High-order entropy measures and spin-free quantum entanglement for molecular problems

On the notion of strong correlation in electronic structure theory

Strong correlation has been said to have many faces, and appears to have many synonyms of questionable suitability. In this work we aim not to define the term once and for all, but to highlight one possibility that is both rigorously defined and physically transparent, and remains so in reference to molecules and quantum lattice models. We survey both molecular examples - hydrogen systems (Hn, n = 2, 4, 6), Be2, H-He-H, and benzene - and the half-filled Hubbard model over a range of correlation regimes. Various quantities are examined including the extent of spin symmetry breaking in correlated single-reference wave functions, energetic ratios inspired by the Hubbard model and the Virial theorem, and metrics derived from the one- and two-electron reduced density matrices (RDMs). The trace and the square norm of the cumulant of the two-electron reduced density matrix capture what may well be defined as strong correlation. Accordingly, strong correlation is understood as a statistical dependence between two electrons, and is distinct from the concepts of "correlation energy" and more general than entanglement quantities that require a partitioning of a quantum system into distinguishable subspaces. This work enables us to build a bridge between a rigorous and quantifiable regime of strong electron correlation and more familiar chemical concepts such as anti-aromaticity in the context of Baird's rule.

Atomic Group Decomposition of Charge Transfer Excitation Global Indexes

A model for decomposing the Le Bahers, Adamo, and Ciofini Charge Transfer (CT) Excitations global indexes ( J. Chem. Theory Comput. 2011, 7, 2498-2506) into molecular subdomains contributions is presented and a software, DOCTRINE (atomic group Decomposition Of the Charge TRansfer INdExes) for the implementation of this novel model has been coded. Although our method applies to any fuzzy or to any disjoint exhaustive partitioning of the real space, it is here applied using a definition of chemically relevant molecular subdomains based on the Atoms in Molecules Bader basins. This choice has the relevant advantage of associating intra or inter subdomain contributions to rigorously defined quantum objects, yet bearing a clear chemical meaning. Our method allows for a quantitative evaluation of the subdomain contributions to the charge transfer, the charge transfer excitation length and the dipole moment change upon excitation. All these global indexes may be obtained either from the electron density increment or the electron density depletion upon excitation. However, the subdomain contributions obtained from the two distributions generally differ, therefore allowing to distinguish whether the contribution to a given property of a given subdomain is dominated by one of the two distributions or if both are playing a significant role. As a toy system for the first application of our model, a typical [D-π-A, π = conjugated bridge] compound belonging to the merocyanine dyes family is selected, and the first four excited states of this compound in a strongly polar protic solvent and in a weakly polar solvent are thoroughly investigated.

Challenges for variational reduced-density-matrix theory with three-particle N-representability conditions

The direct variational optimization of the two-electron reduced density matrix (2RDM) can provide a reference-independent description of the electronic structure of many-electron systems that naturally capture strong or nondynamic correlation effects. Such variational 2RDM approaches can often provide a highly accurate description of strong electron correlation, provided that the 2RDMs satisfy at least partial three-particle N-representability conditions (e.g., the T2 condition). However, recent benchmark calculations on hydrogen clusters [N. H. Stair and F. A. Evangelista, J. Chem. Phys. 153, 104108 (2020)] suggest that even the T2 condition leads to unacceptably inaccurate results in the case of two- and three-dimensional clusters. We demonstrate that these failures persist under the application of full three-particle N-representability conditions (3POS). A variety of correlation metrics are explored in order to identify regimes under which 3POS calculations become unreliable, and we find that the relative squared magnitudes of the cumulant three- and two-particle reduced density matrices correlate reasonably well with the energy error in these systems. However, calculations on other molecular systems reveal that this metric is not a universal indicator for the reliability of the reduced-density-matrix theory with 3POS conditions.

Real Space-Real Time Evolution of Excitonic States Based on the Bethe-Salpeter Equation Method

We introduce a method for constructing localized excitations and simulating the real time dynamics of excitons at the Many-Body Perturbation Theory Bethe-Salpeter Equation level. We track, on the femto-seconds scale, electron injection from a photoexcited dye into a semiconducting slab. From the time-dependent many-body wave function we compute the spatial evolution of the electron and of the hole; full electron injection is attained within 5 fs. Time-resolved analysis of the electron density and electron-hole interaction energy hints at a two-step charge transfer mechanism through an intermediary partially injected state. We adopt the Von-Neumann entropy for analyzing how the electron and hole entangle. We find that the excitation of the dye-semiconductor model may be represented by a four-level system and register a decrease in entanglement upon electron injection. At full injection, the electron and the hole exhibit only a small degree of entanglement indicative of pure electron and hole states.

Correlation-driven phenomena in periodic molecular systems from variational two-electron reduced density matrix theory

Correlation-driven phenomena in molecular periodic systems are challenging to predict computationally not only because such systems are periodically infinite but also because they are typically strongly correlated. Here, we generalize the variational two-electron reduced density matrix (2-RDM) theory to compute the energies and properties of strongly correlated periodic systems. The 2-RDM of the unit cell is directly computed subject to necessary N-representability conditions such that the unit-cell 2-RDM represents at least one N-electron density matrix. Two canonical but non-trivial systems, periodic metallic hydrogen chains and periodic acenes, are treated to demonstrate the methodology. We show that while single-reference correlation theories do not capture the strong (static) correlation effects in either of these molecular systems, the periodic variational 2-RDM theory predicts the Mott metal-to-insulator transition in the hydrogen chains and the length-dependent polyradical formation in acenes. For both hydrogen chains and acenes, the periodic calculations are compared with previous non-periodic calculations with the results showing a significant change in energies and increase in the electron correlation from the periodic boundary conditions. The 2-RDM theory, which allows for much larger active spaces than are traditionally possible, is applicable to studying correlation-driven phenomena in general periodic molecular solids and materials.

TheoDORE: A toolbox for a detailed and automated analysis of electronic excited state computations

The advent of ever more powerful excited-state electronic structure methods has led to a tremendous increase in the predictive power of computation, but it has also rendered the analysis of these computations much more challenging and time-consuming. TheoDORE tackles this problem through providing tools for post-processing excited-state computations, which automate repetitive tasks and provide rigorous and reproducible descriptors. Interfaces are available for ten different quantum chemistry codes and a range of excited-state methods implemented therein. This article provides an overview of three popular functionalities within TheoDORE, a fragment-based analysis for assigning state character, the computation of exciton sizes for measuring charge transfer, and the natural transition orbitals used not only for visualization but also for quantifying multiconfigurational character. Using the examples of an organic push-pull chromophore and a transition metal complex, it is shown how these tools can be used for a rigorous and automated assignment of excited-state character. In the case of a conjugated polymer, we venture beyond the limits of the traditional molecular orbital picture to uncover spatial correlation effects using electron-hole correlation plots and conditional densities.

Toward an understanding of electronic excitation energies beyond the molecular orbital picture

Can we gain an intuitive understanding of excitation energies beyond the molecular picture?

Entanglement Measures for Single- and Multireference Correlation Effects

Electron correlation effects are essential for an accurate ab initio description of molecules. A quantitative a priori knowledge of the single- or multireference nature of electronic structures as well as of the dominant contributions to the correlation energy can facilitate the decision regarding the optimum quantum chemical method of choice. We propose concepts from quantum information theory as orbital entanglement measures that allow us to evaluate the single- and multireference character of any molecular structure in a given orbital basis set. By studying these measures we can detect possible artifacts of small active spaces.

Statistical measure of complexity and correlated behavior of Fermi systems

We apply the statistical measure of complexity, introduced by López-Ruiz, Mancini, and Calbet (LMC), to uniform Fermi systems. We investigate the connection between information and complexity measures with the strongly correlated behavior of various Fermi systems as nuclear matter, electron gas, and liquid helium. We examine the possibility that LMC complexity can serve as an index quantifying correlations in the specific system and to which extent could be related with experimental quantities. Moreover, we concentrate on thermal effects on the complexity of ideal Fermi systems. We find that complexity behaves, both at low and high values of temperature, in a similar way as the specific heat.