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Pure State v-Representability of Density Matrix Embedding Theory
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    Pure State v-Representability of Density Matrix Embedding Theory
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    • Fabian M. Faulstich
      Fabian M. Faulstich
      Department of Mathematics, University of California, Berkeley, California 94720, United States
    • Raehyun Kim
      Raehyun Kim
      Department of Mathematics, University of California, Berkeley, California 94720, United States
      More by Raehyun Kim
    • Zhi-Hao Cui
      Zhi-Hao Cui
      Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
      More by Zhi-Hao Cui
    • Zaiwen Wen
      Zaiwen Wen
      Beijing International Center for Mathematical Research, BICMR, Peking University, Beijing 100871, China
      More by Zaiwen Wen
    • Garnet Kin-Lic Chan
      Garnet Kin-Lic Chan
      Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
    • Lin Lin*
      Lin Lin
      Department of Mathematics, University of California, Berkeley, California 94720, United States
      Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
      *Email: [email protected]
      More by Lin Lin
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    Journal of Chemical Theory and Computation

    Cite this: J. Chem. Theory Comput. 2022, 18, 2, 851–864
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    https://doi.org/10.1021/acs.jctc.1c01061
    Published January 27, 2022
    Copyright © 2022 American Chemical Society

    Abstract

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    Density matrix embedding theory (DMET) formally requires the matching of density matrix blocks obtained from high-level and low-level theories, but this is sometimes not achievable in practical calculations. In such a case, the global band gap of the low-level theory vanishes, and this can require additional numerical considerations. We find that both the violation of the exact matching condition and the vanishing low-level gap are related to the assumption that the high-level density matrix blocks are noninteracting pure-state v-representable (NI-PS-V), which assumes that the low-level density matrix is constructed following the Aufbau principle. To relax the NI-PS-V condition, we develop an augmented Lagrangian method to match the density matrix blocks without referring to the Aufbau principle. Numerical results for the 2D Hubbard and hydrogen model systems indicate that, in some challenging scenarios, the relaxation of the Aufbau principle directly leads to exact matching of the density matrix blocks, which also yields improved accuracy.

    Copyright © 2022 American Chemical Society

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    This article is cited by 9 publications.

    1. Srinivasan S. Iyengar, Juncheng Harry Zhang, Debadrita Saha, Timothy C. Ricard. Graph-|Q⟩⟨C|: A Quantum Algorithm with Reduced Quantum Circuit Depth for Electronic Structure. The Journal of Physical Chemistry A 2023, 127 (44) , 9334-9345. https://doi.org/10.1021/acs.jpca.3c04261
    2. Shreya Verma, Abhishek Mitra, Yu Jin, Soumi Haldar, Christian Vorwerk, Matthew R. Hermes, Giulia Galli, Laura Gagliardi. Optical Properties of Neutral F Centers in Bulk MgO with Density Matrix Embedding. The Journal of Physical Chemistry Letters 2023, 14 (34) , 7703-7710. https://doi.org/10.1021/acs.jpclett.3c01875
    3. Max Nusspickel, Basil Ibrahim, George H. Booth. Effective Reconstruction of Expectation Values from Ab Initio Quantum Embedding. Journal of Chemical Theory and Computation 2023, 19 (10) , 2769-2791. https://doi.org/10.1021/acs.jctc.2c01063
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    6. Eric Cancès, Fabian M. Faulstich, Alfred Kirsch, Eloïse Letournel, Antoine Levitt. Analysis of density matrix embedding theory around the non‐interacting limit. Communications on Pure and Applied Mathematics 2025, 13 https://doi.org/10.1002/cpa.22244
    7. Sajanthan Sekaran, Oussama Bindech, Emmanuel Fromager. A unified density matrix functional construction of quantum baths in density matrix embedding theory beyond the mean-field approximation. The Journal of Chemical Physics 2023, 159 (3) https://doi.org/10.1063/5.0157746
    8. Dariia Yehorova, Joshua S. Kretchmer. A multi-fragment real-time extension of projected density matrix embedding theory: Non-equilibrium electron dynamics in extended systems. The Journal of Chemical Physics 2023, 158 (13) https://doi.org/10.1063/5.0146973
    9. Sajanthan Sekaran, Matthieu Saubanère, Emmanuel Fromager. Local Potential Functional Embedding Theory: A Self-Consistent Flavor of Density Functional Theory for Lattices without Density Functionals. Computation 2022, 10 (3) , 45. https://doi.org/10.3390/computation10030045

    Journal of Chemical Theory and Computation

    Cite this: J. Chem. Theory Comput. 2022, 18, 2, 851–864
    Click to copy citationCitation copied!
    https://doi.org/10.1021/acs.jctc.1c01061
    Published January 27, 2022
    Copyright © 2022 American Chemical Society

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