Challenges for variational reduced-density-matrix theory with three-particle N-representability conditions

Abstract

The direct variational optimization of the two-electron reduced density matrix (2RDM) can provide a reference-independent description of the electronic structure of many-electron systems that naturally captures strong or nondynamic correlation effects. Such variational 2RDM approaches can often provide a highly accurate description of strong electron correlation, provided that the 2RDMs satisfy at least partial three-particle $N$-representability conditions ({\em e.g.}, the T2 condition). However, recent benchmark calculations on hydrogen clusters [J. Chem. Phys. {\bf 153}, 104108 (2020)] suggest that even the T2 condition leads to unacceptably inaccurate results in the case of 2- and 3-dimensional clusters. We demonstrate that these failures persist under the application of full three-particle $N$-representability conditions (3POS). A variety of correlation metrics are explored in order to identify regimes under which 3POS calculations become unreliable, and we find that the relative squared magnitudes of the cumulant three- and two-particle reduced density matrices correlates reasonably well with the energy error in these systems. However, calculations on other molecular systems reveal that this metric is not a universal indicator for the reliability of reduced-density-matrix theory with 3POS conditions.

References in corpus (4)

• Orbital Optimization in the Density Matrix Renormalization Group, with applications to polyenes and β-carotene
• The Electronic Ground State Energy Problem: a New Reduced Density Matrix Approach
• Variational determination of the second-order density matrix for the isoelectronic series of beryllium, neon and silicon
• Polyradical character and spin frustration in fullerene molecules: An ab initio non-collinear Hartree--Fock study

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