Journal ArticleDOI
The variational calculation of reduced density matrices
Mitja Rosina,Claude Garrod +1 more
TLDR
In this article, the authors discuss the computational problem encountered in making direct variational calculations of the reduced density matrices of many-particle systems, and two different algorithms are presented for which working programs have been written.About:
This article is published in Journal of Computational Physics.The article was published on 1975-07-01. It has received 36 citations till now. The article focuses on the topics: Computational problem & Finite set.read more
Citations
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The reduced density matrix method for electronic structure calculations and the role of three-index representability conditions
TL;DR: The variational approach for electronic structure based on the two-body reduced density matrix is studied, incorporating two representability conditions beyond the previously used P, Q, and G conditions, and it is found that the use of the T1 and T2 conditions gives a significant improvement over just the P,Q, andG conditions.
Journal ArticleDOI
Large-Scale Variational Two-Electron Reduced-Density-Matrix-Driven Complete Active Space Self-Consistent Field Methods
TL;DR: A large-scale implementation of the complete active space self-consistent field (CASSCF) method using the variational two-electron reduced-density-matrix approach is presented and the quality of the results is still far superior to those obtained from standard single-reference approaches.
Journal ArticleDOI
Large-scale semidefinite programs in electronic structure calculation
Mituhiro Fukuda,Bastiaan J. Braams,Maho Nakata,Michael L. Overton,Jerome K. Percus,Makoto Yamashita,Zhengji Zhao +6 more
TL;DR: 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.
Journal ArticleDOI
Two algorithms for the lower bound method of reduced density matrix theory
TL;DR: A theorem giving necessary and sufficient conditions for the optimum for the central optimization problem of the lower bound method of reduced density matrix theory is developed.
References
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Journal ArticleDOI
Reduction of the N‐Particle Variational Problem
TL;DR: In this paper, a variational method is presented which is applicable to N-particle boson or fermion systems with two-body interactions, and it is proven that if Γ(1, 2 | 1′, 2′) and γ(1| 1′) are the twoparticle and oneparticle density matrices of an N−particle system [normalized by tr Γ = N(N − 1) and trγ = N] then the associated operator: G( 1, 2|| 1′,2
Journal ArticleDOI
Linear Inequalities for Density Matrices
TL;DR: In this paper, a set of linear inequalities for the reduced two-body density matrix is presented, and the general problem of finding all such inequalities is discussed, and it is shown that all of the linear inequalities found so far for ensemble representability may be written as a single family of inequalities.
Journal ArticleDOI
A new particle-hole approach to collective states
TL;DR: In this paper, it was shown that the first excited state lies entirely within the particle-hole space generated from the correlated ground state for angularmomentum projection and generator coordinate method in Gaussian overlap approximation.