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. 2025 Feb 10;37(4):1382–1392. doi: 10.1021/acs.chemmater.4c02106

Boron Phosphide Nanotubes for Electrocatalytic CO Reduction to Multicarbon Products

Xiaodong Yan †, Wugang Wang †, Oleg V Prezhdo ‡,*, Lai Xu †,*
PMCID: PMC11866746  PMID: 40026706

Abstract

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Developing an efficient catalyst that can reduce CO to economically viable products provides a pathway to achieve carbon neutrality. For this purpose, we introduce and characterize boron phosphide nanotubes, a class of materials that allow one to reach a goal without costly and toxic metal atoms. The tubular configuration imparts a confining effect, facilitating CO adsorption and catalytic reduction into ethanol. By calculating the transition state conditions under different charging and using grand canonical potential kinetics, we establish the transition state energy barriers in the system at different electrochemical potentials. We further elucidate the kinetics and mechanism of the entire reaction process at the microkinetics level and predict the onset potential to be −0.30 V with the Tafel slope of 93.69 mV/dec. Finally, we demonstrate control over concentrations of the products and intermediate species by the choice of pH and the applied potential. The characterized material class and established chemical mechanisms guide design of electrocatalysts for producing multicarbon products.

Introduction

Fossil fuels, as the primary sources of energy, have facilitated industrial development over the past few centuries. However, they have also led to excessive emissions of greenhouse gases, such as carbon dioxide, further exacerbating climate change and other global environmental issues. Reduction of carbon dioxide (CO2) and carbon monoxide (CO) provides a promising method for converting alternative, renewable energy sources, such as solar energy, into chemical energy in the form of fuel and raw materials.1−8 Currently, catalytic reduction of CO2 is considered as a green and environmentally friendly approach to produce a range of multicarbon products, including carbon monoxide, methane, methanol, ethanol, and ethylene.9−19 The process both solves the problem of carbon imbalance and generates important industrial and medical products, e.g., methane and ethanol, making it a win-win solution to the environmental and energy problems faced by modern society. However, several key challenges need to be addressed to make the catalytic reduction of CO a viable solution. The process has been limited by the high overpotential required for the CO reduction, as well as by the competitive hydrogen evolution reaction (HER), which has resulted in low production efficiency and unfavorable energy utilization.15,20 Therefore, it is particularly important to find catalysts with high activity, stability, and selectivity.

In recent years, significant progress has been made in the reduction of CO2 and CO.21,22 Since the successful synthesis of graphene in 2004,23 significant research efforts have been dedicated to two-dimensional materials, such as transition metal carbides and nitrides (MXenes)24 and transition metal dichalcogenides (TMDCs).25 Two-dimensional materials have a high specific surface area and are therefore promising for applications in electrochemical reactions.26 In comparison with traditional two-dimensional planar materials, nanotubes have been proven a promising platform for promoting catalysis due to their unique tubular structure that facilitates mass diffusion, promotes charge transfer, and provides ultrahigh specific surface area.27−29 Further, transition metal phosphides have a great potential for applications in catalysis.30,31 Boron phosphide nanoparticles can be used for CO reduction reactions,32 and the boron and phosphorus chemical elements can enhance the catalytic properties of materials.33,34

Currently, traditional quantum mechanical (QM) calculations are performed under the assumption of a fixed number of electrons, while there may be significant changes in the number of electrons during the reaction. Grand canonical quantum mechanics allows the charge to vary continuously during the calculation of the reaction properties, representing the constant applied potential experimental conditions. Formulation of the grand canonical potential kinetics (GCP-K) allows one to obtain accurate description of catalytic reactions.35 The accuracy of the GCP-K approach has been validated in recent studies on single-crystal Co/TiO2 nanoparticles, with the experimental results showing a close agreement with the predicted relationship between turnover frequency (TOF) and applied potential, as well as the Tafel slope.36

In this study, we design and characterize boron phosphide nanotubes (BPSWNT), a class of materials for the catalytic reduction of CO, as illustrated in Figure S1. We demonstrate the thermodynamic and dynamic stability of the material using ab initio molecular dynamics (AIMD) and phonon spectroscopy. Leveraging the unique tubular structure of the BPSWNT, we propose a strategy to enhance the CO reduction reaction (CORR) within the confinement of the tube, thereby promoting catalytic performance. The curvature of the inner and outer walls of the tube facilitates favorable CO molecule adsorption as well as subsequent coupling and protonation steps. Employing the GCP-K approach, we report detailed microkinetic simulations, yielding an onset potential of −0.30 V and a Tafel slope of 93.69 mV/dec for the boron phosphide nanotube material at a current density of 10 mA/cm2.

Methods

Spin-polarized density functional theory (DFT) calculations were conducted using the Vienna ab initio simulation package (VASP), employing the Perdew–Burke–Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) to describe exchange-correlation energy.37 Electron–ion interactions were treated with the projector augmented wave (PAW) method,38 while van der Waals interactions between atoms were considered using the DFT-D3 method with Becke–Jonson damping.39 A plane-wave basis with a cutoff energy of 450 eV was utilized. Brillouin zone sampling was achieved employing the Gamma scheme with a 1 × 1 × 3 k-point grid for structural optimizations. Convergence thresholds for energy and forces on each atom were set to 10–5 eV and 0.05 eV/Å, respectively. To account for solvation effects, the VASPsol model40 was integrated, employing a water dielectric constant of 78.50.

In this study, ab initio molecular dynamics (AIMD) simulations were conducted to evaluate the thermodynamic stability of the system. The NVT ensemble was utilized, maintaining a temperature of 300 K over a duration of 10 ps with a time step of 1 fs. Concurrently, we employed phonon spectroscopy software to simulate and assess the dynamic stability of the system. Additionally, the crystal orbital Hamiltonian population (COHP) analysis was conducted using the Lobster 4.0.0 code.41−43 We employed the climbing-image nudged elastic band (CI-NEB) method44 to locate the transition state (TS) and determine the reaction pathway.

Subsequently, we utilized JDFTx45 to compute the single-point energy of the optimized structure obtained from VASP, employing the CANDLE46 solvation model. For the single-point energy calculation in JDFTx, we employed the USPP pseudopotential, set the free energy convergence threshold to 10–6 Hartree, used a k-point grid of 1 × 1 × 3, specified a system cutoff energy of 15 hartree, and the spin type was designated as spin-polarized.47

Results and Discussion

Structure

Previous studies showed that boron phosphide nanoparticles have emerged as promising catalysts.32 In this work, we have designed boron phosphide nanotube (BPSWNT) structures by transforming two-dimensional nanosheets into tubular configurations, aiming to enhance the material’s catalytic activity. The material depicted in Figure S1 consists of a B atom and a P atom. The inner radius of the tube is approximately 5.70 Å. Boron phosphide nanotubes feature a hexagonal honeycomb structure composed of boron and phosphorus atoms with an average B–P bond length of around 1.90 Å.

Boron phosphide nanotubes, composed of boron and phosphorus atoms, share structural similarities with carbon nanotubes. The inner space of these nanotubes provides space for accommodating the CO molecules and the ethanol molecules generated during the reduction reaction. Throughout the carbon monoxide reduction process, the structure of the nanotubes undergoes subtle changes as the reaction proceeds, eventually regaining its original shape after the ethanol is produced. This also indicates that phosphorus boron nanotubes have a certain degree of flexibility, allowing them to withstand certain fluctuations while maintaining their overall integrity.

To determine the stability of boron phosphide nanotubes, the thermodynamic stability of the material was explored through AIMD. Considering that electrochemical CO reduction reactions typically occur in aqueous solutions at room temperature and pressure, we simulated the energy and temperature fluctuations of the material at 300 K over a duration of 10 ps with a time step of 1 fs. Figure 1a presents the geometric structure of the material at 0 and 10 ps during AIMD, revealing minimal structural changes. This observation underscores that under room temperature conditions, boron phosphide nanotube materials maintain a stable state. In addition, phonon spectrum calculations were conducted to evaluate the dynamic stability of the material, as shown in Figure 1b. The calculation results indicate that the material has almost no imaginary frequency under the 0 scale, which provides additional evidence for the dynamic stability of the material. In summary, these findings confirm the stability of the boron phosphide nanotubes.

Figure 1.

Figure 1

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Stability of the BPSWNT. (a) AIMD of BPSWNT at the temperature of 300 K. Left and right coordinate axes represent temperature and energy, respectively. Initial structure of the calculation and the completed structure are shown in the illustration. (b) Phonon dispersion spectrum of BPSWNT.

CO Adsorption

Adsorption serves as a pivotal initial step in reaction pathways, and without adsorption, subsequent reactions will not occur; therefore, determining the adsorption site is crucial. Considering that the material is a repetitive tubular structure composed of boron and phosphorus atoms, two types of CO adsorption scenarios can be considered: one with single B and P atoms acting as active sites and the other with adjacent B and P atoms or two P atoms acting as a two-site mode. In the case of two-site CO adsorption, the distance between the two adsorption sites must match the length of the C–O bond. In the case of double-site CO adsorption, the distance between the two adsorption sites must match the length of the C–O bond. However, the distance between the two B or P atoms is about 2.20 Å, while the C–O bond distance in CO is about 1.14 Å, which is a large difference, thus preventing the successful adsorption of CO. Consequently, such scenarios are excluded from consideration. Subsequently, we optimized the structures for the remaining six configurations individually, as shown in Figure S2. Through calculations, it was determined that when a B atom acts as a single active site for vertical CO adsorption, successful fixation of CO onto the substrate occurs, while other configurations fail to achieve CO adsorption.

After confirmation of the CO adsorption based on B atoms, distinctions arise between the inner and outer walls of the catalyst material due to its tubular structure. Subsequently, we conducted calculations to evaluate the CO adsorption on both the inner and outer walls of the tube with B atoms as the active site. The computational results are depicted in Figure 2. Observations reveal successful CO adsorption on both surfaces; the free energy of the structure adsorbing CO inside the tube wall is −1.18 eV at an applied potential of 0 V. However, when the material adsorbs CO on the outer side, the free energy is −0.99 eV at an applied potential of 0 V, which is 0.19 eV higher than that of the inner side adsorption. This difference indicates that CO is more conducive to reaction inside the tube wall. It is worth noting that during CO adsorption, there is a significant atomic position shift on the substrate, resulting in a boron atom in the material showing a tendency to approach the adsorbed CO molecules, while adjacent phosphorus atoms shift in the opposite direction.

Figure 2.

Figure 2

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(a) Structures of BPSWNT with CO and H adsorbed on the inner and outer sides, respectively. (b) Free energies of the four structures in Figure 2a at 0 V.

At the same time, we calculated the free energy of the adsorption of H on the inner and outer sides of the BPSWNT material, respectively, as shown in Figure 2. It can be found that the free energy of the material is −0.03 eV in the inner adsorption of H, which is 0.26 eV higher than that of −0.29 eV in the outer adsorption of H. However, both cases are higher than that of the material’s adsorption of CO, so that the BPSWNT material is more likely to be subjected to CORR, and it can effectively inhibit the occurrence of HER.48−50 We also calculated the free energy changes of the HER and CORR at different potentials, as shown in Figure S3. It can be observed that under an applied voltage of −0.3 V, the free energy of CORR is −1.15 eV, while that of HER is −0.43 eV, which also proves that the activity of the CORR is still superior to that of the HER at different potentials.

An insight into the electronic properties of this system can be gained by calculating the integrated crystal orbital Hamiltonian population (ICOHP) and Bader charge, as shown in Figures S4 and S5. It is worth noting that the ICOHP value of the C–O bond is highest at −9.90 eV when CO is adsorbed inside the tube. The outer adsorbed C–O bond has an ICOHP value of −9.96 eV, which is lower than the ICOHP value of the inner part of the tubular structure, which also suggests that adsorption of CO in this case presents the highest degree of activation of the C–O bonding state, and its bonding state is located at the rightmost of the two cases as proof, as shown in Figure S4. This observation indicates that the C–O bond is maximally activated in this case, achieving the best adsorption effect, confirming our early findings, as shown in Figure 2.

In addition, the study of Figure S5 reveals interesting insights into the Bader charge distribution when CO is adsorbed on the inner side of the tubular structure. It is worth noting that this configuration exhibits the lowest total Bader charge value of the CO molecule, which is −0.48 |e|, lower than the −0.31 |e| adsorbed on the outer side of the tubular structure, indicating that the maximum electron supply from the tubular structure to the adsorbed CO molecules can be achieved on the inner side. This difference illustrates the excellent electron supply capacity of the tubular structure, which further enhances its effectiveness in adsorbing CO.

C–C Coupling

Building upon the successful adsorption of CO, the pivotal step in generating a multicarbon product containing two carbon atoms is C–C coupling. By combining the carbon atoms from two single carbon structures are combined in a coupled form, a dual carbon product can be formed. This paper primarily focuses on the coupling step of two CO molecules, ultimately yielding COCO, from which subsequent multicarbon products are generated. Given the significance of coupling in the reaction pathway, this section specifically conducts transition state calculations on the coupling steps to further investigate the mechanism of coupling.

The coupling method considered in this paper is to adsorb a CO molecule on a B atom and then directly capture another free CO with the adsorbed CO and then couple to form COCO, which is shown in Figure S6, with a calculated transition-state barrier of 0.43 eV. From the transition state structure in Figure S6, it can be seen that the free CO initially approaches the adsorbed CO from the air, and at this time, the C–C distance between them is 3.60 Å. Then, the C atom in the two CO molecules couple, so that the free CO is captured by the adsorbed CO, and the transition state structure is formed; at this time, the C–C distance is 1.99 Å. After the C–C coupling to form COCO, the C atom is finally adsorbed by the P atom of the neighboring B atom. Finally, the boron and phosphorus nanotubes adsorb the two C atoms of COCO onto the neighboring boron and phosphorus atoms, completing the reaction step with a C–C distance of 1.59 Å.

At the same time, we also considered the addition of more H to the reaction environment, as shown in Figures S7 and S8. It can be seen that in the path calculations under two H environments, the highest required energy is −0.60 eV, and then, the highest energy required for H to react with intermediates is −0.71 eV, indicating that it is more likely to occur. Further, our calculations indicate that the interaction between H and CO–CO coupling intermediates is better than that between H and the material, as shown in Figure S9.

Following the discussion of adsorption and coupling reactions above, we performed transition state search calculations for the subsequent 8-electron pathway to the C2 product ethanol (CH3CH2OH) over boron phosphide nanotube catalysts. The transition state barriers for the subsequent hydrogenation and protonation steps are all close to zero, except for the hydrogenation of *CH3COH to *CH3CHOH, which has a higher transition state barrier of 0.42 eV. The main reason for the generation of the high-energy barrier is the change in the reaction site, the C atom on the substrate of the CH3COH linkage is in a tetra-coordinated state, and the reaction site needs to be reduced by one to provide a position for the H in the process of hydrogenation, as shown in Figure S10. Also, Figures S11–S16 show the structure of the initial, transition, and final states with transition state energy barrier close to 0.

Grand Canonical DFT Calculation

At the same time, we also carried out calculations for the transition states with different charges and listed the change of the transition states with different charges for the steps with higher energy barriers, as shown in Figures S17–S18. From the figures, it can be found that for the transition state energy barriers of different steps, the effects of different charges on them are different, the step of coupling has a smaller change for the charge effect, and the transition state energy barriers are almost similar to the change of charge, which basically remains at 0.43 eV from −0.25 to 0.25 e. For the step of *CH3COH hydrogenation to *CH3CHOH, the transition state energy barrier is affected by the change of charge, as shown in Figure S14, the transition state energy barrier is more affected by the charge, and in the case of going from −0.25 to 0.10 e, the transition state energy barrier decreases from 0.49 to 0.40 eV. In the discussion above, the transition state energy barrier of the coupling is the highest in the case of zero charge. However, from the calculations of different charges, it can be found that in the case of −0.25 e, the *CH3COH hydrogenation is 0.06 eV higher than the transition state barrier of the coupling step. The transition state barrier of *CH3COH hydrogenation is 0.03 eV lower than the transition state barrier of the coupling step at 0.10 e. Therefore, the study of the situation at different charges can be beneficial to a more in-depth understanding of the reaction mechanism of the catalytic process.

In order to further investigate the effect of different charges on the transition state, we plotted the effect of charge on the structural change of the transition state, as shown in Figure S19. O–H bond distance versus net charge change for the transition state structure of *CO*COH hydrogenated to generate *COH*COH. It can be found that for the transition state for the hydrogenation of COCOH to generate COHCOH, its O–H bonding distance changes from 2.72 to 2.67 Å in the range of charge change from 0 to 1 e, which is a shortening of the distance by 0.05 Å. This also indicates that the bonding distance required for the transition state decreases gradually with the increase of charge, which means that the reaction gets closer to the product and vice versa to the reactant.

In traditional density functional theory (DFT), it typically employs a fixed number of electrons. However, real experimental responses tend to keep the potential constant.35 In our study, we introduced GCP (U) to consider electronic changes of the system by establishing an invariant potential, thereby obtaining a more realistic representation of catalytic reactions. Initially, we optimized the structure of systems with different charges by using VASP software. Subsequently, we derived the free energy of the system using the JDFT method45 for grand canonical DFT energy calculations under the CANDLE46 implicit solvent model conditions.

Recently, the grand canonical potential kinetics (GCP-K) methodology has been developed to characterize the change in response with an applied potential as the independent variable.51 GCP-K transforms F(n), which describes the free energy in terms of charge as a variable, into G (n; U) in terms of applied potential and charge by means of the Legendre transformation, which is defined as52,53

graphic file with name cm4c02106_m001.jpg (1)

where G is the grand canonical potential free energy, which is obtained from the function F(n) describing the total free energy in terms of charge as a variable, the number of electrons (n), the energy of the electrons Inline graphic at the standard hydrogen electrode (SHE), and the applied potential (U vs SHE). In order for G to be described by an applied potential, this would require matching the electron Fermi energy level with the energy level of the applied potential by varying the occupation of the electron band and thus the number of electrons.46 And that means

graphic file with name cm4c02106_m003.jpg (2)

Therefore, according to formulas S21–S23, the grand canonical potential as a function of U can be defined as

graphic file with name cm4c02106_m004.jpg (3)

Following these calculations, we observed a linear relationship between the reaction free energy F(n) obtained through the JDFT method and the net charge of the system, as shown in Figure 3a. Subsequently, by subtracting the contribution of each electron at the standard hydrogen electrode (SHE), a plot of the corrected free energy against the net charge of the system was constructed, as shown in Figure 3b. It can be found that the free energy of the system at this point is quadratically related to the net charge. The minimum value of free energy is at −0.50 e net charge, which reduces it by 0.44 eV compared to the free energy at 0.75 e net charge. Lastly, the reaction continues to occur and proceeds under an external potential. As shown in Figure 3c, G(n) also exhibits a quadratic relationship with net charge. At this point, the lowest point of the quadratic function is located near the 0 net charge, which is shifted to the right by 0.50 e net charge compared to the case without an applied potential, which also indicates that for the *CH2COH intermediate, the application of an external potential of −0.30 V is equivalent to an increase of the system by approximately 0.50 e net charge. At the same time, it can be noticed that the quadratic relationship between energy and charge in the system is enhanced and made more pronounced with the introduction of the applied potential.

Figure 3.

Figure 3

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Relationship between free energy and net electron number of the structure of *CH2COH in BPSWNT under the grand canonical potential. (a) Relationship between total free energy and the net number of electrons. (b) Relationship between free energy and the net number of electrons after removing electron contributions under standard hydrogen electrode (SHE) conditions. (c) Relationship between free energy and net electron number obtained by increasing the potential to −0.30 V.

By fitting the relationship between the free energy and charge of the system, we obtained the corresponding parameters a, b, and c for each intermediate species, as shown in Tables S1–S3. Using these parameters, we established the relationship between the applied potential and energy. After completing the calculation of intermediates, we also performed corresponding calculations on the transition states of each step in the entire reaction and obtained similar patterns. We have listed in Figure 4 the free energy and transition state barriers of key steps under applied potentials of −0.10, −0.30, and −0.50 V. It can be observed that the influence of the transition state barrier of the coupling step on the potential change is relatively small. With the increase of the applied potential, the transition state barrier basically remains at 0.43 eV, but the free energy will decrease under the influence of potential, from the original 0.11 to 0.07 eV. At potential of −0.10 V, the highest energy barrier step is the step of *CH3COH hydrogenation to generate *CH3CHOH, it is greatly affected by potential changes, and as the applied potential is more negative, its transition state energy barrier will decrease from 0.72 to 0.46 eV.

Figure 4.

Figure 4

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Reaction (a) transition state energy barriers and (b) free energy of FS-IS for the three key steps of C–C coupling to generate *CO*CO, *CO*CO hydrogenation to achieve *CO*COH and *CH3COH hydrogenation to generate *CH3CHOH in BPSWNT at pH = 0 under applied voltages of −0.10, −0.30, and −0.50 V.

All of the intermediates and transition state free energies in the reactions are calculated using the quadratic transformation of the energy obtained through grand canonical calculations. Given that the reaction rate for each step is directly influenced by the applied potential, we derived rate equations to understand the variation rates at each step of the reaction. Finally, we established a microkinetic model to obtain the overall reaction rate and concentrations. The rate equation for each intermediate state in the reaction is shown in formulas S1–S10 in the Supporting Information.

Microkinetics

The Eyring rate equation is used to express the rate constant of a chemical reaction and is given by the following expression: Inline graphic. Among them, kB is the Boltzmann constant, h is the Planck constant, T is the reaction temperature (room temperature = 298.15 K), and ΔG is the energy barrier for each transition state of the reaction. xi represents the concentration of each species in the reaction, and we have established constraint conditions ∑ixi = 1. At the same time, because we are considering steady-state conditions, the left side of the above rate equation is 0, so we can solve for the species concentration in each step of the reaction. By solving the above equation, we obtained the reaction rates of each intermediate state in the total reaction under steady-state approximation conditions. We ultimately derived the function of the current density variation with applied external potential, represented as the I–V curve and Tafel slope plot, as shown in Figure 5. From the graph, it is observed that at a current density of 10 mA/cm2, the onset potential of the system is −0.30 V, with a corresponding Tafel slope of 93.69 mV/dec.

Figure 5.

Figure 5

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(a) Relationship between applied potential and current density of BPSWNT under acidic conditions. (b) Corresponding Tafel curve.

Meanwhile, as shown in Tables S4 and S5, we listed the relevant values of the onset potential and Tafel slope for electrocatalytic reduction of CO or CO2 with other materials, thus illustrating the superior performance of the BPSWNT material for the electrocatalytic reduction reaction. The onset potential of the BPSWNT material was −0.30 eV, the Tafel slope was 93.69 mV/dec, and both the onset potential and the Tafel slope of BPSWNT are better than most of the current electrocatalysts.

We plotted Figure 6 to obtain the concentration of species at a key step of the reaction at different potentials. As seen from Figure 6, the highest concentration of intermediate structures in *CH3COH was observed under low potential conditions. It can also be seen from Figure 4 that the hydrogenation of *CH3COH is the highest energy barrier to be crossed among all the intermediates, under 0 to −0.30 V applied potential conditions. As a result, at an applied potential of 0 V, the highest concentration fraction of the *CH3COH intermediate is close to 1 and the concentration fractions of the other intermediates are near 0. Then, when the applied potential reaches the onset potential of −0.30 V, the reaction starts to proceed and the concentration fractions of the other intermediates begin to increase. Because the energy barrier of the coupling step is less affected with potential and basically stays at 0.43 eV and the energy barrier of the *CH3COH hydrogenation step is greatly affected by potential, the *CO concentration starts to increase at an applied potential of −0.43 V. It can be found that at an applied potential of −0.60 V, the *CO intermediate has become the main component. *CO intermediate has become the main component with a concentration of 59%, and the concentration component of BPSWNT-CH3COH intermediate decreases from 100% to 39%.

Figure 6.

Figure 6

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Changes in the concentration components of reaction intermediates at different potentials at pH = 0 (concentrations normalized to 1).

From Figure 7, it can be found that at an applied potential of −0.10 V, there is almost no change in the intermediate species except that the concentration starts to change when approaching the neutral condition. This is because it can be found in Figure S20 that at −0.10 V applied potential at pH = 3.50, the energy barrier for the hydrogenation of *CH3COH still remains the highest at 0.57 eV, so the concentration of *CH3COH intermediate has been dominant and close to 1. At pH 7, the energy barrier for the hydrogenation of *CH3COH to form *CH3CHOH is 0.45 eV, and the coupling energy barrier is 0.43 eV, so the *CH3COH intermediate no longer dominates and the CO intermediate fraction starts to increase, but since it is still 0.02 eV lower, the *CH3COH and *CO concentrations are 82% and 18%, respectively, at pH = 7.

Figure 7.

Figure 7

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Changes in the concentration composition of reaction intermediates (concentration normalized to 1) at different pH values with applied potentials of −0.10, −0.30, and −0.50 V.

When the applied potential reaches −0.30 V, it can be found that at pH = 0, the energy barrier of *CH3COH hydrogenation stays the highest at 0.58 eV in Figure S21, so the concentration fraction of *CH3COH is close to 1. At a pH of 3.5 and an applied voltage of −0.30 V, the energy barrier of *CH3COH hydrogenation is still the highest at 0.46 eV, but the coupling barrier is just lower by 0.03 eV, so the *CO intermediate component starts to increase to 16%. When pH is 7, the energy barrier of *CH3COH hydrogenation becomes 0.36 eV, the coupling energy barrier is 0.43 eV, and the hydrogenation energy barrier after coupling is 0.51 eV. So, *CH3COH intermediate component decreases, and the concentration components of *CO and *COCO intermediates increase, which are 78% and 22%, respectively.

When the applied potential reaches −0.50 V, at pH = 0, the coupling energy barrier is close to that of CH3COH hydrogenation to produce CH3CHOH, which is 0.43 and 0.46 eV, respectively, as shown in Figure S22. CH3COH intermediate no longer directly dominates as before, and its concentration fraction is 86%. When the pH is 3.50, its transition state energy barrier of 0.36 eV has been the smallest of the three key transition state energy barriers, so its concentration component in this interval decreases rapidly. The energy barrier of hydrogenation after coupling is 0.07 eV higher than the coupling energy barrier, so the concentration of *CO intermediate begins to decline and the concentration of *COCO intermediate begins to rise. Until pH = 7, *CO and *COCO intermediates together occupy the main position, and the concentration components are 49% and 51%, respectively.

In the meantime, we also considered the possibility of generating C1 and C2 products. For the C1 product, we considered CO hydrogenation to form COH and CHO, and we determined that the BPSWNT material is more likely to produce CHO. The energy required to produce COH is higher than that for the rate-determining step of the C2 pathway. On this basis, we calculated the free energy of each reaction step in the subsequent generation of CH4 products, as shown in Figure S23. We also calculated the transition states of the CO hydrogenation to generate CHO and the transition states of the CHO and CO coupling, as shown in Figure S24. These energy barriers at zero charge are 2.18 and 1.06 eV, respectively, while the transition state energy barrier for the CO–CO coupling is 0.43 eV. This indicates that the two CO couplings are more likely to occur, proving that for BPSWNT materials, C2 reactions are more favorable.

On this basis, we also considered ethylene and calculated its path structure free energies, as shown in Figure S25. We find that ethylene can adsorb on the substrate, while ethanol cannot adsorb on the substrate and will be directly desorbed, as shown in Figure S26. This also indicates that for BPSWNT materials, producing ethylene is more difficult than producing ethanol. Therefore, this article mainly discusses the reaction pathway for producing ethanol. Similarly, we calculated alternative pathways for generating ethanol and considered using *C*CO instead of *COH*COH to generate *C*COH, as shown in Figure S27. The energy required to generate *C*COH through *COH*COH is −0.95 eV, and the energy required to generate *C*COH through *C*CO is −0.66 eV. Therefore, *COH*COH is more easily formed. Hence, we adopt the current pathway to generate ethanol.

Conclusions

In summary, we have designed a boron phosphide nanotube material for catalytic CO reduction reactions. The thermodynamic and dynamic stability of the material has been confirmed through ab initio molecular dynamics and phonon spectroscopy, demonstrating feasibility for experimental synthesis. Subsequently, we have reported an extensive investigation of the electronic characteristics of CO adsorption on the tubular structure. Our results show that the material is able to adsorb CO more easily on the inner side by utilizing the confinement effect unique to its tubular structure, which improves the adsorption performance. Subsequently, we characterized the coupling methodology of the material, ultimately identifying the optimal coupling approach. Lastly, we have established the reaction mechanism and kinetics of boron phosphide nanotubes in CO reduction reactions using a grand canonical potential kinetic approach (GCP-K). Through this method, we have predicted that the onset potential of the material for the CORR is −0.30 V, and the Tafel slope is 93.69 mV/dec. We have demonstrated control over the reaction step barriers, free energies, and concentration of reaction intermediates by the applied potential and pH value. The designed material is efficient and stable, providing a promising route to electrochemical CO reduction and related chemical processes.

Acknowledgments

L.X. acknowledges financial support from National Natural Science Foundation of China-General Program (22273063), Major Program in Jiangsu University Natural Science Research (21KJA150004), Suzhou Technology Innovation Policy Independent Program, Suzhou Key Laboratory of Functional Nano & Soft Materials, Collaborative Innovation Center of Suzhou Nano Science & Technology, and the 111 Project. O.V.P. acknowledges support of the US National Science Foundation (CHE-2154367).

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.chemmater.4c02106.

  • Structural information, computational methods, adsorption pattern, crystal orbital Hamilton population analyses, Bader charge, energy barrier diagrams, reaction equations, rate equations, fitted parameters of the grand canonical potential or free energy for BPSWNT, comparison with other catalysts, and changes in the concentration components (PDF)

Author Contributions

# X.Y. and W.W. contributed equally to this work.

The authors declare no competing financial interest.

Supplementary Material

cm4c02106_si_001.pdf (2.7MB, pdf)

References

  1. Luo W.; Nie X.; Janik M. J.; Asthagiri A. Facet dependence of CO2 reduction paths on Cu electrodes. ACS Catal. 2016, 6 (1), 219–229. 10.1021/acscatal.5b01967. [DOI] [Google Scholar]
  2. Das A.; Mandal S. C.; Pathak B. Organic additive for the selective C2-product formation on Cu(100): a density functional theory mechanistic study. Catal. Sci. Technol. 2023, 13 (18), 5365–5373. 10.1039/D3CY00857F. [DOI] [Google Scholar]
  3. Bagchi D.; Riyaz M.; Raj J.; Roy S.; Singh A. K.; Cherevotan A.; Vinod C. P.; Peter S. C. Unraveling the cooperative mechanisms in ultralow copper-loaded WC@NGC for enhanced CO2 electroreduction to acetic acid. Chem. Mater. 2024, 36 (7), 3464–3476. 10.1021/acs.chemmater.4c00405. [DOI] [Google Scholar]
  4. Vichou E.; Perazio A.; Adjez Y.; Gomez-Mingot M.; Schreiber M. W.; Sánchez-Sánchez C. M.; Fontecave M. Tuning selectivity of acidic carbon dioxide electrolysis via surface modification. Chem. Mater. 2023, 35 (17), 7060–7068. 10.1021/acs.chemmater.3c01326. [DOI] [Google Scholar]
  5. Feld L. G.; Boehme S. C.; Morad V.; Sahin Y.; Kaul C. J.; Dirin D. N.; Raino G.; Kovalenko M. V. Quantifying forster resonance energy transfer from single perovskite quantum dots to organic dyes. ACS Nano 2024, 18 (14), 9997–10007. 10.1021/acsnano.3c11359. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Arenas Esteban D.; Pacquets L.; Choukroun D.; Hoekx S.; Kadu A. A.; Schalck J.; Daems N.; Breugelmans T.; Bals S. 3D characterization of the structural transformation undergone by Cu@Ag core–shell nanoparticles following CO2 reduction reaction. Chem. Mater. 2023, 35 (17), 6682–6691. 10.1021/acs.chemmater.3c00649. [DOI] [Google Scholar]
  7. Vos R. l E.; Kolmeijer K. E.; Jacobs T. S.; van der Stam W.; Weckhuysen B. M.; Koper M. T. M. How temperature affects the selectivity of the electrochemical CO2 reduction on copper. ACS Catal. 2023, 13 (12), 8080–8091. 10.1021/acscatal.3c00706. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Pham T. H. M.; Zhang J.; Li M.; Shen T.-H.; Ko Y.; Tileli V.; Luo W.; Zuttel A. Enhanced electrocatalytic CO2 reduction to C2+ products by adjusting the local reaction environment with polymer binders. Adv. Energy Mater. 2022, 12 (9), 2103663 10.1002/aenm.202103663. [DOI] [Google Scholar]
  9. Gao D.; Arán-Ais R. M.; Jeon H. S.; Roldan Cuenya B. Rational catalyst and electrolyte design for CO2 electroreduction towards multicarbon products. Nat. Catal. 2019, 2 (3), 198–210. 10.1038/s41929-019-0235-5. [DOI] [Google Scholar]
  10. Gauthier J. A.; Lin Z.; Head-Gordon M.; Bell A. T. Pathways for the Formation of C2+ Products under Alkaline Conditions during the Electrochemical Reduction of CO2. ACS Energy Letters 2022, 7 (5), 1679–1686. 10.1021/acsenergylett.2c00167. [DOI] [Google Scholar]
  11. Mandal S. C.; Das A.; Roy D.; Das S.; Nair A. S.; Pathak B. Developments of the heterogeneous and homogeneous CO2 hydrogenation to value-added C2+-based hydrocarbons and oxygenated products. Coordin. Chem. Rev. 2022, 471, 214737 10.1016/j.ccr.2022.214737. [DOI] [Google Scholar]
  12. Garza A. J.; Bell A. T.; Head-Gordon M. Mechanism of CO2 reduction at copper surfaces: pathways to C2 products. ACS Catal. 2018, 8 (2), 1490–1499. 10.1021/acscatal.7b03477. [DOI] [Google Scholar]
  13. Liu X.; Schlexer P.; Xiao J.; Ji Y.; Wang L.; Sandberg R. B.; Tang M.; Brown K. S.; Peng H.; Ringe S.; Hahn C.; Jaramillo T. F.; Norskov J. K.; Chan K. pH effects on the electrochemical reduction of CO2 towards C2 products on stepped copper. Nat. Commun. 2019, 10 (1), 32. 10.1038/s41467-018-07970-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Das A.; Mandal S. C.; Das S.; Pathak B. Ga and Zn atom-doped CuAl2O4(111) surface-catalyzed CO2 conversion to dimethyl ether: Importance of acidic sites. J. Phys. Chem. C 2022, 126 (51), 21628–21637. 10.1021/acs.jpcc.2c07240. [DOI] [Google Scholar]
  15. Kortlever R.; Shen J.; Schouten K. J.; Calle-Vallejo F.; Koper M. T. Catalysts and reaction pathways for the electrochemical reduction of carbon dioxide. J. Phys. Chem. Lett. 2015, 6 (20), 4073–4082. 10.1021/acs.jpclett.5b01559. [DOI] [PubMed] [Google Scholar]
  16. Li F.; Thevenon A.; Rosas-Hernandez A.; Wang Z.; Li Y.; Gabardo C. M.; Ozden A.; Dinh C. T.; Li J.; Wang Y.; Edwards J. P.; Xu Y.; McCallum C.; Tao L.; Liang Z. Q.; Luo M.; Wang X.; Li H.; O’Brien C. P.; Tan C. S.; Nam D. H.; Quintero-Bermudez R.; Zhuang T. T.; Li Y. C.; Han Z.; Britt R. D.; Sinton D.; Agapie T.; Peters J. C.; Sargent E. H. Molecular tuning of CO2-to-ethylene conversion. Nature 2020, 577 (7791), 509–513. 10.1038/s41586-019-1782-2. [DOI] [PubMed] [Google Scholar]
  17. Chen X.; Chen J.; Alghoraibi N. M.; Henckel D. A.; Zhang R.; Nwabara U. O.; Madsen K. E.; Kenis P. J. A.; Zimmerman S. C.; Gewirth A. A. Electrochemical CO2-to-ethylene conversion on polyamine-incorporated Cu electrodes. Nat. Catal. 2021, 4 (1), 20–27. 10.1038/s41929-020-00547-0. [DOI] [Google Scholar]
  18. Wang Z.; Li Y.; Zhao X.; Chen S.; Nian Q.; Luo X.; Fan J.; Ruan D.; Xiong B. Q.; Ren X. Localized alkaline environment via In situ electrostatic confinement for enhanced CO2-to-ethylene conversion in neutral medium. J. Am. Chem. Soc. 2023, 145 (11), 6339–6348. 10.1021/jacs.2c13384. [DOI] [PubMed] [Google Scholar]
  19. Hoang T. T. H.; Verma S.; Ma S.; Fister T. T.; Timoshenko J.; Frenkel A. I.; Kenis P. J. A.; Gewirth A. A. Nanoporous copper-silver alloys by additive-controlled electrodeposition for the selective electroreduction of CO2 to ethylene and ethanol. J. Am. Chem. Soc. 2018, 140 (17), 5791–5797. 10.1021/jacs.8b01868. [DOI] [PubMed] [Google Scholar]
  20. Clark E. L.; Hahn C.; Jaramillo T. F.; Bell A. T. Electrochemical CO2 reduction over compressively strained CuAg surface alloys with enhanced multi-carbon oxygenate selectivity. J. Am. Chem. Soc. 2017, 139 (44), 15848–15857. 10.1021/jacs.7b08607. [DOI] [PubMed] [Google Scholar]
  21. Woldu A. R.; Huang Z.; Zhao P.; Hu L.; Astruc D. Electrochemical CO2 reduction (CO2RR) to multi-carbon products over copper-based catalysts. Coord. Chem. Rev. 2022, 454, 214340 10.1016/j.ccr.2021.214340. [DOI] [Google Scholar]
  22. Amirbeigiarab R.; Tian J.; Herzog A.; Qiu C.; Bergmann A.; Cuenya B. R.; Magnussen O. M. Atomic-scale surface restructuring of copper electrodes under CO2 electroreduction conditions. Nat. Catal. 2023, 6 (9), 837–846. 10.1038/s41929-023-01009-z. [DOI] [Google Scholar]
  23. Novoselov K. S.; Geim A. K.; Morozov S. V.; Jiang D.; Zhang Y.; Dubonos S. V.; Grigorieva I. V.; Firsov A. A. Electric field effect in atomically thin carbon films. Science 2004, 306 (5696), 666–669. 10.1126/science.1102896. [DOI] [PubMed] [Google Scholar]
  24. Meng L.; Yan L.-K.; Vines F.; Illas F. Surface termination dependent carbon dioxide reduction reaction on Ti3C2 MXene. J. Mater. Chem. A 2024, 12 (13), 7856–7874. 10.1039/D4TA00320A. [DOI] [Google Scholar]
  25. Li Z.; Attanayake N. H.; Blackburn J. L.; Miller E. M. Carbon dioxide and nitrogen reduction reactions using 2D transition metal dichalcogenide (TMDC) and carbide/nitride (MXene) catalysts. Energy Environ. Sci. 2021, 14 (12), 6242–6286. 10.1039/D1EE03211A. [DOI] [Google Scholar]
  26. Chia X.; Pumera M. Characteristics and performance of two-dimensional materials for electrocatalysis. Nat. Catal. 2018, 1 (12), 909–921. 10.1038/s41929-018-0181-7. [DOI] [Google Scholar]
  27. Zhao R.; Wang Y.; Ji G.; Zhong J.; Zhang F.; Chen M.; Tong S.; Wang P.; Wu Z.; Han B.; Liu Z. Partially nitrided Ni nanoclusters achieve energy-efficient electrocatalytic CO2 reduction to CO at ultralow overpotential. Adv. Mater. 2023, 35 (5), 2205262 10.1002/adma.202205262. [DOI] [PubMed] [Google Scholar]
  28. Fan K.; Jia Y.; Ji Y.; Kuang P.; Zhu B.; Liu X.; Yu J. Curved surface boosts electrochemical CO2 reduction to formate via bismuth nanotubes in a wide potential window. ACS Catal. 2020, 10 (1), 358–364. 10.1021/acscatal.9b04516. [DOI] [Google Scholar]
  29. Chaipornchalerm P.; Nunthakitgoson W.; Mano P.; Kidkhunthod P.; Montoya A.; Namuangruk S.; Wattanakit C. Rational design of Fe single sites supported on hierarchical zeolites via atomic layer deposition for few-walled carbon nanotube production. ACS Appl. Mater. Interfaces. 2024, 16 (26), 33590–33600. 10.1021/acsami.4c06105. [DOI] [PubMed] [Google Scholar]
  30. Pu Z.; Liu T.; Amiinu I. S.; Cheng R.; Wang P.; Zhang C.; Ji P.; Hu W.; Liu J.; Mu S. Transition-metal phosphides: Activity origin, energy-related electrocatalysis applications, and synthetic strategies. Adv. Funct. Mater. 2020, 30 (45), 2004009 10.1002/adfm.202004009. [DOI] [Google Scholar]
  31. Batugedara T. N.; Brock S. L. Role of noble- and base-metal speciation and surface segregation in Ni2–xRhxP nanocrystals on electrocatalytic water splitting reactions in alkaline media. Chem. Mater. 2022, 34 (10), 4414–4427. 10.1021/acs.chemmater.2c00041. [DOI] [Google Scholar]
  32. Mou S.; Wu T.; Xie J.; Zhang Y.; Ji L.; Huang H.; Wang T.; Luo Y.; Xiong X.; Tang B.; Sun X. Boron phosphide nanoparticles: A nonmetal catalyst for high-selectivity electrochemical reduction of CO2 to CH3OH. Adv. Mater. 2019, 31 (36), 1903499 10.1002/adma.201903499. [DOI] [PubMed] [Google Scholar]
  33. Hussien M. K.; Sabbah A.; Qorbani M.; Putikam R.; Kholimatussadiah S.; Tzou D. M.; Elsayed M. H.; Lu Y. J.; Wang Y. Y.; Lee X. H.; Lin T. Y.; Thang N. Q.; Wu H. L.; Haw S. C.; Wu K. C.; Lin M. C.; Chen K. H.; Chen L. C. Constructing B-N-P Bonds in ultrathin holey g-C3N4 for regulating the local chemical environment in photocatalytic CO2 reduction to CO. Small 2024, 20 (35), 2400724 10.1002/smll.202400724. [DOI] [PubMed] [Google Scholar]
  34. Song J.; Lei X.; Mu J.; Li J.; Song X.; Yan L.; Ding Y. Boron-doped nickel-nitrogen-carbon single-atom catalyst for boosting electrochemical CO2 reduction. Small 2023, 19 (52), 2305666 10.1002/smll.202305666. [DOI] [PubMed] [Google Scholar]
  35. Sundararaman R.; Goddard W. A.; Arias T. A. Grand canonical electronic density-functional theory: Algorithms and applications to electrochemistry. J. Chem. Phys. 2017, 146 (11), 114104. 10.1063/1.4978411. [DOI] [PubMed] [Google Scholar]
  36. Liu C.; Qian J.; Ye Y.; Zhou H.; Sun C.-J.; Sheehan C.; Zhang Z.; Wan G.; Liu Y.-S.; Guo J.; Li S.; Shin H.; Hwang S.; Gunnoe T. B.; Goddard W. A. III; Zhang S. Oxygen evolution reaction over catalytic single-site Co in a well-defined brookite TiO2 nanorod surface. Nat. Catal. 2021, 4 (1), 36–45. 10.1038/s41929-020-00550-5. [DOI] [Google Scholar]
  37. Perdew J. P.; Burke K.; Ernzerhof M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1997, 78 (7), 1396–1396. 10.1103/PhysRevLett.78.1396. [DOI] [PubMed] [Google Scholar]
  38. Blochl P. E. Projector augmented-wave method. Phys. Rev. B 1994, 50 (24), 17953–17979. 10.1103/PhysRevB.50.17953. [DOI] [PubMed] [Google Scholar]
  39. Grimme S.; Antony J.; Ehrlich S.; Krieg H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 2010, 132 (15), 154104. 10.1063/1.3382344. [DOI] [PubMed] [Google Scholar]
  40. Mathew K.; Sundararaman R.; Letchworth-Weaver K.; Arias T. A.; Hennig R. G. Implicit solvation model for density-functional study of nanocrystal surfaces and reaction pathways. J. Chem. Phys. 2014, 140 (8), 084106 10.1063/1.4865107. [DOI] [PubMed] [Google Scholar]
  41. Dronskowski R.; Blochl P. E. Crystal orbital hamilton populations (COHP) - energy-resolved visualization of chemical bonding in solids based on density-functional calculations. J. Phys. Chem. C 1993, 97 (33), 8617–8624. 10.1021/j100135a014. [DOI] [Google Scholar]
  42. Maintz S.; Deringer V. L.; Tchougréeff A. L.; Dronskowski R. LOBSTER: A tool to extract chemical bonding from plane-wave based DFT. J. Comput. Chem. 2016, 37 (11), 1030–1035. 10.1002/jcc.24300. [DOI] [PMC free article] [PubMed] [Google Scholar]
  43. Deringer V. L.; Tchougreeff A. L.; Dronskowski R. Crystal orbital hamilton population (COHP) analysis as projected from plane-wave basis sets. J. Phys. Chem. A 2011, 115 (21), 5461–5466. 10.1021/jp202489s. [DOI] [PubMed] [Google Scholar]
  44. Henkelman G.; Uberuaga B. P.; Jónsson H. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys. 2000, 113 (22), 9901–9904. 10.1063/1.1329672. [DOI] [Google Scholar]
  45. Sundararaman R.; Letchworth-Weaver K.; Schwarz K. A.; Gunceler D.; Ozhabes Y.; Arias T. A. JDFTx: Software for joint density-functional theory. SoftwareX 2017, 6, 278–284. 10.1016/j.softx.2017.10.006. [DOI] [PMC free article] [PubMed] [Google Scholar]
  46. Sundararaman R.; Goddard W. A. The charge-asymmetric nonlocally determined local-electric (CANDLE) solvation model. J. Chem. Phys. 2015, 142 (6), 064107 10.1063/1.4907731. [DOI] [PubMed] [Google Scholar]
  47. Letchworth-Weaver K.; Arias T. A. Joint density functional theory of the electrode-electrolyte interface: Application to fixed electrode potentials, interfacial capacitances, and potentials of zero charge. Phys. Rev. B 2012, 86 (7), 075140 10.1103/PhysRevB.86.075140. [DOI] [Google Scholar]
  48. Yang P.; Zhao Z. J.; Chang X.; Mu R.; Zha S.; Zhang G.; Gong J. The Functionality of surface hydroxy groups on the selectivity and activity of carbon dioxide reduction over cuprous oxide in aqueous solutions. Angew. Chem., Int. Ed. Engl. 2018, 57 (26), 7724–7728. 10.1002/anie.201801463. [DOI] [PubMed] [Google Scholar]
  49. Liu J.; Sun L.; Sun Y.; Sun J.; Pan Y.; Xu M.; Lang Y.; Zhai D.; Deng W.; Li Y.; Yang L. Theoretical insights into lanthanide rare earth single-atom catalysts for electrochemical CO2 reduction. J. Mater. Chem. A 2024, 12 (26), 16183–16189. 10.1039/D4TA02381A. [DOI] [Google Scholar]
  50. Pei J.; Wang T.; Sui R.; Zhang X.; Zhou D.; Qin F.; Zhao X.; Liu Q.; Yan W.; Dong J.; Zheng L.; Li A.; Mao J.; Zhu W.; Chen W.; Zhuang Z. N-Bridged Co–N–Ni: new bimetallic sites for promoting electrochemical CO2 reduction. Energy Environ. Sci. 2021, 14 (5), 3019–3028. 10.1039/D0EE03947K. [DOI] [Google Scholar]
  51. Huang Y.; Nielsen R. J.; Goddard W. A. III Reaction mechanism for the hydrogen evolution reaction on the basal plane sulfur vacancy site of MoS2 using grand canonical potential kinetics. J. Am. Chem. Soc. 2018, 140 (48), 16773–16782. 10.1021/jacs.8b10016. [DOI] [PubMed] [Google Scholar]
  52. Jinnouchi R.; Anderson A. B. Electronic structure calculations of liquid-solid interfaces: Combination of density functional theory and modified Poisson-Boltzmann theory. Phys. Rev. B 2008, 77 (24), 245417 10.1103/PhysRevB.77.245417. [DOI] [Google Scholar]
  53. Gunceler D.; Letchworth-Weaver K.; Sundararaman R.; Schwarz K. A.; Arias T. A. The importance of nonlinear fluid response in joint density-functional theory studies of battery systems. Model. Simul. Mater. Sci. Eng. 2013, 21 (7), 074005 10.1088/0965-0393/21/7/074005. [DOI] [Google Scholar]

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