Orbital Entanglement in Bond-Formation Processes

Abstract

The accurate calculation of the (differential) correlation energy is central to the quantum chemical description of bond-formation and bond-dissociation processes. In order to estimate the quality of single- and multireference approaches for this purpose, various diagnostic tools have been developed. In this work, we elaborate on our previous observation [J. Phys. Chem. Lett.2012, 3, 3129] that one- and two-orbital-based entanglement measures provide quantitative means for the assessment and classification of electron correlation effects among molecular orbitals. The dissociation behavior of some prototypical diatomic molecules features all types of correlation effects relevant for chemical bonding. We demonstrate that our entanglement analysis is convenient to dissect these electron correlation effects and to provide a conceptual understanding of bond-forming and bond-breaking processes from the point of view of quantum information theory.

Benchmark of Dynamic Electron Correlation Models for Seniority-Zero Wave Functions and Their Application to Thermochemistry

“…Their electronic structures have been extensively discussed in the literature and we refer the interested reader to, for instances, refs. [73][74][75][76][77] for more details. Table II summarizes the spectroscopic constants for the C 2 , N 2 , and BN molecules.…”

Spectral properties of reduced fermionic density operators and parity superselection rule

“…Let us clarify the relation between the introduced definition of the mode-reduced states and the orbital reduced density matrices used in quantum chemistry [61,62]. In quantum chemistry, the mode is a composite of the space orbital state and the electron spin projection (| ↑ or | ↓ ), and the whole system state vector is written in the form |Ψ = n1,...,nL ψ n1,...,nL |n 1 ⊗ .…”

“…The reduced 2-mode state reads Tr e1,e2,e3 |Ψ Ψ| as each vector |e 1 ⊗ |n i ⊗ |e 2 ⊗ |n j ⊗ |e 3 does have a tensor product structure. Using the orbit basis |n i = {|0 , | ↑ , | ↓ , | ↑↓ }, one gets the 2-orbital reduced density operator [61]. In our approach, the global basis states |j 1 .…”

“…Similarly, the action of mode operators a t and a † t is nonlocal. Since transitions between the states with different numbers of particles are prohibited in quantum chemistry [61,62], both quantum-chemical and our definitions of reduced states do coincide for systems with a fixed number of electrons. The downside of the quantum-chemical definition may only appear for systems with variable number of particles, since the creation and annihilation operators cannot be represented in the tensor product form I⊗.…”

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.…”