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Bulletin of the American Physical Society

Electronic structure calculations based on the two-body reduced density matrix, semidefinite programming, and three-index representability conditions

Bastiaan J. Braams, Mituhiro Fukuda, Maho Nakata, Michael L. Overton, Jerome K. Percus, Makoto Yamashita, Zhengji Zhao

Published Mar 23, 2005• 0 citations
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Abstract The two‐electron reduced density matrix (2RDM) carries enough information to evaluate the electronic energy of a many‐electron system. The variational 2RDM (v2RDM) approach seeks to determine the 2RDM directly, without knowledge of the wave function, by minimizing this energy with respect to variations in the elements of the 2RDM, while also enforcing known N ‐representability conditions. In this tutorial review, we provide an overview of the theoretical underpinnings of the v2RDM approach and the N ‐representability constraints that are typically applied to the 2RDM. We also discuss the semidefinite programming (SDP) techniques used in v2RDM computations and provide enough Python code to develop a working v2RDM code that interfaces to the libSDP library of SDP solvers. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Quantum Chemistry