Dual-Cone Variational Calculation of the 2-Electron Reduced Density Matrix

• URL: http://arxiv.org/abs/2103.17155v1
• Date: Wed, 31 Mar 2021 15:20:34 GMT
• Title: Dual-Cone Variational Calculation of the 2-Electron Reduced Density Matrix
• Authors: David A. Mazziotti
• Abstract summary: Variational calculation of the two-electron reduced density matrix (2RDM) without the many-electron wave function exploits the pairwise nature of the electronic Coulomb interaction. Here we generalize the dual-cone variational 2-RDM method to compute not only the ground-state energy but also the 2-RDM. We apply the method to computing the energies and properties of strongly correlated electrons in an illustrative hydrogen chain and the nitrogen-fixation catalyst FeMoco.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The computation of strongly correlated quantum systems is challenging because of its potentially exponential scaling in the number of electron configurations. Variational calculation of the two-electron reduced density matrix (2-RDM) without the many-electron wave function exploits the pairwise nature of the electronic Coulomb interaction to compute a lower bound on the ground-state energy with polynomial computational scaling. Recently, a dual-cone formulation of the variational 2-RDM calculation was shown to generate the ground-state energy, albeit not the 2-RDM, at a substantially reduced computational cost, especially for higher $N$-representability conditions such as the T2 constraint. Here we generalize the dual-cone variational 2-RDM method to compute not only the ground-state energy but also the 2-RDM. The central result is that we can compute the 2-RDM from a generalization of the Hellmann-Feynman theorem. Specifically, we prove that in the Lagrangian formulation of the dual-cone optimization the 2-RDM is the Lagrange multiplier. We apply the method to computing the energies and properties of strongly correlated electrons -- including atomic charges, electron densities, dipole moments, and orbital occupations -- in an illustrative hydrogen chain and the nitrogen-fixation catalyst FeMoco. The dual variational computation of the 2-RDM with T2 or higher $N$-representability conditions provides a polynomially scaling approach to strongly correlated molecules and materials with significant applications in atomic and molecular and condensed-matter chemistry and physics.

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