Large-scale semidefinite programs in electronic structure calculation
Large-scale semidefinite programs in electronic structure calculation
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DOI：
10.1007/s10107-006-0027-y
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发表时间：
2007-01
影响因子：
2.7
通讯作者：
Mituhiro Fukuda;B. Braams;Maho Nakata;Michael L. Overton;J. Percus;Makoto Yamashita;Zhengji Zhao
中科院分区：
文献类型：
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作者：
Mituhiro Fukuda;B. Braams;Maho Nakata;Michael L. Overton;J. Percus;Makoto Yamashita;Zhengji Zhao
以二体降密度矩阵（RDM）为未知变量，采用变分方法计算原子和分子系统的基态能量，是物理化学/化学物理电子结构理论长期以来的梦想。RDM方法的实现很大程度上得益于半确定规划（SDP）的最新发展。我们介绍了SDP新应用的实际情况以及这些SDP的公式，这些SDP可以任意大。给出了在高性能计算机上并行计算的数值结果。与传统的电子结构方法相比，RDM方法具有鲁棒性和精度高的优点，但其计算时间和内存消耗仍然非常大。
It has been a long-time dream in electronic structure theory in physical chemistry/chemical physics to compute ground state energies of atomic and molecular systems by employing a variational approach in which the two-body reduced density matrix (RDM) is the unknown variable. Realization of the RDM approach has benefited greatly from recent developments in semidefinite programming (SDP). We present the actual state of this new application of SDP as well as the formulation of these SDPs, which can be arbitrarily large. Numerical results using parallel computation on high performance computers are given. The RDM method has several advantages including robustness and provision of high accuracy compared to traditional electronic structure methods, although its computational time and memory consumption are still extremely large.