A computational elucidation of the Structure-Property Relationships in Graphene-Organic 2D Crystal Heterostructures

A computational elucidation of the Structure-Property Relationships in Graphene-Organic 2D Crystal Heterostructures | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article A computational elucidation of the Structure-Property Relationships in Graphene-Organic 2D Crystal Heterostructures Shuangjie Zhao, Miroslav Polozij, Thomas Heine This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8172814/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract The integration of graphene with porous organic 2D crystals (O2DCs) represents an emerging class of van der Waals heterostructures that can possess controllable superlattice effects without complex moiré engineering. In this work, we investigate the structure-property relationships in graphene-O2DC (G-O2DC) heterostructures and the role of substrate interactions through computational studies. We demonstrate how O2DCs impose well-defined corrugation on graphene. The amplitude and superlattice of the graphene layer are directly governed by O2DC pore dimensions and substrate, with larger pores and substrate interactions significantly enhancing the corrugation effect. Despite significant structural modulation, the Dirac cone and linear band dispersion of graphene stay only slightly perturbed across all investigated configurations, demonstrating a decoupling between structural corrugation and electronic properties. These insights establish G-O2DC heterostructures as a viable platform for superlattice engineering in graphene, providing a robust foundation for their rational design and optimization and paving the way for applications in diverse fields such as electronics, catalysis, and energy storage. Physical sciences/Materials science Physical sciences/Nanoscience and technology Physical sciences/Physics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1 Introduction Van der Waals (vdW) heterostructures have drawn a lot of attention as a way to combine and enhance unique properties of 2D materials 1 . Graphene, the most extensively studied 2D materials, has demonstrated exceptional mechanical and electronic properties but also faces inherent limitations due to the absence of a bandgap in its pristine form 2 – 6 . Studies in moiré physics have revealed that superlattice formation can dramatically affect the properties of graphene 7 – 9 . However, moiré engineering requires precise angular control and sophisticated fabrication techniques that remain challenging to implement reliably 10 . Alternative, technically easier approaches resulting in formation of well-defined superlattice could be a significant addition to the field. Structural modulation of graphene using organic 2D crystals (O2DCs), offering tunable pore sizes ranging from 0.3 11 to 10 nm 12 , was recently shown to lead to exactly this tailorability and impose periodic potential on graphene through induced corrugation 13 , but their effect on the graphene electronic structure remains unexplored. The almost unlimited variety of O2DC topologies and the possibility for versatile functionalization could thus open a huge potential playing field for tailoring G-O2DC heterostructures for specific applications 14 , 15 . This unique combination of controllable superlattice engineering and chemical versatility makes G-O2DC heterostructures highly intriguing for systematic investigations aimed at unlocking their full potential. Constructing well-defined heterostructure devices faces significant obstacles, including the difficulty of precise control over the synthesis process, the inevitable existence of defects and impurities, and the inherent structural complexity and uncertainty as 2D heterostructures are very hard to characterize. Commonly used techniques such as diffraction or electron microscopy lack resolution along the z-axis for such thin materials due to both technical limitations and material properties, making it almost impossible to resolve the precise nature of the graphene-organic 2D crystal interface. A less obvious challenge lies in the immense configurational space of the O2DC structures, making the selection of structure one of the crucial tasks. Computational chemistry offers a powerful means to the characterization of experimentally realized structures, which are not easily accessible through experimental techniques alone, meanwhile predicting their target properties before lengthy experiments. However, such an investigation presents a fundamental challenge: balancing physical accuracy with computational feasibility when handling lattice commensurability between layers. An inherent technical obstacle in simulating vdW heterostructures is lattice incommensurability, which originates from the need to constrain two materials with different crystal lattices within a single periodic simulation cell. The large size of O2DC lattice and difference between graphene's honeycomb lattice and variable symmetry of O2DC (e.g., square lattice, distorted honeycomb etc.) make it particularly problematic to find coincidence cells. Such exact cells are often prohibitively large for quantum mechanical calculations. A common compromise is to accept a small amount of mismatch, which, though, introduces artificial strain in the structure, compromising its physical accuracy. Aside from the size of the two lattices in the vdW heterostructure, their orientation also has to be considered when constructing coincidence cells. Such orientation is very important for inorganic vdW heterostructures, even causing phenomena due to the moiré effect 16 . In the case of O2DCs, the question of the orientation with respect to graphene is more complicated, as their monolayer films are typically polycrystalline 17 , 18 and thus a single structure would contain multiple orientations. However, this actually simplifies the computational challenge of lattice coincidence, as specific combinations of lattice dimensions and orientations can be represented by compact periodic models amenable to precise DFT methods 19 . In experimental setups, heterostructures often require the use of substrates to support the material. For inorganic heterostructures, these substrates are selected so they do not affect structural properties of the heterostructure, and consequently neither the vibronic and electronic ones. In the case where one of the heterostructure parts is porous, such as O2DC, these substrates will significantly affect the structure of the assembled system, facilitating interaction of the top heterostructure layer through the pore directly with the substrate (Fig. 1 ). The resulting deformation is highly correlated to the pore size, with larger pores leading to greater deformation. This additional interaction, while non-negligible, is typically absent in simulations conducted under vacuum. In this work we design and validate a complete workflow to simulate G-O2DC heterostructures in experimentally relevant configurations, explicitly including substrate effects and addressing the challenges of lattice incommensurability, while maintaining computational tractability. By exploring the pore size ranging from 2.6 to 22.6 Å and pore geometry with honeycomb and square lattices, we investigate structure-property relationships that reveal how pore dimensions and substrate interactions cause and govern periodic corrugation on graphene. Our investigation demonstrates that while O2DC porosity and substrate effects create significant periodic structural modulation of graphene, no significant modifications are made to its intrinsic electronic properties, contrasting with conventional corrugated graphene systems where structural and electronic effects are intrinsically coupled. The weak electronic response to structural corrugation in G-O2DC heterostructures suggests that geometric modulation alone is insufficient to substantially modify graphene's electronic features, thereby leading the way to functionalization of the templating O2DCs. This framework establishes G-O2DC heterostructures as a platform for structural templating and highlights the critical role of the support in shaping the material structure, an aspect that warrants careful consideration in both materials design and theoretical investigations. 2 Results and Discussion 2.1 Structures and Structure Models We selected and designed a set of model O2DCs with pore sizes ranging from 2.6 to 22.6 Å (Fig. 2 , Figure S1 ) having a perfectly flat structure. Pore sizes were defined as the distance between symmetrically equivalent hydrogen atoms on opposing linkers, corrected by subtracting twice the van der Waals radius of hydrogen (2 × 1.20 Å) to represent the actual accessible space. These model structures include both theoretically constructed and experimentally realized materials and encompass a range of relevant structural motifs including polycyclic aromatic framework ( h1 to h3 ), boronate ester-linked macrocyclic system COF-5 ( h4 ) 20 , and porphyrin-based architectures ( s1 to s6 ). Models h1 to h3 were designed as commensurate structures to graphene, while h4 (COF-5), an experimentally available material, represents an incommensurate case with honeycomb lattice. Models s1 to s6 are designed as totally incommensurate structures with square lattice. During the construction of the heterostructures, the incommensurability was handled by choosing the ones with minimum lattice mismatch from available structures obtained from various orientations of layers at different rotational angles. The rotational angle screening and coincidence cell searching was done by hetbuilder 21 . The rotational angles between graphene and O2DCs are shown in SI (Figure S6, S7, Table S1 , S2). In this code, coincidence lattices are determined with the algorithm outlined by Schwalbe-Koda 22 to find all possible heterostructures with different rotational angles and supercell sizes. Since in experiment, controlling the rotational angle is challenging, as the transfer of organic 2D crystals onto graphene is in most cases random 23 , we selected structures with minimal strain regardless of angle. We have found that mismatches of ≤ 2% generally only have minor effect on the structure. Larger strain will cause distortion of the corrugation pattern of graphene. Instead of conforming to the pore geometry of the O2DC and leading to a corrugation templated by the pore structure, large strain causes additional corrugation not aligned with the pore shape (Figure S1 2). To verify whether rotational orientation significantly impacts properties, we tested two examples of selected O2DCs at different rotational angles (Figure S2), as different lattice orientations can induce different heterostructure properties, due to strain and specific interactions. The porous nature of O2DCs makes them less mechanically stiff than graphene, allowing strain to be more easily imposed on the organic layer during heterostructure formation. In order to incorporate substrate effects into our theoretical models, two commonly used substrates, graphene and silicon dioxide, were selected. They represent a substrate with a good lattice match and one with a different lattice than the O2DCs, respectively. Throughout this work, we denote resulting structures as follows: i) G-O2DC or G-O2DC( x ) is the base heterostructure, where x stands for the particular polymer as shown in Fig. 1 ), ii) G-O2DC-Substrate for structures with substrate on the polymer side of the heterostructure (Fig. 1 b, c); and iii) O2DC-G-Substrate with substrate on the graphene side of the heterostructure (Fig. 1 d, e). The substrate can be a rigid graphene monolayer simulating a bulk surface (Gr) or a silicon dioxide bilayer (SiO 2 ) 24 (Fig. 1 , S3). To validate the graphene corrugation in the structures on substrates, we addressed artifacts arising from unit cell approximations in both substrate-free and substrate-supported systems. For the substrate-free case, we minimized artificial strain by depositing a O2DC flake onto a large graphene flake and optimizing the resulting structure (Fig. 3 . a, b). To avoid flake edge interactions that could introduce artifacts, we maintained 30 Å separation between the edges of the graphene and O2DC flakes. This setup ensures that the G-O2DC interface retains its intrinsic structural fidelity, which is critical for using it as a reliable precursor to construct G-O2DC-substrate heterostructures. For systems involving substrates, we positioned a finite graphene flake onto a periodic O2DC-substrate framework to keep graphene strain-free (Fig. 3 c, d). The distance between the cut edge of graphene flake and unit cell boundary was set again at 30 Å. In both scenarios, the cut edges of O2DC and graphene were saturated by adding hydrogen atoms (Figure S8 a, b). 2.2 Geometry and Interaction Energy of G-O2DC heterostructures We expect three possible effects arising from the heterostructure formation: (i) the proximity effect, which is the impact of interlayer interactions on the electronic structure, (ii) the superlattice effect, where the induced superstructure creates a new periodic potential that modifies the electronic properties of graphene, and (iii) the structural effect, referring to the physical deformation or corrugation of graphene caused by its interaction with the O2DC, altering its electronic structure. We anticipate that the proximity effect will be stronger for small pores, while the superlattice and structural effects will be more significant for large pores. Additionally, we aim to understand the impact of substrate commensurability on the behavior of G-O2DC heterostructures by comparing two distinct substrate classes: silicon dioxide (SiO 2 ) and crystalline graphite represented by rigid graphene. These substrates are chosen to model the effects of structural mismatch and commensurability, respectively, on the properties of G-O2DC systems. When the pore is large enough to allow substantial graphene corrugation inside the pores of O2DC, direct interaction between substrate and graphene will occur as well as proximity effect between these two layers. In all tested standalone G-O2DC heterostructures for organic 2D crystals h1 to h4 and s1 to s6 , the O2DC pore structure induces a weak corrugation on the graphene. This is caused by the dispersion interaction of graphene towards the O2DC pore voids. The amplitude of the corrugation strongly depends on the pore size of O2DC. It ranges from 0.06 Å to 1.45 Å, correlating with the rising of pore diameter from 2.6 Å to 22.6 Å (Figure S4). It is important to note that this consistent effect comes from dispersion interaction and is not an artifact of the computational supercell construction. Artificial corrugation can occur in computational models when lattice mismatch is introduced between O2DC and graphene supercells in the heterostructure, inducing an artificial strain on the structure, 25 and with it a corrugation of graphene similar to the one observed. To rule out such effect, we have plotted the inherent mismatch against the corrugation size and found no correlation (Figure S4), showing the corrugation does not originate from lattice mismatch. The presence of a substrate significantly influences graphene corrugation patterns in G-O2DC heterostructures, with distinct effects depending on the layer sequence. Especially, when the O2DC layer is positioned between graphene and the substrate (G-O2DC-substrate), strong dispersion interaction through the O2DC pores induces pronounced graphene corrugation. The magnitude of this effect scales with pore size: larger pores lead to stronger corrugation (Fig. 4 ). For honeycomb O2DCs, the total graphene corrugation amplitude varies from Δd = 0.22 Å (Δd is defined as the difference between maximum and minimum of z coordinates of corrugated graphene layer) for h1 (5.6 Å) to Δd = 0.66 Å for h3 (15.6 Å), reaching a substantial Δd = 1.19 Å for h4 (22.6 Å) (Fig. 3 b). The observed corrugation amplitudes in the simulated G-O2DC heterostructures are in the range that could be measured using e.g. atomic force microscopy in non-contact mode (typically achieves vertical resolutions of ~ 0.1 Å 26,27 . In pores larger than 22.6 Å, the corrugation shape of graphene changes, forming a plateau in the center of the pore, as the graphene starts touching the substrate. For very large pores on flat substrates, the maximum corrugation is expected to approach ~ 3.5 Å, corresponding to the full interlayer separation distance. The shape of the corrugation of graphene is perfectly templated by the O2DC pore system, as is illustrated in Fig. 5 for graphene on h3 (15.6 Å pores) and s6 (19.6 Å pores) O2DCs on rigid graphene and SiO 2 surface. The observed corrugation amplitude does not depend strongly on the substrate; it is around 0.65 Å and 1.45 Å for the pore sizes of tested honeycomb and square O2DC, respectively, when substrate is included (See also Figure S5). The newly formed corrugation superlattice on graphene reflects the geometry of the underlying O2DC. A honeycomb O2DC will introduce a new hexagonal superlattice on graphene corresponding to its pore arrangement, due to the dispersion through pores and hindrance from frame. The same applies to organic 2D crystals with square pores (Figure S6, S7). To verify if the observed superlattice formation and corrugation are inherent properties of the G-O2DC heterostructure and not computational artifacts arising from periodic boundary conditions, we performed validation tests using finite-size, non-periodic flakes. Example structures of G-O2DC( h2 ) are shown in Supporting Information (Figure S8). The tested non-periodic G-O2DC( h2 ) structure showed roughly the same amplitude of 0.25 Å as the periodic G-O2DC( h2 ) heterostructure. Similarly, the tested graphene flake on the O2DC( h2 )-SiO2 structure and the G-O2DC( h2 )-SiO2 structure both exhibited an amplitude of 0.35 Å. This confirms that the corrugation of the graphene is a native heterostructure property and is not caused by any artificial strain in the model. To investigate the general effects of superlattice formation and corrugation on the electronic structure of the heterostructures, we calculated band structures for all G-O2DC-substrate (Gr and SiO 2 ) heterostructures. Due to the large system size, we had to limit ourselves to only calculate band structure of the G-O2DC moiety without explicitly including the substrate. The substrate is thus effectively used only as a force field to induce geometric change in the heterostructure. This is a safe assumption as our calculations show no obvious electronic effects from SiO 2 around the Fermi level (Figure S9). We aimed to identify any possible modifications to the graphene band structure induced by the interaction with the O2DC layer. No significant band gap was found near the Dirac point, with values ranging from 0.8 to 8.6 meV for h1 to h4 and 1.0 to 12.1 meV for s1 to s6 (Fig. 6 , Figures S10, S11, Tables S1, S2). While no clear correlation was found between the degree of lattice mismatch and band gap opening or corrugation amplitude, the structures with the strongest corrugation exhibited the largest band gaps ( h4 : 8.6 meV; s6 : 12.1 meV). Choice of the substrate does not affect the observed results (Fig. 6 b and c). This preservation of electronic structure is observed for both honeycomb and square O2DC lattices, suggesting that these regular-shaped lattices do not lead to changes in the electronic properties of the heterostructures. Conclusions In this work, we developed a comprehensive computational modeling approach to investigate the structure and electronic properties of graphene-organic 2D crystal (G-O2DC) heterostructures. Our findings demonstrate that the pore structure of the organic 2D crystal always induces corrugation on graphene that is exactly templated by the shape of the O2DC pore structure, allowing for precise tailoring of the heterostructure. This effect is significantly enhanced in the presence of a substrate, where the substrate interacts directly with graphene across the pores, amplifying the corrugation amplitude. The corrugation magnitude is directly controlled by the O2DC pore size, providing a systematic approach to tune the superlattice periodicity and amplitude. It should be noted that under experimental conditions, the corrugation of graphene can be impacted by multiple factors, such as solvent or other guest molecules that can remain inside the pores of O2DCs and block interaction of graphene with the underlying substrates, therefore counteracting the corrugation formation observed in this work. Remarkably, despite substantial corrugation, graphene's electronic band structure remains preserved across all studied configurations, suggesting that sole geometric modulation is not sufficient to significantly modify the electronic features of graphene. Our results also indicate that rotational angles do not play a significant effect for these studied types of structures, thus making precision angle control less important in the fabrication procedure, providing valuable insights for both experimental and theoretical studies on material and device design in G-O2DC heterostructures. Methods The organic 2D crystal (O2DC) unit cells were obtained by performing geometry optimization, including both atomic positions and lattice parameters. The G-O2DC heterostructures were then generated using the hetbuilder code 21 by rotating and expanding the optimized unit cells of O2DC and graphene to find the shared coincident supercell. Specifically, the G-O2DC-substrate structures were generated by rotating and expanding the fully-optimized G-O2DC structure with the unit cell of the substrate. When constructing heterostructure models with substrate, we treat the substrate as a rigid entity that primarily serves as an external force field acting on the G-O2DC moiety. We first optimized the isolated G-O2DC moiety to obtain its optimal unit cell parameters. Subsequently, we rescaled the substrate structure to match the optimized lattice and combine them to form the substrate-supported model. Crucially, we did not further optimize the lattice of the resulting system. By adopting this strategy, we can effectively capture the essential effects of the substrate on the G-O2DC heterostructure while maintaining a computationally tractable model. The geometries of all multi-layer structures were optimized with lattice parameter being fixed by density functional based tight binding method (DFTB). 28 DFTB+, 29 a code of DFTB, and Amsterdam Modeling Suite (AMS) 30 was used to perform geometry optimizations. Particularly, DFTB2, 31,32 a second generation of DFTB coupled with an empirical dispersion correction of universal force-field (UFF) 33 was used, with QUASINANO2015 34 for structures of h4 with SiO 2 substrate and matsci-0-3 parameter set 35 for the rest. Matsci-0-3 parameter set was used for majority of structures in this study, which has been shown before to perform well for similar systems 36 – 38 . QUASINANO2015 was used only for the structure G-h4-SiO2 as it is the only available DFTB parameter set that includes all present species (particularly C, H, B, O, and Si) together. To investigate the electronic properties of the optimized structures, band structures calculations were performed by Fritz-Haber-Institute ab-initio materials simulations package (FHI-aims 39 ) with PBE 40 . Tier 2 basis set and tight integration mesh were used. Deformation analysis was done by a self-made script using atomic simulation environment python package 41 . The script is available on GitHub ( https://github.com/AK-Heine/StrainAnalysis ). Declarations Competing Interests All authors declare no financial or non-financial competing interests. Funding This study was funded by DFG priority program SPP 2244 and CRC 1415. The funder played no role in study design, data collection, analysis and interpretation of data, or the writing of this manuscript. Author Contribution SZ carried out all calculations and provided the first draft, MP supervised the research, TH conceived the project, all authors discussed the results and reviewed manuscript. Data Availability Statement All source data of the quantum chemistry calculations reported in this study are available in the NOMAD repository under DOI: 10.17172/NOMAD/2025.07.28-1 . Acknowledgment T.H. and S.Z. acknowledge funding of the DFG priority program SPP 2244 and CRC 1415. 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Supplementary Files SIrevised.pdf Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 09 Feb, 2026 Reviews received at journal 02 Feb, 2026 Reviewers agreed at journal 18 Jan, 2026 Reviewers invited by journal 17 Dec, 2025 Editor assigned by journal 10 Dec, 2025 Submission checks completed at journal 09 Dec, 2025 First submitted to journal 21 Nov, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8172814","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":561793558,"identity":"fa5c5dab-6764-4d67-a3f2-016a43369640","order_by":0,"name":"Shuangjie Zhao","email":"","orcid":"","institution":"TU Dresden","correspondingAuthor":false,"prefix":"","firstName":"Shuangjie","middleName":"","lastName":"Zhao","suffix":""},{"id":561793563,"identity":"c32400d8-1130-4458-9f60-c1b7cb6394c2","order_by":1,"name":"Miroslav Polozij","email":"","orcid":"","institution":"Center for Advanced Systems 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17:26:18","extension":"png","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":89270,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8172814/v1/92bfa04d92b9d656ea119d07.png"},{"id":98635678,"identity":"1386a621-7c54-4797-a0ab-a3ada9cf4c24","added_by":"auto","created_at":"2025-12-19 17:26:25","extension":"png","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":292437,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8172814/v1/4329206ddc9dac877a541c98.png"},{"id":98635414,"identity":"522d7a7c-dcc6-495f-ac16-2fc8a5e24d21","added_by":"auto","created_at":"2025-12-19 17:26:12","extension":"png","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":140647,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-8172814/v1/912379723ebf860a2b53f7f3.png"},{"id":98635478,"identity":"86bdc62d-7c92-484c-946a-de42bf10d146","added_by":"auto","created_at":"2025-12-19 17:26:14","extension":"xml","order_by":16,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":96553,"visible":true,"origin":"","legend":"","description":"","filename":"0ae16df446cd4c90ab3a8918e89470721structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-8172814/v1/02513c738a9a63121d4c0ce0.xml"},{"id":98635783,"identity":"6731165e-bde0-4655-89cb-70f49a682a98","added_by":"auto","created_at":"2025-12-19 17:26:29","extension":"html","order_by":17,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":109350,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-8172814/v1/9d7f0d51e6bce8f373453524.html"},{"id":98634748,"identity":"fa355aa5-de9d-4309-a5f0-551b0a6adefd","added_by":"auto","created_at":"2025-12-19 17:25:51","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":601720,"visible":true,"origin":"","legend":"\u003cp\u003eScheme of investigated structures. All structures below are generated from (a) original G-O2DC heterostructure. (b), (c) G-O2DC supported on the polymer side and (d), (e) G-O2DC supported on the graphene side by a rigid graphene (Gr) simulating bulk surface and SiO\u003csub\u003e2\u003c/sub\u003e bilayer, respectively.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8172814/v1/6a32729a16d99daac8174a56.png"},{"id":98635641,"identity":"ae13ce0d-7e4a-461c-8e62-7e430121f928","added_by":"auto","created_at":"2025-12-19 17:26:23","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":659595,"visible":true,"origin":"","legend":"\u003cp\u003eMolecular structures of studied O2DCs with honeycomb lattice (\u003cstrong\u003eh1\u003c/strong\u003e to \u003cstrong\u003eh4\u003c/strong\u003e) and square lattice (\u003cstrong\u003es1\u003c/strong\u003e to \u003cstrong\u003es6\u003c/strong\u003e).\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8172814/v1/212d7cc1fc0f36378b9153f4.png"},{"id":98635732,"identity":"d2bd58ae-e8f1-48d1-9b6d-58725d7aafef","added_by":"auto","created_at":"2025-12-19 17:26:28","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":356507,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic representation of the strategy employed for generating flake models with and without a substrate for strain tests. (a) Model of periodic G-O2DC heterostructure. (b) Model of extended, non-periodic G-O2DC flake. (c) Model of periodic G-O2DC-substrate structure. (d) Model of G-O2DC-substrate structure with finite graphene flake on continuous periodic O2DC and substrate layers within the extended cell.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8172814/v1/d9e6ad61b6ba16a6bf64c58a.png"},{"id":98635581,"identity":"95a065f4-3cde-4e54-be57-57814c9e1dd2","added_by":"auto","created_at":"2025-12-19 17:26:17","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":649059,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Schematic representation of graphene corrugation induced by organic 2D crystal (O2DC) pore sizes. Larger pore induces stronger corrugation due to heightened surface interaction. In heterostructures with large-pore O2DCs, the graphene layer can flatten inside the pores (maximum corrugation). Δd: Corrugation amplitude on graphene, defined as the difference between maximum and minimum of its z coordinates. (b) Molecular structures of O2DCs with varying pore sizes and their corresponding G-O2DC-Gr structures with rotational angles (RA) between G and O2DC at 18.9°, 23.0° and 8.0°, respectively\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8172814/v1/0d5af1a475dda80d2b589fa6.jpeg"},{"id":98635676,"identity":"c1b13181-9b82-4577-bfb5-4cb24ade1b6b","added_by":"auto","created_at":"2025-12-19 17:26:25","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":1862334,"visible":true,"origin":"","legend":"\u003cp\u003eExamples of interaction analysis and visualization. (a), (d): Molecular structures of honeycomb shaped O2DC and square shaped O2DC. (b), (e): Models of their corresponding G-O2DC-Gr structures and the qualitative analysis of corrugation of graphene. (c), (f): Models of their corresponding G-O2DC-SiO\u003csub\u003e2\u003c/sub\u003e structures and the qualitative analysis of corrugation of graphene.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8172814/v1/68753a4579bc212a52b0f6ac.png"},{"id":98634744,"identity":"79ea8485-bb8c-4a3e-b694-b48a086f08f9","added_by":"auto","created_at":"2025-12-19 17:25:50","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":900743,"visible":true,"origin":"","legend":"\u003cp\u003eBand structure of graphene part and graphene+O2DC part for the honeycomb shaped and square shaped O2DC examples on different substrates. The substrate structure was not included in the band structure calculations. (a) Molecular structures of the investigated O2DC examples with honeycomb and square lattices. (b) Band structures for the graphene part and the graphene + O2DC part of the corresponding G-O2DC-Gr heterostructures. (c) Band structures for the graphene part and the graphene + O2DC part of the corresponding G-O2DC-SiO\u003csub\u003e2\u003c/sub\u003e heterostructures.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-8172814/v1/59d2bbb408355f19d9d49655.png"},{"id":98636267,"identity":"8f3d71c4-900a-4833-9003-dbf110aff83d","added_by":"auto","created_at":"2025-12-19 17:27:50","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5557276,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8172814/v1/daf8447c-b90c-4508-bed9-be299cb10cfd.pdf"},{"id":98635711,"identity":"1a279f46-b1ed-4588-a562-070697425a46","added_by":"auto","created_at":"2025-12-19 17:26:27","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":6814377,"visible":true,"origin":"","legend":"","description":"","filename":"SIrevised.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8172814/v1/33b52db7249cbcb467b4ab7d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A computational elucidation of the Structure-Property Relationships in Graphene-Organic 2D Crystal Heterostructures","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eVan der Waals (vdW) heterostructures have drawn a lot of attention as a way to combine and enhance unique properties of 2D materials\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. Graphene, the most extensively studied 2D materials, has demonstrated exceptional mechanical and electronic properties but also faces inherent limitations due to the absence of a bandgap in its pristine form\u003csup\u003e\u003cspan additionalcitationids=\"CR3 CR4 CR5\" citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. Studies in moir\u0026eacute; physics have revealed that superlattice formation can dramatically affect the properties of graphene\u003csup\u003e\u003cspan additionalcitationids=\"CR8\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. However, moir\u0026eacute; engineering requires precise angular control and sophisticated fabrication techniques that remain challenging to implement reliably\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. Alternative, technically easier approaches resulting in formation of well-defined superlattice could be a significant addition to the field. Structural modulation of graphene using organic 2D crystals (O2DCs), offering tunable pore sizes ranging from 0.3\u003csup\u003e11\u003c/sup\u003e to 10 nm\u003csup\u003e12\u003c/sup\u003e, was recently shown to lead to exactly this tailorability and impose periodic potential on graphene through induced corrugation\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e, but their effect on the graphene electronic structure remains unexplored. The almost unlimited variety of O2DC topologies and the possibility for versatile functionalization could thus open a huge potential playing field for tailoring G-O2DC heterostructures for specific applications\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e,\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. This unique combination of controllable superlattice engineering and chemical versatility makes G-O2DC heterostructures highly intriguing for systematic investigations aimed at unlocking their full potential.\u003c/p\u003e \u003cp\u003eConstructing well-defined heterostructure devices faces significant obstacles, including the difficulty of precise control over the synthesis process, the inevitable existence of defects and impurities, and the inherent structural complexity and uncertainty as 2D heterostructures are very hard to characterize. Commonly used techniques such as diffraction or electron microscopy lack resolution along the z-axis for such thin materials due to both technical limitations and material properties, making it almost impossible to resolve the precise nature of the graphene-organic 2D crystal interface. A less obvious challenge lies in the immense configurational space of the O2DC structures, making the selection of structure one of the crucial tasks. Computational chemistry offers a powerful means to the characterization of experimentally realized structures, which are not easily accessible through experimental techniques alone, meanwhile predicting their target properties before lengthy experiments. However, such an investigation presents a fundamental challenge: balancing physical accuracy with computational feasibility when handling lattice commensurability between layers.\u003c/p\u003e \u003cp\u003eAn inherent technical obstacle in simulating vdW heterostructures is lattice incommensurability, which originates from the need to constrain two materials with different crystal lattices within a single periodic simulation cell. The large size of O2DC lattice and difference between graphene's honeycomb lattice and variable symmetry of O2DC (e.g., square lattice, distorted honeycomb etc.) make it particularly problematic to find coincidence cells. Such exact cells are often prohibitively large for quantum mechanical calculations. A common compromise is to accept a small amount of mismatch, which, though, introduces artificial strain in the structure, compromising its physical accuracy. Aside from the size of the two lattices in the vdW heterostructure, their orientation also has to be considered when constructing coincidence cells. Such orientation is very important for inorganic vdW heterostructures, even causing phenomena due to the moir\u0026eacute; effect\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. In the case of O2DCs, the question of the orientation with respect to graphene is more complicated, as their monolayer films are typically polycrystalline\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e and thus a single structure would contain multiple orientations. However, this actually simplifies the computational challenge of lattice coincidence, as specific combinations of lattice dimensions and orientations can be represented by compact periodic models amenable to precise DFT methods\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIn experimental setups, heterostructures often require the use of substrates to support the material. For inorganic heterostructures, these substrates are selected so they do not affect structural properties of the heterostructure, and consequently neither the vibronic and electronic ones. In the case where one of the heterostructure parts is porous, such as O2DC, these substrates will significantly affect the structure of the assembled system, facilitating interaction of the top heterostructure layer through the pore directly with the substrate (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The resulting deformation is highly correlated to the pore size, with larger pores leading to greater deformation. This additional interaction, while non-negligible, is typically absent in simulations conducted under vacuum.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn this work we design and validate a complete workflow to simulate G-O2DC heterostructures in experimentally relevant configurations, explicitly including substrate effects and addressing the challenges of lattice incommensurability, while maintaining computational tractability. By exploring the pore size ranging from 2.6 to 22.6 \u0026Aring; and pore geometry with honeycomb and square lattices, we investigate structure-property relationships that reveal how pore dimensions and substrate interactions cause and govern periodic corrugation on graphene. Our investigation demonstrates that while O2DC porosity and substrate effects create significant periodic structural modulation of graphene, no significant modifications are made to its intrinsic electronic properties, contrasting with conventional corrugated graphene systems where structural and electronic effects are intrinsically coupled. The weak electronic response to structural corrugation in G-O2DC heterostructures suggests that geometric modulation alone is insufficient to substantially modify graphene's electronic features, thereby leading the way to functionalization of the templating O2DCs. This framework establishes G-O2DC heterostructures as a platform for structural templating and highlights the critical role of the support in shaping the material structure, an aspect that warrants careful consideration in both materials design and theoretical investigations.\u003c/p\u003e"},{"header":"2 Results and Discussion","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Structures and Structure Models\u003c/h2\u003e \u003cp\u003eWe selected and designed a set of model O2DCs with pore sizes ranging from 2.6 to 22.6 \u0026Aring; (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, Figure \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e) having a perfectly flat structure. Pore sizes were defined as the distance between symmetrically equivalent hydrogen atoms on opposing linkers, corrected by subtracting twice the van der Waals radius of hydrogen (2 \u0026times; 1.20 \u0026Aring;) to represent the actual accessible space. These model structures include both theoretically constructed and experimentally realized materials and encompass a range of relevant structural motifs including polycyclic aromatic framework (\u003cb\u003eh1\u003c/b\u003e to \u003cb\u003eh3\u003c/b\u003e), boronate ester-linked macrocyclic system COF-5 (\u003cb\u003eh4\u003c/b\u003e)\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e, and porphyrin-based architectures (\u003cb\u003es1\u003c/b\u003e to \u003cb\u003es6\u003c/b\u003e). Models \u003cb\u003eh1\u003c/b\u003e to \u003cb\u003eh3\u003c/b\u003e were designed as commensurate structures to graphene, while \u003cb\u003eh4\u003c/b\u003e (COF-5), an experimentally available material, represents an incommensurate case with honeycomb lattice. Models \u003cb\u003es1\u003c/b\u003e to \u003cb\u003es6\u003c/b\u003e are designed as totally incommensurate structures with square lattice. During the construction of the heterostructures, the incommensurability was handled by choosing the ones with minimum lattice mismatch from available structures obtained from various orientations of layers at different rotational angles. The rotational angle screening and coincidence cell searching was done by hetbuilder\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. The rotational angles between graphene and O2DCs are shown in SI (Figure S6, S7, Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e, S2). In this code, coincidence lattices are determined with the algorithm outlined by Schwalbe-Koda\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e to find all possible heterostructures with different rotational angles and supercell sizes. Since in experiment, controlling the rotational angle is challenging, as the transfer of organic 2D crystals onto graphene is in most cases random\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e, we selected structures with minimal strain regardless of angle. We have found that mismatches of \u0026le;\u0026thinsp;2% generally only have minor effect on the structure. Larger strain will cause distortion of the corrugation pattern of graphene. Instead of conforming to the pore geometry of the O2DC and leading to a corrugation templated by the pore structure, large strain causes additional corrugation not aligned with the pore shape (Figure \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e2). To verify whether rotational orientation significantly impacts properties, we tested two examples of selected O2DCs at different rotational angles (Figure S2), as different lattice orientations can induce different heterostructure properties, due to strain and specific interactions. The porous nature of O2DCs makes them less mechanically stiff than graphene, allowing strain to be more easily imposed on the organic layer during heterostructure formation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn order to incorporate substrate effects into our theoretical models, two commonly used substrates, graphene and silicon dioxide, were selected. They represent a substrate with a good lattice match and one with a different lattice than the O2DCs, respectively. Throughout this work, we denote resulting structures as follows: i) G-O2DC or G-O2DC(\u003cem\u003ex\u003c/em\u003e) is the base heterostructure, where \u003cem\u003ex\u003c/em\u003e stands for the particular polymer as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), ii) G-O2DC-Substrate for structures with substrate on the polymer side of the heterostructure (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb, c); and iii) O2DC-G-Substrate with substrate on the graphene side of the heterostructure (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed, e). The substrate can be a rigid graphene monolayer simulating a bulk surface (Gr) or a silicon dioxide bilayer (SiO\u003csub\u003e2\u003c/sub\u003e) \u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, S3).\u003c/p\u003e \u003cp\u003eTo validate the graphene corrugation in the structures on substrates, we addressed artifacts arising from unit cell approximations in both substrate-free and substrate-supported systems. For the substrate-free case, we minimized artificial strain by depositing a O2DC flake onto a large graphene flake and optimizing the resulting structure (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. a, b). To avoid flake edge interactions that could introduce artifacts, we maintained 30 \u0026Aring; separation between the edges of the graphene and O2DC flakes. This setup ensures that the G-O2DC interface retains its intrinsic structural fidelity, which is critical for using it as a reliable precursor to construct G-O2DC-substrate heterostructures. For systems involving substrates, we positioned a finite graphene flake onto a periodic O2DC-substrate framework to keep graphene strain-free (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec, d). The distance between the cut edge of graphene flake and unit cell boundary was set again at 30 \u0026Aring;. In both scenarios, the cut edges of O2DC and graphene were saturated by adding hydrogen atoms (Figure S8 a, b).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Geometry and Interaction Energy of G-O2DC heterostructures\u003c/h2\u003e \u003cp\u003eWe expect three possible effects arising from the heterostructure formation: (i) the proximity effect, which is the impact of interlayer interactions on the electronic structure, (ii) the superlattice effect, where the induced superstructure creates a new periodic potential that modifies the electronic properties of graphene, and (iii) the structural effect, referring to the physical deformation or corrugation of graphene caused by its interaction with the O2DC, altering its electronic structure. We anticipate that the proximity effect will be stronger for small pores, while the superlattice and structural effects will be more significant for large pores. Additionally, we aim to understand the impact of substrate commensurability on the behavior of G-O2DC heterostructures by comparing two distinct substrate classes: silicon dioxide (SiO\u003csub\u003e2\u003c/sub\u003e) and crystalline graphite represented by rigid graphene. These substrates are chosen to model the effects of structural mismatch and commensurability, respectively, on the properties of G-O2DC systems. When the pore is large enough to allow substantial graphene corrugation inside the pores of O2DC, direct interaction between substrate and graphene will occur as well as proximity effect between these two layers.\u003c/p\u003e \u003cp\u003eIn all tested standalone G-O2DC heterostructures for organic 2D crystals \u003cb\u003eh1\u003c/b\u003e to \u003cb\u003eh4\u003c/b\u003e and \u003cb\u003es1\u003c/b\u003e to \u003cb\u003es6\u003c/b\u003e, the O2DC pore structure induces a weak corrugation on the graphene. This is caused by the dispersion interaction of graphene towards the O2DC pore voids. The amplitude of the corrugation strongly depends on the pore size of O2DC. It ranges from 0.06 \u0026Aring; to 1.45 \u0026Aring;, correlating with the rising of pore diameter from 2.6 \u0026Aring; to 22.6 \u0026Aring; (Figure S4). It is important to note that this consistent effect comes from dispersion interaction and is not an artifact of the computational supercell construction. Artificial corrugation can occur in computational models when lattice mismatch is introduced between O2DC and graphene supercells in the heterostructure, inducing an artificial strain on the structure,\u003csup\u003e25\u003c/sup\u003e and with it a corrugation of graphene similar to the one observed. To rule out such effect, we have plotted the inherent mismatch against the corrugation size and found no correlation (Figure S4), showing the corrugation does not originate from lattice mismatch. The presence of a substrate significantly influences graphene corrugation patterns in G-O2DC heterostructures, with distinct effects depending on the layer sequence. Especially, when the O2DC layer is positioned between graphene and the substrate (G-O2DC-substrate), strong dispersion interaction through the O2DC pores induces pronounced graphene corrugation. The magnitude of this effect scales with pore size: larger pores lead to stronger corrugation (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). For honeycomb O2DCs, the total graphene corrugation amplitude varies from Δd\u0026thinsp;=\u0026thinsp;0.22 \u0026Aring; (Δd is defined as the difference between maximum and minimum of z coordinates of corrugated graphene layer) for \u003cb\u003eh1\u003c/b\u003e (5.6 \u0026Aring;) to Δd\u0026thinsp;=\u0026thinsp;0.66 \u0026Aring; for \u003cb\u003eh3\u003c/b\u003e (15.6 \u0026Aring;), reaching a substantial Δd\u0026thinsp;=\u0026thinsp;1.19 \u0026Aring; for \u003cb\u003eh4\u003c/b\u003e (22.6 \u0026Aring;) (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). The observed corrugation amplitudes in the simulated G-O2DC heterostructures are in the range that could be measured using e.g. atomic force microscopy in non-contact mode (typically achieves vertical resolutions of ~\u0026thinsp;0.1 \u0026Aring; \u003csup\u003e26,27\u003c/sup\u003e. In pores larger than 22.6 \u0026Aring;, the corrugation shape of graphene changes, forming a plateau in the center of the pore, as the graphene starts touching the substrate. For very large pores on flat substrates, the maximum corrugation is expected to approach\u0026thinsp;~\u0026thinsp;3.5 \u0026Aring;, corresponding to the full interlayer separation distance.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe shape of the corrugation of graphene is perfectly templated by the O2DC pore system, as is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e for graphene on \u003cb\u003eh3\u003c/b\u003e (15.6 \u0026Aring; pores) and \u003cb\u003es6\u003c/b\u003e (19.6 \u0026Aring; pores) O2DCs on rigid graphene and SiO\u003csub\u003e2\u003c/sub\u003e surface. The observed corrugation amplitude does not depend strongly on the substrate; it is around 0.65 \u0026Aring; and 1.45 \u0026Aring; for the pore sizes of tested honeycomb and square O2DC, respectively, when substrate is included (See also Figure S5). The newly formed corrugation superlattice on graphene reflects the geometry of the underlying O2DC. A honeycomb O2DC will introduce a new hexagonal superlattice on graphene corresponding to its pore arrangement, due to the dispersion through pores and hindrance from frame. The same applies to organic 2D crystals with square pores (Figure S6, S7).\u003c/p\u003e \u003cp\u003eTo verify if the observed superlattice formation and corrugation are inherent properties of the G-O2DC heterostructure and not computational artifacts arising from periodic boundary conditions, we performed validation tests using finite-size, non-periodic flakes. Example structures of G-O2DC(\u003cb\u003eh2\u003c/b\u003e) are shown in Supporting Information (Figure S8). The tested non-periodic G-O2DC(\u003cb\u003eh2\u003c/b\u003e) structure showed roughly the same amplitude of 0.25 \u0026Aring; as the periodic G-O2DC(\u003cb\u003eh2\u003c/b\u003e) heterostructure. Similarly, the tested graphene flake on the O2DC(\u003cb\u003eh2\u003c/b\u003e)-SiO2 structure and the G-O2DC(\u003cb\u003eh2\u003c/b\u003e)-SiO2 structure both exhibited an amplitude of 0.35 \u0026Aring;. This confirms that the corrugation of the graphene is a native heterostructure property and is not caused by any artificial strain in the model.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo investigate the general effects of superlattice formation and corrugation on the electronic structure of the heterostructures, we calculated band structures for all G-O2DC-substrate (Gr and SiO\u003csub\u003e2\u003c/sub\u003e) heterostructures. Due to the large system size, we had to limit ourselves to only calculate band structure of the G-O2DC moiety without explicitly including the substrate. The substrate is thus effectively used only as a force field to induce geometric change in the heterostructure. This is a safe assumption as our calculations show no obvious electronic effects from SiO\u003csub\u003e2\u003c/sub\u003e around the Fermi level (Figure S9). We aimed to identify any possible modifications to the graphene band structure induced by the interaction with the O2DC layer. No significant band gap was found near the Dirac point, with values ranging from 0.8 to 8.6 meV for \u003cb\u003eh1\u003c/b\u003e to \u003cb\u003eh4\u003c/b\u003e and 1.0 to 12.1 meV for \u003cb\u003es1\u003c/b\u003e to \u003cb\u003es6\u003c/b\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, Figures S10, S11, Tables S1, S2). While no clear correlation was found between the degree of lattice mismatch and band gap opening or corrugation amplitude, the structures with the strongest corrugation exhibited the largest band gaps (\u003cb\u003eh4\u003c/b\u003e: 8.6 meV; \u003cb\u003es6\u003c/b\u003e: 12.1 meV). Choice of the substrate does not affect the observed results (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb and c). This preservation of electronic structure is observed for both honeycomb and square O2DC lattices, suggesting that these regular-shaped lattices do not lead to changes in the electronic properties of the heterostructures.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusions","content":"\u003cp\u003eIn this work, we developed a comprehensive computational modeling approach to investigate the structure and electronic properties of graphene-organic 2D crystal (G-O2DC) heterostructures. Our findings demonstrate that the pore structure of the organic 2D crystal always induces corrugation on graphene that is exactly templated by the shape of the O2DC pore structure, allowing for precise tailoring of the heterostructure. This effect is significantly enhanced in the presence of a substrate, where the substrate interacts directly with graphene across the pores, amplifying the corrugation amplitude. The corrugation magnitude is directly controlled by the O2DC pore size, providing a systematic approach to tune the superlattice periodicity and amplitude. It should be noted that under experimental conditions, the corrugation of graphene can be impacted by multiple factors, such as solvent or other guest molecules that can remain inside the pores of O2DCs and block interaction of graphene with the underlying substrates, therefore counteracting the corrugation formation observed in this work. Remarkably, despite substantial corrugation, graphene's electronic band structure remains preserved across all studied configurations, suggesting that sole geometric modulation is not sufficient to significantly modify the electronic features of graphene. Our results also indicate that rotational angles do not play a significant effect for these studied types of structures, thus making precision angle control less important in the fabrication procedure, providing valuable insights for both experimental and theoretical studies on material and device design in G-O2DC heterostructures.\u003c/p\u003e"},{"header":"Methods","content":" \u003cp\u003eThe organic 2D crystal (O2DC) unit cells were obtained by performing geometry optimization, including both atomic positions and lattice parameters. The G-O2DC heterostructures were then generated using the hetbuilder code\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e by rotating and expanding the optimized unit cells of O2DC and graphene to find the shared coincident supercell. Specifically, the G-O2DC-substrate structures were generated by rotating and expanding the fully-optimized G-O2DC structure with the unit cell of the substrate. When constructing heterostructure models with substrate, we treat the substrate as a rigid entity that primarily serves as an external force field acting on the G-O2DC moiety. We first optimized the isolated G-O2DC moiety to obtain its optimal unit cell parameters. Subsequently, we rescaled the substrate structure to match the optimized lattice and combine them to form the substrate-supported model. Crucially, we did not further optimize the lattice of the resulting system. By adopting this strategy, we can effectively capture the essential effects of the substrate on the G-O2DC heterostructure while maintaining a computationally tractable model.\u003c/p\u003e \u003cp\u003eThe geometries of all multi-layer structures were optimized with lattice parameter being fixed by density functional based tight binding method (DFTB).\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e DFTB+,\u003csup\u003e29\u003c/sup\u003e a code of DFTB, and Amsterdam Modeling Suite (AMS) \u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e was used to perform geometry optimizations. Particularly, DFTB2,\u003csup\u003e31,32\u003c/sup\u003e a second generation of DFTB coupled with an empirical dispersion correction of universal force-field (UFF) \u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e was used, with QUASINANO2015 \u003csup\u003e34\u003c/sup\u003e for structures of h4 with SiO\u003csub\u003e2\u003c/sub\u003e substrate and matsci-0-3 parameter set \u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e for the rest. Matsci-0-3 parameter set was used for majority of structures in this study, which has been shown before to perform well for similar systems\u003csup\u003e\u003cspan additionalcitationids=\"CR37\" citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. QUASINANO2015 was used only for the structure G-h4-SiO2 as it is the only available DFTB parameter set that includes all present species (particularly C, H, B, O, and Si) together. To investigate the electronic properties of the optimized structures, band structures calculations were performed by Fritz-Haber-Institute ab-initio materials simulations package (FHI-aims \u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e) with PBE \u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e. Tier 2 basis set and tight integration mesh were used. Deformation analysis was done by a self-made script using atomic simulation environment python package \u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. The script is available on GitHub (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/AK-Heine/StrainAnalysis\u003c/span\u003e\u003cspan address=\"https://github.com/AK-Heine/StrainAnalysis\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e).\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting Interests\u003c/h2\u003e \u003cp\u003eAll authors declare no financial or non-financial competing interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis study was funded by DFG priority program SPP 2244 and CRC 1415. The funder played no role in study design, data collection, analysis and interpretation of data, or the writing of this manuscript.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eSZ carried out all calculations and provided the first draft, MP supervised the research, TH conceived the project, all authors discussed the results and reviewed manuscript.\u003c/p\u003e\u003ch2\u003eData Availability Statement\u003c/h2\u003e \u003cp\u003eAll source data of the quantum chemistry calculations reported in this study are available in the NOMAD repository under DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.17172/NOMAD/2025.07.28-1\u003c/span\u003e\u003cspan address=\"10.17172/NOMAD/2025.07.28-1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eAcknowledgment\u003c/p\u003e \u003cp\u003eT.H. and S.Z. acknowledge funding of the DFG priority program SPP 2244 and CRC 1415. The authors gratefully acknowledge the computing time made available to them on the high-performance computers at the NHR Centers at TU Dresden and NHR Center PC\u003csup\u003e2\u003c/sup\u003e. These are funded by the Federal Ministry of Education and Research and the state governments participating on the basis of the resolutions of the GWK for the national high-performance computing at universities (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ewww.nhr-verein.de/unsere-partner\u003c/a\u003e\u003c/span\u003e\u003cspan address=\"http://www.nhr-verein.de/unsere-partner\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eNovoselov, K. S., Mishchenko, A., Carvalho, A. \u0026amp; Castro Neto, A. 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In this work, we investigate the structure-property relationships in graphene-O2DC (G-O2DC) heterostructures and the role of substrate interactions through computational studies. We demonstrate how O2DCs impose well-defined corrugation on graphene. The amplitude and superlattice of the graphene layer are directly governed by O2DC pore dimensions and substrate, with larger pores and substrate interactions significantly enhancing the corrugation effect. Despite significant structural modulation, the Dirac cone and linear band dispersion of graphene stay only slightly perturbed across all investigated configurations, demonstrating a decoupling between structural corrugation and electronic properties. These insights establish G-O2DC heterostructures as a viable platform for superlattice engineering in graphene, providing a robust foundation for their rational design and optimization and paving the way for applications in diverse fields such as electronics, catalysis, and energy storage.\u003c/p\u003e","manuscriptTitle":"A computational elucidation of the Structure-Property Relationships in Graphene-Organic 2D Crystal Heterostructures","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-19 17:17:05","doi":"10.21203/rs.3.rs-8172814/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-02-09T08:36:17+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-02T07:30:10+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"273523355131320936683397763570223094472","date":"2026-01-18T21:26:35+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-12-17T12:54:34+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-12-10T17:09:58+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-12-10T04:52:29+00:00","index":"","fulltext":""},{"type":"submitted","content":"npj 2D Materials and Applications","date":"2025-11-21T10:44:09+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"npj-2d-materials-and-applications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"npj2dmaterials","sideBox":"Learn more about [npj 2D Materials and Applications](http://www.nature.com/npj2dmaterials/)","snPcode":"41699","submissionUrl":"https://submission.springernature.com/new-submission/41699/3","title":"npj 2D Materials and Applications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"c3bc82ae-5575-4135-9552-eff1a294fd66","owner":[],"postedDate":"December 19th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":59820889,"name":"Physical sciences/Materials science"},{"id":59820890,"name":"Physical sciences/Nanoscience and technology"},{"id":59820891,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-05-21T10:53:10+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-19 17:17:05","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8172814","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8172814","identity":"rs-8172814","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}