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

TL;DR

This paper investigates the limitations of variational reduced-density-matrix theory with three-particle N-representability conditions, showing that even full 3POS conditions fail to improve accuracy for certain strongly correlated systems.

Contribution

It demonstrates the persistent challenges of applying full three-particle N-representability conditions in variational 2RDM methods for strongly correlated systems, highlighting the limitations of current correlation metrics.

Findings

3POS conditions do not always improve results over T2 conditions.

Correlation metrics based on cumulant RDMs are not universally reliable indicators.

Failures are observed in hydrogen clusters and other molecular systems.

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.