Development of Linear-Scaling Relativistic Quantum Chemistry Covering the Periodic Table

Hiromi Nakai*

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

3 Citations (Scopus)


This Award Account focuses on the author's studies on the theoretical developments of two-component (2c) relativistic quantum chemistry calculations for large systems with high efficiency and high accuracy, with a review of related studies as the background. The local unitary transformation scheme allows the linear-scaling computation cost to be applied to construct a 2c Hamiltonian, such as an infinite-order twocomponent version. The divide-and-conquer scheme can lead to linear-scaling computation costs to apply not only a Hartree-Fock (HF) method but also post-HF methods such as the second-order Møller-Plesset perturbation and couple cluster theory with singles and doubles for the 2c Hamiltonian in addition to a non-relativistic version. The frozen core potential scheme can naturally connect pseudopotential calculations with all-electron calculations. The accompanying coordinate expansion with a transfer recurrence relation scheme provides an efficient algorithm for the rapid evaluation of electron repulsion integrals for systems including heavy elements, the orbitals of which have long contractions and high angular momenta, such as f- A nd g-orbitals. Illustrative applications will help readers realize the advantages and usefulness of these schemes.

Original languageEnglish
Pages (from-to)1664-1681
Number of pages18
JournalBulletin of the Chemical Society of Japan
Issue number6
Publication statusPublished - 2021 Jun


  • Divide-and-conquer
  • Infinite-order two-component
  • Local unitary transformation

ASJC Scopus subject areas

  • Chemistry(all)


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