Variational second order density matrix study of $\mathrm{F_3^-}$F3−: Importance of subspace constraints for size-consistency

Abstract

Variational second order density matrix theory under '2-positivity' tends to dissociate molecules into unphysical fractionally charged products with too low energies. We aim to construct a qualitatively correct potential energy surface for F − 3 by applying subspace energy constraints on mono-and diatomic subspaces of the molecular basis space. Mono-atomic subspace constraints do not guarantee correct dissociation: the constraints are thus geometry dependent. Furthermore, the number of subspace constraints needed for correct dissociation does not grow linearly with the number of atoms. The subspace constraints do impose correct chemical properties in the dissociation limit and size-consistency, but the structure of the resulting DM2 does not exactly correspond to a system of non-interacting units.

Considerations on describing non-singlet spin states in variational second order density matrix methods

“…Additionally, the inconsistencies that arise in the dissociation limit of the maximal spin projections of degenerate spin states, such as those occurring in the dissociation limit of the oxygen and carbon dimer, can be corrected by imposing subspace energy conditions. 12,13,30 At the same time, these constraints will correct size-consistency defects and incorrect dissociation-in contrast to the molecules under consideration here, non-homonuclear molecules gener- FIG. 9.…”

“…10 An approach taken by Hammond and Mazziotti avoids the problem of dealing with a non-singlet spin states by coupling them to an overall singlet state. 10 However, because of the inherent size-inconsistency of approximate N-representability constraints (and, more importantly, of approximate S-representability constraints, as we will show here) and their tendency to allow fractional charges in non-interacting systems, [11][12][13] this approach is problematic.…”

“…This type of constraint has been introduced in previous work, and has been shown to correct size-consistency defects and produce correctly charged dissociation products. 12,13 …”

“…The condition (13) for maximal spin projection is a special case of this condition. Just like the maximal spin projection condition (13), it imposes K 2 additional conditions on the 2DM and imposes correctŜ 2 expectation value when combined with the contraction condition, except for states with zero spin projection. In those cases, the condition (14) is already satisfied by the zero spin projection's symmetry.…”

Accuracy of two-particleN-representability conditions for describing different spin states and the singlet–triplet gap in the linear acene series

“…It has been repeatedly demonstrated that v-2RDM methods are not size-consistent, a deficiency which manifests itself in the tendency of the methods to favour fractional charges in non-interacting subsystems [30]. Additional subsystem constraints can alleviate the problem in certain limits but not universally [31][32][33]. Further, the description of open-shell systems is hardly standardised.…”