arXiv subjects

Sara Giarrusso

Publications and source records attributed to Sara Giarrusso.

10 recordsLinked to original sources

arXiv2026

Exact factorization of a many-body wavefunction beyond the electron-nuclear problem

This Review is devoted to the presentation of the exact factorization as a framework employed to study a variety of quantum-mechanical many-body problems. Since its original formulation in the 70s, the main applications of the exact factorization were directed towards understanding the properties of multi-component systems, e.g. electron-nuclear systems. Especially in the electron-nuclear case, the exact factorization is viewed as an exactification of the Born-Oppenheimer approximation, thus it was, and still is, largely employed in nonadiabatic dynamics. Nonetheless, as early as the 80s, the formalism was employed to study many-electron interacting systems and, quite recently, i.e. less than a decade ago, it was extended to study the behavior of molecules in the context in cavity quantum electrodynamics. These formulations, perhaps less popular than the electron-nuclear formulation, have attracted a lot of attention over the years. Therefore, we review here the exact electron-only factorization and the exact photon-electron-nuclear factorization.

physics.chem-ph↗

arXiv2024

Excited-State-Specific Kohn-Sham Formalism for the Asymmetric Hubbard Dimer

Building on our recent study [https://doi.org/10.1021/acs.jpclett.3c02052, J. Phys. Chem. Lett. 14, 8780 (2023)], we explore the generalization of the ground-state Kohn-Sham (KS) formalism of density-functional theory (DFT) to the (singlet) excited states of the asymmetric Hubbard dimer at half-filling. While we found that the KS-DFT framework can be straightforwardly generalized to the highest-lying doubly-excited state, the treatment of the first excited state presents significant challenges. Specifically, using a density-fixed adiabatic connection, we show that the density of the first excited state lacks non-interacting $v$-representability. However, by employing an analytic continuation of the adiabatic path, we demonstrate that the density of the first excited state can be generated by a complex-valued external potential in the non-interacting case. More practically, by performing state-specific KS calculations with exact and approximate correlation functionals -- each state possessing a distinct correlation functional -- we observe that spurious stationary solutions of the KS equations may arise due to the approximate nature of the functional.

physics.chem-ph↗

arXiv2024

Modelling the Kohn-Sham potential for molecular dissociation with orbital-independent functionals: a proof of principle

We model the Hartree-exchange-correlation potential of Kohn-Sham density-functional theory adopting a novel strategy inspired by the strictly-correlated-electrons limit and relying on the exact decomposition of the potential based on the exact factorization formalism. Starting with accurate density and conditional potential for a one-dimensional model of a stretched heteronuclear molecule, we provide a proof-of-principle example of an approximation that accurately reproduces the step of the exact Kohn-Sham potential without resorting to the Kohn-Sham orbitals, virtual or occupied. We also test our strategy using the approximate conditional potentials corresponding to the strictly-correlated-electron and the exact-exchange functionals. The results are encouraging in that the initial approximations are modified in the qualitatively correct way: decreasing correlation in the former and increasing it in the latter.

physics.chem-ph↗

arXiv2023

Exact Excited-State Functionals of the Asymmetric Hubbard Dimer

The exact functionals associated with the (singlet) ground and the two singlet excited states of the asymmetric Hubbard dimer at half-filling are calculated using both Levy's constrained search and Lieb's convex formulation. While the ground-state functional is, as commonly known, a convex function with respect to the density (or, more precisely, the site occupation), the functional associated with the (highest) doubly-excited state is found to be concave. Also, because the density of the first-excited state is non-invertible, its ``functional'' is a partial, multi-valued function composed of one concave and one convex branch that correspond to two separate sets of values of the external potential. Remarkably, it is found that, although the one-to-one mapping between density and external potential may not apply (as in the case of the first excited state), each state-specific energy and corresponding universal functional are ``functions'' whose derivatives are each other's inverse, just as in the ground state formalism. These findings offer insight into the challenges of developing state-specific excited-state density functionals for general applications in electronic structure theory.

cond-mat.str-el↗

arXiv2023

Møller-Plesset and density-fixed adiabatic connections for a model diatomic system at different correlation regimes

In recent years, Adiabatic Connection Interpolations developed within Density Functional Theory (DFT) have been found to provide satisfactory performances in the calculation of interaction energies when used with Hartree-Fock (HF) ingredients. The physical and mathematical reasons for such unanticipated performance have been clarified, to some extent, by studying the strong-interaction limit of the Møller-Plesset (MP) adiabatic connection. In this work, we calculate both the MP and the DFT adiabatic connection (AC) integrand for the asymmetric Hubbard dimer, which allows for a systematic investigation at different correlation regimes by varying two simple parameters in the Hamiltonian: the external potential, $Δv$, and the interaction strength, $U$. Noticeably, we find that, while the DFT AC integrand appears to be convex in the full parameter space, the MP integrand may change curvature twice. Furthermore, we discuss different aspects of the second-order expansion of the correlation energy in each adiabatic connection and we demonstrate that the derivative of the $λ$-dependent density in the MP adiabatic connection at $λ=0$ (i.e., at the HF density) is zero. Concerning the strong-interaction limit of both adiabatic connections, we show that while, for a given density, the asymptotic value of the MP adiabatic connection, $W_\infty^\text{HF}$, is lower (or equal) than its DFT analogue, $W_\infty^\text{KS}$, this is not always the case for a given external potential.

physics.chem-ph↗

arXiv2022

Comparing correlation components and approximations in Hartree-Fock and Kohn-Sham theories via an analytical test case study

The asymmetric Hubbard dimer is a model that allows for explicit expressions of the Hartree-Fock (HF) and Kohn-Sham (KS) states as analytical functions of the external potential, $Δv$, and of the interaction strength, $U$. We use this unique circumstance to establish a rigorous comparison between the individual contributions to the correlation energies stemming from the two theories in the $\{U,Δv\}$ parameter space. Within this analysis of the Hubbard dimer, we observe a change in the sign of the HF kinetic correlation energy, compare the indirect repulsion energies, and derive an expression for the 'traditional' correlation energy, i.e. the one that corrects the HF estimate, in a pure site-occupation function theory spirit [Eq. (43)]. Next, we test the performances of the Liu-Burke and the Seidl-Perdew-Levy functionals, which model the correlation energy based on its weak- and strong-interaction limit expansions and can be used for both the traditional and the KS correlation energies. Our results show that, in the Hubbard dimer setting, they typically work better for the HF reference, despite having been originally devised for KS. These conclusions are somewhat in line with prior assessments of these functionals on various chemical data sets. However, the Hubbard dimer model allows us to show the extent of the error that may occur in using the strong-interaction ingredient for the KS reference in place of the one for the HF reference, as has been carried out in most of the prior assessments.

physics.chem-ph↗

arXiv2022

Secondary kinetic peak in the Kohn-Sham potential and its connection to the response step

We consider a prototypical 1D model Hamiltonian for a stretched heteronuclear molecule and construct individual components of the corresponding KS potential, namely: the kinetic, the N - 1, and the conditional potentials. These components show very special features, such as peaks and steps, in regions where the density is drastically low. Some of these features are quite well known, whereas others, such as a secondary peak in the kinetic potential or a second bump in the conditional potential, are less or not known at all. We discuss these features building on the analytical model treated in J. Chem. Theory Comput. 14, 4151 (2018). In particular, we provide an explanation for the underlying mechanism which determines the appearance of both peaks in the kinetic potential and elucidate why these peaks delineate the region over which the plateau structure, due to the N - 1 potential, stretches. We assess the validity of the Heitler-London Ansatz at large but finite internuclear distance, showing that, if optimal orbitals are used, this model is an excellent approximation to the exact wavefunction. Notably, we find that the second natural orbital presents an extra node very far out on the side of the more electronegative atom.

physics.chem-ph↗

arXiv2018

Strong-interaction limit of an adiabatic connection in Hartree-Fock theory

We show that the leading term in the strong-interaction limit of the adiabatic connection that has as weak-interaction expansion the Moeller-Plesset perturbation theory can be fully determined from a functional of the Hartree-Fock density. We analyze this functional and highlight similarities and differences with the strong-interaction limit of the density-fixed adiabatic connection case of Kohn-Sham density functional theory.

physics.chem-ph↗

arXiv2018

Sum-rules of the response potential in the strongly-interacting limit of DFT

The response part of the exchange-correlation potential of Kohn-Sham density functional theory plays a very important role, for example for the calculation of accurate band gaps and excitation energies. Here we analyze this part of the potential in the limit of infinite interaction in density functional theory, showing that in the one-dimensional case it satisfies a very simple sum rule.

physics.chem-ph↗

arXiv2018

Response potential in the strong-interaction limit of DFT: Analysis and comparison with the coupling-constant average

Using the formalism of the conditional amplitude, we study the response part of the exchange-correlation potential in the strong-coupling limit of density functional theory, analysing its peculiar features and comparing it with the response potential averaged over the coupling constant for small atoms and for the hydrogen molecule. We also use a simple one-dimensional model of a stretched heteronuclear molecule to derive exact properties of the response potential in the strong-coupling limit. The simplicity of the model allows us to unveil relevant features also of the exact Kohn-Sham potential and its different components, namely the appearance of a second peak in the correlation kinetic potential on the side of the most electronegative atom.

physics.chem-ph↗