2, thus the defect-state 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@MoS2 and OH@Ln-MoS2 are 5.0 and 7.1–7.3 eV, respectively, but both ~10.7 eV in O@MoS2 and O@Ln-MoS2. This quantitatively proves the defect-state 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 O2-dissociative and the OOH-associative ones (see section D in SI for a detailed description). On Ln-MoS2, 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 N-doped graphene, an excellent ORR catalyst realized in experiment37. It is indispensable to have a conductive surface to freely exchange electrons during an ORR process. As seen from the pDOSs of Ln-MoS2 (Figs. 2h and S22), the defect states at the Fermi level brought by Ln doping indeed will result in the p-type conductivity of MoS2, which is consistent with a recent experimental result from field-effect measurement on Sm-MoS211. In addition, the electron transfer from Ln dopant onto MoS2 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 free-energy change associated with each step is defined as ΔG, and the electron-involved step with the maximum-ΔG is the potential-limiting 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 MoS2 and Sm-MoS2 are shown in Fig. 3a, and the FED profiles and potential-limiting steps for other Ln-MoS2 surfaces are all the same as those of the representative Sm-MoS2 surface (see section I in SI, Fig. S25). For the ORR on pristine MoS2 in vacuum (i.e., neglecting water effect), the potential-limiting 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 potential-limiting step. When the water effect is considered, the ΔGs of these two steps on Sm-MoS2 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 Ulimits for all the 15 Ln-MoS2 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 ΔGads(OOH) (Fig. 2f). These Ulimits are a little lower than that of Pt (0.78 V)38 and close to those of MoS2 edges (~0.57 V)16,17. In addition, although the possible byproduct H2O2 often has a negative impact on ORR performance, we find it difficult to be produced on Ln-MoS2, because the endothermic OOH* → H2O2 step (ΔG ~ 0.56 eV) cannot compete with the exothermic OOH* → O* step (ΔG ~ −1.69 eV).

Fig. 3: Thermodynamic analyses for the ORR activity and adsorption state of Ln-MoS2 surfaces.
figure 3

a The FEDs (at U = 1.23 V) for the associative ORR pathway on pristine MoS2 (without water) and Sm-MoS2 (with and without water), b the variation of Ulimit with respect to Ln type, and c, d the surface Pourbaix diagram and involved potential-dependent chemical potentials (μ, at pH = 0) on Sm-MoS2. The FEDs, surface Pourbaix diagrams, and μs for other Ln-MoS2 systems can be found in Figs. S25–S27, respectively. Source data are provided as a Source Data file.

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The surface Pourbaix diagram (see section J in SI for calculation formula)4,39 can be used to reveal the electrochemical stability of Ln-MoS2 surface state. The diagram and associated chemical potentials (μ) for the representative Sm-MoS2 surface are shown in Fig. 3c, d, and the similar electrochemical results for all the 15 Ln-MoS2 surfaces are summarized in Figs. S26–S28. In addition, the possible release of H2S from defective sites of MoS240 is also considered in our electrochemical simulation here, where an active S atom (bonding with the Ln dopant) is extracted out to form an H2S molecule, leaving an S vacancy (VS) behind. From the persistent large positive μ(H2S + VS)s for all Ln-MoS2 surfaces at 0 ~ 1.23 VRHE (Figs. 3d and S27), it is clear that the active S atoms are very stable against the formation of H2S. It is interesting to observe that μ(H2S + VS) also has a biperiodic chemical trend (Fig. S29) reverse to that of Ef (Fig. 1c) because the weaker an Ln–S bond is (higher in Ef), the less energy cost to form H2S. According to the surface Pourbaix diagrams, any adsorbate is metastable at a potential around Ulimit 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 inter-adsorbate repulsion of 0.07 eV, making the double-O* configuration less stable than single O*. Therefore, the Ln-MoS2 surfaces will be stably preserved during the ORR process, and it is valid to consider the single adsorbate as the ORR reactant here.

Polarization-curve 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 single-Fe-atom catalyst on N-doped graphene may be predicted to be ORR inactive according to its low Ulimit (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 Ulimit at 0.79 V41,42. Furthermore, in many previous theoretical simulations of different material surfaces, certain simplified water configurations are frequently used41 or the kinetic barriers for ORR steps on Pt(111) are simply borrowed42. However, the above analysis of water effects and the following kinetic results can show that it is highly desired to use the appropriate water-molecular structure for the Ln-MoS2/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 multiple-step ORR processes on Ln-MoS2 surfaces are carried out here to obtain the potential-dependent current densities ( j)34,41. The activation energy (Ea) 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 Eas for various ORR steps on representative Sm-MoS2 surface with three different water configurations (labeled as R-25, H-20, and R-45) are shown in Fig. 4a, and the corresponding atomic-structure evolutions for these steps are shown in Fig. S30. The adsorption process of a O2 molecule in the double layer, i.e., O2(dl) → O\({}_{2}^{*}\), is proved to be not the rate-limiting step (see Fig. S31 and the description above it) and its atomic-structure 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 Eas (about 1.4 and 0.5 eV) much higher than those of the competing associative steps of O\({}_{2}^{*}\to\) OOH* and OOH* → O* + H2O (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 ≳ 107 times and can be excluded from the possible ORR pathway. The H-20 water configuration is chosen to carry out the kinetic calculations for six more Ln-MoS2 systems (Ln = La, Ce, Pr, Dy, Yb, Lu) due to the medium Ea values yielded for Sm-MoS2 (Fig. 4a). As shown in Figs. 4b and S32, S33, on these Ln-MoS2 surfaces, the obtained Eas for the O* → OH* step almost keep constant (~0.12 eV); the OOH* → O* + H2O step has very low Eas of ~ 0.03 eV; for the \({{{{{{{{\rm{O}}}}}}}}}_{2}^{*}\to {{{{{{{{\rm{OOH}}}}}}}}}^{*}\) and OH* → H2O steps, their Eas have the linear Brønsted–Evans–Polanyi relationships31 with their reaction energies (ΔE). These observed data tendencies are used to estimate the Eas for the remaining eight Ln-MoS2 systems, which can speed up the kinetic simulations here with the numerical accuracy safely guaranteed.

Fig. 4: The simulated and analyzed results for polarization curves.
figure 4

a The Eas for various reactions on Sm-MoS2 under three different water configurations and b the linear Ea–ΔE relationship for the \({{{{{{{{\rm{O}}}}}}}}}_{2}^{*}\to {{{{{{{{\rm{OOH}}}}}}}}}^{*}\) step. c, d The simulated polarization curves for Ln-MoS2 surfaces at 25 °C (disc rotation at 1600 rpm) and the derived Uhalfs, and the experimental polarization curves for porous, O-, and P-doped MoS2 samples43, 44 are compared in panel (c). e, f The simulated XRC and coverage curves for Sm-MoS2. Source data are provided as a Source Data file.

Full size image

The simulated j–U polarization curves for different Ln-MoS2 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 (Uonset), 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 MoS2, O-MoS2, and P-MoS243,44 are also shown in Fig. 4c, and their similar potential dependence as those for Ln-MoS2 surfaces can validate the microkinetic simulations here. As an effective kinetic indicator for ORR activity, the half-wave potential (Uhalf) tells the potential at which j reaches half of its maximum value (i.e., the diffusion-limited value). The calculated Uhalfs for Ln-MoS2 surfaces (Fig. 4d) exhibit a similar biperiodic chemical trend as that in Ulimit (Fig. 3b) and are close to or even higher than those of Pt(111), O-MoS2, and P-MoS231,43,44, indicating the superior ORR activity of Ln-MoS2 surfaces. Furthermore, as another similar kinetic indicator, the derived Uonsets (Fig. S35) exhibit the same biperiodic trend and can also effectively reveal high ORR activity. The Uonsets are higher than the Ulimits 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 (XRC, see Eq. (6) in the “Methods” section)45 is used to reveal the sensitivity of total ORR rate (rtot) to the rate-constant change of each step. The XRC curves for the representative Sm-MoS2 surface are shown in Fig. 4e, where the dominating role of O2 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 potential-limiting step, Fig. 3a) that determines the ORR rate here. The OOH* → O* step (Ea ≲ 0.03 eV) is almost spontaneous at room temperature, thus it actually is the \({{{{{{{{\rm{O}}}}}}}}}_{2}^{*}\to {{{{{{{{\rm{OOH}}}}}}}}}^{*}\) step with a secondary XRC value at U = Uhalf that brings the biperiodic Ln-type dependence of ORR activity, and then it is the biperiodic chemical trend in ΔGads(OOH) (Fig. 2f) that leads to the opposite trends in Uhalf and Uonset. The simulated curves for surface-state 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 plot33, which well indicates that both too strong and too weak surface adsorptions will make ORR difficult to happen. Using the linear relationships between ΔGadss of different ORR intermediates and the Ea–ΔE relationships discussed above, the analytical variation of j within a given range of ΔGads(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 Uonset of Pt(111)), positioning the reference ΔGads(OH) at 0.8 eV, and normalizing the j values (jPt = 1.2 mA/cm2)31,34. The j–ΔGads(OH) data for various noble-metal surfaces are also collected from literature for comparison in Fig. 5a, and their numerical data are listed in Table S3. According to the volcano-type curve, the highest j can be obtained on a surface having a ΔGads(OH) higher than that of Pt(111) by 0.0–0.2 eV, quantitatively consistent with the previous claim for metal surfaces31,33,34. Nine kinds of Ln-MoS2 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/cm2), and the other six kinds of surfaces (Ln = Ce, Pr, Nd, Tb, Dy, Ho) in the nearby region (relative ΔGads(OH) at 0.2–0.3 eV) have moderate js (0.03–0.6 mA/cm2). 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 ORR-activity indicators, e.g., Ulimit (Fig. 3b), Uhalf (Fig. 4d), and Uonset (Fig. S35), but opposite to the biperiodic trends in ΔGadss (Fig. 2e and f).

Fig. 5: The volcano plot and rate control analyses for the polarization current densities of Ln-MoS2 surfaces.
figure 5

a The volcano curve describing the j–ΔGads(OH) relationship (at the standard 0.9 V) and the calculated results for all the fifteen Ln-MoS2 surfaces, together with many reported results (experimental j plus theoretical ΔGads(OH)) for various noble-metal surfaces34, 38, 60,61,62,63,64,65,66,67,68,69. The j and ΔGads(OH) on Pt(111) surface is used as the references. b The variation of j at 0.9 V with respect to Ln type. c, d The variations of XRC and XTRC curves with respect to ΔGads(OH). Source data are provided as a Source Data file.

Full size image

To reveal the microkinetic mechanisms underlying the volcano plot, we calculate the XRC curves in terms of ΔGads(OH) (Fig. 5c), as well as the curves for thermodynamic rate control (XTRC, Eq. (7) in the “Methods” section)46 to measure the sensitivity of rtot to the free-energy change of any surface state (Fig. 5d). A positive (negative) XTRC indicates that the increase in rtot needs to further stabilize (destabilize) the corresponding surface state. On the strong-adsorption side of the volcano plot (relative ΔGads(OH) < 0.0 eV), the negative XTRCs of OH* and O* indicate that their destabilization can lead to the increase in rtot, while XRC is mainly dominated by the O2 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 weak-adsorption side (relative ΔGads(OH) > 0.2 eV), the largely positive XTRC of OOH* indicates that it still needs to be stabilized for the increase in rtot. This is the reason why the six Ln-MoS2 surfaces (Ln = Ce, Pr, Nd, Tb, Dy, Ho) with the highest ΔGadss have the lowest js. In the optimal region (relative ΔGads(OH) at 0.0–0.2 eV), rtot is mainly determined by the O2 diffusion in water and becomes almost surface-chemistry independent. This is the reason why various materials (e.g., doped MoS2 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 Ln-MoS2 surfaces. We not only have found the considerably enhanced ORR activity of MoS2 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, ORR-intermediate adsorption strength, free energies of reaction for ORR intermediates (and Ulimit), characteristic potentials for polarization curve (Uhalf and Uonset), and current density. Based on the electronic-structure analysis, we find that the high ORR activity on Ln-MoS2 originates from a defect-state 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 orbital-chemistry mechanism that can closely correlate those simultaneous biperiodic trends in different properties. The ORR behaviors and key fundamental mechanisms revealed on Ln-MoS2 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 package47, where the ionic potential is described by the projector augmented-wave method48. The electronic exchange-correlation potential is expressed by the spin-polarized PBE functional in the generalized-gradient approximation (GGA)49, and the dispersive van de Waals force is described using the zero-damping DFT-D3 functional50. The valence configurations in the used Mo, S, O, and H pseudopotentials are 4d55s15p04f0, 3s23p43d0, 2s22p43d0, and 1s12p0, respectively, and those in the Ln pseudopotentials include 5s, 6s, 5p, 5d, and 4f orbitals. The plane-wave 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 MoS2 layer (12.61 × 10.92 Å2) with an interlayer vacuum spacing of 20 Å is constructed as the structural model, and its Brillouin zone is spanned by a reciprocal-point grid of 2 × 2 × 1.

Reaction paths and activation energies are calculated using the climbing-image nudged elastic band (CI-NEB) method51 with a force convergence threshold of 0.05 eV/Å. The protonation rate of a surface adsorbate is limited by the reaction at water/MoS2 interface because a proton can quickly reach the electrical double layer due to its very low diffusion barrier in water (0.07–0.11 eV52). To model this rate-limiting interfacial step, an H atom is placed on a water molecule nearby the adsorbate to form an H3O unit, and the relaxed structural model is used as the initial state for the CI-NEB path (see Fig. S30). Crystal orbital Hamilton population analysis as implemented in the LOBSTER code package35,36 is used to study the bonding and antibonding characters of atomic bonds, and atomic charges are calculated using Bader charge analysis53. The effect of electronic self-interaction problem intrinsic in the GGA functional for Ln atoms is tested by using the GGA plus HubbardUeff method54, 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, reciprocal-point 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 (Ef) of an Ln dopant in MoS2 is defined as the energy change associated with the filling of a Mo vacancy by a free Ln atom, which is expressed as

$${E}_{{{{{{{{\rm{f}}}}}}}}}={\varepsilon }_{{{{{{{{\rm{d}}}}}}}}}-{\varepsilon }_{0}-{\mu }_{{{{{{{{\rm{Ln}}}}}}}}},$$
(1)

where εd and ε0 are the total electronic energies of Ln-MoS2 and MoS2 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 Ef will have a direct correlation with the interatomic bonding strength in Ln-MoS2, which is highly useful for exploring the orbital-chemistry mechanism in both dopant stability and surface reactivity here.

The radial electron density distribution (Δρr)55 is calculated by

$$\Delta {\rho }_{{{{{{{{\rm{r}}}}}}}}}(r)=\frac{1}{4\pi {r}^{2}}{\iint }_{|\tilde{{{{{{{{\bf{r}}}}}}}}} |=r}\Delta \rho (\tilde{{{{{{{{\bf{r}}}}}}}}}){{{{{{{\rm{d}}}}}}}}\sigma,$$
(2)

where Δρr(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 spherical-surface area.

The surface potential shown in Fig. 1e is calculated by referring the surface work function (Φ) to that of the SHE (ΦSHE), which is expressed as

$$U=\frac{\Phi -{\Phi }_{{{{{{{{\rm{SHE}}}}}}}}}}{|e|},$$
(3)

where ΦSHE is measured to be 4.44 eV in experiment56.

Water-structure statistical sampling

MoS2 will form a relatively weak interface with water, thus the interfacial H2O 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 metal-water interfaces, leading to some stable ordered interfacial water configurations57. We exploit the ab-initio molecular dynamics (AIMD) method to simulate such a dynamically disordered H2O environment on Ln-MoS2, where a thick enough water film with 32 H2O molecules (thickness ~ 7 Å) is considered. It is thicker than that of the electrical double layer at the solid-water interface (~3 Å38). Two kinds of seed water structures are provided to initialize two threads of MD simulations: (1) the H atoms in H2O molecules at the interface pointing to the surface S atom (labeled as “H water”), and (2) the interfacial H2O 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 thermostat58 is used in the AIMD simulations at 300 K for 45,000 steps (0.5 fs/step). There is no structural damage on the Ln-MoS2 substrates during the AIMD simulations, indicating the preferred dynamical stability of doped structures. We sample the simulated Ln-MoS2/water structures every 5000 steps and label them as H-05, H-10, …, and H-45 (R-05, R-10, …, and R-45) for the H-water (R-water) group, for which the atomic structures are shown in Fig. S12. The calculated electrostatic potentials along the normal direction of the Ln-MoS2/water structures also clearly exhibit a two-layered morphology (Fig. S10) that is well-known as a typical solvent character on solid surfaces59.

Microkinetic modeling

The simultaneous rate equations for an ORR process can be briefly summarized as

$$\frac{\partial {\theta }_{n}}{\partial t}=\mathop{\sum}\limits_{i}{\nu }_{ni}{r}_{i}=\mathop{\sum}\limits_{i}{\nu }_{ni}\left({k}_{i}\mathop{\prod}\limits_{R}{\theta }_{R}-{k}_{-i}\mathop{\prod}\limits_{P}{\theta }_{P}\right),$$
(4)

where n indexes the species, and ri is the reaction rate of an elementary ORR step (i) involving the species n; νni is the stoichiometric coefficient of species n in step i, where νni is positive (negative) if the species n is a product (reactant); θR and θP represent the coverages of involved reactants and products in step i, respectively; and ki 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 O2 (\({{{{{{{{\rm{TOF}}}}}}}}}_{{{{{{{{{\rm{O}}}}}}}}}_{2}}\)) equals the total net reaction rate (rtot), and is used to derive the current density (j) by

$$j=4e\cdot \rho \cdot {{{{{{{{\rm{TOF}}}}}}}}}_{{{{{{{{{\rm{O}}}}}}}}}_{2}},$$
(5)

where 4 is the number of transferred electrons, and ρ is the surface density of active sites.

The sensitivities of rtot to the rate-constant change of each step (e.g., ki) and the free-energy change of each species (e.g., \({G}_{n}^{0}\)) can be revealed by the degree of kinetic rate control (XRC) and thermodynamic rate control (XTRC), respectively, defined as45,46

$${X}_{{{{{{{{\rm{RC}}}}}}}},i}=\frac{{k}_{i}}{{r}_{{{{{{{{\rm{tot}}}}}}}}}}{\left(\frac{\partial {r}_{{{{{{{{\rm{tot}}}}}}}}}}{\partial {k}_{i}}\right)}_{{k}_{j\ne i},{K}_{i}}$$
(6)

and

$${X}_{{{{{{{{\rm{TRC}}}}}}}},n}=\frac{1}{{r}_{{{{{{{{\rm{tot}}}}}}}}}}{\left[\frac{\partial {r}_{{{{{{{{\rm{tot}}}}}}}}}}{\partial \left(\frac{-{G}_{n}^{0}}{{k}_{{{{{{{{\rm{B}}}}}}}}}T}\right)}\right]}_{{G}_{m\ne n}^{0},{E}_{{{{{{{{\rm{a}}}}}}}}}},$$
(7)

where Ki is the equilibrium constant of step i; kB is the Boltzmann constant; and a small variation of 1.0% in both ki and \({G}_{n}^{0}\) is used for the calculations of partial derivatives.