arXiv subjects

Thibaud Etienne

Publications and source records attributed to Thibaud Etienne.

10 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

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↗

arXiv2022

Natural-orbital representation of molecular electronic transitions

This paper aims at introducing the formal foundations of the application of reduced density-matrix theory and Green's function theory to the analysis of molecular electronic transitions. For this sake, their mechanics, applied to specific objects containing information related to the passage and the interference between electronic states - the difference and the transition density operators - are rigorously introduced in a self-contained way. After reducing the corresponding $N$-body operators (where $N$ is the number of electrons in the system) using an operator partial-trace procedure, we derive the kernel of the reduced one-body difference and transition density operators, as well as the matrix representation of these operators in a finite-dimensional one-particle-state basis. These derivations are done in first and second quantization for the sake of completeness - the two formulations are equivalently present in the literature - and because second quantization is extensively used in a second part of the paper. Natural orbitals are introduced as appropriate bases for reducing the dimensionality of the problem and the complexity of the analysis of the transition phenomenon. Natural-orbital representation of density operators are often used as a tool to characterize the nature of molecular electronic transitions, so we suggest with this contribution to revisit their theoretical foundations in order to better understand the origin and nature of these tools.

physics.chem-ph↗

arXiv2021

A comprehensive, self-contained derivation of the one-body density matrices from single-reference excited-state calculation methods using the equation-of-motion formalism

In this contribution we review in a rigorous, yet comprehensive fashion the assessment of the one-body reduced density matrices derived from the most used single-reference excited-state calculation methods in the framework of the equation-of-motion formalism. Those methods are separated into two types: those which involve the coupling of a deexcitation operator to a single-excitation transition operator, and those which do not involve such a coupling. The case of many-body auxiliary wave functions for excited states is also addressed. For each of these approaches we were interested in deriving the elements of the one-body transition and difference density matrices, and to highlight their particular structure. This has been accomplished by applying a decomposition of integrals involving one-determinant quantum electronic states on which two or three pairs of second quantization operators can act. Such a decomposition has been done according to a corollary to Wick's theorem, which is brought in a comprehensive and detailed manner. A comment is also given about the consequences of using the equation-of-motion formulation in this context, and the two types of excited-state calculation methods (with and without coupling excitations to deexcitations) are finally compared from the point of view of the structure of their transition and difference density matrices.

physics.chem-ph↗

arXiv2021

Diagnosis of two evaluation paths to density-based descriptors of molecular electronic transitions

In this paper we discuss the reliability of two computational methods (numerical integration on Cartesian grids, and population analysis) used for evaluating scalar quantities related to the nature of electronic transitions. These descriptors are integrals of charge density functions built from the detachment and attachment density matrices projected in the Euclidean space using a finite basis of orbitals. While the numerical integration on Cartesian grids is easily considered to be converged for medium-sized density grids, the population analysis approximation to the numerical integration values is diagnosed using eight diagnostic tests performed on fifty-nine molecules with a combination of fifteen Gaussian basis sets and six exchange-correlation functionals.

physics.chem-ph↗

arXiv2019

Charge separation: From the topology of molecular electronic transitions to the dye/semiconductor interfacial energetics and kinetics

Charge separation properties, that is the ability of a chromophore, or a chromophore/semiconductor interface, to separate charges upon light absorption, are crucial characteristics for an efficient photovoltaic device. Starting from this concept, we devote the first part of this book chapter to the topological analysis of molecular electronic transitions induced by photon capture. Such analysis can be either qualitative or quantitative, and is presented here in the framework of the reduced density matrix theory applied to single-reference, multiconfigurational excited states. The qualitative strategies are separated into density-based and wave function-based approaches, while the quantitative methods reported here for analysing the photoinduced charge transfer nature are either fragment-based, global or statistical. In the second part of this chapter we extend the analysis to dye-sensitized metal oxide surface models, discussing interfacial charge separation, energetics and electron injection kinetics from the dye excited state to the semiconductor conduction band states.

physics.chem-ph↗

arXiv2018

Theoretical insights into the topology of molecular excitons from single-reference excited states calculation methods

This chapter gives an introduction to qualitative and quantitative topological analyses of molecular electronic transitions. Among the possibilities for qualitatively describing how the electronic structure of a molecule is reorganized upon light-absorption, we chose to detail two of them, namely the detachment/attachment density matrix analysis and the natural transition orbitals strategy. While these tools are often introduced separately, we decided to formally detail the connection existing between the two paradigms in the case of excited states calculation methods expressing any excited state as a linear combination of singly excited Slater determinants, written based on a single-reference ground state wave function. In this context, we show how the molecular exciton wave function plays a central role in the topological analysis of the electronic transition process.

physics.chem-ph↗