arXiv subjects

Jérémy Morere

Publications and source records attributed to Jérémy Morere.

6 recordsLinked to original sources

arXiv2026

Is the TDDFRT representation of a molecular electronic transition unique?

In this article a piece of the reference time-dependent density-functional response theory (TDDFRT) representation of molecular electronic transitions is studied through the one-body reduced difference density matrix. A first derivation route for that object has been reported in the literature based on the substitution of TDDFRT-related objects into an exact functional expression. We show in the text that the functional providing the exact object is not unique, and we question whether substituting the same TDDFRT-related objects into the alternative functional expressions leads to acceptable candidates for the approximate TDDFRT one-body reduced difference density matrix, which would question the unequivocality of the TDDFRT representation of molecular electronic transitions. We first directly address the problem using a novel diagrammatic language, inspired by Dyck languages, and specifically designed for dealing with this kind of issue. In the last part of the article we question whether it is possible or not to recast the problem in a more general framework - the equations-of-motion framework. Through all the text, the case of time-dependent Hartree-Fock is compared with that of TDDFRT to highlight what makes them so different when those questions are at stake.

physics.chem-ph↗

arXiv2026

Dyck language and fermionic second quantization: I. Theory

This paper proposes a novel framework connecting fermionic second quantization and Dyck languages. By defining translations of creation and annihilation operators using bracket alphabets, the study establishes nullity criteria for expectation values of chains of second quantization operators. Those translations are designed to reveal sufficient conditions for the nullity of the expectation values relatively to one-determinant states or to the physical vacuum. The nullity criteria are purely syntactic, and simply reduce to the inspection of sequences of opening and closing brackets. Moreover, numbers and transformations in Dyck languages can be imported in the context of fermionic second quantization. One of these numbers, the depth, originally absent from second quantization, can be used to introduce more nullity criteria.

physics.chem-ph↗

arXiv2026

Dyck language and fermionic second quantization: II. Applications

In this work, we establish a direct connection between supplemented Dyck language and the signed expectation value of chains of second quantization operators relatively to the physical vacuum and relatively to a one-determinant state. Inspired by the fact that Dyck language provides an example of the emergence of the Catalan numbers in linguistic framework analysis, we show that these numbers are central when numbering the terms remaining when eliminating vanishing contributions detected by our application of Dyck language to fermionic second quantization. From the translation of creation and annihilation operator - or of pairs of operators - into a bracket alphabet, we derive simple and intuitive sufficient conditions for the nullity of expectation values that does not require an explicit application of Wick's theorem. This is done here with respect to the physical vacuum or relatively to a one-determinant state. We also extend this translation into a diagrammatic framework that allows a visual determination of the signature of fully contracted terms, reproducing the results of Wick's theorem. This approach has been extended to the case of (nested) commutators of pairs of fermionic second quantization including at least one excitation or deexcitation operator. Our results have been implemented in a software, MobiDyck, whose source code is freely available on the web. The algorithmic approach inspired by our work on Dyck language is detailed in this paper. Finally, a comparison of our diagrammatic approach with Goldstone diagrams is provided and closes the article.

physics.chem-ph↗

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

Boundary values for the charge transferred during an electronic transition: insights from matrix analysis

In this contribution we start by proving and generalizing a conjecture that has been established few decades ago, relating the value of the integral of the detachment/attachment density in two pictures - one accounting for transition-induced basis relaxation and one which does not account for such a relaxation. To this end, we show that it is possible to follow two ways: one combines Haynsworth and Courant-Fischer theorems with a corollary to Lidskii-Wielandt theorem, the other combines two twin theorems extending Cauchy's interlacing theorem, together with the abovementioned corollary to Lidskii-Wielandt theorem. These derivations allow us to provide an upper bound for the electronic charge that is effectively displaced during the molecular electronic transition from one electronic quantum state to another. This quantity can be regarded as the neat charge that has been transferred during the transition. Our derivations ultimately show that this boundary value can be determined from a simple singular value decomposition and at most two matrix trace-computing operations.

physics.chem-ph↗

arXiv2025

Auxiliary many-body wavefunctions for TDDFRT electronic excited states: Consequences for the representation of molecular electronic transitions

This contribution reports the study of a set of molecular electronic-structure reorganization representations related to light-induced electronic transitions, modeled in the framework of time-dependent density-functional response theory. More precisely, the work related in this paper deals with the consequences, for the electronic transitions natural-orbital characterization, that are inherent to the use of auxiliary many-body wavefunctions constructed a posteriori and assigned to excited states - since time-dependent density-functional response theory does not provide excited state ansatze in its native formulation. Three types of such auxiliary many-body wavefunctions are studied, and the structure and spectral properties of the relevant matrices (the one-electron reduced difference and transition density matrices) is discussed and compared with the native equation-of-motion time-dependent density functional response theory picture of an electronic transition - we see for instance that within this framework the detachment and attachment density matrices can be derived without diagonalizing the one-body reduced difference density matrix. The common ''departure/arrival'' wavefunction-based representations of electronic transitions are also extensively discussed.

physics.chem-ph↗