Structural models of carbon-based materials generated with molecular augmented dynamics

These are atomic-scale models of disordered carbon-based materials generated using molecular augmented dynamics (MAD) using experimental constraints (X-ray diffraction, neutron diffraction, X-ray photoelectron spectroscopy) and a control simulation protocol based on regular molecular dynamics (MD) without the experimental constraints. The materials include pure carbon forms: tetrahedral amorphous carbon (ta-C); glassy carbon; nanoporous carbon; as well as binary mixtures of carbon compounds: deuterated/hydrogenated amorphous carbon (a-C:D, a-C:H); oxygen-rich amorphous carbon (a-COx). For a-C:H, experimental a-C:D data was used in the structure generation because of the difficulty in matching the available a-C:H data due to the non-trivial interaction of hydrogen's most common isotope (protium, 1H) with neutrons. Thus, available experimental data with deuterium (2H) was used instead. The XYZ structures labeled as "aCD" and "aCH" are the same, generated with target a-C:D data, with deuterium ("D") or hydrogen ("H") labels, respectively. This is to ensure the XYZ files can be imported with common atomistic manipulation software that might give errors with "D" labels. The structures where generated with the TurboGAP code (turbogap.fi) using GAP potentials trained for pure-C [1], C-H mixtures [2], C-O mixtures [3] and a core-electron binding energy model trained for C-H-O [3, 4]. The methodology used is a modified Hamiltonian dynamics approach [3] whose extension to analytical forces is known as MAD, with all the details provided in the following pair of papers: T. Zarrouk and M.A. Caro. Molecular augmented dynamics: Generating experimentally consistent atomistic structures by design. arXiv:2508.17132 T. Zarrouk and M.A. Caro. Linear-scaling calculation of experimental observables for molecular augmented dynamics simulations. arXiv:2509.22388 A gallery of the structures, plotted using ASE [5], Ovito [6] and ase_tools [7], is provided with file name "gallery.png". All other files use an obvious naming ocnvention. The experimental data were obtained from the literature [8-12]. All the details are given in the reference papers [13, 14]. Contact You can get in contact with either or both the authors at firstname.lastname(at)aalto.fi Funding The authors acknowledge financial support from the Research Council of Finland under projects 330488, 347252, 352484, 355301 and 364778, from the European Union’s M-ERA.NET 3 program (NACAB project under grant agreement No 958174). We acknowledge the EuroHPC Joint Undertaking for awarding this project (XCALE innovation study within the Inno4scale project under grant agreement No 101118139) access to the EuroHPC supercomputer LUMI, hosted by CSC (Finland) and the LUMI consortium through a EuroHPC Regular Access call. The authors also acknowledge other computational resources from CSC – the Finnish IT Center for Science and Aalto University’s Science-IT project. References H. Muhli, X. Chen, A. P. Bartók, P. Hernández-León, G. Csányi, T. Ala-Nissila, and M. A. Caro. Machine learning force fields based on local parametrization of dispersion interactions: Application to the phase diagram of C60. Phys. Rev. B 104, 054106 (2021). R. Ibragimova, M. S. Kuklin, T. Zarrouk, and M. A. Caro. Unifying the Description of Hydrocarbons and Hydrogenated Carbon Materials with a Chemically Reactive Machine Learning Interatomic Potential. Chem. Mater. 37, 1094 (2025). T. Zarrouk, R. Ibragimova, A. P. Bartók, and M. A. Caro. Experiment-driven atomistic materials modeling: A case study combining x-ray photoelectron spectroscopy and machine learning potentials to infer the structure of oxygen-rich amorphous carbon. J. Am. Chem. Soc. 146, 14645 (2024). D. Golze, M. Hirvensalo, Hernández-León P., A. Aarva, J. Etula, T. Susi, P. Rinke, T. Laurila, and M. A. Caro. Accurate computational prediction of core-electron binding energies in carbon-based materials: A machine-learning model combining DFT and GW. Chem. Mater. 34, 6240 (2022). A. H. Larsen, J. J. Mortensen, J. Blomqvist, I. E. Castelli, R. Christensen, M. Dulak, J. Friis, M. N. Groves, B. Hammer, C. Hargus, E. D. Hermes, P. C. Jennings, P. B. Jensen, J. Kermode, J. R. Kitchin, E. L. Kolsbjerg, J. Kubal, K. Kaasbjerg, S. Lysgaard, J. B. Maronsson, T. Maxson, T. Olsen, L. Pastewka, A. Peterson, C. Rostgaard, J. Schiøtz, O. Schütt, M. Strange, K. S. Thygesen, T. Vegge, L. Vilhelmsen, M. Walter, Z. Zeng, and K. W. Jacobsen. The Atomic Simulation Environment – A Python library for working with atoms. J. Phys.: Condens. Matter 29, 273002 (2017). A. Stukowski. Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool. Modelling Simul. Mater. Sci. Eng. 18, 015012 (2009). github.com/mcaroba/ase_tools Z. Zeng, L. Yang, Q. Zeng, H. Lou, H. Sheng, J. Wen, D. J. Miller, Y. Meng, W. Yang, W. L. Mao, and H.-K. Mao. Synthesis of quenchable amorphous diamond. Nat. Commun. 8, 322 (2017). K. W. R. Gilkes, P. H. Gaskell, and J. Robertson. Comparison of neutron-scattering data for tetrahedral amorphous carbon with structural models. Phys. Rev. B 51, 12303 (1995). T. M. Burke, R. J. Newport, W. S. Howells, K. W. R. Gilkes, and P. H. Gaskell. The structure of a-C:H(D) by neutron diffraction and isotropic enrichment. J. Non-Cryst. Solids 164, 1139 (1993). C. A. Santini, A. Sebastian, C. Marchiori, V. P. Jonnalagadda, L. Dellmann, W. W. Koelmans, M. D. Rossell, C. P. Rossel, and E. Eleftheriou. Oxygenated amorphous carbon for resistive memory applications. Nat. Commun. 6, 1 (2015). A. C. Forse, C. Merlet, P. K. Allan, E. K. Humphreys, J. M. Griffin, M. Aslan, M. Zeiger, V. Presser, Y. Gogotsi, and C. P. Grey. New insights into the structure of nanoporous carbons from NMR, Raman, and pair distribution function analysis. Chem. Mater. 27, 6848 (2015). T. Zarrouk and M. A. Caro. Molecular augmented dynamics: Generating experimentally consistent atomistic structures by design. arXiv:2508.17132. T. Zarrouk and M. A. Caro. Linear-scaling calculation of experimental observables for molecular augmented dynamics simulations. arXiv:2509.22388.本数据集包含通过分子增强动力学（molecular augmented dynamics, MAD）生成的无序碳基材料原子级模型，生成过程结合了实验约束条件（X射线衍射、中子衍射、X射线光电子能谱），以及基于常规分子动力学（molecular dynamics, MD）、无实验约束的控制模拟协议。 所涵盖的材料包括纯碳形式： 四面体无定形碳（tetrahedral amorphous carbon, ta-C）、玻璃碳、纳米多孔碳； 以及碳化合物二元混合物： 氘代/氢化无定形碳（a-C:D, a-C:H）、富氧无定形碳（a-COₓ）。 针对氢化无定形碳（a-C:H），由于氢最常见的同位素（氕，¹H）与中子存在非平凡相互作用，难以匹配现有a-C:H实验数据，因此结构生成时实际采用了氘（²H）的实验数据。标注为"aCD"与"aCH"的XYZ结构完全一致，均基于目标a-C:D数据生成，仅分别以氘（"D"）或氢（"H"）作为原子标签，此举可确保XYZ文件能被常见原子级操控软件正常导入，避免因"D"标签引发报错。 本数据集的结构通过TurboGAP代码（turbogap.fi）生成，所用的GAP势分别针对纯碳体系[1]、碳氢混合物[2]、碳氧混合物[3]进行训练，同时采用了针对碳氢氧体系训练的核心电子结合能模型[3,4]。所采用的方法为改进型哈密顿动力学方法[3]，其解析力扩展形式即为分子增强动力学（MAD），完整细节见以下两篇论文： 1. T. Zarrouk与M.A. Caro，《分子增强动力学：按需生成与实验一致的原子级结构》，arXiv:2508.17132 2. T. Zarrouk与M.A. Caro，《分子增强动力学模拟中实验可观测量的线性标度计算》，arXiv:2509.22388 本数据集附带结构可视化图集（文件名为"gallery.png"），图集使用ASE[5]、OVITO[6]与ase_tools[7]绘制。其余文件均遵循直观的命名规则。 本数据集所用的实验数据取自文献[8-12]，完整细节见参考文献[13,14]。 ## 联系方式 可通过firstname.lastname(at)aalto.fi联系任意一位或两位作者。 ## 资助说明 作者感谢芬兰研究理事会资助的项目330488、347252、352484、355301与364778，以及欧盟M-ERA.NET 3计划（NACAB项目，资助协议编号958174）提供的经费支持。作者感谢欧洲高性能计算联合倡议（EuroHPC Joint Undertaking）为本次项目（Inno4scale项目内的XCALE创新研究，资助协议编号101118139）分配了由芬兰CSC与LUMI联盟运营的欧洲超算LUMI的使用权限，该权限通过EuroHPC常规访问计划申请获得。此外，作者感谢芬兰IT科学中心CSC与阿尔托大学Science-IT项目提供的其他计算资源。 ## 参考文献 [1] H. Muhli, X. Chen, A. P. Bartók, P. Hernández-León, G. Csányi, T. Ala-Nissila, and M. A. Caro. 基于色散相互作用局域参数化的机器学习力场：在C₆₀相图研究中的应用. 《物理评论B》, 104, 054106 (2021). [2] R. Ibragimova, M. S. Kuklin, T. Zarrouk, and M. A. Caro. 反应性机器学习原子间势统一描述烃类与氢化碳材料. 《化学材料》, 37, 1094 (2025). [3] T. Zarrouk, R. Ibragimova, A. P. Bartók, and M. A. Caro. 实验驱动的原子级材料建模：结合X射线光电子能谱与机器学习势推断富氧无定形碳结构的案例研究. 《美国化学会志》, 146, 14645 (2024). [4] D. Golze, M. Hirvensalo, Hernández-León P., A. Aarva, J. Etula, T. Susi, P. Rinke, T. Laurila, and M. A. Caro. 碳基材料核心电子结合能的精准计算预测：结合DFT与GW的机器学习模型. 《化学材料》, 34, 6240 (2022). [5] A. H. Larsen, J. J. Mortensen, J. Blomqvist, I. E. Castelli, R. Christensen, M. Dulak, J. Friis, M. N. Groves, B. Hammer, C. Hargus, E. D. Hermes, P. C. Jennings, P. B. Jensen, J. Kermode, J. R. Kitchin, E. L. Kolsbjerg, J. Kubal, K. Kaasbjerg, S. Lysgaard, J. B. Maronsson, T. Maxson, T. Olsen, L. Pastewka, A. Peterson, C. Rostgaard, J. Schiøtz, O. Schütt, M. Strange, K. S. Thygesen, T. Vegge, L. Vilhelmsen, M. Walter, Z. Zeng, and K. W. Jacobsen. 原子模拟环境：用于原子操作的Python库. 《物理学报：凝聚态分册》, 29, 273002 (2017). [6] A. Stukowski. 利用OVITO——开放可视化工具对原子级模拟数据进行可视化与分析. 《建模与仿真材料科学与工程》, 18, 015012 (2009). [7] github.com/mcaroba/ase_tools [8] Z. Zeng, L. Yang, Q. Zeng, H. Lou, H. Sheng, J. Wen, D. J. Miller, Y. Meng, W. Yang, W. L. Mao, and H.-K. Mao. 可淬冷无定形金刚石的合成. 《自然·通讯》, 8, 322 (2017). [9] K. W. R. Gilkes, P. H. Gaskell, and J. Robertson. 四面体无定形碳的中子散射数据与结构模型对比. 《物理评论B》, 51, 12303 (1995). [10] T. M. Burke, R. J. Newport, W. S. Howells, K. W. R. Gilkes, and P. H. Gaskell. 中子衍射与同位素富集法研究a-C:H(D)的结构. 《非晶态固体杂志》, 164, 1139 (1993). [11] C. A. Santini, A. Sebastian, C. Marchiori, V. P. Jonnalagadda, L. Dellmann, W. W. Koelmans, M. D. Rossell, C. P. Rossel, and E. Eleftheriou. 用于阻变存储器应用的含氧无定形碳. 《自然·通讯》, 6, 1 (2015). [12] A. C. Forse, C. Merlet, P. K. Allan, E. K. Humphreys, J. M. Griffin, M. Aslan, M. Zeiger, V. Presser, Y. Gogotsi, and C. P. Grey. 从NMR、拉曼与对分布函数分析探究纳米多孔碳的结构新认知. 《化学材料》, 27, 6848 (2015). [13] T. Zarrouk and M.A. Caro. 分子增强动力学：按需生成与实验一致的原子级结构. arXiv:2508.17132. [14] T. Zarrouk and M.A. Caro. 分子增强动力学模拟中实验可观测量的线性标度计算. arXiv:2509.22388.