Analysis of two-orbital correlations in wave functions restricted to electron-pair states

Abstract

Wavefunctions constructed from electron-pair states can accurately model strong electron correlation effects and are promising approaches especially for larger many-body systems. In this article, we analyze the nature and the type of electron correlation effects that can be captured by wavefunctions restricted to electron-pair states. We focus on the Antisymmetric Product of 1-reference orbital Geminal (AP1roG) method combined with an orbital optimization protocol presented in [Phys. Rev. B, 89, 201106(R), 2014] whose performance is assessed against electronic structures obtained form DMRG reference data. Our numerical analysis covers model systems for strong correlation: the one-dimensional Hubbard model with periodic boundary condition as well as metallic and molecular hydrogen rings. Specifically, the accuracy of AP1roG is benchmarked using the single-orbital entropy, the orbital-pair mutual information as well as the eigenvalue spectrum of the one-orbital and two-orbital reduced density matrices. Our study indicates that contributions from singly occupied states become important in the strong correlation regime which highlights the limitations of the AP1roG method. Furthermore, we examine the effect of orbital rotations within the AP1roG model on correlations between orbital pairs.

Measuring multi-configurational character by orbital entanglement

“…This scaling allows us to compare the diagnostic between different active space sizes which was not the case for some previous definitions of entanglement based diagnostics. 14,15 The single-orbital entropies can easily be evaluated from a density matrix renormalization group (DMRG) [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] wave function but can also be implemented for other methods like standard complete active space self-consistent field (CASSCF) calculations or the antisymmetric product of the 1-reference orbitalbased geminals 39 .…”

On the multi-reference nature of plutonium oxides: PuO22+, PuO2, PuO3 and PuO2(OH)2

“…Furthermore, when combined with concepts of quantum information theory, DMRG allows us to quantify orbital entanglement [32] and orbital-pair correlations [30,[33][34][35][36][37][38][39] that enable us to gain a better understanding of electron correlation effects, [36,40,41] elucidate chemical bonding in molecules, [37,[42][43][44][45][46][47] and detect changes in the electronic wave function. [48][49][50] The suitability of DMRG for helping to understand the electronic structure of actinides can be seen in a recent study of the changes in the ground-state for the CUO molecule when diluted in different noble gas matrices.…”

An efficient method for strongly correlated electrons in one dimension

“…The number of sites varies from 14 to 122 in small and intermediate correlation regimes. For comparison, OO-AP1roG results [9] have been included. The data sets used in this figure can be found in the Supplemental Material (Table III).…”