Integer electron-count cuts in variational second-order reduced-density-matrix theory. I. Molecular dissociation with fixed real-space and orbital partitions
Abstract
Van Aggelen et al. [Phys. Chem. Chem. Phys. 11, 5558 (2009)] showed that variational second-order reduced-density-matrix (2-RDM) calculations with the standard two-index conditions dissociate diatomic molecules into fractionally charged atoms with energies far below the exact limit, a drastic violation of size consistency; the proposed subsystem constraints require auxiliary calculations with the physical fragment Hamiltonians. We show that two long-known ingredients, combined, remove most of this failure without such calculations: the requirement that the number of electrons in a part of the molecule be an integer, imposed as linear conditions on the 2-RDM, and a chemically motivated partition of the molecule into atomic regions bounded at the bond critical point of the Hartree-Fock density. In a minimal basis, compared with full configuration interaction, a single such condition reduces the energy errors of NO+ and CN- at 6 Å from 108.9 and 80.7 mEh to less than 0.02 mEh. In N2+, whose fragments have the correct mean population but too small a fluctuation, the region and three-index conditions act complementarily, reducing the error at 4 Å from 138.0 to 1.6 mEh. At the separated-atom limit, the region cuts make the P, Q, G energy additive over the fragments to within 0.2 mEh in 7 of 10 systems, 3 already nearly additive without cuts; adding the T1 and T2 conditions also makes CO nearly additive, while a nonadditive error remains for N2+ and CO+. Effective partitions are those whose condition is nearly saturated by the exact state.
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BibTeX
@misc{nakata2026integer,
title = {{Integer electron-count cuts in variational second-order reduced-density-matrix theory. I. Molecular dissociation with fixed real-space and orbital partitions}},
author = {Maho Nakata},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36514},
eprint = {2610.36514},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36514},
}
RIS
TY - UNPB
TI - Integer electron-count cuts in variational second-order reduced-density-matrix theory. I. Molecular dissociation with fixed real-space and orbital partitions
AU - Maho Nakata
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36514
UR - https://arxiv.org/abs/2610.36514
AB - Van Aggelen et al. [Phys. Chem. Chem. Phys. 11, 5558 (2009)] showed that variational second-order reduced-density-matrix (2-RDM) calculations with the standard two-index conditions dissociate diatomic molecules into fractionally charged atoms with energies far below the exact limit, a drastic violation of size consistency; the proposed subsystem constraints require auxiliary calculations with the physical fragment Hamiltonians. We show that two long-known ingredients, combined, remove most of this failure without such calculations: the requirement that the number of electrons in a part of the molecule be an integer, imposed as linear conditions on the 2-RDM, and a chemically motivated partition of the molecule into atomic regions bounded at the bond critical point of the Hartree-Fock density. In a minimal basis, compared with full configuration interaction, a single such condition reduces the energy errors of NO^+ and CN^- at 6 Å from 108.9 and 80.7 mE_h to less than 0.02 mE_h. In N_2^+, whose fragments have the correct mean population but too small a fluctuation, the region and three-index conditions act complementarily, reducing the error at 4 Å from 138.0 to 1.6 mE_h. At the separated-atom limit, the region cuts make the P, Q, G energy additive over the fragments to within 0.2 mE_h in 7 of 10 systems, 3 already nearly additive without cuts; adding the T_1 and T_2 conditions also makes CO nearly additive, while a nonadditive error remains for N_2^+ and CO^+. Effective partitions are those whose condition is nearly saturated by the exact state.
ER -