Orbital entanglement in quantum chemistry

Abstract

The basic concepts of orbital entanglement and its application to chemistry are briefly reviewed. The calculation of orbital entanglement measures from correlated wavefunctions is discussed in terms of reduced n-particle density matrices. Possible simplifications in their evaluation are highlighted in case of seniority-zero wavefunctions. Specifically, orbital entanglement allows us to dissect electron correlation effects in its strong and weak contributions, to determine bond orders, to assess the quality and stability of active space calculations, to monitor chemical reactions, and to identify points along the reaction coordinate where electronic wavefunctions change drastically. Thus, orbital entanglement represents a useful and intuitive tool to interpret complex electronic wavefunctions and to facilitate a qualitative understanding of electronic structure and how it changes in chemical processes.

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

“…In the case of spatial orbitals, we have four different one-particle states (either unoccupied, singly occupied with a spin-up or spin-down electron, or doubly occupied orbitals) and the one-orbital reduced density matrix is a 4 × 4 matrix. Its elements can be calculated from the one-and two-particle reduced density matrices [39] or from generalized correlation functions. [35,37] We refer the interested reader to refs 30, 37-39 for more details on how to calculate orbital-reduced density matrices.…”

“…Moreover, we will seek active orbital spaces that allow for an accurate description of static/nondynamic electron correlation effects in all investigated plutonium oxides. One possibility to define stable and reliable active spaces in correlation calculations was proposed by some of us [36,39] and recently applied to facilitate black-box DMRG calculations. [79] In contrast to ref.…”

“…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.…”

Density matrix renormalization group with efficient dynamical electron correlation through range separation

“…In addition, significant deviations (> ±0.02) of NOONs from the Hartree-Fock limit of 2 (occupied orbitals) and 0 (virtual orbitals) have been considered as multireference indicators. In the framework of DMRG, two other measures, namely the single-orbital entropy 12 and the mutual information 14,61 , have become popular 62 . These entropy measures are calculated from the oneorbital RDM -in the latter case, also from the twoorbital RDM -and can be exploited to examine the multireference character of a wave function and/or trace the amount of static and dynamic electron correlation in an electronic wave function 63 .…”

Doubly Excited Resonance States of Helium Atom: Complex Entropies

“…In particular, there has been a remarkable increase of interest in exploring properties of various quantum composite systems [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In recent years, both the entanglement and Shannon Entropy in helium and helium-like ions have also accelerated a great research attention [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33].…”