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Vincent Robert

Publications and source records attributed to Vincent Robert.

18 recordsLinked to original sources
arXiv2026

Quantification of Tides in Giant Planets from Observations

Quantifying tidal effects on giant planets has recently made significant advances, thanks in particular to the Cassini space probe. During its thirteen-year orbit around Saturn, numerous measurements from different instruments made it possible to characterize fundamental parameters such as Saturn\'s Love number $k_2$ and quality factor $Q$ at different frequencies. In this article, we summarize the various measurements and methods that have allowed to arrive at such a result, as well as the extrapolations that can be deduced for other systems. More generally, the state of the art concerning the four giant planets of the Solar System is presented, as well as the case of exoplanets.

astro-ph.EP↗
arXiv2026

Orthogonally Constrained CASSCF Framework: Newton-Raphson Orbital Optimization and Nuclear Gradients

In a recent work, we introduced the foundations of an orthogonally constrained complete active space self-consistent field (OC-CASSCF) framework that produces state-specific molecular orbitals for mutually orthogonal multiconfigurational electronic states. In the present study, we extend this approach by incorporating a Newton-Raphson orbital-optimization scheme, for which we derive analytical expressions of the orbital gradient and Hessian. Furthermore, we outline a practical route toward the evaluation of analytical nuclear gradients, enabling geometry optimizations within the OC-CASSCF formalism. Benchmark calculations on the three lowest singlet states of LiH and H$_2$O molecules demonstrate a systematic improvement as compared to conventional state-averaged CASSCF, even when using modestly sized active spaces.

physics.chem-ph↗
arXiv2025

A State-Specific Iterative Decoupling Scheme Based on Perturbation Theory for Low-Energy Electronic States

In this work, we introduce a selective and scalable extension of the multi-step Rayleigh-Schrodinger and Brillouin-Wigner perturbative scheme (see arXiv:2408.16505), designed to efficiently access the low-energy spectrum of molecular systems. The method proceeds by combining successive effective Hamiltonian diagonalizations inspired by second-order Rayleigh-Schrodinger perturbation theory, with a Brillouin-Wigner correction applied to individually optimized states using an updated partitioning of the Hamiltonian. At each step, a zeroth-order state is identified and progressively decoupled from the remaining higher-lying states, thereby enabling a well-conditioned Brillouin-Wigner expansion for the energy correction. In contrast to previous approaches, the method selectively targets a small number of low-lying states, significantly reducing the numerical overhead while maintaining spectroscopic accuracy. The robustness of the method is demonstrated on the LiH and H4 molecules, where accurate excitation energies are obtained for the lowest singlet states using compact model spaces, confirming its potential for realistic applications.

physics.chem-ph↗
arXiv2024

Combining Effective Hamiltonians and Brillouin-Wigner Approach: A Perturbative Approach to Spectroscopy

The numerical cost of variational methods suggests using perturbative approaches to determine the electronic structure of molecular systems. In this work, a sequential construction of effective Hamiltonians drives the definition of approximate model functions and energies in a multi-state Rayleigh-Schr\"odinger perturbative scheme. A second step takes advantage of an updated partitioning of the Hamiltonian to perform a state-specific Brillouin-Wigner energy correction based on a well-tempered perturbation expansion. The multi-step RSBW method is exemplified on model-Hamiltonians to stress its robustness, efficiency and applicability to spectroscopy determination.

physics.chem-ph↗
arXiv2023

A Two-Step Rayleigh-Schr\"odinger Brillouin-Wigner Approach to Transition Energies

Perturbative methods are attractive to describe the electronic structure of molecular systems because of their low-computational cost and systematically improvable character. In this work, a two-step perturbative approach is introduced combining multi-state Rayleigh-Schr\"odinger (effective Hamiltonian theory) and state-specific Brillouin-Wigner schemes to treat degenerate configurations and yield an efficient evaluation of multiple energies. The first step produces model functions and an updated definition of the perturbative partitioning of the Hamiltonian. The second step inherits the improved starting point provided in the first step, enabling then faster processing of the perturbative corrections for each individual state. The here-proposed two-step method is exemplified on a model-Hamiltonian of increasing complexity.

physics.chem-ph↗
arXiv2022

Orthogonally Constrained Orbital Optimization: assessing changes of optimal orbitals for orthogonal multi-reference states

The choice of molecular orbitals is decisive in configuration interaction calculations. In this letter, a democratic description of the ground and excited states follows an orthogonally constrained orbitals optimization to produce state-specific orbitals. The approach faithfully recovers the excitation energy of afour-electron Hubbard trimer, whereas state-average calculations can miss the value by a factor 2.5. The method emphasises the need for orbitals optimizationto reduce expansions and to reach spectroscopic accuracy.

quant-ph↗
arXiv2022

Modifications of Tanabe-Sugano d$^6$ diagram induced by radical ligand field: ab initio inspection of a Fe(II)-verdazyl molecular complex

Quantum entanglement between the spin states of a metal centre and radical ligands is suggested in an iron(II) [Fe(dipyvd)$_2$]$^{2+}$ compound (dipyvd = 1-isopropyl-3,5-dipyridil-6-oxoverdazyl). Wavefunction \textit{ab initio} (Difference Dedicated Configuration Interaction, DDCI) inspections were carried out to stress the versatility of local spin states. We named this phenonmenon \textit{excited state spinmerism}, in reference to our previous work (see Roseiro et. al., ChemPhysChem 2022, e202200478) where we introduced the concept of spinmerism as an extension of mesomerism to spin degrees of freedom. The construction of localized molecular orbitals allows for a reading of the wavefunctions and projections onto the local spin states. The low-energy spectrum is well-depicted by a Heisenberg picture. A 60 cm$^{-1}$ ferromagnetic interaction is calculated between the radical ligands with the $S_{total} = 0$ and $1$ states largely dominated by a local low-spin $S_{Fe} = 0$. In contrast, the higher-lying $S_{total} = 2$ states are superpositions of the local $S_{Fe} = 1$ (17%, 62%) and $S_{Fe} = 2$ (72%, 21%) spin states. Such mixing extends the traditional picture of a high-field $d^6$ Tanabe-Sugano diagram. Even in the absence of spin-orbit coupling, the avoided crossing between different local spin states is triggered by the field generated by radical ligands. This puzzling scenario emerges from versatile local spin states in compounds which extend the traditional views in molecular magnetism.

quant-ph↗
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↗
arXiv2020

A multi-decadal view of the heat and mass budget of a volcano in unrest: La Soufrière de Guadeloupe (French West Indies)

Particularly in the presence of a hydrothermal system, many volcanoes output large quantities of heat through the transport of water from deep within the edifice to the surface. Thus, heat flux is a prime tool for evaluating volcanic activity and unrest. We review the volcanic unrest at La Soufrière de Guadeloupe (French West Indies) using an airborne thermal camera survey, and in-situ measurements of temperature and flow rate through temperature probes, Pitot-tube and MultiGAS measurements. We deduce mass and heat fluxes for the fumarolic, ground and thermal spring outputs and follow these over a period spanning 2000--2020. Our results are compared with published data and we performed a retrospective analysis of the temporal variations in heat flux over this period using the literature data. We find that the heat emitted by the volcano is 36.5 +/- 7.9 MW, of which the fumarolic heat flux is dominant at 28.3 +/- 6.8 MW. Given a total heated area of 26780 m2, this equates to a heat flux density of 627 +/- 94 W/m2, which is amongst the highest established for worldwide volcanoes with hydrothermal systems, particularly for dome volcanoes. A major change at La Soufrière de Guadeloupe, however, is the development of a widespread region of ground heating at the summit where heat output has increased from 0.2 +/- 0.1 MW in 2010 to 5.7 +/- 0.9 MW in 2020. This change is concurrent with accelerating unrest at the volcano, and the emergence of two new high-flux fumaroles in recent years. Our findings highlight the importance of continued and enhanced surveillance and research strategies at La Soufrière de Guadeloupe, the results of which can be used to better understand hydrothermal volcanism the world over.

physics.geo-ph↗
arXiv2020

Resonance locking in giant planets indicated by the rapid orbital expansion of Titan

Tidal effects in planetary systems are the main driver in the orbital migration of natural satellites. They result from physical processes occurring deep inside celestial bodies, whose effects are rarely observable from surface imaging. For giant planet systems, the tidal migration rate is determined by poorly understood dissipative processes in the planet, and standard theories suggest an orbital expansion rate inversely proportional to the power 11/2 in distance, implying little migration for outer moons such as Saturn's largest moon, Titan. Here, we use two independent measurements obtained with the Cassini spacecraft to measure Titan's orbital expansion rate. We find Titan migrates away from Saturn at 11.3 $\pm$ 2.0 cm/year, corresponding to a tidal quality factor of Saturn of Q $\simeq$ 100, and a migration timescale of roughly 10 Gyr. This rapid orbital expansion suggests Titan formed significantly closer to Saturn and has migrated outward to its current position. Our results for Titan and five other moons agree with the predictions of a resonance locking tidal theory, sustained by excitation of inertial waves inside the planet. The associated tidal expansion is only weakly sensitive to orbital distance, motivating a revision of the evolutionary history of Saturn's moon system. The resonance locking mechanism could operate in other systems such as stellar binaries and exoplanet systems, and it may allow for tidal dissipation to occur at larger orbital separations than previously believed.

astro-ph.EP↗
arXiv2016

Local density approximation in site-occupation embedding theory

Site-occupation embedding theory (SOET) is a density-functional theory (DFT)-based method which aims at modelling strongly correlated electrons. It is in principle exact and applicable to model and quantum chemical Hamiltonians. The theory is presented here for the Hubbard Hamiltonian. In contrast to conventional DFT approaches, the site (or orbital) occupations are deduced in SOET from a partially-interacting system consisting of one (or more) impurity site(s) and non-interacting bath sites. The correlation energy of the bath is then treated implicitly by means of a site-occupation functional. In this work, we propose a simple impurity-occupation functional approximation based on the two-level (2L) Hubbard model which is referred to as two-level impurity local density approximation (2L-ILDA). Results obtained on a prototypical uniform 8-site Hubbard ring are promising. The extension of the method to larger systems and more sophisticated model Hamiltonians is currently in progress.

cond-mat.str-el↗
arXiv2015

New constraints on Saturn's interior from Cassini astrometric data

Using astrometric observations spanning more than a century and including a large set of Cassini data, we determine Saturn's tidal parameters through their current effects on the orbits of the eight main and four coorbital moons. We have used the latter to make the first determination of Saturn's Love number, $k_2=0.390 \pm 0.024$, a value larger than the commonly used theoretical value of 0.341 (Gavrilov & Zharkov, 1977), but compatible with more recent models (Helled & Guillot, 2013) for which $k_2$ ranges from 0.355 to 0.382. Depending on the assumed spin for Saturn's interior, the new constraint can lead to a reduction of up to 80% in the number of potential models, offering great opportunities to probe the planet's interior. In addition, significant tidal dissipation within Saturn is confirmed (Lainey et al., 2012) corresponding to a high present-day tidal ratio $k_2/Q=(1.59 \pm 0.74) \times 10^{-4}$ and implying fast orbital expansions of the moons. This high dissipation, with no obvious variations for tidal frequencies corresponding to those of Enceladus and Dione, may be explained by viscous friction in a solid core, implying a core viscosity typically ranging between $10^{14}$ and $10^{16}$ Pa.s (Remus et al., 2012). However, a dissipation increase by one order of magnitude at Rhea's frequency could suggest the existence of an additional, frequency-dependent, dissipation process, possibly from turbulent friction acting on tidal waves in the fluid envelope of Saturn (Ogilvie & Li, 2004). Alternatively, a few of Saturn's moons might themselves experience large tidal dissipation.

astro-ph.EP↗
arXiv2012

Ab initio derivation of multi-orbital extended Hubbard model for molecular crystals

From configuration interaction (CI) ab initio calculations, we derive an effective two-orbital extended Hubbard model based on the gerade (g) and ungerade (u) molecular orbitals (MOs) of the charge-transfer molecular conductor (TTM-TTP)I_3 and the single-component molecular conductor [Au(tmdt)_2]. First, by focusing on the isolated molecule, we determine the parameters for the model Hamiltonian so as to reproduce the CI Hamiltonian matrix. Next, we extend the analysis to two neighboring molecule pairs in the crystal and we perform similar calculations to evaluate the inter-molecular interactions. From the resulting tight-binding parameters, we analyze the band structure to confirm that two bands overlap and mix in together, supporting the multi-band feature. Furthermore, using a fragment decomposition, we derive the effective model based on the fragment MOs and show that the staking TTM-TTP molecules can be described by the zig-zag two-leg ladder with the inter-molecular transfer integral being larger than the intra-fragment transfer integral within the molecule. The inter-site interactions between the fragments follow a Coulomb law, supporting the fragment decomposition strategy.

cond-mat.mtrl-sci↗
arXiv2010

Multi-Orbital Molecular Compound (TTM-TTP)I_3: Effective Model and Fragment Decomposition

The electronic structure of the molecular compound (TTM-TTP)I_3, which exhibits a peculiar intra-molecular charge ordering, has been studied using multi-configuration ab initio calculations. First we derive an effective Hubbard-type model based on the molecular orbitals (MOs) of TTM-TTP; we set up a two-orbital Hamiltonian for the two MOs near the Fermi energy and determine its full parameters: the transfer integrals, the Coulomb and exchange interactions. The tight-binding band structure obtained from these transfer integrals is consistent with the result of the direct band calculation based on density functional theory. Then, by decomposing the frontier MOs into two parts, i.e., fragments, we find that the stacked TTM-TTP molecules can be described by a two-leg ladder model, while the inter-fragment Coulomb energies are scaled to the inverse of their distances. This result indicates that the fragment picture that we proposed earlier [M.-L. Bonnet et al.: J. Chem. Phys. 132 (2010) 214705] successfully describes the low-energy properties of this compound.

cond-mat.mtrl-sci↗
arXiv2010

Intramolecular charge ordering in the multi molecular orbital system (TTM-TTP)I_3

Starting from the structure of the (TTM-TTP)I_3 molecular-based material, we examine the characteristics of frontier molecular orbitals using ab initio (CASSCF/CASPT2) configurations interaction calculations. It is shown that the singly-occupied and second-highest-occupied molecular orbitals are close to each other, i.e., this compound should be regarded as a two-orbital system. By dividing virtually the [TTM-TTP] molecule into three fragments, an effective model is constructed to rationalize the origin of this picture. In order to investigate the low-temperature symmetry breaking experimentally observed in the crystal, the electronic distribution in a pair of [TTM-TTP] molecules is analyzed from CASPT2 calculations. Our inspection supports and explains the speculated intramolecular charge ordering which is likely to give rise to low-energy magnetic properties.

cond-mat.mtrl-sci↗
arXiv2003

Magnetic ligands in the $Pt_2(dta)_4I$ compound

We report a reinterpretation of the electronic structure of the $(Pt)_2I(dta)_4$ compound, based on {\em ab initio} embedded fragment calculations. Our major results are the following. First, the usually assumed electronic intra-dimer charge ordering is unrealistic. Second, the $(dta)$ ligands take part actively in the magnetic properties of the system. The proposed electronic structure is favorably confronted to experimental data. In particular, the unexplained $3:1$ $Pt^{2+}/Pt^{3+}$ abundances ratio of the XPS spectra is rationalized.

cond-mat.str-el↗
arXiv2003

Environment effects on effective magnetic exchange integrals and local spectroscopy of extended strongly correlated systems

The present work analyzes the importance of the different components of the environment effects on the local spectroscopy of extended strongly correlated systems. It has been found that the usual formal charge definition of the charge transfer and Madelung potential are far too crude for an accurate determination of the local excitation energies in embedded fragment calculations. A criterion for the validation of the embedding against the infinite system density of states has been proposed.

cond-mat.str-el↗