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Time-dependent hole states in multiconfigurational time-dependent Hartree-Fock approaches: Applications in photoionization of water molecule

Zhao-Han Zhang1, Yang Li1,*, Himadri Pathak3,4, Takeshi Sato5,6,7, Kenichi L. Ishikawa5,6,7,8, and Feng He1,2,†

  • 1Key Laboratory for Laser Plasmas (Ministry of Education) and School of Physics and Astronomy, Collaborative Innovation Center for IFSA (CICIFSA), Shanghai Jiao Tong University, Shanghai 200240, China
  • 2Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 201210, China
  • 3Quantum Mathematical Science Team, Division of Applied Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), 2-1 Hirosawa Wako, Saitama 351-0198, Japan
  • 4Computational Molecular Science Research Team, RIKEN Center for Computational Science (R-CCS), 7-1-26 Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
  • 5Department of Nuclear Engineering and Management, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
  • 6Photon Science Center, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
  • 7Research Institute for Photon Science and Laser Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
  • 8Institute for Attosecond Laser Facility, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

  • *Contact author: liyang22@sjtu.edu.cn
  • †Contact author: fhe@sjtu.edu.cn
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Phys. Rev. Research 8, 013016 – Published 12 January, 2026

DOI: https://doi.org/10.1103/q5zy-pm5d

Abstract

By simulating the real-time multi-electron wavefunction with the multiconfigurational time-dependent Hartree-Fock (MCTDHF) approach, we conduct an ab initio study of the single-photon ionization process of a body-fixed water molecule (H2O) driven by attosecond pulses. To this end, we present a full-dimensional implementation of the MCTDHF method based on one-center expansions, allowing for the simulation of arbitrarily polarized lasers and multicenter polyatomic potentials. With a rigorous definition of the time-dependent hole state (TDHS) using the time-domain generalization of extended Koopmans' theorem, we derive the reduced ion density matrix within the MCTDHF framework, which inherently encodes the total and channel-resolved photoionization cross sections of H2O. The cross sections obtained are benchmarked against existing experimental and theoretical results, validating the TDHS formalism. Furthermore, by adjusting the phase delay and intensity ratio of a pair of orthogonally polarized attosecond pulses, we explore the ultrafast control of attosecond coherence between electronic states of H2O+.

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Time-Dependent Hole States in Multiconfigurational Time-Dependent Hartree-Fock Approaches: A Time-Domain Generalization of Extended Koopmans’ Theorem

Zhao-Han Zhang, Yang Li, Himadri Pathak, Takeshi Sato, Kenichi L. Ishikawa, and Feng He
Phys. Rev. Lett. 136, 013204 (2026)

Article Text

References (84)

  1. A. U. Lode, C. Lévêque, L. B. Madsen, A. I. Streltsov, and O. E. Alon, Colloquium: Multiconfigurational time-dependent Hartree approaches for indistinguishable particles, Rev. Mod. Phys. 92, 011001 (2020).
  2. K. L. Ishikawa and T. Sato, A review on ab initio approaches for multielectron dynamics, IEEE J. Sel. Top. Quantum Electron. 21, 1 (2015).
  3. J. Zanghellini, M. Kitzler, C. Fabian, T. Brabec, and A. Scrinzi, An MCTDHF approach to multielectron dynamics in laser fields, Laser Phys. 13, 1064 (2003).
  4. T. Kato and H. Kono, Time-dependent multiconfiguration theory for electronic dynamics of molecules in an intense laser field, Chem. Phys. Lett. 392, 533 (2004).
  5. J. Caillat, J. Zanghellini, M. Kitzler, O. Koch, W. Kreuzer, and A. Scrinzi, Correlated multielectron systems in strong laser fields: A multiconfiguration time-dependent Hartree-Fock approach, Phys. Rev. A 71, 012712 (2005).
  6. T. Kato and H. Kono, Time-dependent multiconfiguration theory for electronic dynamics of molecules in intense laser fields: A description in terms of numerical orbital functions, J. Chem. Phys. 128, 184102 (2008).
  7. G. Jordan and A. Scrinzi, Core-polarization effects in molecular high harmonic generation, New J. Phys. 10, 025035 (2008).
  8. S. Sukiasyan, C. McDonald, C. Destefani, M. Y. Ivanov, and T. Brabec, Multielectron correlation in high-harmonic generation: A 2D model analysis, Phys. Rev. Lett. 102, 223002 (2009).
  9. D. J. Haxton, K. V. Lawler, and C. W. McCurdy, Multiconfiguration time-dependent Hartree-Fock treatment of electronic and nuclear dynamics in diatomic molecules, Phys. Rev. A 83, 063416 (2011).
  10. D. Haxton, K. Lawler, and C. McCurdy, Single photoionization of Be and HF using the multiconfiguration time-dependent Hartree-Fock method, Phys. Rev. A 86, 013406 (2012).
  11. D. Hochstuhl, C. M. Hinz, and M. Bonitz, Time-dependent multiconfiguration methods for the numerical simulation of photoionization processes of many-electron atoms, Eur. Phys. J.: Spec. Top. 223, 177 (2014).
  12. R. Sawada, T. Sato, and K. L. Ishikawa, Implementation of the multiconfiguration time-dependent Hartree-Fock method for general molecules on a multiresolution Cartesian grid, Phys. Rev. A 93, 023434 (2016).
  13. T. Sato and K. L. Ishikawa, Time-dependent complete-active-space self-consistent-field method for multielectron dynamics in intense laser fields, Phys. Rev. A 88, 023402 (2013).
  14. H. Miyagi and L. B. Madsen, Time-dependent restricted-active-space self-consistent-field theory for laser-driven many-electron dynamics, Phys. Rev. A 87, 062511 (2013).
  15. H. Miyagi and L. B. Madsen, Time-dependent restricted-active-space self-consistent-field theory for laser-driven many-electron dynamics. II. Extended formulation and numerical analysis, Phys. Rev. A 89, 063416 (2014).
  16. T. Sato and K. L. Ishikawa, Time-dependent multiconfiguration self-consistent-field method based on the occupation-restricted multiple-active-space model for multielectron dynamics in intense laser fields, Phys. Rev. A 91, 023417 (2015).
  17. T. Sato, K. L. Ishikawa, I. Březinová, F. Lackner, S. Nagele, and J. Burgdörfer, Time-dependent complete-active-space self-consistent-field method for atoms: Application to high-order harmonic generation, Phys. Rev. A 94, 023405 (2016).
  18. J. J. Omiste and L. B. Madsen, Attosecond photoionization dynamics in neon, Phys. Rev. A 97, 013422 (2018).
  19. X. Li, D. Haxton, M. B. Gaarde, K. Schafer, and C. McCurdy, Direct extraction of intense-field-induced polarization in the continuum on the attosecond time scale from transient absorption, Phys. Rev. A 93, 023401 (2016).
  20. J. J. Omiste, W. Li, and L. B. Madsen, Electron correlation in beryllium: Effects in the ground state, short-pulse photoionization, and time-delay studies, Phys. Rev. A 95, 053422 (2017).
  21. J. J. Omiste and L. B. Madsen, Effects of core space and excitation levels on ground-state correlation and photoionization dynamics of Be and Ne, J. Chem. Phys. 150, 084305 (2019).
  22. I. Tikhomirov, T. Sato, and K. L. Ishikawa, High-harmonic generation enhanced by dynamical electron correlation, Phys. Rev. Lett. 118, 203202 (2017).
  23. Y. Orimo, T. Sato, and K. L. Ishikawa, Application of the time-dependent surface flux method to the time-dependent multiconfiguration self-consistent-field method, Phys. Rev. A 100, 013419 (2019).
  24. Y. Orimo, K. Tökési, T. Sato, and K. L. Ishikawa, Comparison between quantum and classical calculations for above threshold ionization of argon, Eur. Phys. J. D 73, 153 (2019).
  25. Y. Li, F. He, T. Sato, and K. L. Ishikawa, Implementation of the time-dependent complete-active-space self-consistent-field method for diatomic molecules, J. Phys. Chem. A 128, 1523 (2024).
  26. G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta et al., Isolated single-cycle attosecond pulses, Science 314, 443 (2006).
  27. M. Chini, K. Zhao, and Z. Chang, The generation, characterization and applications of broadband isolated attosecond pulses, Nat. Photon. 8, 178 (2014).
  28. T. Gaumnitz, A. Jain, Y. Pertot, M. Huppert, I. Jordan, F. Ardana-Lamas, and H. J. Wörner, Streaking of 43-attosecond soft-x-ray pulses generated by a passively cep-stable mid-infrared driver, Opt. Express 25, 27506 (2017).
  29. X. Wang, F. Xiao, J. Wang, L. Wang, B. Zhang, J. Liu, J. Zhao, and Z. Zhao, Ultrashort isolated attosecond pulse generation with 750-nm free-carrier envelope phase near-infrared pulses, Ultrafast Sci. 4, 0080 (2024).
  30. M. J. Vrakking, Control of attosecond entanglement and coherence, Phys. Rev. Lett. 126, 113203 (2021).
  31. L.-M. Koll, L. Maikowski, L. Drescher, T. Witting, and M. J. Vrakking, Experimental control of quantum-mechanical entanglement in an attosecond pump-probe experiment, Phys. Rev. Lett. 128, 043201 (2022).
  32. K. L. Ishikawa, K. C. Prince, and K. Ueda, Control of ion-photoelectron entanglement and coherence via Rabi oscillations, J. Phys. Chem. A 127, 10638 (2023).
  33. M. Ruberti, V. Averbukh, and F. Mintert, Bell test of quantum entanglement in attosecond photoionization, Phys. Rev. X 14, 041042 (2024).
  34. H. Laurell, S. Luo, R. Weissenbilder, M. Ammitzböll, S. Ahmed, H. Söderberg, C. L. M. Petersson, V. Poulain, C. Guo, C. Dittel et al., Measuring the quantum state of photoelectrons, Nat. Photon. 19, 352 (2025).
  35. D. Clarke, G. Armstrong, A. Brown, and H. Van Der Hart, R-matrix-with-time-dependence theory for ultrafast atomic processes in arbitrary light fields, Phys. Rev. A 98, 053442 (2018).
  36. R. Dörner, V. Mergel, O. Jagutzki, L. Spielberger, J. Ullrich, R. Moshammer, and H. Schmidt-Böcking, Cold target recoil ion momentum spectroscopy: A ‘momentum microscope’ to view atomic collision dynamics, Phys. Rep. 330, 95 (2000).
  37. Z.-H. Zhang, Y. Li, H. Pathak, T. Sato, K. L. Ishikawa, and F. He, Time-dependent hole states in multiconfigurational time-dependent Hartree-Fock approaches: A time-domain generalization of extended Koopmans' theorem, Phys. Rev. Lett. 136, 013204 (2026).
  38. L. Madsen, L. Nikolopoulos, T. Kjeldsen, and J. Fernández, Extracting continuum information from ψ (t) in time-dependent wave-packet calculations, Phys. Rev. A 76, 063407 (2007).
  39. L. Argenti, R. Pazourek, J. Feist, S. Nagele, M. Liertzer, E. Persson, J. Burgdörfer, and E. Lindroth, Photoionization of helium by attosecond pulses: Extraction of spectra from correlated wave functions, Phys. Rev. A 87, 053405 (2013).
  40. L. Tao and A. Scrinzi, Photo-electron momentum spectra from minimal volumes: The time-dependent surface flux method, New J. Phys. 14, 013021 (2012).
  41. A. Scrinzi, t-SURFF: Fully differential two-electron photo-emission spectra, New J. Phys. 14, 085008 (2012).
  42. P. A. Dirac, Note on exchange phenomena in the thomas atom, Math. Proc. Cambridge Philos. Soc. 26, 376 (1930).
  43. J. Frenkel, Wave Mechanics: Advanced General Theory (Oxford University Press, Oxford, 1934), Vol. 436.
  44. A. McLachlan, A variational solution of the time-dependent Schrodinger equation, Mol. Phys. 8, 39 (1964).
  45. H.-D. Meyer, U. Manthe, and L. S. Cederbaum, The multi-configurational time-dependent Hartree approach, Chem. Phys. Lett. 165, 73 (1990).
  46. T. Koopmans, Über die zuordnung von wellenfunktionen und eigenwerten zu den einzelnen elektronen eines atoms, Physica 1, 104 (1934).
  47. O. W. Day, D. W. Smith, and C. Garrod, A generalization of the Hartree-Fock one-particle potential, Int. J. Quantum Chem. 8, 501 (1974).
  48. D. W. Smith and O. W. Day, Extension of Koopmans’ theorem. I. Derivation, J. Chem. Phys. 62, 113 (1975).
  49. M. M. Morrell, R. G. Parr, and M. Levy, Calculation of ionization potentials from density matrices and natural functions, and the long-range behavior of natural orbitals and electron density, J. Chem. Phys. 62, 549 (1975).
  50. H. Bachau, E. Cormier, P. Decleva, J. Hansen, and F. Martín, Applications of B-splines in atomic and molecular physics, Rep. Prog. Phys. 64, 1815 (2001).
  51. Z.-H. Zhang, Y. Li, Y.-J. Mao, and F. He, QPC-TDSE: A parallel TDSE solver for atoms and small molecules in strong lasers, Comput. Phys. Commun. 290, 108787 (2023).
  52. D. Toffoli, M. Stener, G. Fronzoni, and P. Decleva, Convergence of the multicenter B-spline DFT approach for the continuum, Chem. Phys. 276, 25 (2002).
  53. C. W. McCurdy and F. Martin, Implementation of exterior complex scaling in B-splines to solve atomic and molecular collision problems, J. Phys. B: At. Mol. Opt. Phys. 37, 917 (2004).
  54. S. Sukiasyan and H.-D. Meyer, On the effect of initial rotation on reactivity. A multi-configuration time-dependent Hartree (mctdh) wave packet propagation study on the H + D2 and D+H2 reactive scattering systems, J. Phys. Chem. A 105, 2604 (2001).
  55. D. J. Haxton, Lebedev discrete variable representation, J. Phys. B: At. Mol. Opt. Phys. 40, 4443 (2007).
  56. S. Krogstad, Generalized integrating factor methods for stiff pdes, J. Comput. Phys. 203, 72 (2005).
  57. D. Kidd, C. Covington, and K. Varga, Exponential integrators in time-dependent density-functional calculations, Phys. Rev. E 96, 063307 (2017).
  58. Y. Li, T. Sato, and K. L. Ishikawa, Implementation of a time-dependent multiconfiguration self-consistent-field method for coupled electron-nuclear dynamics in diatomic molecules driven by intense laser pulses, Phys. Rev. A 104, 043104 (2021).
  59. Y. Saad, Iterative Methods for Sparse Linear Systems (SIAM, Philadelphia, Pennsylvania, 2003).
  60. E. Rodríguez-Cuenca, A. Picón, S. Oberli, A. I. Kuleff, and O. Vendrell, Core-hole coherent spectroscopy in molecules, Phys. Rev. Lett. 132, 263202 (2024).
  61. F. Calegari, D. Ayuso, A. Trabattoni, L. Belshaw, S. De Camillis, S. Anumula, F. Frassetto, L. Poletto, A. Palacios, P. Decleva et al., Ultrafast electron dynamics in phenylalanine initiated by attosecond pulses, Science 346, 336 (2014).
  62. P. M. Kraus, B. Mignolet, D. Baykusheva, A. Rupenyan, L. Horný, E. F. Penka, G. Grassi, O. I. Tolstikhin, J. Schneider, F. Jensen et al., Measurement and laser control of attosecond charge migration in ionized iodoacetylene, Science 350, 790 (2015).
  63. L. He, S. Sun, P. Lan, Y. He, B. Wang, P. Wang, X. Zhu, L. Li, W. Cao, P. Lu et al., Filming movies of attosecond charge migration in single molecules with high harmonic spectroscopy, Nat. Commun. 13, 4595 (2022).
  64. Q. Sun, T. C. Berkelbach, N. S. Blunt, G. H. Booth, S. Guo, Z. Li, J. Liu, J. D. McClain, E. R. Sayfutyarova, S. Sharma et al., Pyscf: The Python-based simulations of chemistry framework, WIREs Comput. Mol. Sci. 8, e1340 (2018).
  65. C. Brundle and D. W. Turner, High resolution molecular photoelectron spectroscopy. II. Water and deuterium oxide, Proc. R. Soc. London A 307, 27 (1968).
  66. A. Potts and W. C. Price, Photoelectron spectra and valence shell orbital structures of groups V and VI hydrides, Proc. R. Soc. London A 326, 181 (1972).
  67. K. A. Peterson, D. E. Woon, and T. H. Dunning, Jr., Benchmark calculations with correlated molecular wave functions. IV. The classical barrier height of the H+H2→H2+H reaction, J. Chem. Phys. 100, 7410 (1994).
  68. A. K. Wilson, T. Van Mourik, and T. H. Dunning, Jr., Gaussian basis sets for use in correlated molecular calculations. VI. Sextuple zeta correlation consistent basis sets for boron through neon, J. Mol. Struct. THEOCHEM 388, 339 (1996).
  69. G. Diercksen, W. Kraemer, T. Rescigno, C. Bender, B. McKoy, S. Langhoff, and P. Langhoff, Theoretical studies of photoexcitation and ionization in H2O, J. Chem. Phys. 76, 1043 (1982).
  70. I. Cacelli, V. Carravetta, and R. Moccia, Molecular differential photoionization cross-section calculations with L2 basis functions in the random-phase approximation. Results for H2O, J. Chem. Phys. 97, 320 (1992).
  71. M. Ruberti, R. Yun, K. Gokhberg, S. Kopelke, L. Cederbaum, F. Tarantelli, and V. Averbukh, Total molecular photoionization cross-sections by algebraic diagrammatic construction-Stieltjes-Lanczos method: Benchmark calculations, J. Chem. Phys. 139, 144107 (2013).
  72. B. N. C. Tenorio, M. A. C. Nascimento, S. Coriani, and A. B. Rocha, Coupled cluster study of photoionization and photodetachment cross sections, J. Chem. Theory Comput. 12, 4440 (2016).
  73. P. Modak and B. Antony, Probing photon interaction with H2O and D2O, J. Phys. B: At. Mol. Opt. Phys. 53, 045202 (2020).
  74. J. Benda, J. D. Gorfinkiel, Z. Mašín, G. S. J. Armstrong, A. C. Brown, D. D. A. Clarke, H. W. van der Hart, and J. Wragg, Perturbative and nonperturbative photoionization of H2 and H2O using the molecular R-matrix-with-time method, Phys. Rev. A 102, 052826 (2020).
  75. P. Fernández-Milán, V. Borràs, J. González-Vázquez, and F. Martín, Photoionization of the water molecule with XCHEM, J. Chem. Phys. 158, 134305 (2023).
  76. K. Tan, C. Brion, P. E. Van der Leeuw, and M. Van der Wiel, Absolute oscillator strengths (10–60 eV) for the photoabsorption, photoionisation and fragmentation of H2O, Chem. Phys. 29, 299 (1978).
  77. G. Haddad and J. A. Samson, Total absorption and photoionization cross sections of water vapor between 100 and 1000 å, J. Chem. Phys. 84, 6623 (1986).
  78. W. Chan, G. Cooper, and C. Brion, The electronic spectrum of water in the discrete and continuum regions. Absolute optical oscillator strengths for photoabsorption (6–200 eV), Chem. Phys. 178, 387 (1993).
  79. A. Palacios, J. L. Sanz-Vicario, and F. Martín, Theoretical methods for attosecond electron and nuclear dynamics: Applications to the H2 molecule, J. Phys. B: At. Mol. Opt. Phys. 48, 242001 (2015).
  80. J. Colgan, M. Pindzola, and F. Robicheaux, Time-dependent studies of single and multiple photoionization of H2+, Phys. Rev. A 68, 063413 (2003).
  81. C. Truesdale, S. Southworth, P. Kobrin, D. Lindle, G. Thornton, and D. Shirley, Photoelectron angular distributions of H2O, J. Chem. Phys. 76, 860 (1982).
  82. M. Banna, B. McQuaide, R. Malutzki, and V. Schmidt, The photoelectron spectrum of water in the 30 to 140 eV photon energy range, J. Chem. Phys. 84, 4739 (1986).
  83. M. Stener, G. Fronzoni, D. Toffoli, and P. Decleva, Time dependent density functional photoionization of CH4, NH3, H2O and HF, Chem. Phys. 282, 337 (2002).
  84. Z.-H. Zhang, Y. Li, H. Pathak, T. Sato, K. L. Ishikawa, and F. He, Time-dependent hole states in multiconfigurational time-dependent Hartree-Fock approaches: Applications in photoionization of water molecule [Data set], Zenodo (2025), https://doi.org/10.5281/zenodo.15301436.

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Phys. Rev. Research 8, 013016– Published 12 January, 2026
  • Received 10 May 2025
  • Accepted 30 June 2025
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