# Variational approach for the electronic structure calculation on the second-order reduced density matrices and the $N$-representability problem

@article{Nakata2010VariationalAF, title={Variational approach for the electronic structure calculation on the second-order reduced density matrices and the \$N\$-representability problem}, author={Maho Nakata and Mituhiro Fukuda and Katsuki Fujisawa}, journal={arXiv: Strongly Correlated Electrons}, year={2010} }

The reduced-density-matrix method is an promising candidate for the next generation electronic structure calculation method; it is equivalent to solve the Schr\"odinger equation for the ground state. The number of variables is the same as a four electron system and constant regardless of the electrons in the system. Thus many researchers have been dreaming of a much simpler method for quantum mechanics. In this chapter, we give a overview of the reduced-density matrix method; details of the…

## 4 Citations

### Functional N -Representability in 2-Matrix, 1-Matrix, and Density Functional Theories

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A brand-new version of the parallel SDP solver, SDPARA, is described, which has been equipped with a Cholesky factorization implementation and demonstrated 1.7PFlops performance with over two million constraints by using 4,080 GPUs.

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The primal-dual interior-point method (PDIPM) is one of the most powerful algorithms for solving SDP problems, and many research groups have employed it for developing software packages, and the largest SDP problem was solved, thereby creating a new world record.

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