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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.

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.

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.

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.

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., Comment: The present review article (81 pages, 5 figures) is part of the "Topics in Current Chemistry'' topical collection entitled "New Horizon in Computational Chemistry Software''

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 Soufri\`ere 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 Soufri\`ere 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 Soufri\`ere de Guadeloupe, the results of which can be used to better understand hydrothermal volcanism the world over.

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., Comment: Published in Nature Astronomy, SharedIt link: https://rdcu.be/b4I3Q

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., Comment: 27 pages, 11 figures

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.