ISSN 0253-2778

CN 34-1054/N

open
Free to Publish. Free to Read.
Open AccessOpen Access JUSTC Original Paper

A Hamiltonian matrix based algorithm for simulating evolution of electronic wave functions

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2020.06.013
  • Received Date: 10 March 2020
  • Accepted Date: 20 June 2020
  • Rev Recd Date: 20 June 2020
  • Publish Date: 30 June 2020
    Abstract

  • Abstract

    Accurate simulation and analysis of electronic motion and evolution are the key to developing efficient electron modulation methods for practical applications.Some traditional methods, such as TDHF(time-dependent Hartree-Fock) and TDDFT (time-dependent density functional theory), work well when dealing with small scale systems. However, they are not suitable enough for large scale systems, in terms of computational complexity and costs.Considering that in some large systems the relative position of atoms are quite stable, and perturbations have limited effect on inner interaction Hamiltonian, a simple yet effective method is proposed capable of quickly simulating the evolution of electronic wave function based on Hamiltonian matrix. The method is applied in four different systems and the results demonstrate the applicability of this algorithm to treat the charge evolution behavior in large systems, providing a new perspective for the development of electron modulation.

    Abstract

    Accurate simulation and analysis of electronic motion and evolution are the key to developing efficient electron modulation methods for practical applications.Some traditional methods, such as TDHF(time-dependent Hartree-Fock) and TDDFT (time-dependent density functional theory), work well when dealing with small scale systems. However, they are not suitable enough for large scale systems, in terms of computational complexity and costs.Considering that in some large systems the relative position of atoms are quite stable, and perturbations have limited effect on inner interaction Hamiltonian, a simple yet effective method is proposed capable of quickly simulating the evolution of electronic wave function based on Hamiltonian matrix. The method is applied in four different systems and the results demonstrate the applicability of this algorithm to treat the charge evolution behavior in large systems, providing a new perspective for the development of electron modulation.
    • FullText(HTML)
  • loading
    • References(22)
  • [1]
    NGUYEN V, NGUYEN T, BACH L, et al. Effective photocatalytic activity of mixed Ni/Fe-base metal-organic framework under a compact fluorescent daylight lamp[J]. Catalysts, 2018, 8(11): 487.
    [2]
    FISCHER M C, WILSON J W, ROBLES F E, et al. Invited review article: pump-probe microscopy[J]. Review of Scientific Instruments, 2016, 87(3): 031101.
    [3]
    PICN A, LEHMANN C S, BOSTEDT C, et al. Hetero-site-specific X-ray pump-probe spectroscopy for femtosecond intramolecular dynamics[J]. Nature Communications, 2016, 7: 11652.
    [4]
    HERINK G, JALALI B, ROPERS C, et al. Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate[J]. Nature Photonics, 2016, 10(5): 321-326.
    [5]
    MUKAMEL S, BAKKER H J. Preface: Special topic on multidimensional spectroscopy[J]. The Journal of Chemical Physics, 2015,142: 212101.
    [6]
    SAURABH P, MUKAMEL S. Two-dimensional infrared spectroscopy of vibrational polaritons of molecules in an optical cavity[J]. The Journal of Chemical Physics, 2016, 144(12): 124115.
    [7]
    TSUCHIMOCHI T, VAN VOORHIS T. Time-dependent projected Hartree-Fock[J]. The Journal of Chemical Physics, 2015, 142(12): 124103.
    [8]
    MAITRA N T. Perspective: Fundamental aspects of time-dependent density functional theory[J]. The Journal of Chemical Physics, 2016, 144(22): 220901.
    [9]
    MORRISON A F, HERBERT J M. Low-scaling quantum chemistry approach to excited-state properties via an ab initio exciton model: Application to excitation energy transfer in a self-assembled nanotube[J]. The Journal of Physical Chemistry Letters, 2015, 6:4390-4396.
    [10]
    HOHENBERG P, KOHN W. Inhomogeneous electron gas[J]. Physical Review, 1964, 136: B864.
    [11]
    KOHN W, SHAM L J. Self-consistent equations including exchange and correlation effects[J]. Physical Review, 1965, 140: A1133.
    [12]
    RUNGE E, GROSS E K U. Density-functional theory for time-dependent systems[J]. Physical Review Letters, 1984, 52(12): 997-1000.
    [13]
    LAGER G A, JORGENSEN J D, ROTELLA F J. Crystal structure and thermal expansion of α-quartz SiO2 at low temperatures[J]. Journal of Applied Physics, 1982, 53(10): 6751-6756.
    [14]
    SHI A, LI H, YIN S, et al. Effect of conjugation degree and delocalized π-system on the photocatalytic activity of single layer g-C3N4[J]. Applied Catalysis B: Environmental, 2017, 218: 137-146.
    [15]
    DAVID W I F, IBBERSON R M, MATTHEWMAN J C, et al. Crystal structure and bonding of ordered C60[J]. Nature, 1991, 353(6340): 147.
    [16]
    GEIM A K. Graphene: status and prospects[J]. Science, 2009, 324(5934): 1530-1534.
    [17]
    PIPEK J, MEZEY P G. A fast intrinsic localization procedure applicable for abinitio and semiempirical linear combination of atomic orbital wave functions[J]. The Journal of Chemical Physics, 1989, 90(9): 4916-4926.
    [18]
    HUZINAGA S, SAKAI Y, MIYOSHI E, et al. Extended Mulliken electron population analysis[J]. The Journal of Chemical Physics, 1990, 93(5): 3319-3325.
    [19]
    YU M, TRINKLE D R. Accurate and efficient algorithm for Bader charge integration[J]. The Journal of Chemical Physics, 2011, 134(6): 064111.
    [20]
    YANG L, LI X, ZHANG G, et al. Combining photocatalytic hydrogen generation and capsule storage in graphene based sandwich structures[J]. Nature Communications, 2017, 8: 16049.
    [21]
    MANNA A K, BALAMURUGAN D, CHEUNG M S, et al. Unraveling the mechanism of photoinduced charge transfer in carotenoid-porphyrin-C60 molecular triad[J]. The Journal of Physical Chemistry Letters, 2015, 6(7): 1231-1237.
    [22]
    GARG V, KODIS G, CHACHISVILIS M, et al. Conformationally constrained macrocyclic diporphyrin-fullerene artificial photosynthetic reaction center[J]. Journal of the American Chemical Society, 2011, 133(9): 2944-2954.)
    • Supplements(0)
    • Related Articles
    • Track Citations
  • 加载中

Catalog

    |
    Get Citation
    PDF
    XML
    [1]
    NGUYEN V, NGUYEN T, BACH L, et al. Effective photocatalytic activity of mixed Ni/Fe-base metal-organic framework under a compact fluorescent daylight lamp[J]. Catalysts, 2018, 8(11): 487.
    [2]
    FISCHER M C, WILSON J W, ROBLES F E, et al. Invited review article: pump-probe microscopy[J]. Review of Scientific Instruments, 2016, 87(3): 031101.
    [3]
    PICN A, LEHMANN C S, BOSTEDT C, et al. Hetero-site-specific X-ray pump-probe spectroscopy for femtosecond intramolecular dynamics[J]. Nature Communications, 2016, 7: 11652.
    [4]
    HERINK G, JALALI B, ROPERS C, et al. Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate[J]. Nature Photonics, 2016, 10(5): 321-326.
    [5]
    MUKAMEL S, BAKKER H J. Preface: Special topic on multidimensional spectroscopy[J]. The Journal of Chemical Physics, 2015,142: 212101.
    [6]
    SAURABH P, MUKAMEL S. Two-dimensional infrared spectroscopy of vibrational polaritons of molecules in an optical cavity[J]. The Journal of Chemical Physics, 2016, 144(12): 124115.
    [7]
    TSUCHIMOCHI T, VAN VOORHIS T. Time-dependent projected Hartree-Fock[J]. The Journal of Chemical Physics, 2015, 142(12): 124103.
    [8]
    MAITRA N T. Perspective: Fundamental aspects of time-dependent density functional theory[J]. The Journal of Chemical Physics, 2016, 144(22): 220901.
    [9]
    MORRISON A F, HERBERT J M. Low-scaling quantum chemistry approach to excited-state properties via an ab initio exciton model: Application to excitation energy transfer in a self-assembled nanotube[J]. The Journal of Physical Chemistry Letters, 2015, 6:4390-4396.
    [10]
    HOHENBERG P, KOHN W. Inhomogeneous electron gas[J]. Physical Review, 1964, 136: B864.
    [11]
    KOHN W, SHAM L J. Self-consistent equations including exchange and correlation effects[J]. Physical Review, 1965, 140: A1133.
    [12]
    RUNGE E, GROSS E K U. Density-functional theory for time-dependent systems[J]. Physical Review Letters, 1984, 52(12): 997-1000.
    [13]
    LAGER G A, JORGENSEN J D, ROTELLA F J. Crystal structure and thermal expansion of α-quartz SiO2 at low temperatures[J]. Journal of Applied Physics, 1982, 53(10): 6751-6756.
    [14]
    SHI A, LI H, YIN S, et al. Effect of conjugation degree and delocalized π-system on the photocatalytic activity of single layer g-C3N4[J]. Applied Catalysis B: Environmental, 2017, 218: 137-146.
    [15]
    DAVID W I F, IBBERSON R M, MATTHEWMAN J C, et al. Crystal structure and bonding of ordered C60[J]. Nature, 1991, 353(6340): 147.
    [16]
    GEIM A K. Graphene: status and prospects[J]. Science, 2009, 324(5934): 1530-1534.
    [17]
    PIPEK J, MEZEY P G. A fast intrinsic localization procedure applicable for abinitio and semiempirical linear combination of atomic orbital wave functions[J]. The Journal of Chemical Physics, 1989, 90(9): 4916-4926.
    [18]
    HUZINAGA S, SAKAI Y, MIYOSHI E, et al. Extended Mulliken electron population analysis[J]. The Journal of Chemical Physics, 1990, 93(5): 3319-3325.
    [19]
    YU M, TRINKLE D R. Accurate and efficient algorithm for Bader charge integration[J]. The Journal of Chemical Physics, 2011, 134(6): 064111.
    [20]
    YANG L, LI X, ZHANG G, et al. Combining photocatalytic hydrogen generation and capsule storage in graphene based sandwich structures[J]. Nature Communications, 2017, 8: 16049.
    [21]
    MANNA A K, BALAMURUGAN D, CHEUNG M S, et al. Unraveling the mechanism of photoinduced charge transfer in carotenoid-porphyrin-C60 molecular triad[J]. The Journal of Physical Chemistry Letters, 2015, 6(7): 1231-1237.
    [22]
    GARG V, KODIS G, CHACHISVILIS M, et al. Conformationally constrained macrocyclic diporphyrin-fullerene artificial photosynthetic reaction center[J]. Journal of the American Chemical Society, 2011, 133(9): 2944-2954.)
    Recommended articles
    TrendMD
    Volume 50 Issue 6 page: 811-818
    Cover

    Article Metrics

    Article views (20) PDF downloads(126)
    Proportional views

    Copyright © Editorial Office of JUSTC, All Rights Reserved. 皖ICP备05002528号

    Supported by: Beijing Renhe Information Technology Co. Ltd    

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return