Direct variational determination of the two-electron reduced density matrix for doubly occupied-configuration-interaction wave functions: The influence of three-index <i>N</i>-representability conditions

J. Chem. Theory Comput.

Capuzzi

et al. 2018

The variational reduced density matrix theory has been recently applied with great success to models within the truncated doubly occupied configuration interaction space, which corresponds to the seniority zero subspace. Conservation of the seniority quantum number restricts the Hamiltonians to be based on the SU(2) algebra. Among them there is a whole family of exactly solvable Richardson-Gaudin pairing Hamiltonians. We benchmark the variational theory against two different exactly solvable models, the Richardson-Gaudin-Kitaev and the reduced BCS Hamiltonians. We obtain exact numerical results for the so-called [Formula: see text] N-representability conditions in both cases for systems that go from 10 to 100 particles. However, when random single-particle energies as appropriate for small superconducting grains are considered, the exactness is lost but still a high accuracy is obtained.

Section: Introductionmentioning

confidence: 99%

Benchmarking the Variational Reduced Density Matrix Theory in the Doubly Occupied Configuration Interaction Space with Integrable Pairing Models

Rubio-García

J. Chem. Theory Comput.

Capuzzi

et al. 2018

“…Apart from these basic conditions, more restrictive higher‐index N ‐representability conditions can be added. [ 26,27,30–33,35–37 ]…”

Section: Theorymentioning

confidence: 99%

“…The remainder of the 2‐RDM elements

^{2} {\overset{false˜}{D}}_{jl}^{ik}

are zero. Moreover, the seniority number for DOCI wave functions is zero, and consequently, the expectation value of the corresponding seniority‐number operator

\overset{Ω}{true}

[ 31 ] is

\begin{matrix} lefttrue \\ {(〈〉, \overset{false^}{normalΩ})}_{DOCI} = {(〈〉, (\underset{σ}{false\sum} \underset{i^{σ}}{false\sum} a_{i^{σ}}^{†} a_{i^{σ}} - \underset{σ}{false\sum} \underset{i^{σ}}{false\sum} a_{i^{σ}}^{†} a_{i^{\overset{false¯}{σ}}}^{†} a_{i^{\overset{false¯}{σ}}} a_{i^{σ}}))}_{DOCI} = \\ = N - 2 \underset{σ}{false\sum} {\sum_{i^{σ}}}^{2} {\overset{D}{true}}_{i^{σ} i^{\overset{σ}{true}}}^{i^{σ} i^{\overset{σ}{true}}} = 0 \end{matrix}

…”

Section: Theorymentioning

confidence: 99%

Incorporating dynamic correlation into the variational determination method of the second‐order reduced density matrix in the doubly occupied configuration interaction space

Int J of Quantum Chemistry

Torre

Laín

et al. 2020

Self Cite

The variational determination of the second‐order reduced density matrices arising from N‐electron doubly occupied configuration interaction wave functions has recently been proposed as a method to describe systems possessing static correlation in their ground states. In this work, we propose to combine this approach with the on‐top pair density functional theory in order to incorporate dynamic correlations and improve the description of systems possessing both types of electron correlation. The procedure requires ensuring that the second‐order reduced density matrix elements satisfy determined N‐representability variational conditions, as well as other constraints arising from the doubly‐occupied configuration interaction wave function features. An analysis of the results obtained through this method, in studies of strongly correlated many‐electron systems, shows the usefulness of our proposals.

“…The values arising from the 2-POS and (2,3)-POS v2RDM-DOCI procedures have been previously reported by us in Ref. 33; they have been included in this and other Tables in order to make an easier comparison with the results obtained from the method proposed in this work. As can be seen, in all cases, the full 3-POS conditions improve the energies from those using the 2-and (2,3)-POS by at least three and two orders of magnitude, respectively.…”

Section: B Molecular Systemsmentioning

confidence: 99%

“…Usually, the variational 2-RDM (v2RDM) calculations use a set of necessary N-representability constraints involving p-particle RDMs (p-RDM), known as p-positivity conditions. [28][29][30] In the DOCI space, recent calculations with molecular systems [31][32][33] and pairing models [34][35][36] have shown that the lower bounds on the ground-state energies obtained from v2RDM calculations converge rapidly with the number p of particles. Moreover, for attractive pairing interactions twopositivity conditions together with a subset of three-positivity conditions have shown to provide exact numerical results for a large variety of integrable models.…”

Section: Introductionmentioning

confidence: 99%

Variational reduced density matrix method in the doubly occupied configuration interaction space using three-particle N-representability conditions

The Journal of Chemical Physics

Capuzzi

Rubio-García

et al. 2018

Self Cite