arXiv subjects

Julien Toulouse

Publications and source records attributed to Julien Toulouse.

At least 19 recordsLinked to original sources

arXiv2026

Linear-response time-dependent density-functional theory with local range separation: Core and valence resonances of the neon atom

We investigate range-separated hybrids (RSHs) and locally range-separated hybrids (LRSHs) for linear-response time-dependent density-functional theory (TDDFT) Sternheimer calculations of the photoionization spectrum of the Ne atom. This system constitutes a stringent test for approximate exchange-correlation treatments because it exhibits both valence and core resonances with very different energy scales. Building on previous work employing a simple one-parameter local range-separation function, we assess here a more flexible two-parameter range-separation function designed to improve the high-density limit. We compare photoionization spectra and resonance parameters obtained with RSHs and LRSHs. We find that the LRSH approach with the two-parameter range-separation function provides an overall satisfactory description of the photoionization spectrum, including energies for both valence and core resonances. The lifetimes of the 2s $\rightarrow$ np valence resonances are also reasonably reproduced since their decay does not involve double excitations. In contrast, the lifetimes of the 1s $\rightarrow$ np core resonances are overestimated by orders of magnitude because their Auger decay channels involve double excitations that are absent in adiabatic, single-determinant TDDFT. Obtaining more accurate resonance widths within linear-response range-separated TDDFT would require using multideterminant schemes and/or adding a frequency-dependent response kernel.

physics.chem-ph↗

arXiv2026

Strictly localized orbitals from spatial partitioning with the discontinuous Galerkin method

We present a rigorous electronic-structure theory of strictly localized orbitals associated with a spatial partition of the one-electron Hilbert space that remains well defined in the complete basis-set limit. Each strictly localized orbital is supported on a spatial domain and may be discontinuous at domain interfaces. Using the interior-penalty discontinuous Galerkin method, these strictly localized orbitals can be employed in variational electronic-structure calculations despite their discontinuities at domain interfaces. As a proof of concept, we present numerical illustrations on one-dimensional diatomic model systems. They show that variational calculations can be carried out in a basis of strictly localized orbitals while maintaining good agreement with conventional calculations. Moreover, these strictly localized orbitals naturally lead to chemically intuitive representations of many-electron wave functions in the spirit of valence-bond theory.

physics.chem-ph↗

arXiv2026

Geometric theory of constrained Schr\"odinger dynamics with application to time-dependent density-functional theory on a finite lattice

Time-dependent density-functional theory (TDDFT) is a central tool for studying the dynamical electronic structure of molecules and solids, yet aspects of its mathematical foundations remain insufficiently understood. In this work, we revisit the foundations of TDDFT within a finite-dimensional setting by developing a general geometric framework for Schr\"odinger dynamics subject to prescribed expectation values of selected observables. We show that multiple natural definitions of such constrained dynamics arise from the underlying geometry of the state manifold. The conventional TDDFT formulation emerges from demanding stationarity of the action functional, while an alternative, purely geometric construction leads to a distinct form of constrained Schr\"odinger evolution that has not been previously explored. This alternative dynamics may provide a more mathematically robust route to TDDFT and may suggest new strategies for constructing nonadiabatic approximations. Applying the theory to interacting fermions on finite lattices, we derive novel Kohn--Sham schemes in which the density constraint is enforced via an imaginary potential or, equivalently, a nonlocal Hermitian operator. Numerical illustrations for the Hubbard dimer demonstrate the behavior of these new approaches.

cond-mat.mtrl-sci↗

arXiv2026

Geometric Time-Dependent Density Functional Theory

We provide a new formulation of Time-Dependent Density Functional Theory (TDDFT) based on the geometric structure of the set of states constrained to have a fixed density. Orbital-free TDDFT is formulated using a hydrodynamics equation involving a new density-to-current functional map. In the corresponding Kohn--Sham equation, the density is reproduced using a non-local operator. Finally, we present numerical simulations for one-dimensional soft-Coulomb systems.

cond-mat.mtrl-sci↗

arXiv2025

Time-dependent ab__initio molecular-orbital decomposition for high-harmonic generation spectroscopy

We propose a real-time time-dependent ab__initio approach within a configuration-interaction-singles ansatz to decompose the high-harmonic generation (HHG) signal of molecules in terms of individual molecular-orbital (MO) contributions. Calculations have been performed by propagating the time-dependent Schr{ö}dinger equation with complex energies, in order to account for ionization of the system, and by using tailored Gaussian basis sets for high-energy and continuum states. We have studied the strong-field electron dynamics and the HHG spectra in aligned CO2 and H2O molecules. Contribution from MOs in the strong-field dynamics depends on the interplay between the MO ionization energy and the coupling between the MO and the laser-pulse symmetries. Such contributions characterize different portions of the HHG spectrum, indicating that the orbital decomposition encodes nontrivial information on the modulation of the strong-field dynamics. Our results correctly reproduce the MO contributions to HHG for CO2 as described in the literature experimental and theoretical data and lead to an original analysis of the role of the highest occupied molecular orbitals HOMO, HOMO-1, and HOMO-2 of H2O according to the polarization direction of the laser pulse.

physics.chem-ph↗

arXiv2025

Double-hybrid density-functional theory with density-based basis-set correction

We develop the theory justifying the application of the density-based basis-set correction (DBBSC) method to double-hybrid approximations in order to accelerate their basis convergence. We show that, for the oneparameter double hybrids based on the adiabatic connection, the exact dependence of the basis-set correction functional on the coupling-constant parameter $λ$ involves a uniform coordinate scaling by a factor 1/$λ$ of the density and of the basis functions. Neglecting this uniform coordinate scaling corresponds essentially to the recent work of Mester and K{á}llay [J. Phys. Chem. Lett. 16, 2136 (2025)] on the application of the DBBSC method to double-hybrid approximations. Test calculations on molecular atomization energies and reaction barrier heights confirm that the DBBSC method efficiently accelerates the basis convergence of double-hybrid approximations, and also show that neglecting the uniform coordinate scaling is a reasonable approximation.

physics.chem-ph↗

arXiv2025

Vacuum polarization in a one-dimensional effective quantum-electrodynamics model

With the aim of progressing toward a practical implementation of an effective quantum-electrodynamics (QED) theory of atoms and molecules, which includes the effects of vacuum polarization through the creation of virtual electron-positron pairs but without the explicit photon degrees of freedom, we study a one-dimensional effective QED model of the hydrogen-like atom with delta-potential interactions. This model resembles the three-dimensional effective QED theory with Coulomb interactions while being substantially simpler. We provide some mathematical details about the definition of this model, calculate the vacuum-polarization density, and the Lamb-type shift of the bound-state energy, correcting and extending results of previous works. We also study the approximation of the model in a finite plane-wave basis, and in particular we discuss the basis convergence of the bound-state energy and eigenfunction, of the vacuum-polarization density, and of the Lamb-type shift of the bound-state energy. We highlight the difficulty of converging the vacuum-polarization density in a finite basis and we propose a way to improve it. The present work could give hints on how to perform similar calculations for the three-dimensional effective QED theory of atoms and molecules.

quant-ph↗

arXiv2024

Shortcut to Chemically Accurate Quantum Computing via Density-based Basis-set Correction

Using GPU-accelerated state-vector emulation, we propose to embed a quantum computing ansatz into density-functional theory via density-based basis-set corrections (DBBSC) to obtain quantitative quantum-chemistry results on molecules that would otherwise require brute-force quantum calculations using hundreds of logical qubits. Indeed, accessing a quantitative description of chemical systems while minimizing quantum resources is an essential challenge given the limited qubit capabilities of current quantum processors. We provide a shortcut towards chemically accurate quantum computations by approaching the complete-basis-set limit through coupling the DBBSC approach, applied to any given variational ansatz, to an on-the-fly crafting of basis sets specifically adapted to a given system and user-defined qubit budget. The resulting approach self-consistently accelerates the basis-set convergence, improving electronic densities, ground-state energies, and first-order properties (e.g. dipole moments), but can also serve as a classical, a posteriori, energy correction to quantum hardware calculations with expected applications in drug design and materials science.

physics.chem-ph↗

arXiv2024

Accelerated basis-set convergence of coupled-cluster excitation energies using the density-based basis-set correction method

We present the first application to real molecular systems of the recently proposed linear-response theory for the density-based basis-set correction method [J. Chem. Phys. 158, 234107 (2023)]. We apply this approach to accelerate the basis-set convergence of excitation energies in the equation-of-motion coupled-cluster singles doubles (EOM-CCSD) method. We use an approximate linear-response framework which neglects the second-order derivative of the basis-set correction density functional and consists in simply adding to the usual Hamiltonian the one-electron potential generated by the first-order derivative of the functional. This additional basis-set correction potential is evaluated at the Hartree-Fock density, leading to a very computationally cheap basis-set correction. We tested this approach over a set of about 30 excitation energies computed for five small molecular systems and found that the excitation energies from the ground state to Rydberg states are the main source of basis-set error. These excitation energies systematically increase when the size of the basis set is increased, suggesting a biased description in favour of the excited state. Despite the simplicity of the present approach, the results obtained with the basis-set corrected EOM-CCSD method are encouraging as they yield to a mean absolute deviation of 0.02 eV for the aug-cc-pVTZ basis set, while it is of 0.04 eV using the standard EOM-CCSD method. This might open the path to an alternative to explicitly correlated approaches to accelerate the basis-set convergence of excitation energies.

physics.chem-ph↗

arXiv2024

A density-fitting implementation of the density-based basis-set correction method

This work reports an efficient density-fitting implementation of the density-based basis-set correction (DBBSC) method in the MOLPRO software. This method consists in correcting the energy calculated by a wave-function method with a given basis set by an adapted basis-set correction density functional incorporating the short-range electron correlation effects missing in the basis set, resulting in an accelerated convergence to the complete-basis-set limit. Different basis-set correction density-functional approximations are explored and the complementary-auxiliary-basis-set single-excitation correction is added. The method is tested on a benchmark set of reaction energies at the second-order Møller-Plesset (MP2) level and a comparison with the explicitly correlated MP2-F12 method is provided. The results show that the DBBSC method greatly accelerates the basis convergence of MP2 reaction energies, without reaching the accuracy of the MP2-F12 method but with a lower computational cost.

physics.chem-ph↗

arXiv2023

Effective quantum electrodynamics: One-dimensional model of the relativistic hydrogen-like atom

We consider a one-dimensional effective quantum electrodynamics (QED) model of the relativistic hydrogen-like atom using delta-potential interactions. We discuss the general exact theory and the Hartree-Fock approximation. The present one-dimensional effective QED model shares the essential physical feature of the three-dimensional theory: the nuclear charge polarizes the vacuum state (creation of electron-positron pairs) which results in a QED Lamb-type shift of the bound-state energy. Yet, this 1D effective QED model eliminates some of the most serious technical difficulties of the three-dimensional theory coming from renormalization. We show how to calculate the vacuum-polarization density at zeroth order in the two-particle interaction and the QED Lamb-type shift of the bound-state energy at first order in the two-particle interaction. The present work may be considered as a step toward the development of a quantum-chemistry effective QED theory of atoms and molecules.

math-ph↗

arXiv2023

Basis-set correction based on density-functional theory: Linear-response formalism for excited-state energies

The basis-set correction method based on density-functional theory consists in correcting the energy calculated by a wave-function method with a given basis set by a density functional. This basis-set correction density functional incorporates the short-range electron correlation effects missing in the basis set. This results in accelerated basis convergences of ground-state energies to the complete-basis-set limit. In this work, we extend the basis-set correction method to a linear-response formalism for calculating excited-state energies. We give the general linear-response equations, as well as the more specific equations for configuration-interaction wave functions. As a proof of concept, we apply this approach to the calculations of excited-state energies in a one-dimensional two-electron model system with harmonic potential and a Dirac-delta electron-electron interaction. The results obtained with full-configuration-interaction wave functions expanded in a basis of Hermite functions and a local-density-approximation basis-set correction functional show that the present approach does not help in accelerating the basis convergence of excitation energies. However, we show that it significantly accelerates basis convergences of excited-state total energies.

physics.chem-ph↗

arXiv2023

Semiclassical approximations of photoabsorption cross sections beyond the continuum threshold

We develop semiclassical approximations for calculating photoabsorption cross sections beyond the continuum threshold in quantum many-body systems. These approximations use the fully quantum-mechanical Wigner function of the ground state and semiclassical expansions only for the part of the cross section depending on the continuum states, thus avoiding the difficult explicit calculation of the continuum states. Even though the approach is general, we test it in electronic-structure theory for the photoionization cross sections of the hydrogen and helium atoms. The results suggest that these semiclassical approximations can be used to obtain good estimates of cross sections at high energy.

physics.atom-ph↗

arXiv2022

Photoionization and core resonances from range-separated time-dependent density-functional theory for open-shell states: Example of the lithium atom

We consider the calculations of photoionization spectra and core resonances of open-shell systems using range-separated time-dependent density-functional theory. Specifically, we use the time-dependent range-separated hybrid (TDRSH) scheme, combining a long-range Hartree-Fock (HF) exchange potential and kernel with a short-range potential and kernel from a local density-functional approximation, and the time-dependent locally range-separated hybrid (TDLRSH) scheme, which uses a local range-separation parameter. To efficiently perform the calculations, we formulate a spin-unrestricted linear-response Sternheimer approach in a non-orthogonal B-spline basis set and using appropriate frequency-dependent boundary conditions. We illustrate this approach on the Li atom, which suggests that TDRSH and TDLRSH are adequate simple methods for estimating single-electron photoionization spectra of open-shell systems.

physics.chem-ph↗

arXiv2022

Review of approximations for the exchange-correlation energy in density-functional theory

In this chapter, we provide a review of ground-state Kohn-Sham density-functional theory of electronic systems and some of its extensions, we present exact expressions and constraints for the exchange and correlation density functionals, and we discuss the main families of approximations for the exchange-correlation energy: semilocal approximations, single-determinant hybrid approximations, multideterminant hybrid approximations, dispersion-corrected approximations, as well as orbital-dependent exchange-correlation density functionals. The chapter aims at providing both a consistent bird's-eye view of the field and a detailed description of some of the most used approximations. It is intended to be readable by chemists/physicists and applied mathematicians.

physics.chem-ph↗

arXiv2022

Systematic lowering of the scaling of Monte Carlo calculations by partitioning andsubsampling

We propose to compute physical properties by Monte Carlo calculations using conditional expectation values. The latter are obtained on top of the usual Monte Carlo sampling by partitioning the physical space in several subspaces or fragments, and subsampling each fragment (i.e., performing side walks) while freezing the environment. No bias is introduced and a zero-variance principle holds in the limit of separability, i.e. when the fragments are independent. In practice, the usual bottleneck of Monte Carlo calculations -- the scaling of the statistical fluctuations as a function of the number of particles N -- is relieved for extensive observables. We illustrate the method in variational Monte Carlo on the 2D Hubbard model and on metallic hydrogen chains using Jastrow-Slater wave functions. A factor O(N) is gained in numerical efficiency.

physics.chem-ph↗

arXiv2022

The Valence-Bond Quantum Monte Carlo Method

The VB-QMC method is presented in this chapter. It consists of using in quantum Monte Carlo (QMC) approaches with a wave function expressed as a usually short expansion of classical Valence-Bond (VB) structures supplemented by a Jastrow factor to account for dynamical correlation. Two variants exist: the VB-VMC (using variational Monte Carlo) and VB-DMC (using diffusion Monte Carlo) methods. QMC algorithms circumvent the notorious non-orthogonality issue of classical VB approaches, and allow highly efficient calculations on massively parallel machines. Calculation of VB weights and resonance energies are possible at the VB-VMC level, which makes VB-VMC a correlated method retaining all the interpretative capabilities of classical VB methods. Several recent applications are shown to illustrate the potential of this method as a modern alternative to classical VB methods to study ground and excited states of molecules.

physics.chem-ph↗

arXiv2022

Photoionization and core resonances from range-separated density-functional theory: General formalism and example of the beryllium atom

We explore the merits of linear-response range-separated time-dependent density-functional theory (TDDFT) for the calculation of photoionization spectra. We consider two variants of range-separated TDDFT, namely the timedependent range-separated hybrid (TDRSH) scheme which uses a global range-separation parameter and the timedependent locally range-separated hybrid (TDLRSH) which uses a local range-separation parameter, and compare with standard time-dependent local-density approximation (TDLDA) and time-dependent Hartree-Fock (TDHF). We show how to calculate photoionization spectra with these methods using the Sternheimer approach formulated in a nonorthogonal B-spline basis set with appropriate frequency-dependent boundary conditions. We illustrate these methods on the photoionization spectrum of the Be atom, focusing in particular on the core resonances. Both the TDRSH and TDLRSH photoionization spectra are found to constitute a large improvement over the TDLDA photoionization spectrum and a more modest improvement over the TDHF photoionization spectrum.

physics.chem-ph↗