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Computerized implementation of higher-order electron-correlation methods and their linear-scaling divide-and-conquer

Masahiko Nakano1, Takeshi Yoshikawa1, So Hirata2,3

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Journal of Computational Chemistry
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We developed efficient computational methods for quantum chemistry, reducing costs for accurate electronic structure calculations. These new techniques provide reliable results for complex molecular systems with significantly less computational expense.

Keywords:
divide-and-conquer methodelectron-correlation theorylinear-scalingtensor contraction engine

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Area of Science:

  • Computational quantum chemistry
  • Theoretical chemistry
  • Electronic structure theory

Background:

  • Higher-order coupled-cluster (CC) and Møller-Plesset perturbation theories (MPPT) are essential for accurate electronic structure calculations.
  • Conventional implementations of these methods scale poorly with system size, limiting their applicability.
  • Linear-scaling methods are needed to overcome the computational bottlenecks of traditional quantum chemistry approaches.

Purpose of the Study:

  • To implement and assess linear-scaling divide-and-conquer (DC) based higher-order CC and MPPT methods.
  • To develop automated computational schemes using a tensor contraction engine.
  • To evaluate the accuracy and efficiency of DC-based methods for various molecular systems.

Main Methods:

  • Implementation of linear-scaling divide-and-conquer (DC) based higher-order coupled-cluster (CC) and Møller-Plesset perturbation theories (MPPT).
  • Utilized a tensor contraction engine for automated implementation of CC and MPPT methods and their combinations.
  • Developed DC-based energy expressions for standard CC and MPPT, including augmented CC methods up to high excitation orders (e.g., CCSDTQ, MP4, CCSD(2)TQ).

Main Results:

  • Successfully implemented DC-based higher-order CC and MPPT methods with automated symbolic computation.
  • Numerical assessments on hydrogen halide chains, polyene chains, and a model of photoactive yellow protein were performed.
  • DC-based correlation methods yielded reliable correlation energies comparable to conventional methods.

Conclusions:

  • Linear-scaling DC-based CC and MPPT methods offer a significant reduction in computational cost.
  • These methods provide accurate correlation energies for chemical systems.
  • The developed approach enables efficient and reliable electronic structure calculations for larger and more complex molecules.