Development of the electronic structure calculation using the particle method

2018 Fiscal Year Final Research Report

• Project/Area Number: 16K05047
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Computational science
• Research Institution: Hosei University
• Principal Investigator: ZEMPO Yasunari 法政大学, 情報科学部, 教授 (60557859)
• Co-Investigator(Kenkyū-buntansha): 狩野 覚 法政大学, 情報科学部, 教授 (30107700) ; 岩沢 美佐子 法政大学, 理工学部, 助手 (40566816)
• Research Collaborator: ISHIDA masaya ; AKINO nobuhiko
• Project Period (FY): 2016-04-01 – 2019-03-31
• Keywords: 粒子法 / SPH / 電子状態計算 / Bohm形式 / 線形結合 / 粒子の追加と削除

Outline of Final Research Achievements

The particle method has no restriction on the particle arrangement, where the calculation is performed. The purpose is, by using this feature, to develop the method to analyze the dynamics of the electronic state. In order to describe the time evolution of the electronic state, we have developed a new method to solve the time-dependent wave equation, using the Bohmian that is very compatible with the particle method. In this form, there is also numerical instability in the region, where the value of the wave function was very small. However, we have successfully solved these difficulties by a linear combination of the ground state and the other excited states, where there is no node． When the particles are, on the other hand, too densely or sparsely distributed, the accuracy in the particle method are degraded. This also solved, by dynamic addition and deletion of the particles, to maintain the calculation accuracy.

Free Research Field

計算材料科学

Academic Significance and Societal Importance of the Research Achievements

電子状態計算は実空間で解析するためには、一般に解析領域をあらかじめ等間隔のメッシュを切って、全域で計算が行われる。原子や分子では電子密度がほぼゼロに近い領域でも計算を行うことになり、かなり無駄な計算が行われており改善の余地があった。我々は、このような領域へ粒子（計算点）を配置することなく、電子状態に合わせ高精度な計算が必要な領域へ集中的に粒子を配置する改善をおこなった。更に電子状態の動的な変化をとらえるためには時間依存の波動方程式を解く必要があるが、粒子法との相性が非常に良いBohm形式を用いることで、計算点が自動的に移動する手法を開発し、計算精度を維持することが可能となった。