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Simulating real-time molecular electron dynamics efficiently using the time-dependent density matrix renormalization group

Published 9 Sep 2024 in physics.chem-ph, cond-mat.str-el, and physics.comp-ph | (2409.05959v3)

Abstract: Compared to ground state electronic structure optimizations, accurate simulations of molecular real-time electron dynamics are usually much more difficult to perform. To simulate electron dynamics, the time-dependent density matrix renormalization group (TDDMRG) has been shown to offer an attractive compromise between accuracy and cost. However, many simulation parameters significantly affect the quality and efficiency of a TDDMRG simulation. So far, it is unclear whether common wisdom from ground state DMRG carries over to the TDDMRG, and a guideline on how to choose these parameters is missing. Here, in order to establish such a guideline, we investigate the convergence behavior of the main TDDMRG simulation parameters, such as time integrator, the choice of orbitals, and the choice of matrix-product-state representation for complex-valued non-singlet states. In addition, we propose a method to select orbitals that are tailored to optimize the dynamics. Lastly, we showcase the TDDMRG by applying it to charge migration ionization dynamics in furfural, where we reveal a rapid conversion from an ionized state with a $\sigma$ character to one with a $\pi$ character within less than a femtosecond.

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References (170)
  1. L. Cederbaum and J. Zobeley, “Ultrafast charge migration by electron correlation,” Chem. Phys. Lett. 307, 205–210 (1999).
  2. A. I. Kuleff and L. S. Cederbaum, “Ultrafast correlation-driven electron dynamics,” J. Phys. B 47, 124002 (2014).
  3. F. Calegari, D. Ayuso, A. Trabattoni, L. Belshaw, S. D. Camillis, S. Anumula, F. Frassetto, L. Poletto, A. Palacios, P. Decleva, J. B. Greenwood, F. Martín, and M. Nisoli, “Ultrafast electron dynamics in phenylalanine initiated by attosecond pulses,” Science 346, 336–339 (2014).
  4. P. M. Kraus, B. Mignolet, D. Baykusheva, A. Rupenyan, L. Horný, E. F. Penka, G. Grassi, O. I. Tolstikhin, J. Schneider, F. Jensen, L. B. Madsen, A. D. Bandrauk, F. Remacle, and H. J. Wörner, “Measurement and laser control of attosecond charge migration in ionized iodoacetylene,” Science 350, 790–795 (2015).
  5. P. M. Kraus, M. Zürch, S. K. Cushing, D. M. Neumark, and S. R. Leone, “The ultrafast X-ray spectroscopic revolution in chemical dynamics,” Nat. Rev. Chem. 2, 82–94 (2018).
  6. A. Palacios and F. Martín, “The quantum chemistry of attosecond molecular science,” Wiley Interdiscip. Rev.: Comput. Mol. Sci. 10, e1430 (2020).
  7. X. Li, N. Govind, C. Isborn, A. E. DePrince III, and K. Lopata, “Real-time time-dependent electronic structure theory,” Chem. Rev. 120, 9951–9993 (2020).
  8. I. Ross, P. Matousek, M. Towrie, A. Langley, and J. Collier, “The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplifiers,” Opt. Commun. 144, 125–133 (1997).
  9. E. Saldin, E. Schneidmiller, and M. Yurkov, The Physics of Free Electron Lasers, Advanced Texts in Physics (Springer Berlin Heidelberg, 2010).
  10. J. Rothhardt, S. Demmler, S. Hädrich, J. Limpert, and A. Tünnermann, “Octave-spanning OPCPA system delivering CEP-stable few-cycle pulses and 22 W of average power at 1 MHz repetition rate,” Opt. Express 20, 10870–10878 (2012).
  11. D. J. Tannor and S. A. Rice, “Control of selectivity of chemical reaction via control of wave packet evolution,” J. Chem. Phys. 83, 5013–5018 (1985).
  12. D. J. Tannor, R. Kosloff, and S. A. Rice, “Coherent pulse sequence induced control of selectivity of reactions: Exact quantum mechanical calculations,” J. Chem. Phys. 85, 5805–5820 (1986).
  13. R. J. Levis, G. M. Menkir, and H. Rabitz, “Selective bond dissociation and rearrangement with optimally tailored, strong-field laser pulses,” Science 292, 709–713 (2001).
  14. A. P. Pati, I. S. Wahyutama, and A. N. Pfeiffer, “Subcycle-resolved probe retardation in strong-field pumped dielectrics,” Nat. Commun. 6, 7746 (2015).
  15. M. Lara-Astiaso, D. Ayuso, I. Tavernelli, P. Decleva, A. Palacios, and F. Martín, “Decoherence, control and attosecond probing of XUV-induced charge migration in biomolecules. A theoretical outlook,” Faraday Discuss. 194, 41–59 (2016).
  16. A. Trabattoni, M. Galli, M. Lara-Astiaso, A. Palacios, J. Greenwood, I. Tavernelli, P. Decleva, M. Nisoli, F. Martín, and F. Calegari, “Charge migration in photo-ionized aromatic amino acids,” Philos. Trans. R. Soc. 377, 20170472 (2019).
  17. K. Chordiya, V. Despré, B. Nagyillés, F. Zeller, Z. Diveki, A. I. Kuleff, and M. U. Kahaly, “Photo-ionization initiated differential ultrafast charge migration: impacts of molecular symmetries and tautomeric forms,” Phys. Chem. Chem. Phys. 25, 4472–4480 (2023).
  18. E. Runge and E. K. U. Gross, “Density-functional theory for time-dependent systems,” Phys. Rev. Lett. 52, 997–1000 (1984).
  19. K. Yabana and G. F. Bertsch, “Time-dependent local-density approximation in real time,” Phys. Rev. B 54, 4484–4487 (1996).
  20. K. Burke, J. Werschnik, and E. K. U. Gross, “Time-dependent density functional theory: Past, present, and future,” J. Chem. Phys. 123, 062206 (2005).
  21. K. Lopata and N. Govind, “Modeling fast electron dynamics with real-time time-dependent density functional theory: Application to small molecules and chromophores,” J. Chem. Theory Comput. 7, 1344–1355 (2011).
  22. N. Helbig, J. Fuks, I. Tokatly, H. Appel, E. Gross, and A. Rubio, “Time-dependent density-functional and reduced density-matrix methods for few electrons: Exact versus adiabatic approximations,” Chem. Phys. 391, 1–10 (2011).
  23. M. R. Provorse and C. M. Isborn, “Electron dynamics with real-time time-dependent density functional theory,” Int. J. Quantum Chem. 116, 739–749 (2016).
  24. A. I. Kuleff, J. Breidbach, and L. S. Cederbaum, “Multielectron wave-packet propagation: General theory and application,” J. Chem. Phys. 123, 044111 (2005).
  25. M. Ruberti, V. Averbukh, and P. Decleva, “B-spline algebraic diagrammatic construction: Application to photoionization cross-sections and high-order harmonic generation,” J. Chem. Phys. 141, 164126 (2014).
  26. N. V. Golubev and A. I. Kuleff, “Control of charge migration in molecules by ultrashort laser pulses,” Phys. Rev. A 91, 051401 (2015).
  27. N. Rohringer, A. Gordon, and R. Santra, “Configuration-interaction-based time-dependent orbital approach for ab initio treatment of electronic dynamics in a strong optical laser field,” Phys. Rev. A 74, 043420 (2006).
  28. L. Greenman, P. J. Ho, S. Pabst, E. Kamarchik, D. A. Mazziotti, and R. Santra, “Implementation of the time-dependent configuration-interaction singles method for atomic strong-field processes,” Phys. Rev. A 82, 023406 (2010).
  29. D. Hochstuhl and M. Bonitz, “Time-dependent restricted-active-space configuration-interaction method for the photoionization of many-electron atoms,” Phys. Rev. A 86, 053424 (2012).
  30. P. Krause, J. A. Sonk, and H. B. Schlegel, “Strong field ionization rates simulated with time-dependent configuration interaction and an absorbing potential,” J. Chem. Phys. 140, 174113 (2014).
  31. S. Bauch, L. K. Sørensen, and L. B. Madsen, “Time-dependent generalized-active-space configuration-interaction approach to photoionization dynamics of atoms and molecules,” Phys. Rev. A 90, 062508 (2014).
  32. S. Bauch, H. R. Larsson, C. Hinz, and M. Bonitz, “The time-dependent generalized active space configuration interaction approach to correlated ionization dynamics of diatomic molecules,” J. Phys.: Conf. Ser. 696, 012008 (2016).
  33. H. R. Larsson, S. Bauch, L. K. Sørensen, and M. Bonitz, “Correlation effects in strong-field ionization of heteronuclear diatomic molecules,” Phys. Rev. A 93, 013426 (2016).
  34. J. B. Schriber and F. A. Evangelista, “Time dependent adaptive configuration interaction applied to attosecond charge migration,” J. Chem. Phys. 151, 171102 (2019).
  35. H. B. Schlegel, P. Hoerner, and W. Li, “Ionization of HCCI Neutral and Cations by Strong Laser Fields Simulated With Time Dependent Configuration Interaction,” Front. Chem. 10, 866137 (2022).
  36. A. S. Durden and B. G. Levine, “Floquet time-dependent configuration interaction for modeling ultrafast electron dynamics,” J. Chem. Theory Comput. 18, 795–806 (2022).
  37. S. Carlström, M. Spanner, and S. Patchkovskii, “General time-dependent configuration-interaction singles. I. Molecular case,” Phys. Rev. A 106, 043104 (2022).
  38. 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).
  39. 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).
  40. 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).
  41. 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).
  42. I. S. Wahyutama, T. Sato, and K. L. Ishikawa, “Time-dependent multiconfiguration self-consistent-field study on resonantly enhanced high-order harmonic generation from transition-metal elements,” Phys. Rev. A 99, 063420 (2019).
  43. J. Zanghellini, M. Kitzler, C. Fabian, T. Brabec, and A. Scrinzi, “An MCTDHF Approach to Multielectron Dynamics in Laser Fields,” Laser Phys. 13, 1064 (2002).
  44. T. Kato and H. Kono, “Time-dependent multiconfiguration theory for electronic dynamics of molecules in an intense laser field,” Chem. Phys. Lett. 392, 533–540 (2004).
  45. 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).
  46. M. Nest, T. Klamroth, and P. Saalfrank, “The multiconfiguration time-dependent Hartree–Fock method for quantum chemical calculations,” J. Chem. Phys. 122, 124102 (2005).
  47. H.-D. Meyer, F. Gatti, and G. A. Worth, Multidimensional quantum dynamics: MCTDH theory and applications (John Wiley & Sons, 2009).
  48. D. Hochstuhl and M. Bonitz, “Two-photon ionization of helium studied with the multiconfigurational time-dependent Hartree–Fock method,” J. Chem. Phys. 134, 084106 (2011).
  49. 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, 177–336 (2014).
  50. D. J. Haxton and C. W. McCurdy, “Two methods for restricted configuration spaces within the multiconfiguration time-dependent Hartree-Fock method,” Phys. Rev. A 91, 012509 (2015).
  51. A. U. J. 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).
  52. T. Sato, H. Pathak, Y. Orimo, and K. L. Ishikawa, “Communication: Time-dependent optimized coupled-cluster method for multielectron dynamics,” J. Chem. Phys. 148, 051101 (2018).
  53. H. Pathak, T. Sato, and K. L. Ishikawa, “Time-dependent optimized coupled-cluster method for multielectron dynamics. II. A coupled electron-pair approximation,” J. Chem. Phys. 152, 124115 (2020).
  54. H. Pathak, T. Sato, and K. L. Ishikawa, “Time-dependent optimized coupled-cluster method for multielectron dynamics. IV. Approximate consideration of the triple excitation amplitudes,” J. Chem. Phys. 154, 234104 (2021).
  55. B. Sverdrup Ofstad, E. Aurbakken, O. Sigmundson Schøyen, H. E. Kristiansen, S. Kvaal, and T. B. Pedersen, “Time-dependent coupled-cluster theory,” Wiley Interdiscip. Rev.: Comput. Mol. Sci. 13, e1666 (2023).
  56. J. S. Kretchmer and G. K.-L. Chan, “A real-time extension of density matrix embedding theory for non-equilibrium electron dynamics,” J. Chem. Phys. 148, 054108 (2018).
  57. A. E. Feiguin and S. R. White, “Time-step targeting methods for real-time dynamics using the density matrix renormalization group,” Phys. Rev. B 72, 020404 (2005).
  58. J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, “Time-dependent variational principle for quantum lattices,” Phys. Rev. Lett. 107, 070601 (2011).
  59. C. Lubich, T. Rohwedder, R. Schneider, and B. Vandereycken, “Dynamical approximation by hierarchical tucker and tensor-train tensors,” SIAM J. Matrix Anal. Appl. 34, 470–494 (2013).
  60. C. Lubich, I. V. Oseledets, and B. Vandereycken, “Time integration of tensor trains,” SIAM J. Numer. Anal. 53, 917–941 (2015).
  61. J. Haegeman, C. Lubich, I. Oseledets, B. Vandereycken, and F. Verstraete, “Unifying time evolution and optimization with matrix product states,” Phys. Rev. B 94, 165116 (2016).
  62. E. Ronca, Z. Li, C. A. Jimenez-Hoyos, and G. K.-L. Chan, “Time-step targeting time-dependent and dynamical density matrix renormalization group algorithms with ab initio hamiltonians,” J. Chem. Theory Comput. 13, 5560–5571 (2017).
  63. S. Paeckel, T. Köhler, A. Swoboda, S. R. Manmana, U. Schollwöck, and C. Hubig, “Time-evolution methods for matrix-product states,” Ann. Phys. 411, 167998 (2019).
  64. L.-H. Frahm and D. Pfannkuche, “Ultrafast ab initio quantum chemistry using matrix product states,” J. Chem. Theory Comput. 15, 2154–2165 (2019).
  65. A. Baiardi, “Electron dynamics with the time-dependent density matrix renormalization group,” J. Chem. Theory Comput. 17, 3320–3334 (2021).
  66. H. R. Larsson, “A tensor network view of multilayer multiconfiguration time-dependent Hartree methods,” Mol. Phys. 122, e2306881 (2024).
  67. X. Chu and S.-I. Chu, “Time-dependent density-functional theory for molecular processes in strong fields: Study of multiphoton processes and dynamical response of individual valence electrons of N2subscriptN2{\mathrm{N}}_{2}roman_N start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT in intense laser fields,” Phys. Rev. A 64, 063404 (2001).
  68. E. Plésiat, P. Decleva, and F. Martín, “Vibrational branching ratios in the photoelectron spectra of N2 and CO: interference and diffraction effects,” Phys. Chem. Chem. Phys. 14, 10853–10871 (2012).
  69. P. López-Tarifa, M.-A. H. du Penhoat, R. Vuilleumier, M.-P. Gaigeot, U. Rothlisberger, I. Tavernelli, A. L. Padellec, J.-P. Champeaux, M. Alcamí, P. Moretto-Capelle, F. Martín, and M.-F. Politis, “Time-dependent density functional theory molecular dynamics simulation of doubly charged uracil in gas phase,” Cent. Eur. J. Phys. 12, 97–102 (2014).
  70. A. Bruner, S. Hernandez, F. Mauger, P. M. Abanador, D. J. LaMaster, M. B. Gaarde, K. J. Schafer, and K. Lopata, “Attosecond Charge Migration with TDDFT: Accurate Dynamics from a Well-Defined Initial State,” J. Phys. Chem. Lett. 8, 3991–3996 (2017).
  71. A. S. Folorunso, A. Bruner, F. Mauger, K. A. Hamer, S. Hernandez, R. R. Jones, L. F. DiMauro, M. B. Gaarde, K. J. Schafer, and K. Lopata, “Molecular modes of attosecond charge migration,” Phys. Rev. Lett. 126, 133002 (2021).
  72. F. Mauger, A. S. Folorunso, K. A. Hamer, C. Chandre, M. B. Gaarde, K. Lopata, and K. J. Schafer, “Charge migration and attosecond solitons in conjugated organic molecules,” Phys. Rev. Res. 4, 013073 (2022).
  73. K. A. Hamer, F. Mauger, A. S. Folorunso, K. Lopata, R. R. Jones, L. F. DiMauro, K. J. Schafer, and M. B. Gaarde, “Characterizing particle-like charge-migration dynamics with high-order harmonic sideband spectroscopy,” Phys. Rev. A 106, 013103 (2022).
  74. A. S. Folorunso, F. Mauger, K. A. Hamer, D. D. Jayasinghe, I. S. Wahyutama, J. R. Ragains, R. R. Jones, L. F. DiMauro, M. B. Gaarde, K. J. Schafer, and K. Lopata, “Attochemistry regulation of charge migration,” J. Phys. Chem. A 127, 1894–1900 (2023).
  75. Y.-S. Wang, J. X. Zhong Manis, M. C. Rohan, T. M. Orlando, and J. S. Kretchmer, “Modeling intermolecular coulombic decay with non-hermitian real-time time-dependent density functional theory,” J. Phys. Chem. Lett. 15, 7806–7813 (2024).
  76. S. Grimme and M. Parac, “Substantial errors from time-dependent density functional theory for the calculation of excited states of large π𝜋\piitalic_π systems,” Chem. Phys. Chem. 4, 292–295 (2003).
  77. J. Schirmer and A. Dreuw, “Critique of the foundations of time-dependent density-functional theory,” Phys. Rev. A 75, 022513 (2007).
  78. A. I. Kuleff and A. Dreuw, “Theoretical description of charge migration with a single Slater-determinant and beyond,” J. Chem. Phys. 130, 034102 (2009).
  79. B. F. Habenicht, N. P. Tani, M. R. Provorse, and C. M. Isborn, “Two-electron Rabi oscillations in real-time time-dependent density-functional theory,” J. Chem. Phys. 141, 184112 (2014).
  80. K. Ranka and C. M. Isborn, “Size-dependent errors in real-time electron density propagation,” J. Chem. Phys. 158, 174102 (2023).
  81. V. V. Kim, G. S. Boltaev, M. Iqbal, N. A. Abbasi, H. Al-Harmi, I. S. Wahyutama, T. Sato, K. L. Ishikawa, R. A. Ganeev, and A. S. Alnaser, “Resonance enhancement of harmonics in the vicinity of 32 nm spectral range during propagation of femtosecond pulses through the molybdenum plasma,” J. Phys. B 53, 195401 (2020).
  82. W.-T. Peng, B. S. Fales, and B. G. Levine, “Simulating electron dynamics of complex molecules with time-dependent complete active space configuration interaction,” J. Chem. Theory Comput. 14, 4129–4138 (2018).
  83. S. R. White, “Density matrix formulation for quantum renormalization groups,” Phys. Rev. Lett. 69, 2863–2866 (1992).
  84. S. R. White, “Density-matrix algorithms for quantum renormalization groups,” Phys. Rev. B 48, 10345–10356 (1993).
  85. G. K.-L. Chan, “An algorithm for large scale density matrix renormalization group calculations,” J. Chem. Phys. 120, 3172–3178 (2004).
  86. G. K.-L. Chan, J. J. Dorando, D. Ghosh, J. Hachmann, E. Neuscamman, H. Wang, and T. Yanai, “An introduction to the density matrix renormalization group ansatz in quantum chemistry,” in Frontiers in Quantum Systems in Chemistry and Physics, edited by S. Wilson, P. J. Grout, J. Maruani, G. Delgado-Barrio, and P. Piecuch (Springer Netherlands, Dordrecht, 2008) pp. 49–65.
  87. S. Wouters and D. Van Neck, “The density matrix renormalization group for ab initio quantum chemistry,” Eur. Phys. J. D 68, 1–20 (2014).
  88. R. Olivares-Amaya, W. Hu, N. Nakatani, S. Sharma, J. Yang, and G. K.-L. Chan, “The ab-initio density matrix renormalization group in practice,” J. Chem. Phys. 142, 034102 (2015).
  89. N. Nakatani and S. Guo, “Density matrix renormalization group (DMRG) method as a common tool for large active-space CASSCF/CASPT2 calculations,” J. Chem. Phys. 146, 094102 (2017).
  90. A. Baiardi and M. Reiher, “The density matrix renormalization group in chemistry and molecular physics: Recent developments and new challenges,” J. Chem. Phys. 152, 040903 (2020).
  91. H. R. Larsson, H. Zhai, K. Gunst, and G. K.-L. Chan, “Matrix product states with large sites,” J. Chem. Theory Comput. 18, 749–762 (2022a).
  92. Note that different algorithms exist that exploit DMRG-like approaches for time evolution. Here, we use “TDDMRG” to generically refer to all of them.
  93. N. Nakatani, S. Wouters, D. Van Neck, and G. K.-L. Chan, “Linear response theory for the density matrix renormalization group: Efficient algorithms for strongly correlated excited states,” J. Chem. Phys. 140, 024108 (2014).
  94. J. Hachmann, J. J. Dorando, M. Avilés, and G. K.-L. Chan, “The radical character of the acenes: A density matrix renormalization group study,” J. Chem. Phys. 127, 134309 (2007).
  95. H. R. Larsson, H. Zhai, C. J. Umrigar, and G. K.-L. Chan, “The chromium dimer: Closing a chapter of quantum chemistry,” J. Am. Chem. Soc. 144, 15932–15937 (2022b).
  96. R. Weinkauf, P. Schanen, A. Metsala, E. W. Schlag, M. Bürgle, and H. Kessler, “Highly efficient charge transfer in peptide cations in the gas phase: Threshold effects and mechanism,” J. Phys. Chem. 100, 18567–18585 (1996).
  97. R. Weinkauf, E. W. Schlag, T. J. Martinez, and R. D. Levine, “Nonstationary electronic states and site-selective reactivity,” J. Phys. Chem. A 101, 7702–7710 (1997).
  98. F. Remacle, R. Levine, and M. Ratner, “Charge directed reactivity: a simple electronic model, exhibiting site selectivity, for the dissociation of ions,” Chem. Phys. Lett. 285, 25–33 (1998).
  99. F. Remacle, R. D. Levine, E. W. Schlag, and R. Weinkauf, “Electronic control of site selective reactivity: A model combining charge migration and dissociation,” J. Phys. Chem. A 103, 10149–10158 (1999).
  100. W. Cui, M. S. Thompson, and J. P. Reilly, “Pathways of peptide ion fragmentation induced by vacuum ultraviolet light,” J. Am. Soc. Mass Spectrom. 16, 1384–1398 (2005).
  101. F. Remacle and R. D. Levine, “Probing ultrafast purely electronic charge migration in small peptides,” Z. Phys. Chem. 221, 647–661 (2007).
  102. J. P. Reilly, “Ultraviolet photofragmentation of biomolecular ions,” Mass Spectrom. Rev. 28, 425–447 (2009).
  103. F. Remacle and R. D. Levine, “Charge migration and control of site selective reactivity: The role of covalent and ionic states,” J. Chem. Phys. 110, 5089–5099 (1999).
  104. M. F. Kling, P. von den Hoff, I. Znakovskaya, and R. de Vivie-Riedle, “(Sub-)femtosecond control of molecular reactions via tailoring the electric field of light,” Phys. Chem. Chem. Phys. 15, 9448–9467 (2013).
  105. V. D. Nikolay V. Golubev and A. I. Kuleff, “Quantum control with smoothly varying pulses: general theory and application to charge migration,” J. Mod. Opt. 64, 1031–1041 (2017).
  106. J. Breidbach and L. S. Cederbaum, “Universal attosecond response to the removal of an electron,” Phys. Rev. Lett. 94, 033901 (2005).
  107. J. Breidbach and L. S. Cederbaum, “Migration of holes: Formalism, mechanisms, and illustrative applications,” J. Chem. Phys. 118, 3983–3996 (2003).
  108. J. Breidbach and L. S. Cederbaum, “Migration of holes: Numerical algorithms and implementation,” J. Chem. Phys. 126, 034101 (2007).
  109. V. Kochetov and S. I. Bokarev, “RhoDyn: A ρ𝜌\rhoitalic_ρ-TD-RASCI Framework to Study Ultrafast Electron Dynamics in Molecules,” J. Chem. Theory Comput. 18, 46–58 (2022).
  110. S. Giri, G. Dixit, and J. C. Tremblay, “Attosecond charge migration in heterocyclic five-membered rings,” Eur. Phys. J.: Spec. Top. 232, 1935–1943 (2023).
  111. H. B. Schlegel, “Charge Migration in HCCI Cations Probed by Strong Field Ionization: Time-Dependent Configuration Interaction and Vibrational Wavepacket Simulations,” J. Phys. Chem. A 127, 6040–6050 (2023).
  112. H. Lischka, D. Nachtigallová, A. J. A. Aquino, P. G. Szalay, F. Plasser, F. B. C. Machado, and M. Barbatti, “Multireference approaches for excited states of molecules,” Chem. Rev. 118, 7293–7361 (2018).
  113. C. Lubich, From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis, Zurich lectures in advanced mathematics (European Mathematical Society, 2008).
  114. M. Beck, A. Jäckle, G. Worth, and H.-D. Meyer, “The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets,” Phys. Rep. 324, 1–105 (2000).
  115. U. Manthe, “The multi-configurational time-dependent Hartree approach revisited,” J. Chem. Phys. 142, 244109 (2015).
  116. H.-D. Meyer and H. Wang, “On regularizing the MCTDH equations of motion,” J. Chem. Phys. 148, 124105 (2018).
  117. D. Ghosh, J. Hachmann, T. Yanai, and G. K.-L. Chan, “Orbital optimization in the density matrix renormalization group, with applications to polyenes and β𝛽\betaitalic_β-carotene,” J. Chem. Phys. 128, 144117 (2008).
  118. D. Zgid and M. Nooijen, “The density matrix renormalization group self-consistent field method: Orbital optimization with the density matrix renormalization group method in the active space,” J. Chem. Phys. 128, 144116 (2008).
  119. C. Lubich, “Time Integration in the Multiconfiguration Time-Dependent Hartree Method of Molecular Quantum Dynamics,” Appl. Math. Res. Express 2015, 311–328 (2015).
  120. B. Kloss, I. Burghardt, and C. Lubich, “Implementation of a novel projector-splitting integrator for the multi-configurational time-dependent Hartree approach,” J. Chem. Phys. 146, 174107 (2017).
  121. L. P. Lindoy, B. Kloss, and D. R. Reichman, “Time evolution of ML-MCTDH wavefunctions. II. Application of the projector splitting integrator,” J. Chem. Phys. 155, 174109 (2021).
  122. C. Leforestier, R. Bisseling, C. Cerjan, M. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, and R. Kosloff, “A comparison of different propagation schemes for the time dependent schrödinger equation,” J. Comput. Phys. 94, 59–80 (1991).
  123. J. J. García-Ripoll, “Time evolution of matrix product states,” New J. Phys. 8, 305 (2006).
  124. R. Peng, A. F. White, H. Zhai, and G. Kin-Lic Chan, “Conservation laws in coupled cluster dynamics at finite temperature,” J. Chem. Phys. 155, 044103 (2021).
  125. H. Zhai, H. R. Larsson, S. Lee, Z.-H. Cui, T. Zhu, C. Sun, L. Peng, R. Peng, K. Liao, J. Tölle, J. Yang, S. Li, and G. K.-L. Chan, “Block2: A comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond,” J. Chem. Phys. 159, 234801 (2023).
  126. J. Provazza, K. Gunst, H. Zhai, G. K.-L. Chan, T. Shiozaki, N. C. Rubin, and A. F. White, “Fast emulation of fermionic circuits with matrix product states,” J. Chem. Theory Comput. 20, 3719–3728 (2024).
  127. M. L. Wall and L. D. Carr, “Out-of-equilibrium dynamics with matrix product states,” New J. Phys. 14, 125015 (2012).
  128. T. J. Park and J. C. Light, “Unitary quantum time evolution by iterative Lanczos reduction,” J. Chem. Phys. 85, 5870–5876 (1986).
  129. D. J. Tannor, Introduction to Quantum Mechanics: A Time-Dependent Perspective (University Science Books, 2007).
  130. P. Silvi, F. Tschirsich, M. Gerster, J. Jünemann, D. Jaschke, M. Rizzi, and S. Montangero, “The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems,” SciPost Phys. Lect. Notes , 8 (2019).
  131. S. Sharma and G. K.-L. Chan, “Spin-adapted density matrix renormalization group algorithms for quantum chemistry,” J. Chem. Phys. 136, 124121 (2012).
  132. Z. Li and G. K.-L. Chan, “Spin-projected matrix product states: Versatile tool for strongly correlated systems,” J. Chem. Theory Comput. 13, 2681–2695 (2017).
  133. H. R. Larsson, C. A. Jiménez-Hoyos, and G. K.-L. Chan, “Minimal matrix product states and generalizations of mean-field and geminal wave functions,” J. Chem. Theory Comput. 16, 5057–5066 (2020).
  134. W. Tatsuaki, “Interaction-round-a-face density-matrix renormalization-group method applied to rotational-invariant quantum spin chains,” Phys. Rev. E 61, 3199–3206 (2000).
  135. H. R. Larsson, “Computing vibrational eigenstates with tree tensor network states (TTNS),” J. Chem. Phys. 151, 204102 (2019).
  136. G. K.-L. Chan and M. Head-Gordon, “Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group,” J. Chem. Phys. 116, 4462–4476 (2002).
  137. M.-S. Dupuy and G. Friesecke, “Inversion symmetry of singular values and a new orbital ordering method in tensor train approximations for quantum chemistry,” SIAM J. Sci. Comput. 43, B108–B131 (2021).
  138. G. Barcza, O. Legeza, K. H. Marti, and M. Reiher, “Quantum-information analysis of electronic states of different molecular structures,” Phys. Rev. A 83, 012508 (2011).
  139. G. Moritz, B. A. Hess, and M. Reiher, “Convergence behavior of the density-matrix renormalization group algorithm for optimized orbital orderings,” J. Chem. Phys. 122, 024107 (2004).
  140. C. Krumnow, L. Veis, O. Legeza, and J. Eisert, “Fermionic orbital optimization in tensor network states,” Phys. Rev. Lett. 117, 210402 (2016).
  141. Y. Ma and H. Ma, “Assessment of various natural orbitals as the basis of large active space density-matrix renormalization group calculations,” J. Chem. Phys. 138, 224105 (2013).
  142. A. O. Mitrushchenkov, G. Fano, R. Linguerri, and P. Palmieri, “On the importance of orbital localization in QC-DMRG calculations,” Int. J. Quantum Chem. 112, 1606–1619 (2012).
  143. “block2,”  (2024), https://github.com/block-hczhai/block2-preview.
  144. 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, S. Wouters, and G. K.-L. Chan, “PySCF: the Python-based simulations of chemistry framework,” Wiley Interdiscip. Rev.: Comput. Mol. Sci. 8, e1340 (2018).
  145. Q. Sun, X. Zhang, S. Banerjee, P. Bao, M. Barbry, N. S. Blunt, N. A. Bogdanov, G. H. Booth, J. Chen, Z.-H. Cui, J. J. Eriksen, Y. Gao, S. Guo, J. Hermann, M. R. Hermes, K. Koh, P. Koval, S. Lehtola, Z. Li, J. Liu, N. Mardirossian, J. D. McClain, M. Motta, B. Mussard, H. Q. Pham, A. Pulkin, W. Purwanto, P. J. Robinson, E. Ronca, E. R. Sayfutyarova, M. Scheurer, H. F. Schurkus, J. E. T. Smith, C. Sun, S.-N. Sun, S. Upadhyay, L. K. Wagner, X. Wang, A. White, J. D. Whitfield, M. J. Williamson, S. Wouters, J. Yang, J. M. Yu, T. Zhu, T. C. Berkelbach, S. Sharma, A. Y. Sokolov, and G. K.-L. Chan, “Recent developments in the PySCF program package,” J. Chem. Phys. 153, 024109 (2020).
  146. “Pyscf,”  (2024), https://github.com/pyscf/pyscf.
  147. Q. Sun, “Libcint: An efficient general integral library for gaussian basis functions,” J. Comput. Chem. 36, 1664–1671 (2015).
  148. “libcint,”  (2024), https://github.com/sunqm/libcint.
  149. R. Ditchfield, W. J. Hehre, and J. A. Pople, “Self-Consistent Molecular-Orbital Methods. IX. An Extended Gaussian-Type Basis for Molecular-Orbital Studies of Organic Molecules,” J. Chem. Phys. 54, 724–728 (1971).
  150. W. J. Hehre, R. Ditchfield, and J. A. Pople, “Self-Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian-Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules,” J. Chem. Phys. 56, 2257–2261 (1972).
  151. F. Weigend and R. Ahlrichs, “Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy,” Phys. Chem. Chem. Phys. 7, 3297–3305 (2005).
  152. O. I. Tolstikhin, L. B. Madsen, and T. Morishita, “Weak-field asymptotic theory of tunneling ionization in many-electron atomic and molecular systems,” Phys. Rev. A 89, 013421 (2014).
  153. I. S. Wahyutama, D. D. Jayasinghe, F. Mauger, K. Lopata, M. B. Gaarde, and K. J. Schafer, “All-electron, density-functional-based method for angle-resolved tunneling ionization in the adiabatic regime,” Phys. Rev. A 106, 052211 (2022).
  154. G. Knizia, “Intrinsic atomic orbitals: An unbiased bridge between quantum theory and chemical concepts,” J. Chem. Theory Comput. 9, 4834–4843 (2013).
  155. R. B. Sidje, “Expokit: a software package for computing matrix exponentials,” ACM Trans. Math. Softw. 24, 130–156 (1998).
  156. A. Szabo and N. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, Dover Books on Chemistry (Dover Publications, 1996).
  157. P. Löwdin, “On the Non-Orthogonality Problem Connected with the Use of Atomic Wave Functions in the Theory of Molecules and Crystals,” J. Chem. Phys. 18, 365–375 (1950).
  158. N. J. Higham, “Stability of a method for multiplying complex matrices with three real matrix multiplications,” SIAM J. Matrix Anal. Appl. 13, 681–687 (1992).
  159. J. Pipek and P. G. Mezey, “A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions,” J. Chem. Phys. 90, 4916–4926 (1989).
  160. P. Pulay and T. P. Hamilton, “UHF natural orbitals for defining and starting MC-SCF calculations,” J. Chem. Phys. 88, 4926–4933 (1988).
  161. D. M. Potts, C. M. Taylor, R. K. Chaudhuri, and K. F. Freed, “The improved virtual orbital-complete active space configuration interaction method, a “packageable” efficient ab initio many-body method for describing electronically excited states,” J. Chem. Phys. 114, 2592–2600 (2001).
  162. O. Legeza and J. Sólyom, “Optimizing the density-matrix renormalization group method using quantum information entropy,” Phys. Rev. B 68, 195116 (2003).
  163. P. Slavíček and T. J. Martínez, “Ab initio floating occupation molecular orbital-complete active space configuration interaction: An efficient approximation to CASSCF,” J. Chem. Phys. 132, 234102 (2010).
  164. E. R. Sayfutyarova, Q. Sun, G. K.-L. Chan, and G. Knizia, “Automated construction of molecular active spaces from atomic valence orbitals,” J. Chem. Theory Comput. 13, 4063–4078 (2017).
  165. E. R. Sayfutyarova and S. Hammes-Schiffer, “Constructing molecular π𝜋\piitalic_π-orbital active spaces for multireference calculations of conjugated systems,” J. Chem. Theory Comput. 15, 1679–1689 (2019).
  166. A. Khedkar and M. Roemelt, “Active space selection based on natural orbital occupation numbers from n𝑛nitalic_n-electron valence perturbation theory,” J. Chem. Theory Comput. 15, 3522–3536 (2019).
  167. Z. Tóth and P. Pulay, “Comparison of methods for active orbital selection in multiconfigurational calculations,” J. Chem. Theory Comput. 16, 7328–7341 (2020).
  168. L. Ding, S. Knecht, and C. Schilling, “Quantum Information-Assisted Complete Active Space Optimization (QICAS),” J. Phys. Chem. Lett. 14, 11022–11029 (2023).
  169. B. G. Levine, A. S. Durden, M. P. Esch, F. Liang, and Y. Shu, “CAS without SCF—Why to use CASCI and where to get the orbitals,” J. Chem. Phys. 154, 090902 (2021).
  170. C. J. Stein and M. Reiher, “Automated selection of active orbital spaces,” J. Chem. Theory Comput. 12, 1760–1771 (2016).

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