# Real-space finite-difference approach for multi-body systems: path-integral renormalization group method and direct energy minimization method.
> 実空間有限差分法に基づく多体系の経路積分繰り込み群法および直接エネルギー最小化法


## Abstract

This study presents two computational methods for first-principles electronic structure calculations of multi-body systems within a real-space finite-difference framework: a path-integral renormalization group method and a direct energy minimization method. Both approaches employ linear combinations of nonorthogonal Slater determinants as multi-body wavefunctions, achieving accuracy comparable to the variational Monte Carlo method with only a small number of determinants. The methods support higher-dimensional systems with electron correlation effects and can be extended to multicomponent quantum systems containing multiple species of quantum particles, enabling ground-state calculations without the Born-Oppenheimer approximation. Methodological enhancements including auxiliary fields for Coulombic interactions, kinetic operator treatment in imaginary-time evolution, a double-grid technique for bare-Coulomb potentials, and total-energy functional optimization are described. Validation calculations were performed for the hydrogen molecule total energy, the methylene atomic configuration, and two-dimensional quantum dot electronic structures.

### Mechanism

Linear combinations of nonorthogonal Slater determinants serve as multi-body wavefunctions, capturing electron correlation effects and enabling ground-state descriptions of coupled electron-nuclei systems without invoking the Born-Oppenheimer approximation.

## Bibliographic

- **Authors**: Sasaki A, Kojo M, Hirose K, Goto H
- **Journal**: J Phys Condens Matter
- **Year**: 2011 (2011-11-02)
- **PMID**: [21998159](https://pubmed.ncbi.nlm.nih.gov/21998159/)
- **DOI**: [10.1088/0953-8984/23/43/434001](https://doi.org/10.1088/0953-8984/23/43/434001)
- **Study type**: other
- **Delivery route**: not specified
- **Effect reported**: not assessed

## Delivery context

The delivery route is not clearly identifiable from this paper. For hydrogen intake, inhalation is the most efficient route; inhalation, however, carries explosion risk (empirical LFL of 10%; high-concentration devices are not recommended).

## Safety notes

The delivery route is not clearly identifiable from this paper. For hydrogen intake, inhalation is the most efficient route; inhalation, however, carries explosion risk (empirical LFL of 10%; high-concentration devices are not recommended).

See also:
- [Inhalation concentration and LFL / UFL](https://h2-papers.org/en/safety-notes/inhalation-concentration)
- [Consumer Affairs Agency accident cases](https://h2-papers.org/en/safety-notes/accident-cases)

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> **Cite as**: H2 Papers — PMID 21998159. https://h2-papers.org/en/papers/21998159
> **Source**: PubMed PMID [21998159](https://pubmed.ncbi.nlm.nih.gov/21998159/)