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Modern Approaches to Exact Diagonalization and Selected Configuration Interaction with the Adaptive Sampling CI Method

  • Norm M. Tubman
    Norm M. Tubman
    Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
    Chemical Sciences Division, Lawrence Berkeley National Laboratory Berkeley, California 94720, United States
  • C. Daniel Freeman
    C. Daniel Freeman
    Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
    Chemical Sciences Division, Lawrence Berkeley National Laboratory Berkeley, California 94720, United States
  • Daniel S. Levine
    Daniel S. Levine
    Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
    Chemical Sciences Division, Lawrence Berkeley National Laboratory Berkeley, California 94720, United States
  • Diptarka Hait
    Diptarka Hait
    Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
    Chemical Sciences Division, Lawrence Berkeley National Laboratory Berkeley, California 94720, United States
  • Martin Head-Gordon
    Martin Head-Gordon
    Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
    Chemical Sciences Division, Lawrence Berkeley National Laboratory Berkeley, California 94720, United States
  • , and 
  • K. Birgitta Whaley
    K. Birgitta Whaley
    Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
    Chemical Sciences Division, Lawrence Berkeley National Laboratory Berkeley, California 94720, United States
Cite this: J. Chem. Theory Comput. 2020, 16, 4, 2139–2159
Publication Date (Web):March 11, 2020
https://doi.org/10.1021/acs.jctc.8b00536
Copyright © 2020 American Chemical Society

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    Abstract

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    Recent advances in selected configuration interaction methods have made them competitive with the most accurate techniques available and, hence, creating an increasingly powerful tool for solving quantum Hamiltonians. In this work, we build on recent advances from the adaptive sampling configuration interaction (ASCI) algorithm. We show that a useful paradigm for generating efficient selected CI/exact diagonalization algorithms is driven by fast sorting algorithms, much in the same way iterative diagonalization is based on the paradigm of matrix vector multiplication. We present several new algorithms for all parts of performing a selected CI, which includes new ASCI search, dynamic bit masking, fast orbital rotations, fast diagonal matrix elements, and residue arrays. The ASCI search algorithm can be used in several different modes, which includes an integral driven search and a coefficient driven search. The algorithms presented here are fast and scalable, and we find that because they are built on fast sorting algorithms they are more efficient than all other approaches we considered. After introducing these techniques, we present ASCI results applied to a large range of systems and basis sets to demonstrate the types of simulations that can be practically treated at the full-CI level with modern methods and hardware, presenting double- and triple-ζ benchmark data for the G1 data set. The largest of these calculations is Si2H6 which is a simulation of 34 electrons in 152 orbitals. We also present some preliminary results for fast deterministic perturbation theory simulations that use hash functions to maintain high efficiency for treating large basis sets.

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