- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Ternary H-C-N compounds at high pressure featuring sp3-hybridized C-N networks

Bole Chen1,2, Siyu Jin2, Cheng Lu3,*, and Andreas Hermann2,†

  • *Contact author: lucheng@calypso.cn
  • †Contact author: a.hermann@ed.ac.uk
PDF

Phys. Rev. B 114, 034109 – Published 7 July, 2026

DOI: https://doi.org/10.1103/8252-rnzw

Abstract

Hydrogen, carbon, and nitrogen are amongst the most important light elements in the composition of the solar system. They form the organic molecules and atmospheric components of many outer planets. Under the extreme conditions within planets, exploring the H-C-N chemical space is central to understanding the abiotic chemistry and interior structure of icy planets and moons. Here, based on effective crystal structure searches and ab initio calculations, we report the ground state phase diagram of the H-C-N system at pressures up to 500 GPa. Two thermodynamically stable ternary compounds CH2N2 and C2HN3 are predicted to maintain their stability up to the pressure of the mantle-core boundary of Neptune. Upon compression, both CH2N2 and C2HN3 benefit from the formation of a dense tetrahedrally connected network formed from sp3 hybridized carbon and nitrogen, supported by hydrogen bonding. The simplest possible compound, hydrogen cyanide HCN, is found to be metastable. Amongst methane-ammonia mixtures, we identify five metastable compounds: (CH4)2NH3, CH4NH3, CH4(NH3)2, CH4(NH3)3, and CH4(NH3)4. Potential synthesis pathways for the metastable compounds are provided for further discussion on the formation of mixtures based on simple molecules.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (64)

  1. W. B. Hubbard and J. J. MacFarlane, Structure and evolution of Uranus and Neptune, J. Geophys. Res.: Solid Earth 85, 225 (1980).
  2. R. Chau, S. Hamel, and W. J. Nellis, Chemical processes in the deep interior of Uranus, Nat. Commun. 2, 203 (2011).
  3. M. Rahm, J. I. Lunine, D. A. Usher, and D. Shalloway, Polymorphism and electronic structure of polyimine and its potential significance for prebiotic chemistry on Titan, Proc. Natl. Acad. Sci. USA 113, 8121 (2016).
  4. D. Duan, X. Huang, F. Tian, D. Li, H. Yu, Y. Liu, Y. Ma, B. Liu, and T. Cui, Pressure-induced decomposition of solid hydrogen sulfide, Phys. Rev. B 91, 180502(R) (2015).
  5. A. P. Drozdov, M. I. Eremets, I. A. Troyan, V. Ksenofontov, and S. I. Shylin, Conventional superconductivity at 203 Kelvin at high pressures in the sulfur hydride system, Nature (London) 525, 73 (2015).
  6. H. Liu, I. I. Naumov, R. Hoffmann, N. W. Ashcroft, and R. J. Hemley, Potential high-Tc superconducting lanthanum and yttrium hydrides at high pressure, Proc. Natl. Acad. Sci. USA 114, 6990 (2017).
  7. Z. M. Geballe, H. Liu, A. K. Mishra, M. Ahart, M. Somayazulu, Y. Meng, M. Baldini, and R. J. Hemley, Synthesis and stability of lanthanum superhydrides, Angew. Chem. 130, 696 (2018).
  8. A. R. Oganov and S. Ono, Theoretical and experimental evidence for a post-perovskite phase of MgSiO3 in Earth's D” layer, Nature (London) 430, 445 (2004).
  9. A. Hermann and P. Schwerdtfeger, Xenon suboxides stable under pressure, J. Phys. Chem. Lett. 5, 4336 (2014).
  10. A. Dewaele, N. Worth, C. J. Pickard, R. J. Needs, S. Pascarelli, O. Mathon, M. Mezouar, and T. Irifune, Synthesis and stability of xenon oxides Xe2O5 and Xe3O2 under pressure, Nat. Chem. 8, 784 (2016).
  11. W. Xu, V. N. Robinson, X. Zhang, H. C. Zhang, M. E. Donnelly, P. Dalladay-Simpson, A. Hermann, X. D. Liu, and E. Gregoryanz, Ionic phases of ammonia-rich hydrate at high densities, Phys. Rev. Lett. 126, 015702 (2021).
  12. V. Naden Robinson, Y. Wang, Y. Ma, and A. Hermann, Stabilization of ammonia-rich hydrate inside icy planets, Proc. Natl. Acad. Sci. USA 114, 9003 (2017).
  13. A. S. Naumova, S. V. Lepeshkin, P. V. Bushlanov, and A. R. Oganov, Unusual chemistry of the C-H-N-O system under pressure and implications for giant planets, J. Phys. Chem. A 125, 3936 (2021).
  14. L. J. Conway, C. J. Pickard, and A. Hermann, Rules of formation of H-C-N-O compounds at high pressure and the fates of planetary ices, Proc. Natl. Acad. Sci. USA 118, e2026360118 (2021).
  15. K. de Villa, F. Gonzalez-Cataldo, and B. Militzer, Double superionicity in icy compounds at planetary interior conditions, Nat. Commun. 14, 7580 (2023).
  16. V. N. Robinson and A. Hermann, Plastic and superionic phases in ammonia-water mixtures at high pressures and temperatures, J. Phys.: Condens. Matter 32, 184004 (2020).
  17. B. Militzer, Phase separation of planetary ices explains nondipolar magnetic fields of Uranus and Neptune, Proc. Natl. Acad. Sci. USA 121, e2403981121 (2024).
  18. K. de Villa, X. Wang, E. Zurek, and B. Militzer, Superionicity in ammonium polyhydrides at extreme pressures, J. Chem. Phys. 163, 244305 (2025).
  19. T. Thevenet, A. Dian, M. Cioni, A. Markovits, S. Scandolo, A. France-Lanord, and F. Siro Brigiano, From methane to nanodiamond precursors in water: Superacid-like condensation pathways under extreme conditions, Angew. Chem. Int. Ed. 65, e20364 (2026).
  20. L. J. Conway and A. Hermann, High pressure hydrocarbons revisited: From van der Waals compounds to diamond, Geosciences 9, 227 (2019).
  21. G. R. Qian, H. Niu, C. H. Hu, A. R. Oganov, Q. Zeng, and H. Y. Zhou, Diverse chemistry of stable hydronitrogens, and implications for planetary and materials sciences, Sci. Rep. 6, 25947 (2016).
  22. T. Li, N. Stolte, R. Tao, D. A. Sverjensky, I. Daniel, and D. Pan, Synthesis and stability of biomolecules in C-H-O-N fluids under Earth's upper mantle conditions, J. Am. Chem. Soc. 146, 31240 (2024).
  23. X. Wen, L. Hand, V. Labet, T. Yang, R. Hoffmann, N. W. Ashcroft, A. R. Oganov, and A. O. Lyakhov, Graphane sheets and crystals under pressure, Proc. Natl. Acad. Sci. USA 108, 6833 (2011).
  24. D. Laniel, F. Trybel, A. Aslandukov, S. Khandarkhaeva, T. Fedotenko, Y. Yin, N. Miyajima, F. Tasnadi, A. V. Ponomareva, N. Jena, F. I. Akbar, B. Winkler, A. Neri, S. Chariton, V. Prakapenka, V. Milman, W. Schnick, A. N. Rudenko, M. I. Katsnelson, I. A. Abrikosov, et al., Synthesis of ultra-incompressible and recoverable carbon nitrides featuring CN4 tetrahedra, Adv. Mater. 36, 2308030 (2024).
  25. H. Dong, A. R. Oganov, Q. Zhu, and G. R. Qian, The phase diagram and hardness of carbon nitrides, Sci. Rep. 5, 9870 (2015).
  26. T. Kimura and M. Murakami, Fluid-like elastic response of superionic NH3 in Uranus and Neptune, Proc. Natl. Acad. Sci. USA 118, e2021810118 (2021).
  27. C. S. Yoo, Physical and chemical transformations of highly compressed carbon dioxide at bond energies, Phys. Chem. Chem. Phys. 15, 7949 (2013).
  28. C. Lu, M. Miao, and Y. Ma, Structural evolution of carbon dioxide under high pressure, J. Am. Chem. Soc. 135, 14167 (2013).
  29. C. J. Pickard, M. Martinez-Canales, and R. J. Needs, Decomposition and terapascal phases of water ice, Phys. Rev. Lett. 110, 245701 (2013).
  30. G. R. Qian, A. O. Lyakhov, Q. Zhu, A. R. Oganov, and X. Dong, Novel hydrogen hydrate structures under pressure, Sci. Rep. 4, 5606 (2014).
  31. D. Li, A. R. Oganov, X. Dong, X. F. Zhou, Q. Zhu, G. Qian, and H. Dong, Nitrogen oxides under pressure: Stability, ionization, polymerization, and superconductivity, Sci. Rep. 5, 16311 (2015).
  32. G. Saleh and A. R. Oganov, Novel stable compounds in the C-H-O ternary system at high pressure, Sci. Rep. 6, 32486 (2016).
  33. J. Shi, W. Cui, S. Botti, and M. A. L. Marques, Nitrogen-hydrogen-oxygen ternary phase diagram: New phases at high pressure from structural prediction, Phys. Rev. Mater. 2, 023604 (2018).
  34. B. A. Steele and I. I. Oleynik, Ternary inorganic compounds containing carbon, nitrogen, and oxygen at high pressures, Inorg. Chem. 56, 13321 (2017).
  35. E. E. Vaneeva, S. V. Lepeshkin, and A. R. Oganov, Prediction and rationalization of abundant C-N-H molecules in different environments, J. Phys. Chem. Lett. 14, 8367 (2023).
  36. F. Izquierdo-Ruiz, M. L. Cable, R. Hodyss, T. H. Vu, H. Sandstrom, A. Lobato, and M. Rahm, Hydrogen cyanide and hydrocarbons mix on Titan, Proc. Natl. Acad. Sci. USA 122, e2507522122 (2025).
  37. F. Peng, Y. Ma, A. Hermann, and M. Miao, Recoverable high-energy compounds by reacting methane and nitrogen under high pressure, Phys. Rev. Mater. 4, 103610 (2020).
  38. E. Horvath-Bordon, R. Riedel, P. F. McMillan, P. Kroll, G. Miehe, P. A. van Aken, A. Zerr, P. Hoppe, O. Shebanova, I. McLaren, S. Lauterbach, E. Kroke, and R. Boehler, High-pressure synthesis of crystalline carbon nitride imide, Angew. Chem. 119, 1498 (2007).
  39. T. J. Koller, S. Jin, V. Krol, S. J. Ambach, U. Ranieri, S. Khandarkhaeva, J. Spender, S. McWilliams, F. Trybel, N. Giordano, T. Poreba, M. Mezouar, X. Kuang, C. Lu, L. Dubrovinsky, N. Dubrovinskaia, A. Hermann, W. Schnick, and D. Laniel, Simple molecules under high-pressure and high-temperature conditions: Synthesis and characterization of α- and β-C(NH)2 with fully sp3-hybridized carbon, Angew. Chem. Int. Ed. 63, e202318214 (2024).
  40. H. A. Shuttleworth, M. A. Kuzovnikov, L. J. Conway, H. Hu, J. Yan, S. Gallego-Parra, I. Osmond, T. Marqueno, M. Hanfland, D. Laniel, E. Gregoryanz, A. Hermann, M. Pena-Alvarez, and R. T. Howie, Pressure-driven reactivity in dense methane-nitrogen mixtures, Angew. Chem. 137, e202422710 (2025).
  41. A. Hermann, L. J. Conway, and C. J. Pickard, Rules of formation of H–C–N–O compounds at high pressure and the fates of planetary ices [dataset], University of Edinburgh, School of Physics and Astronomy, Institute for Condensed Matter and Complex Systems, 2021, https://doi.org/10.7488/ds/3018.
  42. L. J. Conway, C. J. Pickard, and A. Hermann, Rules of formation of H–C–N–O compounds at high pressure and the fates of planetary ices, Materials Cloud Archive, 2021.62 (2021), https://doi.org/10.24435/materialscloud:p6-zh.
  43. C. J. Pickard and R. J. Needs, Ab initio random structure searching, J. Phys.: Condens. Matter 23, 053201 (2011).
  44. Y. Wang, J. Lv, L. Zhu, and Y. Ma, CALYPSO: A method for crystal structure prediction, Comput. Phys. Commun. 183, 2063 (2012).
  45. H. Wang, Y. Wang, J. Lv, Q. Li, L. Zhang, and Y. Ma, CALYPSO structure prediction method and its wide application, Comput. Mater. Sci. 112, 406 (2016).
  46. C. J. Pickard and R. J. Needs, Highly compressed ammonia forms an ionic crystal, Nat. Mater. 7, 775 (2008).
  47. C. J. Pickard and R. J. Needs, Structure of phase III of solid hydrogen, Nat. Phys. 3, 473 (2007).
  48. M. Martinez-Canales, C. J. Pickard, and R. J. Needs, Thermodynamically stable phases of carbon at multiterapascal pressures, Phys. Rev. Lett. 108, 045704 (2012).
  49. C. J. Pickard and R. J. Needs, High-pressure phases of nitrogen, Phys. Rev. Lett. 102, 125702 (2009).
  50. J. Hafner, Materials simulations using vasp-a quantum perspective to materials science, Comput. Phys. Commun. 177, 6 (2007).
  51. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  52. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  53. A. Togo and I. Tanaka, First principles phonon calculations in materials science, Scr. Mater. 108, 1 (2015).
  54. A. Otero-de-la-Roza, M. A. Blanco, A. M. Pendás, and V. Luaña, Critic: A new program for the topological analysis of solid-state electron densities, Comput. Phys. Commun. 180, 157 (2009).
  55. S. Maintz, V. L. Deringer, A. L. Tchougreeff, and R. Dronskowski, LOBSTER: A tool to extract chemical bonding from plane-wave based DFT, J. Comput. Chem. 37, 1030 (2016).
  56. See Supplemental Material at http://link.aps.org/supplemental/10.1103/8252-rnzw for structure search details, phase diagrams, decomposition reactions, phonon dispersions, ELF plots, and crystallographic information, which includes Refs. [14, 26, 47, 48, 49, 59, 60].
  57. X. Song, K. Yin, Y. Wang, A. Hermann, H. Liu, J. Lv, Q. Li, C. Chen, and Y. Ma, Exotic hydrogen bonding in compressed ammonia hydrides, J. Phys. Chem. Lett. 10, 2761 (2019).
  58. C. J. Pickard, A. Salamat, M. J. Bojdys, R. J. Needs, and P. F. McMillan, Carbon nitride frameworks and dense crystalline polymorphs, Phys. Rev. B 94, 094104 (2016).
  59. E. Gregoryanz, A. F. Goncharov, K. Matsuishi, H.-k. Mao, and R. J. Hemley, Raman spectroscopy of hot dense hydrogen, Phys. Rev. Lett. 90, 175701 (2003).
  60. M. Wang, M. Peña-Alvarez, R. T. Howie, and E. Gregoryanz, Revisiting the phase diagram of methane, Phys. Rev. Lett. 136, 046101 (2026).
  61. A. Salamat, K. Woodhead, P. F. McMillan, R. Q. Cabrera, A. Rahman, D. Adriaens, F. Corà, and J.-P. Perrillat, Tetrahedrally bonded dense C2N3H with a defective wurtzite structure: X-ray diffraction and Raman scattering results at high pressure and ambient conditions, Phys. Rev. B 80, 104106 (2009).
  62. S. Schaack, U. Ranieri, P. Depondt, R. Gaal, W. F. Kuhs, P. Gillet, F. Finocchi, and L. E. Bove, Observation of methane filled hexagonal ice stable up to 150 GPa, Proc. Natl. Acad. Sci. USA 116, 16204 (2019).
  63. A. Hermann, N. W. Ashcroft, and R. Hoffmann, High pressure ices, Proc. Natl. Acad. Sci. USA 109, 745 (2012).
  64. A. Hermann, B. Chen, and S. Jin, Ternary H-C-N compounds at high pressure featuring sp3-hybridized C-N networks [dataset], University of Edinburgh, School of Physics and Astronomy, Institute for Condensed Matter and Complex Systems, 2026, https://doi.org/10.7488/ds/8143.

Outline

Information

Phys. Rev. B 114, 034109– Published 7 July, 2026
  • Received 24 February 2026
  • Revised 29 May 2026
  • Accepted 17 June 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation