arXiv subjects

Emmanuel Fromager

Publications and source records attributed to Emmanuel Fromager.

At least 19 recordsLinked to original sources

arXiv2026

Ensemble density functional theory of excited states: Exact N-centered formalism and practical opportunities

Ground-state electronic structure calculations using Kohn-Sham density functional theory (KS-DFT) offer an unprecedented balance between efficiency and accuracy, now paradigmatic to the fields of quantum chemistry and condensed matter physics. KS-DFT can be extended to model electronic excitations through a density mapping onto a non-interacting ensemble state in which, unlike in thermal theories, the weights assigned to the excited states vary independently. Thanks to its numerous appeals, like the adequate treatment of multiple excitations for which the widely-used time-dependent extension of DFT struggles, ensemble DFT (eDFT) has lately become a vibrant area of research. Recently, an enlarged type of ensemble, referred to as N-centered (Nc) ensemble, has been introduced to describe within the same unified formalism both neutral and charged electronic excitations. This perspective paper provides a detailed exposition of exact Nc-eDFT, with a comprehensive review of its formal developments. To cut practical computational tools out of the exact theory, three original strategies are presented, complementing existing approaches. The first one, related to the design of ensemble density-functional approximations, consists in recycling regular ground-state functionals by dressing them with a weight-dependent scaling function deduced from exact properties of eDFT. We then explore quasi-degenerate formulations of ensemble density-functional perturbation theory, suggesting alternative definitions for the ensemble Hartree, exchange, and correlation energies, individually, and paving the way toward robust orbital-dependent eDFAs. Finally, we revisit and generalize the concept of quantum bath for an ensemble of non-interacting states, laying the foundations of an in-principle exact (in the sense of lattice eDFT) quantum embedding theory of excited states.

physics.chem-ph↗

arXiv2026

Generalized local potential functional embedding theory of localized orbitals

In this work we introduce a generalized flavor, in the sense of generalized Kohn-Sham density functional theory (gKS-DFT), of the recently derived local potential functional embedding theory (LPFET) [J. Chem. Theory Comput. 2025, 21, 20, 10293], where the in-principle exact formalism of DFT is combined with that of density matrix embedding theory (DMET). In generalized LPFET (gLPFET), the embedding clusters are designed from a full-size gKS system where the (in-principle non-local) Hartree-Fock exchange potential is combined with a local (in the localized orbital representation) correlation potential. The latter is optimized self-consistently such that gKS and local embedding cluster's densities match. Unlike in DMET, which uses the same (global) chemical potential value in all clusters, each embedded orbital has its own chemical potential in gLPFET. We show analytically that, when electron correlation is strongly local, the latter potential becomes a simple functional of the correlation potential. Numerical calculations on model systems confirm the high accuracy of gLPFET in this regime, in contrast to DMET. Moreover, we show that gLPFET completely fixes the flaw of LPFET in weaker correlation regimes, through its appropriate description of the Hartree-exchange potential.

cond-mat.str-el↗

arXiv2026

Exactly factorized molecular Kohn-Sham density functional theory

Fromager and Lasorne [Electron. Struct. 6 025002 (2024)] have recently derived an in-principle exact Kohn-Sham density functional theory (KS-DFT) of electrons and nuclei, where the nuclear density and the (so-called conditional) electronic density are mapped onto a fictitious electronically non-interacting KS molecule. In this work, we apply the exact factorization formalism to the molecular KS wavefunction, thus leading to disentangled (but coupled) marginal and conditional KS equations. We show that, while being equivalent to the original theory, these equations open new perspectives in the practical extension of regular (electronic) KS-DFT beyond the Born-Oppenheimer approximation. The importance and treatment of correlations induced in this context by second-order geometrical derivatives is also discussed.

physics.chem-ph↗

arXiv2026

Charged excitations made neutral: N-centered ensemble density functional theory of Fukui functions

An in-principle exact working equation to compute electronic affinity and ionization Fukui functions is derived within the $N$-centered (Nc) ensemble extension of density functional theory (DFT). It circumvents the kernel derivative discontinuity problem of DFT for fractional electron numbers, whose contribution is recovered through weight derivatives of the ensemble density functional potential. Thus, it allows for the design of alternative and effective approximations, such as the weight-dependent scaling of regular functionals or the interpolation between known limits of Nc ensembles

physics.chem-ph↗

arXiv2025

Exact static linear response of excited states from ensemble density functional theory

Following a recent work [E. Fromager, J. Phys. Chem. A 2025, 129, 4, 1143-1155] on the ensemble density functional theory (DFT) of excited electronic energy levels, we derive in this paper the ensuing static linear response theory, thus allowing for an in-principle exact evaluation of excited-state density-density linear response functions in a completely frequency-independent setting. Once individual-state components of the inverse ensemble linear response function have been introduced, a working Dyson-type equation naturally emerges for each state, individually. By considering the zero-weight limit of the theory, which infinitesimally deviates from standard Kohn--Sham DFT, exact excited-state corrections to ground-state linear response DFT can be identified. They involve the first-order weight derivatives of the ensemble Hartree-exchange-correlation (Hxc) potential and kernel, thus confirming the importance in ensemble DFT of both weight and density-functional derivatives of the ensemble Hxc energy functional.

physics.chem-ph↗

arXiv2024

Ensemble density functional theory of ground and excited energy levels

A Kohn-Sham density-functional energy expression is derived for any (ground or excited) state within a given many-electron ensemble along with the stationarity condition it fulfills with respect to the ensemble density, thus giving access to both physical energy levels and individual-state densities, in principle exactly. We also provide working equations for the evaluation of the latter from the true static ensemble density-density linear response function. Unlike in Gould's recent ensemble potential functional approach to excited states [arXiv:2404.12593], we use the ensemble density as sole basic variable. While a state-specific KS potential naturally emerges from the present formalism, at the exact ensemble Hartree-exchange-only (Hx) level of approximation, the standard implementation of orbital-optimized DFT for excited states is recovered when recycling the regular ground-state Hx-correlation functional in this context.

physics.chem-ph↗

arXiv2024

Fragment quantum embedding using the Householder transformation: a multi-state extension based on ensembles

In recent works by Yalouz et al. (J. Chem. Phys. 157, 214112, 2022) and Sekaran et al. (Phys. Rev. B 104, 035121, 2021; Computation 10, 45, 2022), Density Matrix Embedding Theory (DMET) has been reformulated through the use of the Householder transformation as a novel tool to embed a fragment within extended systems. The transformation was applied to a reference non-interacting one-electron reduced density matrix to construct fragments' bath orbitals, which are crucial for subsequent ground state calculations. In the present work, we expand upon these previous developments and extend the utilization of the Householder transformation to the description of multiple electronic states, including ground and excited states. Based on an ensemble noninteracting density matrix, we demonstrate the feasibility of achieving exact fragment embedding through successive Householder transformations, resulting in a larger set of bath orbitals. We analytically prove that the number of additional bath orbitals scales directly with the number of fractionally occupied natural orbitals in the reference ensemble density matrix. A connection with the regular DMET bath construction is also made. Then, we illustrate the use of this ensemble embedding tool in single-shot DMET calculations to describe both ground and first excited states in a Hubbard lattice model and an ab initio hydrogen system. Lastly, we discuss avenues for enhancing ensemble embedding through self-consistency and explore potential future directions.

physics.chem-ph↗

arXiv2024

Extended $N$-centered ensemble density functional theory of double electronic excitations

A recent work [arXiv:2401.04685] has merged $N$-centered ensembles of neutral and charged electronic ground states with ensembles of neutral ground and excited states, thus providing a general and in-principle exact (so-called extended $N$-centered) ensemble density functional theory of neutral and charged electronic excitations. This formalism made it possible to revisit the concept of density-functional derivative discontinuity, in the particular case of single excitations from the highest occupied Kohn-Sham (KS) molecular orbital, without invoking the usual "asymptotic behavior of the density" argument. In this work, we address a broader class of excitations, with a particular focus on double excitations. An exact implementation of the theory is presented for the two-electron Hubbard dimer model. A thorough comparison of the true physical ground- and excited-state electronic structures with that of the fictitious ensemble density-functional KS system is also presented. Depending on the choice of the density-functional ensemble as well as the asymmetry of the dimer and the correlation strength, an inversion of states can be observed. In some other cases, the strong mixture of KS states within the true physical system makes the assignment "single excitation" or "double excitation" irrelevant.

cond-mat.str-el↗

arXiv2024

Neutral electronic excitations and derivative discontinuities: An extended $N$-centered ensemble density functional theory perspective

This work merges two different types of many-electron ensembles, namely the Theophilou-Gross-Oliveira-Kohn ensembles of ground and neutrally-excited states, and the more recent $N$-centered ensembles of neutral and charged ground states. On that basis, an in-principle exact and general, so-called extended $N$-centered, ensemble density-functional theory of charged and neutral electronic excitations is derived. We revisit in this context the concept of density-functional derivative discontinuity for neutral excitations, without ever invoking nor using the asymptotic behavior of the ensemble electronic density. The present mathematical construction fully relies on the weight dependence of the ensemble Hartree-exchange-correlation density-functional energy, which makes the theory applicable to lattice models and opens new perspectives for the description of gaps in mesoscopic systems.

physics.chem-ph↗

arXiv2023

Density functional theory beyond the Born-Oppenheimer approximation: Exact mapping onto an electronically non-interacting Kohn-Sham molecule

This work presents an alternative, general, and in-principle exact extension of electronic Kohn-Sham density functional theory (KS-DFT) to the fully quantum-mechanical molecular problem. Unlike in existing multi-component or exact-factorization-based DFTs of electrons and nuclei, both nuclear and electronic densities are mapped onto a fictitious electronically non-interacting molecule (referred to as KS molecule), where the electrons still interact with the nuclei. Moreover, in the present molecular KS-DFT, no assumption is made about the mathematical form (exactly factorized or not) of the molecular wavefunction. By expanding the KS molecular wavefunction \`a la Born-Huang, we obtain a self-consistent set of "KS beyond Born-Oppenheimer" electronic equations coupled to nuclear equations that describe nuclei interacting among themselves and with non-interacting electrons. An exact adiabatic connection formula is derived for the Hartree-exchange-correlation energy of the electrons within the molecule and, on that basis, a practical adiabatic density-functional approximation is proposed and discussed.

physics.chem-ph↗

arXiv2023

Unitary transformations within density matrix embedding approaches: A novel perspective on the self-consistent scheme for electronic structure calculation

In this work, we introduce an original self-consistent scheme based on the one-body reduced density matrix ($\gamma$) formalism. A significant feature of this methodology is the utilization of an optimal unitary transformation of the Hamiltonian, determined through a self-consistently determined, unitary reflection $\mathbf{R}[\gamma]$. This enables the extraction of all reduced properties of the system from a smaller, accurately solved embedding cluster, and to systematically reconstruct the reduced density matrix of the system. This process ensures that both extended and embedded systems satisfy the local virial-like relation, providing quantitative insight into the correspondence between the fragment in the extended system and its embedded analogue. The performance and convergence of the method, as well as the N-representability of the resulting correlated density matrix, are evaluated and discussed within the context of the one-dimensional Hubbard model, which provides exact results for a comprehensive comparison.

cond-mat.str-el↗

arXiv2023

A unified density-matrix functional construction of quantum baths in density matrix embedding theory beyond the mean-field approximation

The equivalence in one-electron quantum bath between the practical implementation of density matrix embedding theory (DMET) and the more recent Householder-transformed density matrix functional embedding theory has been shown previously in the standard but special case where the reference full-size (one-electron reduced) density matrix, from which the bath is constructed, is idempotent [J. Chem. Phys. 157, 214112 (2022)]. We prove mathematically that the equivalence remains valid when the density matrix is not idempotent anymore, thus allowing for the construction of correlated (one-electron) quantum baths. A density-matrix functional exactification of DMET is derived within the present unified quantum embedding formalism. Numerical examples reveal that the embedding cluster can be quite sensitive to the level of density-matrix functional approximation used for computing the reference density matrix.

physics.chem-ph↗

arXiv2022

Quantum embedding of multi-orbital fragments using the Block-Householder-transformation

Recently, some of the authors introduced the use of the Householder transformation as a simple and intuitive method for the embedding of local molecular fragments (see Sekaran et. al., Phys. Rev. B 104, 035121 (2021), and Sekaran et. al., Computation 10, 45 (2022)). In this work, we present an extension of this approach to the more general case of multi-orbital fragments using the block version of the Householder transformation applied to the one-body reduced density matrix, yet unlocking the applicability to general quantum chemistry/condensed-matter physics Hamiltonians. A step by step construction of the Block-Householder transformation is presented. Both physical and numerical interest of the approach are highlighted. The specific mean-field (non-interacting) case is thoroughly detailed as it is shown that the embedding of a given $N$ spin-orbitals fragment leads to the generation of two separated sub-systems: a $2N$ spin-orbitals "fragment+bath" cluster that exactly contains $N$ electrons, and a remaining cluster's "environment" which is described by so-called core electrons. We illustrate the use of this transformation in different cases of embedding {scheme} for practical applications. We particularly focus on the extension of the previously introduced Local Potential Functional Embedding Theory (LPFET) and Householder-transformed Density Matrix Functional Embedding Theory (Ht-DMFET) to the case of multi-orbital fragments. These calculations are realized on different types of systems such as model Hamiltonians (Hubbard rings) and \textit{ab initio} molecular systems (hydrogen rings).

quant-ph↗

arXiv2022

Reduced density matrix functional theory from an ab initio seniority-zero wave function: Exact and approximate formulations along adiabatic connection paths

Currently, there is a growing interest in the development of a new hierarchy of methods based on the concept of seniority, which has been introduced quite recently in quantum chemistry. Despite the enormous potential of these methods, the accurate description of both dynamical and static correlation effects within a single and in-principle-exact approach remains a challenge. In this work, we propose an alternative formulation of reduced density-matrix functional theory (RDMFT) where the (one-electron reduced) density matrix is mapped onto an ab initio seniority-zero wave function. In this theory, the exact natural orbitals and their occupancies are determined self-consistently from an effective seniority-zero calculation. The latter involves a universal higher-seniority density matrix functional for which an adiabatic connection (AC) formula is derived and implemented under specific constraints that are related to the density matrix. The pronounced curvature of the (constrained) AC integrand, which is numerically observed in prototypical hydrogen chains and the Helium dimer, indicates that a description of higher-seniority correlations within second-order perturbation theory is inadequate in this context. Applying multiple linear interpolations along the AC or connecting second-order perturbation theory to a full-seniority treatment via Pad\'{e} approximants are better strategies. Such information is expected to serve as a guide in the future design of higher-seniority density-matrix functional approximations.

physics.chem-ph↗

arXiv2022

Local Potential Functional Embedding Theory: A Self-Consistent Flavor of Density Functional Theory for Lattices without Density Functionals

The recently proposed Householder transformed density-matrix functional embedding theory (Ht-DMFET) [Sekaran et al., Phys. Rev. B 104, 035121 (2021)], which is equivalent to (but formally simpler than) density matrix embedding theory (DMET) in the non-interacting case, is revisited from the perspective of density-functional theory (DFT). An in-principle-exact density-functional version of Ht-DMFET is derived for the one-dimensional Hubbard lattice with a single embedded impurity. On the basis of well-identified density-functional approximations, a local potential functional embedding theory (LPFET) is formulated and implemented. Even though LPFET performs better than Ht-DMFET in the low-density regime, in particular when electron correlation is strong, both methods are unable to describe the density-driven Mott-Hubbard transition, as expected. These results combined with our formally exact density-functional embedding theory reveal that a single statically embedded impurity can in principle describe the gap opening, provided that the complementary correlation potential (that describes the interaction of the embedding cluster with its environment, which is simply neglected in both Ht-DMFET and LPFET) exhibits a derivative discontinuity (DD) at half filling. The extension of LPFET to multiple impurities (which would enable to circumvent the modeling of DDs) and its generalization to quantum chemical Hamiltonians are left for future work.

cond-mat.str-el↗

arXiv2021

Ensemble Density Functional Theory of Neutral and Charged Excitations

Recent progress in the field of (time-independent) ensemble density-functional theory (DFT) for excited states are reviewed. Both Gross-Oliveira-Kohn (GOK) and $N$-centered ensemble formalisms, which are mathematically very similar and allow for an in-principle-exact description of neutral and charged electronic excitations, respectively, are discussed. Key exact results like, for example, the equivalence between the infamous derivative discontinuity problem and the description of weight dependencies in the ensemble exchange-correlation density functional, are highlighted. The variational evaluation of orbital-dependent ensemble Hartree-exchange (Hx) energies is discussed in detail. We show in passing that state-averaging individual exact Hx energies can lead to severe (solvable though) $v$-representability issues. Finally, we explore the possibility to use the concept of density-driven correlation, which has been recently introduced and does not exist in regular ground-state DFT, for improving state-of-the-art correlation density-functional approximations for ensembles. The present review reflects the efforts of a growing community to turn ensemble DFT into a rigorous and reliable low-cost computational method for excited states. We hope that, in the near future, this contribution will stimulate new formal and practical developments in the field.

physics.chem-ph↗

arXiv2021

Householder transformed density matrix functional embedding theory

Quantum embedding based on the (one-electron reduced) density matrix is revisited by means of the unitary Householder transformation. While being exact and equivalent to (but formally simpler than) density matrix embedding theory (DMET) in the non-interacting case, the resulting Householder transformed density matrix functional embedding theory (Ht-DMFET) preserves, by construction, the single-particle character of the bath when electron correlation is introduced. In Ht-DMFET, the projected "impurity+bath" cluster's Hamiltonian (from which approximate local properties of the interacting lattice can be extracted) becomes an explicit functional of the density matrix. In the spirit of single-impurity DMET, we consider in this work a closed (two-electron) cluster constructed from the full-size non-interacting density matrix. When the (Householder transformed) interaction on the bath site is taken into account, per-site energies obtained for the half-filled one-dimensional Hubbard lattice match almost perfectly the exact Bethe Ansatz results in all correlation regimes. In the strongly correlated regime, the results deteriorate away from half-filling. This can be related to the electron number fluctuations in the (two-site) cluster which are not described neither in Ht-DMFET nor in regular DMET. As expected, the per-site energies dramatically improve when increasing the number of embedded impurities. Formal connections with density/density matrix functional theories have been briefly discussed and should be explored further. Work is currently in progress in this direction.

cond-mat.str-el↗

arXiv2020

Exact exchange-correlation potentials for calculating the fundamental gap with a fixed number of electrons

Capturing the discontinuous shift by $\Delta$ in the exact exchange-correlation (xc) potential is the standard proposal for calculating the fundamental gap, $E_\mathrm{g}$, from the Kohn-Sham (KS) gap, $\varepsilon_\mathrm{g}$, within KS density functional theory (DFT), as $E_\mathrm{g} = \varepsilon_\mathrm{g} + \Delta$, yet this discontinuity is absent from existing approximations. The '$N$-centered' formulation of ensemble DFT artificially maintains a total electron number, $N$, in order to yield $E_\mathrm{g}$ not through a discontinuous shift in the xc potential but via the ensemble-weight derivative of the xc energy. Within the $N$-centered approach we calculate exact xc potentials for a one-dimensional finite system and show analytically that $\Delta$ can in fact be interpreted as a discontinuous shift in the exact $N$-centered ensemble xc potential, thereby extending to charged excitations an exact property of uncharged excitations. We show that applying the Levy-Zahariev 'shift-in-potential' procedure in this context relocates the discontinuous shift to the unimportant periphery of the system, so that the exact xc potential in effect is free of discontinuities and thus the inability of a local functional to capture discontinuous behavior is inconsequential.

cond-mat.mtrl-sci↗