The adsorption characteristics and mechanism of C1 molecules on two-dimensional SrTiO₃ films

Abstract

The microscopic mechanism of molecular adsorption is a key and yet to be fully resolved scientific issue. This study employs density functional theory combined with ab initio molecular dynamics simulations to systematically investigate the adsorption behavior of three representative C1 molecules (CO, CO₂, and CH₂O) on the surface of pristine and point-defective two-dimensional SrTiO₃ films, aiming to further understand the general principles of molecular adsorption. The findings indicate that the adsorption configurations of C1 molecules are primarily governed by electrostatic interactions, i.e., the high potential regions of the molecules tend to combine with the low potential regions of the surface, and vice versa. Besides, the adsorption strength is significantly affected by the distribution of valence electrons and the configuration of molecular orbitals. Moreover, charge transfer effects alter the distribution of electrostatic potential, thereby causing a transition in the configuration of adsorbed molecules. These discoveries are of significant importance for identifying reaction sites and predicting catalytic mechanisms.

---

1. Introduction

With the increasing urgency of environmental pollution control and energy conversion needs, the development of efficient and highly selective gas adsorption materials has become a major focus.^1,2 Two-dimensional (2D) perovskite oxide films characterized by unique quantum confinement effects, abundant surface active sites, and controllable electronic structures exhibit great application potential in gas adsorption, catalysis, sensing, and related fields.^3–6 For instance, oxygen vacancies on the surface of 2D perovskite oxide films can enhance the binding force with CO molecules,⁷ and morphology engineering enables efficient solar-driven water evaporation and catalytic degradation of pollutants.⁸ Furthermore, hetero-integration with materials such as graphene and MXenes can couple light absorption with gas response characteristics to develop multifunctional devices.⁹ These breakthroughs highlight the strong application prospects of 2D perovskite films in gas adsorption and related fields.

However, there are still several key scientific issues that need to be addressed. Structural and electronic reconstructions under 2D confinement, including lattice distortion, electronic reconstruction, and surface polarization, can obviously influence adsorption pathways, yet current theoretical models do not fully capture these effects. For instance, Cheng et al.¹⁰ regulated the stability of quasi-2D perovskite through a stress relaxation strategy, revealing the profound influence of residual stress on material properties, while the detailed regulatory mechanisms remain poorly understood. And although defect engineering approaches, such as oxygen vacancies and adsorbed atoms, can enhance gas adsorption, the underlying microscopic mechanisms are not yet fully clarified.^7,11 Furthermore, molecular adsorption studies are often scattered across different material systems, and there are few systematic comparative analyses based on a unified material platform, hindering the establishment of a universal correlation model for composition–structure–performance relationship.^3,12 For example, while SrTiO₃ (STO) films exhibit excellent photocatalytic and dielectric performance, the relationship between these functionalities and their gas adsorption behavior remains insufficiently explored, constraining their applications in multifunctional devices.

To address the aforementioned challenges, this study focuses on 2D STO films and systematically investigates the adsorption behavior of C1 molecules such as CO, CO₂, and CH₂O on both pristine and point defect-containing surfaces. By analyzing the physical and chemical properties such as the distribution of electrostatic potential, charge transfer, and molecular orbitals, the fundamental principles and intrinsic mechanisms governing the adsorption configurations are elucidated. How point-defect engineering modulates C1 adsorption is further studied, revealing the ways to tune binding strength and selectivity. These insights provide guidelines for optimizing the gas sensitivity of 2D perovskite films and advancing their deployment in gas adsorption, sensing, and related applications.

2. Computational methods

All the calculations were performed in the framework of density functional theory (DFT) using the projector augmented plane-wave (PAW) method,^13,14 as implemented in the Vienna Ab initio Simulation Package (VASP).^15,16 The generalized gradient approximation parameterized by Perdew, Burke and Ernzerhof¹⁷ was selected to describe the exchange correlation between electrons. The cutoff kinetic energy was set at 450 eV. The electronic and ionic loops converged to 10⁻⁵ eV and 0.02 eV × Å⁻¹, respectively. A vacuum layer over 15 Å was applied to avoid artificial interaction between periodic images and dipole correction was employed to improve the convergence.¹⁸ The surface was simulated in a 4 × 4 superlattice model, with a lateral dimension of about 15.6 Å. The Brillouin zone integration was performed using a 1 × 1 × 1, 3 × 3 × 1 Monkhorst-Pack¹⁹k-grid for structural relaxation and static calculations, respectively. The long-range van der Waals interaction was described using the DFT-D3 approach.²⁰ All structures were visualized with VESTA software²¹ and the isovalue of electron density was set to 0.1.

The quench molecular dynamics (QMD) approach was used to determine the optimal adsorption configuration. The QMD simulation was performed in a cononical (NVT) ensemble with the temperature controlled at 300 K by the Nosé–Hoover method.²² The simulation lasted for 15 ps with a time step of 1.5 fs, and the adsorption structure was sampled every 500 steps. More details about this method are provided in the supplementary information.

The adsorption energy of the C1 molecules (E_ad) is defined as E_ad = E(C1@STO) − E(STO) − E(C1), where E(C1@STO), E(STO) and E(C1) represent the total energy of the system after adsorbing the C1 molecules, the energy of the pristine 2D STO film, and the energy of the C1 molecules, respectively.

3. Results and discussion

3.1. Adsorption sites and configurations of C1 molecules

3.1.1. Adsorption on the Ti–O surface. Given the significant role of CO₂ in numerous chemical processes and environmental science, the following text mainly focus on the adsorption behavior of it, while the results for CO and CH₂O are provided in the supplementary information. QMD simulations reveal that both CO₂ and CH₂O molecules exhibit strong adsorption within a few hundred time steps, becoming stably anchored at specific adsorption sites. In contrast, CO molecules remain weakly bound throughout the entire MD simulations, continuously migrating across surface Ti atoms.

CO₂, CO, and CH₂O molecules each exhibit a single predominant adsorption configuration on the Ti–O surface. Fig. 1a and Fig. S1 show the relaxed geometries obtained after QMD. For CO₂ molecules, after adsorption, they are arranged parallel to the Ti–O–Ti atomic chain, with the C atom located directly above the surface O atom. Its two O atoms each form bonds with one surface Ti atom, and the original 180 °C–O–C bond bends, forming a carbonate like structure. In the case of CH₂O, the C–O bonds are also arranged along the Ti–O–Ti atomic chain. Its C atom forms a bond with a surface O atom, and its O atom combines with the adjacent surface Ti atom, forming a structure similar to that of dioxymethylene species. The CO molecule adopts a tilted orientation, with the C atom directed toward a surface Ti atom. Various initial configurations were tested and all converged to similar final adsorption geometries.

Fig. 1 Top view (left) and side view (top right) of the adsorption configurations of CO₂ on the (a) pristine Ti–O, (b) Ti-adatom doped Ti–O, (c) O vacancy doped Ti–O, and (d) pristine Sr–O surfaces of 2D STO film. The bottom right of each panel shows the side view of the electrostatic potential mapped onto the electron density isosurface. High potential regions are shown in red, and low potential regions in blue. This color scheme is consistently used in subsequent electrostatic potential maps.

It is worth pointing out that if CO₂ is initially placed parallel to the Ti–O–Ti chain at a distance of approximately 2.5 Å above the surface and then structurally relaxed, it stays laterally about 3.5 Å above the surface. This relaxed structure was used as the initial state and the adsorbed configuration obtained from QMD simulations was used as the final state, and then the intermediate states between them were searched using the climbing image nudged elastic band (CI-NEB) method. As shown in Fig. 2, the results reveal that CO₂ overcomes an energy barrier of approximately 0.11 eV during its approach toward the Ti–O surface. This explains why CO₂ is repelled from the surface during the structural relaxation process mentioned above. Nevertheless, the barrier is relatively low, suggesting that CO₂ can readily acquire sufficient thermal energy to surpass it and form strong chemisorption with the Ti–O surface. These findings also indicate that it is difficult for only structural relaxation to determine the reliable adsorption configuration of CO₂ on the STO surface. In contrast, CH₂O does not need to cross an energy barrier during the adsorption process, as shown in Fig. S2, indicating that CH₂O molecules are more prone to surface adsorption.

Fig. 2 Variation of relative energy (ΔE) of the CO₂ plus 2D STO film system along the CO₂ adsorption path. The insets show the side view of the initial, intermediate, and final configurations of CO₂ on the Ti–O surface with the corresponding O–C–O bond angles of the CO₂ molecule indicated in each configuration.

It can also be seen from Fig. 2 that the transition from the initial configuration to the final configuration is accompanied by a gradual decrease in the O–C–O bond angle of CO₂ from 180° to about 131.8°. This behavior can be attributed to the enhanced interaction between the C atom and the surface O atom, as indicated by the corresponding integrated crystal orbital Hamilton population (ICOHP) value decreasing from approximately −0.1 eV before adsorption to about −10.0 eV after adsorption. This enhanced C–O (surface) interaction weakens the original intramolecular C–O bonds in CO₂, whose ICOHP values increase from around −18.2 eV to approximately −13.1 eV. It is well-established that CO₂ molecules adopt a linear structure due to the sp hybridization of the central C atom. However, during adsorption, the formation of bonds between the C atom and surface O atoms drives a gradual transition of the C atom toward sp²-like hybridization. Consequently, the linear structure of CO₂ becomes progressively distorted, leading to the observed reduction in the O–C–O bond angle along the adsorption pathway.

By testing, it was found that the Ti adatom at the hollow site is most stable on the Ti–O surface. As shown in Fig. 1b and Fig. S3a, b, CO₂ exhibits three adsorption configurations at the Ti adatom site: two molecular adsorption modes (denoted as type 1 and type 2) and one dissociative adsorption mode. The two molecular configurations are structurally similar, both featuring side-on adsorption of one C–O bond onto the Ti adatom. In the dissociative adsorption configuration, one O atom of CO₂ binds atop the Ti adatom, while the remaining fragment forms a CO molecule, with the C atom oriented toward a surface Ti atom. For CO, its C–O bond interacts with the Ti adatom, which gives rise to a lateral adsorption, as shown in Fig. S3c. For CH₂O, it is also the C–O bond that forms a bond with the Ti adatom, but its C atom points towards an adjacent surface Ti atom rather than a surface O atom, as shown in Fig. S3d.

For clarity, the two surface Ti atoms at the edge of O vacancies were labeled as Ti1 and Ti2, respectively. The CO₂ molecule adopts an adsorption configuration parallel to the Ti–O–Ti chain along the edge of the O vacancies, with its C atom positioned directly above a surface O atom, while its two O atoms form bonds with Ti1 and another surface Ti atom, respectively (Fig. 1c). This configuration closely resembles that of CO₂ adsorbed on the defect-free surface. For CO, its O and C atoms form bonds with Ti1 and Ti2, respectively, as illustrated in Fig. S4a. For CH₂O, two stable adsorption configurations are identified. The first one is similar to that of CO, where the O and C atoms form a bond with Ti1 and Ti2, respectively; in the second configuration, the O atom occupies the O vacancy site, while the C atom is positioned diagonally above this O atom and forms a bond with Ti2 (Fig. S4b, c).

3.1.2. Adsorption on the Sr–O surface. Along the [001] crystal direction, STO has two distinct surface terminations, i.e., Sr–O and Ti–O surfaces, which are referred to as “a cornerstone in surface science and materials physics”²³ and have been widely studied.²⁴ In spite of the reported low catalytic activity of the Sr–O surface,^25,26 the adsorption behavior of C1 molecules on this termination was investigated. As shown in Fig. 1d and Fig. S5, both CO₂ and CH₂O are adsorbed on the Sr–O surface primarily through the bonding of their respective C atoms with surface O atoms. However, CO exhibits weak adsorption on the Sr–O surface. Throughout the QMD simulation, CO continuously migrates across the surface, failing to form a strong adsorption.

A comprehensive analysis of the aforementioned results prompts a fundamental scientific inquiry: why do the C1 molecules adopt specific adsorption configurations rather than other theoretically possible patterns? For example, why does the C atom of CO₂ not adsorb onto Ti sites on the pristine Ti–O surface, and why does CO₂ not adopt a vertical orientation with its O atom bonding to a Ti site? To address these questions, the following section explores the underlying mechanisms by calculating the electrostatic potential distribution and analyzing electronic structures, such as molecular orbitals.

3.2. The impact of electrostatic potential on the adsorption configuration

If molecules form covalent bonds with the surface (such as chemical adsorption), then the reaction sites must have sufficient valence electron density. Additionally, in the early stages of the adsorption process, if there is an electrostatic interaction between the surface and molecules, this interaction has a significant impact on the adsorption configuration. Accordingly, the electrostatic potential (ESP) maps projected onto the electron density were analyzed to capture the combined influence of valence electron density and electrostatic potential on C1 adsorption.

As shown in Fig. 3a, b and Fig. S6, regardless of the presence of point defects, the electron density isosurfaces around the Ti and O atoms on the Ti–O surface are interconnected, revealing some covalent interaction between them; whereas on the Sr–O surface, the electron density around the Sr and O atoms is spherically distributed, exhibiting typical ionic bond characteristics. Moreover, with or without point defects, the ESP is low at the cation (Ti, Sr) sites and high at the anion (O) site. For the C1 molecules, the low-potential region is located at the C atom, while the high-potential region is at the O atom.

Fig. 3 The electronic electrostatic potential mapped electron density isosurface of (a) Ti–O surface, (b) Sr–O surface and (c) CO₂ molecule. The colored isosurfaces in (c) are given in different perspectives.

Analysis of the adsorption configurations reveals that the interaction between C1 molecules and the surface of 2D STO films follows a distinct electrostatic potential matching principle: high-ESP regions of the C1 molecules preferentially approach low-ESP surface sites, and vice versa. Taking CO₂ as an example, the low-ESP regions at the C atom interact with high-ESP surface O sites, while the high-ESP regions at the O atom interact with low-ESP Ti sites. This behavior arises primarily from the electrostatic attraction between the high and low ESP regions, which brings the corresponding sites closer to each other and forms bonds. Although the Sr atoms are also low-ESP sites, they are in the ionic form, lacking valence electrons around them. Therefore, C1 molecules cannot form covalent bonds with Sr atoms when adsorbed on the Sr–O surface, and thus are not anchored at the Sr sites.

To further rationalize the adsorption orientation of CO₂, its density of states (DOS) was computed (Fig. 4a) and then used to construct the molecular orbital energy levels (Fig. 4b). As shown in Fig. 4a, the highest occupied molecular orbital (HOMO) of CO₂ is the non-bonding orbital contributed by the O atom, which has low reactivity. Additionally, the lobes of the wave function of the HOMO have both positive and negative components at the O ends, making it unfavorable for them to bond simultaneously with other orbitals. Therefore, although CO₂ has a high electrostatic potential at the O ends, it does not form a bond with the surface Ti atoms in a vertical manner.

Fig. 4 (a) The calculated DOS and (b) the schematic energy level diagram of molecular orbitals of CO₂. The distribution of electrons and wave functions of HOMO are also shown in (b). The positive and negative components of the wave function are denoted in purple and cyan, respectively. To avoid overlapping of data lines, the negative value of the DOS for C atoms is given in (a).

Compared to the adsorption on the pristine Ti–O surface (Fig. 1b), the adsorption behavior of CH₂O on the Ti adatom has undergone notable changes: its C atom no longer bonds to a high-ESP surface O atom, but instead tilts toward a neighboring low-ESP surface Ti atom. According to the analysis using LOBSTER software,²⁷ the ESP of the C atom of CH₂O increases significantly from approximately 6.5 V when adsorbed on the pristine Ti–O surface to around 3.0 V when adsorbed at the Ti adatom. Therefore, the C atom is more likely to engage in an attractive electrostatic interaction with a nearby surface Ti atom, which exhibits a much lower electrostatic potential (about −18 V), rather than with a surface O atom, whose potential is comparatively higher (around 11 V).

The electrostatic interaction principle described above provides a reasonable explanation for the variations in adsorption sites and configurations of C1 molecules on 2D STO films. However, this approach has inherent limitations in assessing adsorption strength, characterizing the nature of chemical bonding, and distinguishing the spatial distribution of electrostatic potentials. Moreover, it does not offer insight into the underlying mechanisms driving changes in electrostatic potential. To gain a more comprehensive understanding of the adsorption characteristics of C1 molecules, it is essential to further investigate their molecular orbitals and other electronic structure features.

3.3. Adsorption energy and chemical bond properties

Adsorption energy is a critical physical parameter that reflects the thermodynamic stability and interaction strength of adsorption configurations, playing a fundamental role in understanding adsorption behavior. The adsorption energies of the C1 molecules at various surface sites were calculated and are summarized in Table 1 and Table S1. In the pristine region, CO₂ and CH₂O exhibit relatively high adsorption energies (exceeding 1 eV in absolute value), indicating strong chemisorption on the surface. In contrast, CO has a much lower adsorption energy (around 0.3 eV), characteristic of physisorption. This result accounts for the weak binding of CO to the STO surface and its tendency to migrate rather than remain fixed. Upon the introduction of point defects, the adsorption energies of CO₂, CO, and CH₂O all increase at the defect sites, suggesting that defect sites enhance the adsorption of these C1 molecules.

Table 1 The adsorption energy (E_ad) of CO₂ on pristine Ti–O surface (CO₂@Ti–O), pristine Sr–O surface (CO₂@Sr–O), Ti adatom (CO₂@Ti) and O vacancy (CO₂@Vo), respectively, and the average variation in C–O bond length (Δl_C–O), C–O bond ICOHP (ΔICOHP_C–O), and the electron transfer numbers for CO₂ (Δn_tot,), the C atom (Δn_C), and the O atom (Δn_O) after adsorption. The units of E_ad, Δl_C–O, ΔICOHP_C–O, and Δn are eV, Å, eV and e, respectively. e stands for a single electron, and the positive sign indicates an increase in the number of valence electrons

Configuration	E ad	ΔlC–O	ΔICOHPC–O	Δntot	ΔnC	ΔnO
CO2@Ti–O	−1.017	0.091	4.955	+0.41	+0.18	+0.11
CO2@Sr–O	−1.199	0.096	4.608	+0.74	+0.18	+0.28
CO2@Ti (type1)	−1.438	0.108	4.983	+0.75	+0.51	+0.12
CO2@Ti (type2)	−1.594	0.099	4.407	+0.75	+0.61	+0.07
CO2@Vo	−1.258	0.095	4.968	+0.40	+0.17	+0.13

---

It is noteworthy that it is the overall energy effect caused by the structural changes of the system after adsorption that is reflected by adsorption energy, and therefore adsorption energy alone cannot directly reveal the properties of specific chemical bonds.^28,29 In order to more accurately assess the impact of adsorption on chemical bonding, this study compares the C–O length in C1 molecules before and after adsorption, as shown in Table 1 and Table S1. In many cases, variations in bond length can qualitatively indicate the changes in bond strength, stability, and molecular reactivity.³⁰ Overall, an increase in the C–O bond length is observed upon adsorption, suggesting a weakening of the C–O interaction and the activation of the C1 molecules.

In addition, the ICOHP was calculated to quantify specific bond strengths, where an increase in the ICOHP value corresponds to higher bond energy, a reduction in bond strength and weaker atom–atom interactions, and vice versa.^31,32 As summarized in Table 1 and Table S1, the ICOHP values for the C–O bond increase upon adsorption relative to the gas phase, consistent with C–O weakening, and implying the activation of the C1 molecules. These results complement the adsorption-energy and bond-length analyses and provide an intuitive energetic descriptor of reactivity and stability.

As previously discussed, CO and CH₂O exhibit counter-intuitive adsorption configurations in some cases. For CO, as shown in Fig. S7a, the ESP is higher at the O end than at the C end along its molecular axis. From the perspective of electrostatic interaction, the O end should be preferentially adsorbed at the low potential sites on the surface, but in fact, it is the C atom that is closer to the surface. Similarly, for CH₂O, the potential below the C atom is low, so it seems that the C atom should interact with the high potential region on the surface. This is indeed the case on the defect-free Ti–O surface, where the C atom forms bonds with the surface O atom; however, when adsorbed on the Ti adatom, the C atom of CH₂O does not form a bond with the surface O atom, but interacts with the neighbouring surface Ti atom, as shown in Fig. S3d.

These anomalous adsorption behaviors can be rationalized through a detailed analysis of the electronic orbital structures. For CO, its HOMO is primarily contributed by the C atom, and the charge density of the HOMO at the C end is higher than that at the O end, as shown in Fig. S7c. Therefore, adsorption tends to occur at the C end. Furthermore, due to the low activity of the C 2p_z lone pair electrons that occupy the HOMO of CO, the interaction between the C atom and the surface Ti atom is relatively weak, and the adsorption has a negligible impact on the C–O bond (see Table S1). Additionally, as previously mentioned, the electrostatic potential at the C end is lower than that at the O end, which may be another reason for the weak interaction between C and Ti.

Upon adsorbing on a pristine Ti–O surface, only the C atom of CO interacts with the surface (Fig. S1a). However, at the edge of an O vacancy, both the C and O atoms of CO interact with the Ti atoms (see Fig. S4a). This difference can be attributed to the lack of electron receptors in O vacancy-doped STO films, making the systems be electron-excess. These excess electrons occupy the bottom of the conduction band, have high energy (Fig. S9) and thus are reactive. Additionally, the spatial steric hindrance at the O vacancy is small, so both the C and O atoms of CO can form a bond with a Ti atom at the edge of the O vacancy, respectively.

For CH₂O, as mentioned above, when it is adsorbed onto the Ti adatom, the ESP at its C atom increases. This phenomenon can be attributed to the redistribution of electrons after adsorption. Specifically, compared to the gaseous CH₂O, the C atom of the adsorbed CH₂O gains 0.49 valence electron (Table S1), resulting in an increase in its ESP. On the other hand, the ESP of the surface Ti atom is low, so there is an electrostatic attraction between the C atom of CH₂O and the surface Ti atom, which results in their bonding. A similar mechanism governs the bridging adsorption configuration of CH₂O between the two Ti atoms at the O vacancy edge (Fig. S4b).

4. Conclusions

In conclusion, this study employed density functional theory combined with ab initio molecular dynamics simulations to systematically explore the adsorption behavior of C1 molecules, such as CO, CO₂, and CH₂O, on the surface of 2D STO films, revealing the underlying microscopic adsorption mechanisms. The results demonstrate that the adsorption sites and configurations are predominantly governed by electrostatic interactions: the regions in the C1 molecules with high ESP preferentially interact with the surface sites with low ESP, and vice versa. The adsorption strength is correlated with the distribution of valence charge and molecular orbital character. Chemisorption, as observed in CO₂ and CH₂O, leads to activation of the C–O bond, manifested by bond elongation and increased ICOHP values. In contrast, CO exhibits physisorption, characterized by weak interactions and a negligible structural change. Furthermore, surface point defects such as Ti adatoms and O vacancies significantly enhance the adsorption by altering the ESP and electronic structures of the surface sites. Furthermore, charge transfer leads to the reconstruction of the electrostatic potential, thereby changing the adsorption configuration. These insights, which are only based on ordinary physical and chemical properties, are expected to provide a broadly applicable framework for understanding the molecular adsorption behavior on oxide surfaces and other material systems.

Author contributions

Yuanbin Xue: conceptualization, methodology, investigation, writing – original draft, and funding acquisition. Cuihuan Geng: writing – review and editing. Xiaojing Bai: writing – review and editing. Huali Hao: writing – original draft, writing – review and editing, and funding acquisition.

Conflicts of interest

There are no conflicts to declare.

Data availability

All data are presented in the article. They can be obtained from the authors upon reasonable request.

Supplementary information (SI): a detailed explanation of the QMD method; adsorption geometries of CO, CO₂, and CH₂O on pristine Ti–O, defective Ti–O, and Sr–O surfaces; electronic structure analyses, including electrostatic potential isosurfaces, DOS, and molecular orbital diagrams for CO and CH₂O; adsorption energies, C–O bond length changes, ICOHP values, and charge transfer for CO and CH₂O on various surfaces; and element-resolved DOS of O vacancy-doped STO films. See DOI: https://doi.org/10.1039/d5cp03564c.

Acknowledgements

The authors acknowledge the support from the National Natural Science Foundation of China (Grant No. 52408286, 12004009), the Henan International Joint Laboratory of Nanocomposite Sensing Materials, and the Natural Science Foundation of Hubei Province (No. 2025AFB628). The numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center of Wuhan University.

References

1. K. Kacem, J. Casanova-Chafer, S. Ameur, M. F. Nsib and E. Llobet, J. Alloys Compd., 2023, 941, 169011.
2. H. Li, J. Yu, Y. Gong, N. Lin, Q. Yang, X. Zhang and Y. Wang, Sep. Purif. Technol., 2023, 307, 122716.
3. R. Bhardwaj, S. S. Jena, V. S. Srikar, S. Ghosh and A. Hazra, Nanotechnology, 2023, 34, 405502.
4. L. Zhang, S. Li and W. Hu, Modell. Simul. Mater. Sci. Eng., 2023, 31, 055004.
5. L. Zhang and S. Shao, J. Appl. Phys., 2022, 131, 025307.
6. M. Deng, Z. Li, S. Liu, X. Fang and L. Wu, Nat. Commun., 2024, 15, 8789.
7. J. Qi, L. Bian, T. Ting, C. Liu, L. Yang, Y. Xu, J. Peng, X. Song and S. An, J. Power Sources, 2023, 570, 233032.
8. Y. Wang, C. Wang, W. Liang, X. Song, Y. Zhang, M. Huang and H. Jiang, Nano Energy, 2020, 70, 104538.
9. A. Das, B. Maji, S. J. Sahoo, J. Singh and P. Dash, ACS Appl. Electron. Mater., 2024, 6, 5789–5804.
10. Q. Cheng, B. Wang, G. Huang, Y. Li, X. Li, J. Chen, S. Yue, K. Li, H. Zhang, Y. Zhang and H. Zhou, Angew. Chem., Int. Ed., 2022, 61, e202208264.
11. D. Kim, H. Lim, M. Seo, H. Shin, K. Kim, M. Jung, S. Jang, B. Chae, B. Park, J. Lee, Y. Choi, K.-J. Kim, J. Kim, X. Tong, A. Hunt, I. Waluyo and B. S. Mun, ACS Appl. Mater. Interfaces, 2024, 16, 38679–38689.
12. J. Xie, P. Bai, C. Wang, N. Chen, W. Chen, M. Duan and H. Wang, ACS Appl. Energy Mater., 2022, 5, 9559–9570.
13. P. E. Blöchl, Phys. Rev. B: Condens. Matter Mater. Phys., 1994, 50, 17953–17979.
14. G. Kresse and D. Joubert, Phys. Rev. B: Condens. Matter Mater. Phys., 1999, 59, 1758–1775.
15. G. Kresse and J. Furthmuller, Comput. Mater. Sci., 1996, 6, 15–50.
16. G. Kresse and J. Furthmüller, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 11169–11186.
17. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868.
18. L. Bengtsson, Phys. Rev. B: Condens. Matter Mater. Phys., 1999, 59, 12301–12304.
19. H. J. Monkhorst and J. D. Pack, Phys. Rev. B: Solid State, 1976, 13, 5188–5192.
20. S. Grimme, J. Comput. Chem., 2006, 27, 1787–1799.
21. K. Momma and F. Izumi, J. Appl. Crystallogr., 2008, 41, 653–658.
22. D. Bucher, L. C. T. Pierce, J. A. McCammon and P. R. L. Markwick, J. Chem. Theory Comput., 2011, 7, 890–897.
23. S. Wu, C. Zhao, C. He, X. Dong and H. Xu, J. Phys. Chem. Lett., 2025, 16, 3741–3747.
24. M. M. Rahman, S. Oh, P. R. Adhikari and J. Lee, Adv. Sci., 2024, 11, 2405450.
25. S. Carlotto, Appl. Surf. Sci., 2020, 527, 146850.
26. S. Carlotto, M. M. Natile, A. Glisenti and A. Vittadini, Surf. Sci., 2015, 633, 68–76.
27. S. Maintz, V. L. Deringer, A. L. Tchougréeff and R. Dronskowski, J. Comput. Chem., 2016, 37, 1030–1035.
28. C. He, C.-H. Lee, L. Meng, H.-Y. T. Chen and Z. Li, J. Am. Chem. Soc., 2024, 146, 12395–12400.
29. J. Hulva, M. Meier, R. Bliem, Z. Jakub, F. Kraushofer, M. Schmid, U. Diebold, C. Franchini and G. S. Parkinson, Science, 2021, 371, 375–379.
30. M. Kaupp, D. Danovich and S. Shaik, Coord. Chem. Rev., 2017, 344, 355–362.
31. R. Dronskowski and P. E. Blochl, J. Chem. Phys., 1993, 97, 8617–8624.
32. V. L. Deringer, A. L. Tchougréeff and R. Dronskowski, J. Phys. Chem. A, 2011, 115, 5461–5466.

---