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Relativistic Kramers-Unrestricted Exact-Two-Component Density Matrix Renormalization Group

  • Chad E. Hoyer
    Chad E. Hoyer
    Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
  • Hang Hu
    Hang Hu
    Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
    More by Hang Hu
  • Lixin Lu
    Lixin Lu
    Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
    More by Lixin Lu
  • Stefan Knecht*
    Stefan Knecht
    Algorithmiq Ltd., Kanavakatu 3C, FI-00160 Helsinki, Finland
    Abteilung SHE Chemie, GSI Helmholtzzentrum für Schwerionenforschung, DE-64291 Darmstadt, Germany
    Department Chemie, Johannes-Gutenberg Universität Mainz, DE-55128 Mainz, Germany
    *Email: [email protected]
  • , and 
  • Xiaosong Li*
    Xiaosong Li
    Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
    *Email: [email protected]
    More by Xiaosong Li
Cite this: J. Phys. Chem. A 2022, 126, 30, 5011–5020
Publication Date (Web):July 26, 2022
https://doi.org/10.1021/acs.jpca.2c02150
Copyright © 2022 American Chemical Society

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    Abstract

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    In this work we develop a variational relativistic density matrix renormalization group (DMRG) approach within the exact-two-component (X2C) framework (X2C-DMRG), using spinor orbitals optimized with the two-component relativistic complete active space self-consistent field. We investigate fine-structure splittings of p- (Ga, In, Tl) and d-block (Sc, Y, La) atoms and excitation energies of monohydride molecules (GeH, SnH, and TlH) with X2C-DMRG calculations using an all-electron relativistic Hamiltonian in a Kramers-unrestricted basis. We find that X2C-DMRG yields accurate 2P and 2D splittings compared to multireference configuration interaction with singles and doubles (MRCISD). We also investigated the degree of symmetry breaking in the atomic multiplets and convergence of electron correlation in the total energies. Symmetry breaking can be large in some cases (∼30 meV); however, increasing the number of renormalized block states m for the DMRG optimization recovers the symmetry breaking by several orders of magnitude. Encouragingly, we find the convergence of electron correlation to be close to MRCISDTQ5 quality. Relativistic X2C-DMRG approaches are important for cases where spin–orbit coupling is significant and the underlying reference wave function requires a large determinantal space. We are able to obtain quantitatively correct fine-structure splittings for systems up to 1019 number of determinants with traditional CI approaches, which are currently unfeasible to converge for the field.

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    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpca.2c02150.

    • Weights (CI coefficient squared) of the dominant configuration in the CASSCF reference wave functions for atomic multiplet splittings, X2C-CASSCF and X2C-DMRG total energies for atomic systems, and comparison between Kramers-restricted and Kramers-unrestricted X2C-MRCISD for splitting of Ga atom with the A space (PDF)

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    Cited By

    This article is cited by 11 publications.

    1. Tianyuan Zhang, Samragni Banerjee, Lauren N. Koulias, Edward F. Valeev, A. Eugene DePrince, III, Xiaosong Li. Dirac–Coulomb–Breit Molecular Mean-Field Exact-Two-Component Relativistic Equation-of-Motion Coupled-Cluster Theory. The Journal of Physical Chemistry A 2024, 128 (17) , 3408-3418. https://doi.org/10.1021/acs.jpca.3c08167
    2. Kirill D. Shumilov, Andrew J. Jenkins, Henry S. La Pierre, Bess Vlaisavljevich, Xiaosong Li. Overdestabilization vs Overstabilization in the Theoretical Analysis of f-Orbital Covalency. Journal of the American Chemical Society 2024, 146 (17) , 12030-12039. https://doi.org/10.1021/jacs.4c01665
    3. Can Liao, Chad E. Hoyer, Rahoul Banerjee Ghosh, Andrew J. Jenkins, Stefan Knecht, Michael J. Frisch, Xiaosong Li. Comparison of Variational and Perturbative Spin–Orbit Coupling within Two-Component CASSCF. The Journal of Physical Chemistry A 2024, 128 (12) , 2498-2506. https://doi.org/10.1021/acs.jpca.3c08031
    4. Jordan N. Ehrman, Kirill Shumilov, Andrew J. Jenkins, Joseph M. Kasper, Tonya Vitova, Enrique R. Batista, Ping Yang, Xiaosong Li. Unveiling Hidden Shake-Up Features in the Uranyl M4-Edge Spectrum. JACS Au 2024, 4 (3) , 1134-1141. https://doi.org/10.1021/jacsau.3c00838
    5. Rosa Di Felice, Maricris L. Mayes, Ryan M. Richard, David B. Williams-Young, Garnet Kin-Lic Chan, Wibe A. de Jong, Niranjan Govind, Martin Head-Gordon, Matthew R. Hermes, Karol Kowalski, Xiaosong Li, Hans Lischka, Karl T. Mueller, Erdal Mutlu, Anders M. N. Niklasson, Mark R. Pederson, Bo Peng, Ron Shepard, Edward F. Valeev, Mark van Schilfgaarde, Bess Vlaisavljevich, Theresa L. Windus, Sotiris S. Xantheas, Xing Zhang, Paul M. Zimmerman. A Perspective on Sustainable Computational Chemistry Software Development and Integration. Journal of Chemical Theory and Computation 2023, 19 (20) , 7056-7076. https://doi.org/10.1021/acs.jctc.3c00419
    6. Yang Guo, Ning Zhang, Wenjian Liu. SOiCISCF: Combining SOiCI and iCISCF for Variational Treatment of Spin–Orbit Coupling. Journal of Chemical Theory and Computation 2023, 19 (19) , 6668-6685. https://doi.org/10.1021/acs.jctc.3c00789
    7. Jordan Ehrman, Ernesto Martinez-Baez, Andrew J. Jenkins, Xiaosong Li. Improving One-Electron Exact-Two-Component Relativistic Methods with the Dirac–Coulomb–Breit-Parameterized Effective Spin–Orbit Coupling. Journal of Chemical Theory and Computation 2023, 19 (17) , 5785-5790. https://doi.org/10.1021/acs.jctc.3c00479
    8. Zhendong Li. Time-reversal symmetry adaptation in relativistic density matrix renormalization group algorithm. The Journal of Chemical Physics 2023, 158 (4) , 044119. https://doi.org/10.1063/5.0127621
    9. Chad E. Hoyer, Lixin Lu, Hang Hu, Kirill D. Shumilov, Shichao Sun, Stefan Knecht, Xiaosong Li. Correlated Dirac–Coulomb–Breit multiconfigurational self-consistent-field methods. The Journal of Chemical Physics 2023, 158 (4) , 044101. https://doi.org/10.1063/5.0133741
    10. Wenjian Liu. Perspective: Simultaneous treatment of relativity, correlation, and QED. WIREs Computational Molecular Science 2022, 88 https://doi.org/10.1002/wcms.1652
    11. Huanchen Zhai, Garnet Kin-Lic Chan. A comparison between the one- and two-step spin–orbit coupling approaches based on the ab initio density matrix renormalization group. The Journal of Chemical Physics 2022, 157 (16) , 164108. https://doi.org/10.1063/5.0107805

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