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Updated: Dec 30, 2025

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Large-scale excited-state calculation using dynamical polarizability evaluated by divide-and-conquer based coupled

Takeshi Yoshikawa1, Jyunya Yoshihara2, Hiromi Nakai1

  • 1Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan.

The Journal of Chemical Physics
|January 17, 2020
PubMed
Summary

This study introduces an efficient coupled cluster linear response (CCLR) scheme for large-scale excited-state calculations, including nonlocal excitations. The new method, based on dynamical polarizability and divide-and-conquer techniques, offers accurate and efficient computation, with DC-GF showing the best performance.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Spectroscopy

Background:

  • Accurate excited-state calculations are crucial for understanding molecular properties.
  • Standard fragmentation methods in excited-state calculations are limited to local excitations.
  • Previous success in time-dependent density functional theory (TD-DFT) using dynamical polarizability suggests its extension to higher levels of theory.

Purpose of the Study:

  • To develop an efficient scheme at the coupled cluster linear response (CCLR) level for large-scale excited-state calculations.
  • To extend the dynamical polarizability approach to handle both local and nonlocal excited states.
  • To implement and evaluate linear-scaling methods for CCLR calculations.

Main Methods:

  • Evaluation of excited states as poles of dynamical polarizability.
  • Extension of coupled-perturbed self-consistent field (CPSCF), random phase approximation (RPA), and Green's function (GF) formulas to CCLR.
  • Application of the divide-and-conquer (DC) technique for linear-scaling CCLR.
  • Implementation of CCLR with singles and doubles (CCSDLR) for six schemes (standard and DC-type CPSCF, RPA, GF).

Main Results:

  • The standard CCLR methods accurately reproduced conventional results but were computationally expensive.
  • The DC-type CCLR methods achieved quasilinear scaling computational costs.
  • DC-type treatments provided approximate but efficient calculations.
  • The DC-Green's function (DC-GF) method demonstrated the best performance among the developed schemes.

Conclusions:

  • The proposed efficient CCLR scheme enables large-scale excited-state calculations, including nonlocal excitations.
  • Linear-scaling DC-type methods significantly reduce computational cost while maintaining reasonable accuracy.
  • The DC-GF approach is identified as the most promising method for future applications in excited-state calculations.