Quantifying Delocalization and Static Correlation Errors by Imposing (Spin)Population Redistributions through Constraints on Atomic Domains

J. Chem. Theory Comput.

et al. 2023

Self Cite

As a matrix extension of the Fukui function, a reactivity descriptor grounded within Conceptual Density Functional Theory, the Fukui matrix extends Frontier Molecular Orbital Theory to correlated regimes with its eigendecomposition in Fukui occupations and Fukui naturals. Despite successful applications, the questions remain as to whether replacing a quantity derived from a purely density-based framework by its matrix extension is theoretically well-founded and what chemical information is contained in the corresponding eigendecomposition. In this study, we show that the matrix extension of the Fukui function is only well-defined if one also generalizes the external potential to become nonlocal, leading to the introduction of Conceptual First-Order Reduced Density Matrix Functional Theory. By interpreting the Anderson impurity model from an interacting open subsystem perspective, we show how Fukui occupations and Fukui naturals reflect the influence of an increasing (static) correlation and which characteristic patterns we should expect within a molecular context. This study represents a step in generalizing Conceptual Density Functional Theory beyond its density-based perspective.

Section: Methodsmentioning

confidence: 99%

Extending Conceptual Density Functional Theory toward First-Order Reduced Density Matrices: An Open Subsystems Viewpoint on the Fukui Matrix

Acke

Hende

J. Chem. Theory Comput.

et al. 2023

Self Cite

“…The uniform magnetic field lies along the − z direction. These hydrogen models have been used extensively to benchmark electronic structure methods and provide insightful testbeds for studying strong static correlation. ,− …”

Section: Methodsmentioning

confidence: 99%

Section: ■ Theorymentioning

confidence: 99%

“…In order to constrain a particular wave function to a target value S z ,target for the spin expectation value ⟨ Ŝ z ⟩ along the axis of the applied magnetic field, we can use the formalism of constraints. − , In this framework, the Lagrangian is optimized, and the optimality condition for the wave function parameters p (which are the spinor rotation generators κ in the case of GHF and the ONV expansion coefficients c in the case of FCI) causes the usual molecular magnetic Hamiltonian (cf. eq ) to be replaced by the modified Hamiltonian where the term −μ Ŝ z represents an additional one-electron potential .…”

Section: Theorymentioning

confidence: 99%

“…This allows us to determine the energetic costs of only partially allowing for certain spin flips and why certain spin sectors are disfavored energetically. In order to do so, we extend the theory of Li and co-workers with a constrained formalism − that allows us to target states with a particular ⟨ Ŝ z ⟩. The resulting formalism allows us to characterize the electronic structure underlying the spin behavior in magnetic fields in terms of the constrained GHF (CGHF) states and spin phase diagrams that arise from the associated Lagrange multipliers.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analyzing the Behavior of Spin Phases in External Magnetic Fields by Means of Spin-Constrained States

Lemmens

J. Chem. Theory Comput.

Bultinck

et al. 2022

Self Cite

During molecular dissociation in the presence of an external uniform magnetic field, electrons flip their spin antiparallel to the magnetic field because of the stabilizing influence of the spin Zeeman operator. Although generalized Hartree−Fock descriptions furnish the optimal mean-field energetic description of such bond-breaking processes, they are allowed to break S ̂z symmetry, leading to intricate and unexpected spin phases and phase transitions. In this work, we show that the behavior of these molecular spin phases can be interpreted in terms of spin phase diagrams constructed by constraining states to target expectation values of projected spin. The underlying constrained states offer a complete electronic characterization of the spin phases and spin phase transitions, as they can be analyzed using standard quantum chemical tools. Because the constrained states effectively span the entire phase space, they could provide an excellent starting point for post-Hartree−Fock methods aimed at gaining more electron correlation or regaining spin symmetry.

Uncovering phase transitions that underpin the flat-planes in the tilted Hubbard model using subsystems and entanglement measures

The Journal of Chemical Physics

Hende

Baerdemacker

et al. 2022

Self Cite

The failure of many approximate electronic structure methods can be traced to their erroneous description of fractional charge and spin redistributions in the asymptotic limit towards infinity, where violations of the flat-plane conditions lead to delocalization and static correlation errors. Although the energetic consequences of the flat-planes are known, the underlying quantum phase transitions that occur when (spin)charge is redistributed have not been characterized. In this study, we use open subsystems to redistribute (spin)charges in the tilted Hubbard model by imposing suitable Lagrange constraints on the Hamiltonian. We computationally recover the flat-plane conditions and quantify the underlying quantum phase transitions using quantum entanglement measures. The resulting entanglement patterns quantify the phase transition that give rise to the flat-plane conditions and quantify the complexity required to accurately describe charge redistributions in strongly correlated systems. Our study indicates that entanglement patterns can uncover those phase transitions that have to be modelled accurately if the delocalization and static correlation errors of approximate methods are to be reduced.