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Research Article  |  Open Access  |  20 Nov 2023

Investigation of dual atom doped single-layer MoS2 for electrochemical reduction of carbon dioxide by first-principle calculations and machine-learning

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J Mater Inf 2023;3:25.
10.20517/jmi.2023.29 |  © The Author(s) 2023.
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The exploration of efficient electrocatalysts for carbon dioxide reduction reaction (CO2RR) with viable activity and superior selectivity remains a great challenge. The efficiency of CO2RR over traditional transition metal-based catalysts is restricted by their inherent scaling relationships, so breaking this scaling relationship is the key to improving the catalytic performance. In this work, inspired by the recent experimental progress in the synthesis of dual atom catalysts (DACs), we reported a rational design of novel DACs with two transition metal atoms embedded in defective MoS2 with S vacancies for CO2 reduction; 21 metal dimer systems were selected, including six homonuclear catalysts (MoS2-M2, M = Cu, Fe, Ni, Mn, Cr, Co) and 15 heteronuclear catalysts (MoS2-M1M2). First-principles calculations showed that the MoS2-NiCr system not only breaks the linear relationship of key intermediates but also possesses a low overpotential of 0.58 V and superior selectivity in the process of methane generation, which can be used as a promising catalyst for methane formation from CO2 electroreduction. Notably, by combining random forest regression machine learning study, we found that the CO2RR activity of DACs is essentially controlled by some fundamental factors, such as the distance between metal centers and the number of outer electrons in the metal atoms. Our findings provide profound insights for the design of efficient DACs for CO2RR.


Electrocatalysis, CO2RR, dual atom catalysts, random forest regression


The increasing consumption of fossil fuels has induced massive release of carbon dioxide (CO2) in the atmosphere and caused severe energy crisis and environmental pollution on a global scale[1,2]. One sustainable approach is to decrease CO2 emissions while transforming CO2 into value-added products. Nevertheless, the CO2 molecule is very stable, which requires a high activation energy to activate and break the C=O bond[3-7]. Among those developed methods[8,9], the electrochemical CO2 reduction reaction (CO2RR) is one promising solution and has received lots of experimental and theoretical attention owing to its simple operation, controllable selectivity, and practical potential for industrial applications[10,11].

In particular, the single-atom catalysts (SACs) have been a rapidly developing field in recent years owing to their powerful potential for heterogeneous catalysis[12]. The well-defined active sites provide a great platform for investigating the reaction mechanism and establishing the correlation between structures and activity[3,11,13-20]. Significant progress has been made in applying SACs for single-intermediate electrochemical reactions, i.e., the hydrogen evolution reaction (HER)[21-24]. The SACs also exhibit promising electrocatalytic applications in other types of multi-intermediate reactions, including oxygen reduction reactions (ORR)[25-28], CO2RR[29-31], and N2 reduction reactions (NRR)[32,33]. The catalytic activity of SACs, however, is usually limited to the simple electronic structure and low density of metal active sites[34]. Meanwhile, the SACs tend to form metal clusters during experimental synthesis, which causes great challenges in the usage of SACs efficiently[18,35]. Moreover, due to the presence of only one type of active site, it is difficult to break the inherent linear relationship of adsorption strength of intermediates by SACs[36-38]. The catalytic activity can be regulated by balancing the adsorption of reaction intermediates on the catalyst surface[39,40].

In this case, a promising strategy to regulate the adsorption of intermediates is via introducing a secondary metal site, as indicated by prior studies[41-43]. We have termed it as dual atom catalysts (DACs)[44]. On account of the synergetic effects of dual active sites, DACs can better maximize the catalytic potential of SACs for various multi-step reactions, leading to boosted catalytic performance[45-49]. For example, Yan et al. experimentally synthesized the Pt2 dimer dispersed on graphene, which catalyzes the hydrolytic dehydrogenation of ammonia and boron at a reaction rate nearly 17-fold faster than that of a single Pt atom[50]. Ren et al. synthesized Fe-Ni DACs embedded in N-doped porous carbon as a highly efficient catalyst for CO2 reduction[13]. In theory, Zhao et al. predicted that Cu2 dimer loaded on porous C2N nanosheets has high selectivity for CH4 production[51]. The Co-, Ni-, and Cu-based DACs are predicted to exhibit higher activity for O2 reduction than the corresponding single-atom counterparts[45,52]. In order to obtain excellent transition metal (TM)-based DACs, an appropriate stabilizing substrate is essential, which not only offers the coordination sites for stably capturing metal atoms but also acts synergistically with the active center during the electrocatalytic process. Currently, a lot of experimental and theoretical studies focus on the N-doped carbon or graphene as the stabilizing substrate. Notably, during the synthesis of 2D nanosheets of molybdenum disulfide (MoS2), inherent vacancy defects are very common and easy to form, mostly S vacancies[53-55]. Not only the single S vacancy but also the double S vacancies and clustered S vacancy line can be realized experimentally[56]. These S vacancies can be used as the anchor sites for catalytic atoms due to their high binding affinity for atoms and molecules. Experimentally, many isolated metal atoms, such as Co and Pt, have been successfully anchored at the single S vacancy of MoS2[57,58]. Thus, we hypothesized that the MoS2 with available double S vacancies could also be a potential substrate to anchor DACs[59].

In this work, we theoretically explored the CO2RR performance of a series of dual-metal (M: Cu, Fe, Ni, Mn, Cr, Co)-doped single-layered MoS2 (denoted as MoS2-M2 or MoS2-M1M2, Figure 1) via density functional theory (DFT) calculations. In the optimized homonuclear and heteronuclear DACs, some of the adjacent metal atoms will form the metal-metal bond [Figure 1B and D], while others will not [Figure 1A and C]. The results showed that water molecules would first occupy the active site, which is difficult to desorb, and would stabilize MoS2-M2/M1M2 for further CO2 reduction. Among the examined 21 DAC compositions, MoS2-NiCr is identified as a highly promising candidate for catalyzing CO2 reduction to CH4. More importantly, we incorporated random forest regression prediction in a machine learning approach by training the DFT calculated data to identify important feature factors that influence the activity of CO2RR and the adsorption of the key *CO intermediate, where the distance between the two metal centers and the number of electrons in the outer layers of the metal atoms play a significant role.

Investigation of dual atom doped single-layer MoS<sub>2</sub> for electrochemical reduction of carbon dioxide by first-principle calculations and machine-learning

Figure 1. The geometric structure of MoS2-M2 and MoS2-M1M2. Some of the adjacent metal atoms will form metal-metal bonds (B and D), while others will not (A and C). The dark cyan and yellow balls represent Mo and S atoms, respectively, and the dark blue and purple balls represent the two TM atoms. TM: Transition metal.


All the spin-unrestricted DFT calculations are performed in the DMol3 code[60,61]. The exchange-correlation effect is described via the Perdew-Burke-Ernzerhof (PBE)[62] functional of the generalized gradient approximation (GGA)[63]. The double numerical plus polarization (DNP) basis is employed using the DFT semi-core pseudopotential (DSPP) for the core treatment. The van der Waals interaction between CO2RR intermediates and DACs is described by empirical dispersion-corrected DFT (DFT-D3). To simulate the aqueous solvent environment, a conductor-like screening model (COSMO) is adopted[64-66]. In geometric optimization, the convergence threshold of energy is 2 × 10-5 Ha; the maximum displacement is set as 0.005 Å, and the force applied to each atom is 0.004 Ha/Å. A 4 × 4 × 1 rectangular 2H-MoS2 supercell with adjacent double S vacancies was constructed, and a 3 × 3 × 1 Monkhorst-Pack k-mesh was used to sample the Brillouin zone. Moreover, an 18 Å vacuum space was set to avoid interactions of adjacent images. The canonical ensemble (NVT) ab initio molecular dynamics (AIMD) simulations are performed in a Nosé-Hoover thermostat at 300K for five picoseconds (ps) in a time step of one femtosecond (fs).

The formation energies of homonuclear and heteronuclear DACs, Ef, are calculated by the following equation[67]:

$$ E_{f}=\frac{1}{N}\left[E_{total }-\left(E_{M o S_{2}}+N \times E_{T M}\right)+N \times E_{c o h}\right] $$

where N represents the number of doped atoms, Etotal is the total energy of DACs, $$ E_{M o S_{2}} $$ denotes the energy of MoS2 substrate with double S vacancies, and Ecoh is the cohesive energy of the dopant.

According to the computational hydrogen electrode (CHE) model[68], the Gibbs free energy change (ΔG) of each elementary reaction step of CO2RR is calculated by ΔG = ΔE + ΔZPE - TΔS, where ΔE is the reaction energy change calculated by DFT calculations, while ΔZPE and TΔS represent the difference in zero-point and entropy change at 298 K. For gas phase molecules, the entropy is derived from the NIST database and details are provided in the Supporting Information [Supplementary Table 1].

The limiting potential (UL) of the reaction is calculated as UL = -ΔGmax/e, where ΔGmax corresponds to the maximum free energy change among all the CO2RR elementary steps.



According to the above equations, we calculated the formation energy (Ef) [Figure 2A] to assess the thermodynamic stability of the six kinds of homonuclear DACs and 15 kinds of heteronuclear DACs. The Ef of all DACs were negative, ranging from -4.92 to -6.16 eV [Supplementary Table 2], indicating high thermodynamic stability. In addition, the AIMD simulations are carried out to verify the dynamic stability of the DACs. From Figure 2B to E (MoS2-MnCr, MoS2-FeMn, MoS2-CrCo, and MoS2-NiCr), the temperature slightly fluctuates around 300 K, and the energy changes within ± 0.01 eV. No obvious deformation occurs in these frameworks during the AIMD simulation, further confirming the high dynamic stability of the catalysts.

Investigation of dual atom doped single-layer MoS<sub>2</sub> for electrochemical reduction of carbon dioxide by first-principle calculations and machine-learning

Figure 2. (A) The formation energy of different transition metals embedded in MoS2; The energy fluctuations of (B) MoS2-MnCr, (C) MoS2-FeMn, (D) MoS2-CrCo , and (E) MoS2-NiCr in AIMD simulations for 5 ps under 300 K with a time step of 1 fs. AIMD: Ab initio molecular dynamics; fs: femtosecond.

Activation of CO2

The activation of CO2 over the active center is the first step during electrocatalytic CO2RR. However, from Supplementary Table 3, water adsorption is energetically more preferable than CO2 except for MoS2-MnCr. From the optimized structures [Supplementary Figure 1], the O atom of the adsorbed H2O is coordinated to one single metal center or the metal-metal bridge site. Note that the adsorbed water molecule cannot split spontaneously due to its highly endothermic dissociation process (0.28~1.07 eV, Supplementary Table 4). Therefore, we subsequently considered CO2 adsorption and reduction after water molecules first occupy the active site. The binding interaction between CO2 and MoS2-embedded DACs ranges from -0.45 to -0.98 eV [Supplementary Figure 2]. Especially, the binding strength of CO2 on MoS2-NiCr is strong with high adsorption free energy of -0.98 eV and curved O−C−O bond angle of 139.106°, which is accompanied by considerable charge transfer of around 0.6 |e| from catalyst to CO2 [Figure 3A]. Note that in the case of MoS2-NiCr, the two O atoms of CO2 are coordinated to the Ni and Cr centers, respectively. In other DAC systems, only one of the O atoms of CO2 is coordinated to one metal center, which is accompanied by weaker adsorption strength (-0.45~-0.88 eV) and less charge transfer (0.01~0.02 |e|) between the anchored metal dimer and CO2 (MoS2-CrCo is shown as an example in Figure 3B). However, the favorable adsorption proves that CO2 molecules can be effectively captured and activated by the metal dimers embedded in sulfur vacancies of MoS2.

Investigation of dual atom doped single-layer MoS<sub>2</sub> for electrochemical reduction of carbon dioxide by first-principle calculations and machine-learning

Figure 3. The adsorption geometry and charge density difference of CO2 adsorption over (A) MoS2-NiCr and (B) MoS2-CrCo DACs, with an isosurface level of 0.002 e·Å-3. The green and red regions represent electron depletion and accumulation, respectively. DACs: Dual atom catalysts.

Scaling relations

In most cases, the potential limiting step for CO2 electroreduction is the reduction of *COOH to *CO (two-electron reduction) or the reduction of *CO to *CHO (deep reduction). Thus, the overall catalytic efficiency depends strongly on the adsorption energies of *COOH [Eads(COOH)], *CO [Eads(CO)], and *CHO [Eads(CHO)][69,70]. The reduction of CO2 to CO involves a two-step electroreduction, i.e., *CO2 + H+ + e- → *COOH and *COOH + H+ + e- → *CO + H2O, while *CO to *CHO is a hydrogenation reduction step, *CO + H+ + e- → *CHO. The adsorption strengths of *CO and *COOH or *CHO on the conventional metal surfaces are usually linearly correlated, which limits the electrocatalytic activity[36,71]. Therefore, we first examined the adsorption of *CHO, *COOH and *CO. The detailed adsorption energy and the adsorption geometries are given in Supplementary Table 5 and Supplementary Figure 3. From Figure 4, the scaling relations are completely broken compared to those observed in pure metal surfaces. In the linear diagram of Eads(COOH) vs. Eads(CO) [Figure 4A], the scattered points are distributed in the whole region, indicating that the DAC electrocatalysts can effectively break the linear relationship. Note that most of these investigated DACs have strong *CO adsorption, which means that the generated CO would undergo further hydrogenation to form deep reduction products. For the relationship between Eads(CO) and Eads(CHO) [Figure 4B], the scaling relationships are slightly weakened with scattered points compared with those of the pure metal surfaces. In addition, NiCr and CrCo are two special cases that deviate greatly from the linear relationship of pure metal surfaces and show small differences between Eads(CO) and Eads(CHO); thus, they can be used as candidates to achieve the desired low overpotential for deep reduction products. Consequently, we selected these two systems for our subsequent calculations. We also analyzed the projected density of states (PDOS) of the NiCr and CrCo candidates after CO adsorption. From Supplementary Figure 4, within the energy region from -8 to -4 eV below the Fermi level, it can be clearly seen that the p orbital of C in the adsorbed *CO is strongly hybridized with the d orbital of the metal, proving that *CO has strong adsorption with the metal active site, which is beneficial to the deep reduction reaction of CO[72].

Investigation of dual atom doped single-layer MoS<sub>2</sub> for electrochemical reduction of carbon dioxide by first-principle calculations and machine-learning

Figure 4. Relationship between the binding energies (A) Eads(COOH) vs. Eads(CO) and (B) Eads(CHO) vs. Eads(CO) of MoS2 embedded DACs and the transition metal surfaces. The linear proportional relationships between the adsorbents were obtained on Ni, Cu, Ag, Pd, Au, Pt, and Rh surfaces[70]. DACs: Dual atom catalysts.

The pathway of CO2RR

In the following, we systematically investigated the reduction pathway of CO2RR on MoS2-NiCr and MoS2-CrCo after the formation of strongly bound *CO (*CO is firstly produced through the two-electron pathway: CO2 → *COOH → CO). The *CO can be further reduced to other C1 products, such as HCHO, CH3OH, and CH4. The free energy diagrams of all the possible C1 products are shown in Figure 5, the structural schematics are shown in Supplementary Figure 5, and the detailed data of free energy are provided in Supplementary Table 6. One can see that the hydrogenation of *CO to *CHO is energetically more favorable than the formation of *COH. Moreover, for both MoS2-NiCr and MoS2-CrCo, the generation of CH4 needs lower energy input than the generation of HCHO and CH3OH, indicating that CH4 would be the main reduction product of CO2RR. From Figure 5A, the potential limiting step of CH4 formation on MoS2-NiCr corresponds to *CO reduction to *CHO and *OH reduction to H2O, which need comparable endothermic free energy of 0.56 and 0.58 eV, respectively. While on MoS2-CrCo [Figure 5B], the potential limiting step of CH4 formation corresponds to *CO2 reduction to *COOH or *CO reduction to *CHO, which needs comparable endothermic free energy of 0.44 and 0.43 eV, respectively. Figure 6 shows the detailed geometry of reaction intermediates during CH4 formation on MoS2-NiCr and MoS2-CrCo catalysts. On MoS2-NiCr [Figure 6A], the various intermediates (*CHO, *CH2O, *CH3O, *O, and *OH) from a deep reduction of *CO are all coordinated to both the Ni and Cr atoms. In the case of MoS2-CrCo [Figure 6B], the reaction intermediates are mainly singly coordinated to the Cr atom. This indicates that the Ni and Cr centers in MoS2-NiCr work synergistically as dual active sites to affect the adsorption and bonding of CO2RR intermediates, while in MoS2-CrCo, only the Cr center plays the key role and functions as the single active site for CO2RR.

Investigation of dual atom doped single-layer MoS<sub>2</sub> for electrochemical reduction of carbon dioxide by first-principle calculations and machine-learning

Figure 5. Free energy diagrams of the electroreduction of CO2 on (A) MoS2-NiCr and (B) MoS2-CrCo at URHE = 0 eV.

Investigation of dual atom doped single-layer MoS<sub>2</sub> for electrochemical reduction of carbon dioxide by first-principle calculations and machine-learning

Figure 6. Schematics of the reaction pathway of CH4 formation on (A) MoS2-NiCr and (B) MoS2-CrCo catalysts. CO2RR: Carbon dioxide reduction reaction.

Selectivity of CO2RR vs. HER

In CO2RR, the HER always competes with CO2 reduction in an aqueous solution[73]. Firstly, the occupation of sites was initially considered, and as shown in Supplementary Table 7, H adsorption in most dual-atom systems is not as strong as H2O and CO2 adsorption. Therefore, the diatomic sites are more likely to take the CO2RR path. Secondly, it is necessary to assess the selectivity of CO2RR by comparing its limiting potential (UL). In the CO2 reduction process, we consider the comparison between the limiting potential of the electrochemical steps and that of HER. Accordingly, a more positive value of ΔUL [UL(CO2RR) - UL(HER)] implies higher reaction selectivity for CO2 reduction. From Figure 7, the ΔUL of the NiCr dimer (0.26 V) is located in the upper right corner, indicating its high CO2RR selectivity, while the ΔUL of the CrCo dimer is close to 0, indicating its poor selectivity. Furthermore, the ideal electrocatalysts should be well accompanied by effective CO2 activation. In other words, the strong adsorption of CO2 over the catalyst can inhibit H on the catalyst surface, thus hindering the competitive HER as the CO2 will occupy the available active sites[6,74,75]. The calculated adsorption free energies of *H on MoS2-NiCr and MoS2-CrCo metal sites are -0.84 and -0.45 eV, respectively (inset in Figure 7), while the adsorption free energies of CO2 are -0.98 and -0.68 eV, respectively. This indicates that CO2 adsorption is more favorable than H* adsorption. Hence, the adsorption of CO2 is preferred, while the adsorption of *H is hindered. By comparing the reaction activity and selectivity, the MoS2-NiCr is screened to be a promising dual-site electrocatalyst to promote the CH4 formation with moderate rate-determining step (RDS) barriers and high CO2RR selectivity over HER. Our theoretical prediction will provide useful insights for future experimental verification of the high electrocatalytic performance of Ni-Cr DACs supported on MoS2 substrates.

Investigation of dual atom doped single-layer MoS<sub>2</sub> for electrochemical reduction of carbon dioxide by first-principle calculations and machine-learning

Figure 7. The limiting potential difference between CO2 reduction [UL(CO2RR)] and HER [UL(HER)] over MoS2-NiCr and MoS2-CrCo catalysts. The inset in the figure is the free energy diagram of HER. CO2RR: Carbon dioxide reduction reaction; HER: hydrogen evolution reaction; UL: limiting potential.

Machine learning analysis

From the data calculated above, the CO2RR activity of DACs and the binding strength of the intermediate *CO are closely related, with weak CO binding favoring CO gas desorption and strong CO binding facilitating adsorption of added H to *CHO. At present, the underlying factors affecting CO2RR activity remain to be discovered. Furthermore, DAC systems are much more complex than TM surfaces. Therefore, it is difficult to accurately describe the CO2RR activity of DACs with only one descriptor. Without performing intensive DFT calculations, there is a strong need to identify more readily available variables to describe the CO2RR activity of DACs.

Thus, by using a machine learning approach, we investigated the correlation between ΔG*CO or UL(CO) and the intrinsic factors of six homonuclear and 15 heteronuclear catalysts. Proper feature selection is essential for machine learning models to identify the hidden rules behind the input data. In our work, we considered seven very basic parameters to describe the geometric and electronic properties of DACs, including the distance between two metal atoms (dM-M), the average distance between two metal atoms and six Mo atoms (dM-Mo), the radii of two metal atoms (R1 and R2), the number of outer electrons of two metal atoms (Ne1 and Ne2), the Pauling electronegativity (P1 and P2), the first ionization energy (I1 and I2), and the electron affinity (A1 and A2). Importantly, we examined the correlations between the factors, and as can be seen in Supplementary Figure 6, most combinations of factors are poorly related to each other. Some of the factors vary with the regularity of the periodic table, e.g., Ne, R, etc. Thus, these factors and coefficients are variables that can be approximated as independent of each other. It is important to note that we augmented the data for all the DACs studied because MoS2-M1M2 and MoS2-M2M1 correspond to two different sets of variable combinations [Supplementary Table 8]. In this way, each DAC possesses two sets of input features.

We used a random forest regression algorithm from the scikit-learn toolkit[76]. The DFT computed ΔG*CO values were then compared with the values predicted based on the random forest study. The DFT-computed ΔG*CO input data were randomly perturbed and divided into a training set and a test set in a ratio of 6:1. As shown in Figure 8A, the predicted values based on the random forest have a similar trend to the values calculated by DFT, with a lower mean square error of 0.058. There is a high R2 value, 0.93 for the training score and 0.91 for the test score, indicating that the random forest prediction algorithm adequately trained the model by learning the factors inherent in the model to reach an accurate prediction. The importance of the seven features on ΔG*CO was also evaluated. In Figure 8B, the distance between the metals (dM-M) is the most influential on ΔG*CO, with a feature importance value of 0.34, while the sum of feature importance values of the radius of the metal atoms (R1 and R2) and the distance between the metal and the Mo atoms (dM-Mo) is only 0.01. That means that the synergistic effect between the DACs has a strong influence on the catalytic efficiency. In addition, the outer electron number (Ne) of the metal atom also plays an important role, with a sum of feature importance (Ne1 + Ne2) of 0.20, which can be interpreted as forming a metal-metal bond between DACs that cannot efficiently bind the CO2RR intermediates. However, the importance of the remaining three features (P, I, and A) was relatively insignificant. We also predicted the limiting potential in the CO2 → CO process based on the Random Forest algorithm, and the predictions were highly similar to the DFT [Figure 8C and D]. The feature importance pie charts show similarities to those described above. Machine learning links the correlations between the intrinsic structure and the properties, providing powerful insights into the understanding of the CO2RR activity of DACs. Particularly, since the activity of the dual-atom catalyst in the CO2RR process is closely correlated with these important factors, we can apply these descriptors to predict the activity of other dual-atom compositions.

Investigation of dual atom doped single-layer MoS<sub>2</sub> for electrochemical reduction of carbon dioxide by first-principle calculations and machine-learning

Figure 8. Comparison of (A) ΔG*CO and (C) [UL(CO)] obtained by DFT with values predicted by machine learning; (B and D) feature importance based on a random forest regression. DFT: Density functional theory.

Potential limitations

There is one thing that needs to be added: our work is based on first-principles calculations to investigate the activity of electrochemical reduction of CO2 by dual atom doped single-layer MoS2. From a theoretical point of view, the DACs predicted by us have relatively negative formation energies (Ef) and stable structures through AIMD, which indicates that it is feasible to synthesize such structures. Recently, an ingenious approach has successfully assembled DACs of Ni and Fe into the interlayer of MoS2[77]. These DACs exhibit higher catalytic activity toward acidic water splitting. Our predicted MoS2-FeNi structure was confirmed through this experiment. Therefore, these structures that we predict, namely the doping of different dual atoms (Cu, Co, Cr, Mn, etc.) in the single-layer MoS2, are expected to be realized in the future.

Furthermore, our computations rely on a traditional CHE model that neglects the display potential and display solvation factors, which do affect the precision of the performance evaluation to some extent. Although the method has some limitations in the evaluation of activity due to the significant computational cost savings and relatively accurate simulation accuracy of the CHE model, this method is very popular for large-scale prediction and performance screening of new materials[78-83]. In other words, while taking into account the calculation speed and accuracy, the performance evaluation at the same atomic level is also of great reference significance.


In summary, the reaction activity of various dual atoms embedded in defective MoS2 monolayers, named MoS2-M2/M1M2, for CO2 reduction was systematically studied using computational DFT approaches. We theoretically studied 21 dimer electrocatalysts. Our results demonstrate that the defective MoS2 monolayer with double S vacancies can anchor the two TM atoms stably. Through the analysis of the adsorption relationship of key intermediates, it was found that MoS2-CrCo and MoS2-NiCr candidates significantly deviated from the linear relationship; thus, they were selected for further analysis of deep reduction. We found that MoS2-CrCo shows a lower barrier energy for CH4 production (0.44 eV), but its selectivity (ΔUL = 0.02 eV) over competitive HER is low. In contrast, the MoS2-NiCr system possesses superior selectivity (ΔUL = 0.26 eV) and catalytic activity for CH4 production with a low rate-determining electrochemical barrier of 0.58 V. In the whole reaction process, water exists in the form of coordination in the formation process of C1 products. Moreover, our machine learning study demonstrated that adsorption of the key *CO intermediate and CO2RR activity can be well described by some basic parameters, such as the distance between the center of metal atoms and the number of outer electrons of the metal atoms. This work presents an atomic-level investigation of the screening and design of novel DACs supported on defective MoS2, providing useful insights for further investigations, including theoretical and experimental attempts.



We acknowledged the support provided by the National Natural Science Foundation of China (No.21903008) and the Chongqing Science and Technology Commission (cstc2020jcyj-msxmX0382). This research used resources from the National Supercomputer Center in Guangzhou.

Authors’ contributions

Conceived the idea for scientific research: Tang Q

Developed the theoretical models and performed the theoretical calculations: Li H

Assisted in processing the data of DFT calculations: Li H, Ma M

Provided technical support for machine learning and completed analysis and processing of data: Deng C

Wrote the manuscript and finalized it with support: Li H, Deng C, Li F, Ma M, Tang Q

Availability of data and materials

Not applicable.

Financial support and sponsorship

The authors would like to thank the support provided by the National Natural Science Foundation of China (No.21903008) and the Chongqing Science and Technology Commission (cstc2020jcyj-msxmX0382).

Conflicts of interest

All authors declared that there are no conflicts of interest.

Ethical approval and consent to participate

Not applicable.

Consent for publication

Not applicable.


© The Author(s) 2023.

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Cite This Article

OAE Style

Li H, Deng C, Li F, Ma M, Tang Q. Investigation of dual atom doped single-layer MoS2 for electrochemical reduction of carbon dioxide by first-principle calculations and machine-learning. J Mater Inf 2023;3:25.

AMA Style

Li H, Deng C, Li F, Ma M, Tang Q. Investigation of dual atom doped single-layer MoS2 for electrochemical reduction of carbon dioxide by first-principle calculations and machine-learning. Journal of Materials Informatics. 2023; 3(4): 25.

Chicago/Turabian Style

Li, Huidong, Chaofang Deng, Fuhua Li, Mengbo Ma, Qing Tang. 2023. "Investigation of dual atom doped single-layer MoS2 for electrochemical reduction of carbon dioxide by first-principle calculations and machine-learning" Journal of Materials Informatics. 3, no.4: 25.

ACS Style

Li, H.; Deng C.; Li F.; Ma M.; Tang Q. Investigation of dual atom doped single-layer MoS2 for electrochemical reduction of carbon dioxide by first-principle calculations and machine-learning. J. Mater. Inf. 2023, 3, 25.

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