Proposal of new algorithms for the electronic structure calculation based on the reduced-density-matrix method

基于降密度矩阵法的电子结构计算新算法的提出

• 批准号: 21700008
• 负责人: FUKUDA Mituhiro
• 金额: $ 1.83万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21700008/
• 关键词: 情報数理; 量子化学; 電子構造計算; 縮約密度行列法; 半正定値計画問題; 主双対内点法; 大規模最適化問題; 加速勾配法; 凸計画問題; 並列計算; 1次法; 最適化; 凸最適化問題; 縮約密度行列; 数理計画法

One of the most basic problems in quantum chemistry is the electronic structure calculation problem. Using the reduced-density-matrix method, we can obtain an approximate solution solving a convex problem called semidefinite programming problem. This approach is known to be very attractive both in theoretical and numerical aspects. However, its computational time is extremely slow compared to the usual methods and it cannot be used to large-scale problems. We succeed to solve the large-scale semidefinite programming problem with high accuracy using a parallel primal-dual interior-point method. This problem is considered one of the largest semidefinite programming problems solved so far.

量子化学中最基本的问题之一是电子结构计算问题。利用约化密度矩阵方法，我们可以得到一个求解半定规划问题的近似解。这种方法在理论和数值方面都是非常有吸引力的。然而，与通常的方法相比，它的计算时间非常慢，并且不能用于大规模问题。我们成功地解决了大规模半定规划问题的高精度的并行原始-对偶邻点法。这个问题被认为是迄今为止解决的最大的半定规划问题之一。

项目成果

Applications of optimization techniques in quantum chemistry

优化技术在量子化学中的应用

• 发表时间: 2011
• 作者: Mituhiro Fukuda;Maho Nakata;and Katsuki Fujisawa
• 通讯作者: and Katsuki Fujisawa

On the relation between the N-representability conditions in quantum chemistry with the valid inequalities for the cut polytope

量子化学中N-可表示性条件与切割多胞形有效不等式之间的关系

• 发表时间: 2010
• 作者: Mituhiro Fukuda;Maho Nakata;and Katsuki Fujisawa;Mituhiro Fukuda;Mituhiro Fukuda
• 通讯作者: Mituhiro Fukuda

SDP approximation for the electronic structures of atoms and molecules

原子和分子电子结构的 SDP 近似

• 发表时间: 2011
• 作者: Mituhiro Fukuda;Maho Nakata;and Katsuki Fujisawa
• 通讯作者: and Katsuki Fujisawa

On the relation between the N-representability conditionsin quantum chemistry with the valid inequalities for the cut polytope

量子化学中N-可表示性条件与切割多胞形有效不等式之间的关系

• 发表时间: 2010
• 作者: Mituhiro Fukuda;Maho Nakata;and Katsuki Fujisawa;Mituhiro Fukuda
• 通讯作者: Mituhiro Fukuda

Solving large-scale semidefinite programs for the variational calculation of second-order reduced density matrices in fermionic system

求解费米子系统中二阶约化密度矩阵变分计算的大规模半定程序

• 发表时间: 2010
• 作者: Mituhiro Fukuda;Maho Nakata;and Katsuki Fujisawa;Mituhiro Fukuda;Mituhiro Fukuda
• 通讯作者: Mituhiro Fukuda