• Corpus ID: 117851046

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… 
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References

SHOWING 1-10 OF 71 REFERENCES

Variational reduced-density-matrix calculation of the one-dimensional Hubbard model

Variational reduced-density-matrix theory is applied to calculating the ground-state energy and two-electron reduced density matrices (2-RDMs) of the one-dimensional Hubbard model for a range of

A density matrix variational calculation for atomic Be

The ground-state energy of the beryllium atom is calculated using a variational procedure in which the elements of the two-body reduced density matrix (particle–particle matrix) are the variational

The electronic ground-state energy problem: a new reduced density matrix approach.

It is shown that the computation of the ground-state energy reduces to the search of the projection of some two-electron reduced Hamiltonian on the dual cone of N-representability conditions.

The reduced density matrix method for electronic structure calculations and the role of three-index representability conditions.

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.

Realization of quantum chemistry without wave functions through first-order semidefinite programming.

An efficient algorithm with an order-of-magnitude reduction in floating-point operations and memory usage is presented and automatically treats strong, multireference correlation when the optimization occurs on the space of two electrons.

Variational calculation of second-order reduced density matrices by strong N-representability conditions and an accurate semidefinite programming solver.

This work explores the well-known N-representability conditions (P, Q, and G) together with the more recent and much stronger T1 and T2(') conditions and provides physically meaningful results for the Hubbard model in the high correlation limit.

General atomic and molecular electronic structure system

A description of the ab initio quantum chemistry package GAMESS, which can be treated with wave functions ranging from the simplest closed‐shell case up to a general MCSCF case, permitting calculations at the necessary level of sophistication.

Variational minimization of atomic and molecular ground-state energies via the two-particle reduced density matrix

Atomic and molecular ground-state energies are variationally determined by constraining the two-particle reduced density matrix (2-RDM) to satisfy positivity conditions. Because each positivity

Large-scale semidefinite programs in electronic structure calculation

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.

Chemical verification of variational second-order density matrix based potential energy surfaces for the N2 isoelectronic series.

A novel constraint is introduced that imposes the correct dissociation and enforces size consistency on diatomic 14-electron molecules and is illustrated with calculations on NO(+), CO, CN(-), N(2), and O(2)(2+).
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