Perturbative Coordinate Descent Full Configuration Interaction

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Abstract
The coordinate descent full configuration interaction (CDFCI) is an accurate and efficient method for calculating ground-state energies of molecular systems. In this work we introduce two perturbative extensions of original CDFCI. We first propose a direct CDFCI + PT to further correct variational energy by perturbation theory. We also propose an iterative perturbative CDFCI (IP-CDFCI) to avoid evaluating the overlarge perturbative space and catch the information encoded in variational stage. In IP-CDFCI, we store three sparse vectors in a Hash table: c, b and d, where c is the variational wave function, b is the compressed approximation of Hc and d is the perturbative wave function, respectively. By utilizing the redundant memory in the storage of c, we can calculate perturbation without any extra memory compared to original CDFCI. We also use a strategy to eliminate the expensive repetitive evaluation of diagonal elements of Hamiltonian by creating a vector h which stores the diagonal entries of Hamiltonian. This strategy trades memory usage for computational time and reduces the computing time significantly. Furthermore, we use quadruple-precision floating-point numbers to improve the numerical stability of perturbative energy. We demonstrate the effectiveness of the single-threaded IP-CDFCI and the multithreaded CDFCI + PT, respectively, by performing calculations on several small molecular benchmarks as well as challenging correlated system: the chromium dimer.
Funding Information
  • University of Science and Technology of China
  • Ministry of Science and Technology of the People's Republic of China (2021ZD0303306)
  • National Key Research and Development Program of China (2016YFA0200604)
  • National Key Research and Development Program of China (2021YFB0300600)
  • National Natural Science Foundation of China (12271109)
  • National Natural Science Foundation of China (21688102)
  • National Natural Science Foundation of China (22173093)
  • National Natural Science Foundation of China (22288201)
  • National Natural Science Foundation of China (22503093)
  • National Natural Science Foundation of China (42550106)
  • Anhui Provincial Key Research and Development Plan (2022a05020052)
  • Chinese Academy of Sciences (XDB0450101)
  • Chinese Academy of Sciences (XDB1170000)
  • Chinese Academy of Sciences (YSBR-005)
  • Southwest University of Science and Technology
  • Anhui Province Science and Technology Innovation Project (202423k09020010)
  • Anhui Initiative in Quantum Information Technologies (AHY090400)
  • Hefei National Laboratory for Physical Sciences at the Microscale (KF2020003)

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