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The month of May 2024 was characterized by solar energetic particles events directed towards the Earth, especially the big event causing a strong terrestrial geomagnetic storm during the night from 10 to 11 May 2024, with auroras observed everywhere in Europe. This was the strongest storm for the last 20 years with a Disturbed Storm Time index Dst < −400 nT. In the present work, we show with observations of GOES, PROBA-V/EPT and MetOP/MEPED that this exceptional event was associated with the injection of energetic protons in the proton radiation belt, with important consequences for the South part of the South Atlantic Anomaly (SAA). In addition, the geomagnetic storm caused by the solar eruption has had tremendous impacts on the electron radiation belts. Indeed, we show that for 0.3 to 1 MeV electrons, the storm led to a long lasting four belts configuration which was not observed before with EPT launched in 2013, until a smaller geomagnetic storm took place at the end of June 2024. Moreover, for the first time since its launch, observations of the EPT show that ultra-relativistic electrons with E > 2 MeV have been injected into the inner belt down to McIlwain parameter L = 2.4, violating the impenetrable barrier previously estimated to be located at L = 2.8. [ABSTRACT FROM AUTHOR]

When high-energy particles originating from space penetrate the atmosphere, they may interact with atoms and molecules, initiating air showers composed of secondary and tertiary particles propagating towards the ground. They can cause ionization of the atmosphere and contribute to the radiation dose at low altitudes. This work uses the GEANT-4-based Atmospheric Radiation Interaction Simulator (AtRIS) toolkit to compute these quantities in the Earth's atmosphere. We take advantage of the unique Planet Specification File (PSF) of the Atmospheric Radiation Interaction Simulator (AtRIS) to investigate the effect of the state of the atmosphere on the resulting induced ionization and absorbed dose rates from the top of the atmosphere (at 100 km) down to the surface. The atmospheric profiles (density, pressure, temperature, and composition) are computed with the NRLMSISE-00 model at various latitudes and for every month of 2014, corresponding to the last maximum of solar activity. The resulting ionization and dose rates present different profiles that vary with latitude in the atmosphere, with the relative difference between equatorial and high latitude ionization rates reaching 68% in the Pfotzer maximum. We obtain differences of up to 59% between the equator and high latitudes observed at commercial flight altitudes for the radiation dose. Both ionization and absorbed dose rates also feature anti-phased seasonal variations in the two hemispheres throughout 2014. Based on these results, we computed global maps of the ionization and dose rates at fixed altitudes in the atmosphere by using precomputed maps of the effective vertical cutoff rigidities and the results of three AtRIS simulations to consider the effect of latitude. While sharing the same general structure as maps created with a single profile, these new maps also show a clear asymmetry in the ionization and absorbed dose rates in the polar regions. [ABSTRACT FROM AUTHOR]

We introduce for the first time the PROBA‐V/EPT electron flux data to train a deep learning data‐driven model with the purpose of investigating the Earth's radiation belts dynamics. The Long‐Short Term Memory Neural Network is employed to predict the electron fluxes between 1 and 8 Earth Radius (RE) along a Low Earth Orbit. Different combinations of time series inputs involving Solar Wind and geomagnetic data are tested, based on previous knowledge of their impact onto the high energy radiation fluxes. Two Energetic Particle Telescope energy channels feed the learning procedure for nonrelativistic (0.5–0.6 MeV) and relativistic (1.0–2.4 MeV) electron fluxes. A good performance of the model employing different time resolutions from hours to days is demonstrated with a correlation of more than 0.9 between the predicted and out‐of‐sample fluxes, and a prediction efficiency that can attain between 0.6 and 0.9 depending on the L range. The analysis of different input parameters and time resolutions allows to construct the best data set structure and improve the model to identify relevant effects such as dropouts, flux increase and recovery features. Plain Language Summary: The Van Allen belts are regions of intense radiation trapped by the Earth's magnetic field. A continuous stream of charged particles, the solar wind, is ejected from the Sun's outer atmosphere carrying the interplanetary magnetic field. When the solar wind interacts with the Earth's magnetic field, it can have significant effects on the space environment surrounding our planet. Predicting the state of the Van Allen Belts is crucial for satellites orbiting near‐Earth, and to aviation and astronaut operations. Disturbances in the Van Allen Belts can represent a significant hazard to human activities, and can also drive out‐of‐control induced electric currents that can damage equipment on satellites. A Machine Learning model is developed here using electron radiation fluxes measurements from an instrument called Energetic Particle Telescope, onboard the PROBA‐V satellite orbiting at an altitude of 820 km. A good performance of the model is demonstrated with a prediction efficiency between 0.6 and 0.9. The results of the model support the prediction of the space‐time Van Allen belts evolution to prevent serious damage in case of strong external perturbations from particles and electromagnetic fields. Key Points: PROBA‐V/EPT high energy electron fluxes are used to efficiently train a deep learning data‐driven modelThe electron flux forecasts along the PROBA‐V orbit demonstrate a high prediction efficiency depending on the Van Allen belts regionsThe good performance of the models is assessed on different energy ranges, input combinations and time resolutions from hours to days [ABSTRACT FROM AUTHOR]

Relativistic radiation belt electron observations from the Energetic Particle Telescope (EPT) on board the PROBA-V (Project for On-Board Autonomy and Vegetation) satellite are compared to those performed by the Magnetic Electron Ion Spectrometer (MagEIS) on board the Van Allen Probes formerly known as the Radiation Belt Storm Probes (RBSP). Despite their very different orbits, both instruments are able to measure fluxes of electrons trapped on a given magnetic shell. In the outer belt, the comparison of high- and low-altitude fluxes is performed during the first 3 months of 2014, featuring the most intense storms of the year. In the inner belt, measurements from the two instruments are compared only at conjunction, when the satellites are physically close to each other. Due to the low number of conjunctions, the whole period of mutual operation of both instruments is used (i.e., May 2013–October 2019). The comparisons show that flux variations appear simultaneously on both spacecraft, but the fluxes observed by the EPT are almost always lower than for MagEIS, as expected from their different orbits. In addition, this difference in flux intensity increases with electron energy. During geomagnetic storms, it is also shown that dropout events (i.e., sudden depletion of electrons) in the outer belt are more pronounced at low altitudes than near the geomagnetic Equator. The effect of the equatorial pitch angle value of electrons is investigated in the outer belt. Despite the difference in flux intensity observed by the two instruments, especially at high energies, a linear relationship with a linear correlation higher than 0.7 was found. The correlation is at its maximum when low-pitch-angle electrons near the Equator are considered. [ABSTRACT FROM AUTHOR]

The static second hyperpolarizabilities ([gamma]) of the singlet diradical systems with intermediate diradical character involving phenalenyl radicals connected by acetylene and vinylene [pi]-conjugated linkers were investigated. The results provided the possibility of developing a novel control scheme of [gamma] for phenalenyl radical systems involving [pi]-conjugated linkers.

The second hyperpolarizabilities of bisimidazole- and bistriazole-benzene compounds are calculated at different levels of approximation to unravel the effects of diradical character as well as of charge and spin multiplicity. A discussion is presented on the diradical character and the spin state control of third-order nonlinear optical properties of diradical molecular systems.

This contribution reveals the effects of a static electric field on the static second hyperpolarizability γ of symmetric singlet diradical molecules using the valence configuration interaction scheme. It is found that under the effect of a field, the component of γ along the axis joining the two radical sites can be gigantically (approximately two to three orders) enhanced for symmetric diradicals having intermediate diradical characters with respect to those of closed-shell and pure diradical molecules in the absence of a field. Moreover, this electric field enhancement of γ increases as a function of the diradical character. These results and their analysis propose therefore a new strategy to design materials with exceptional nonlinear optical responses. [ABSTRACT FROM AUTHOR]

Within the spin-unrestricted density functional theory (DFT) the long-range correction (LC) scheme combined with the Becke–Lee–Yang–Parr exchange-correlation functional, referred to as LC-UBLYP method, has been applied to the calculation of the second hyperpolarizability (γ) of open-shell singlet diradical systems of increasing complexity and has demonstrated good performance: (i) for the simplest H2 dissociation model, the γ values calculated by the LC-UBLYP method significantly overshoot the full configuration interaction result but reproduce qualitatively the evolution of γ as a function of the diradical character, (ii) for small singlet diradical 1,3-dipole systems, the diradical character dependence of γ determined by the UCCSD and UCCSD(T) reference methods is reproduced semiquantitatively by the LC-UBLYP method except in the small diradical character region, where the spin-unrestricted solutions coincide with spin-restricted solutions, (iii) the LC-UBLYP method also closely reproduces the UCCSD(T) results on the diradical character dependence of γ of the p-quinodimethane model system, particularly in the intermediate and large diradical character regions, whereas it shows an abrupt change for a diradical character (y) close to 0.2 originating from the triplet instability, (iv) the reliability of LC-UBLYP to reproduce reference coupled cluster results on open-shell singlet systems with intermediate and large diradical characters has also been substantiated in the case of γ of 1,4-bis-(imidazol-2-ylidene)-cyclohexa-2,5-diene (BI2Y), then (v), for real systems built from a pair of phenalenyl radicals separated by a conjugated linker, the LC-UBLYP results have been found to closely match the UBHandHLYP values—which, for small systems are in good agreement with those obtained using correlated molecular orbital methods—whereas the UB3LYP results can be much different. These results are not only important from the viewpoint of an efficient determination of the nonlinear optical properties of open-shell singlet systems, but also from the viewpoint of defining new challenges for elaborating improved exchange-correlation functionals. [ABSTRACT FROM AUTHOR]

Remarkable enhancement of two-photon absorption (TPA) peak is theoretically predicted in symmetric open-shell singlet diradical systems with intermediate diradical character as compared to closed-shell and pure diradical systems. It is revealed that the largest TPA peak intensities occur for open-shell singlet diradicals having a ferromagnetically coupled ground state and strongly depend on the ratio between damping factors of the excited states. This result confirms that open-shell singlet conjugated molecules with intermediate diradical characters have precedence over conventional closed-shell conjugated systems in resonant third-order nonlinear optical properties. [ABSTRACT FROM AUTHOR]

The linear and second-order nonlinear susceptibilities of the urea crystal have been evaluated by applying the supermolecule approach. Calculations performed at the time-dependent Hartree–Fock (TDHF) level using the Austin model (AM1) semiempirical Hamiltonian have first demonstrated the almost additive character of the essential polarizability and first hyperpolarizability components. In fact, the only exception concerns the χcc(1) component when stacking urea molecules along the c axis, i.e., the axis of the hydrogen bonds. This behavior has been confirmed by ab initio calculations on small clusters. The macroscopic quantities have then been determined by adopting the multiplicative scheme and by correcting the TDHF/AM1 values for missing electron correlation by means of density functional theory and coupled cluster method. The reliability of the multiplicative scheme was demonstrated for clusters as large as 3a×3b×3c. While the electron correlation correction factors are similar for a single molecule and different small clusters, the global performance of the scheme differs for the linear and nonlinear responses. For the second-order nonlinear susceptibility, our predictions are in good agreement with experiment, while for the linear susceptibility and the associated refractive index, our predictions underestimate the experimental values. The limitations of our approach may be attributed to its inability to account for more subtle cooperative effects, like those associated with a network of hydrogen bonds. Together with other works, the supermolecule calculations confirm that the sign of χabc(2) is negative, contrary to an estimate from band structure calculation. [ABSTRACT FROM AUTHOR]

A general semiempirical scheme has been elaborated to simulate circular dichroism (CD) spectra of supramolecular systems. This approach adopts the analytical method of Beck and Hohlneicher [Theor. Chem. Acc. 101, 297 (1999).] to evaluate the one- and two-center integrals over Slater atomic orbitals. The performance of the method, employing INDO/S and CNDO/S semiempirical parametrizations, has been assessed by considering (i) the effect of the size of the singly excited states manifold, (ii) the origin invariance, and (iii) comparisons with the experimental and other theoretical spectra of several helicenes as well as pyridine-pyrimidine oligomers, which can adopt helical conformations. The main results are (i) the INDO/S parametrization with rather small excitation manifolds is able to reproduce, at low computational costs, the experimental CD spectra of several helicenes as well as CD simulations performed at ab initio and time-dependent density functional theory level of approximation; (ii) in the series of homohelicenes, the rotatory strength of the lowest-energy band increases almost linearly with the size of the helix; (iii) as evidenced by the study of tetradodecyloxy helicene bisquinone, packing effects can change the sign of remarkable CD bands, which are used to assign the structure configuration. [ABSTRACT FROM AUTHOR]

Using density functional theory (DFT) with the B3LYP, PBE, and PBE0 exchange-correlation functionals as well as the Mo\ller-Plesset second-order perturbation theory (MP2) combined with a series of rather extended basis sets, 1H and 13C chemical shifts of small alkanes and chloroalkanes (with different numbers of chlorine atoms on specific positions) have been simulated and compared to experimental data. For the 1H chemical shifts, theory tends to reproduce experiment within the limits of the experimental errors. In the case of 13C chemical shift, the differences between theory and experiment increase monotonically with the number of chlorine atoms and exhibit a deviation from additivity. This behavior is related to the saturation of the experimental 13C chemical shifts with the number of chlorine atoms, whereas the evolution is mostly linear at both DFT and MP2 levels of approximation. This difference has been traced back to the relativistic spin-orbit coupling effects, which are exalted as a result of the enhancement of the s character of the C atom when increasing the number of linked Cl atoms. Thus, it was demonstrated that not only electron correlation but also relativistic effects have to be considered for estimating the 13C chemical shifts when several Cl atoms are directly attached to the C atom. Linear (theory/experiment) regressions have then been performed for the different types of C atoms, i.e., bearing one, two, and three Cl atoms, with excellent correlation coefficients. The linear correlation relationships so obtained can then serve to predict and facilitate the interpretation of the nuclear magnetic resonance spectra of more complex compounds. Furthermore, by investigating the basis set effects, the correlation between the chemical shifts calculated using the 6-311+G(2d,p) basis set and the more extended 6-311+G(2df,p) and aug-cc-pvtz basis sets is excellent, demonstrating that the choice of the 6-311+G(2d,p) basis set for calculating the 1H and 13C chemical shifts is relevant. [ABSTRACT FROM AUTHOR]

The origin of the diradical character dependence of the second hyperpolarizability (γ) of neutral singlet diradical systems is clarified based on the perturbation formula of γ using the simplest diradical molecular model with different diradical characters, i.e., H2 under bond dissociation. The enhancement of γ in the intermediate diradical character region turns out to originate from the increasing magnitude of the transition moment between the first and second excited states and the decrease of that between the ground and first excited states, respectively, with the increase in diradical character. This feature confirms that open-shell singlet conjugated molecules with intermediate diradical characters constitute a new class of third-order nonlinear optical systems, whose γ values can be controlled by the diradical character in addition to the conjugation length. [ABSTRACT FROM AUTHOR]

The mixed electric-magnetic second-order nonlinear optical responses of oriented films of helicenes have been computed ab initio using the random phase approximation method and compared to the pure electric-dipole counterpart. It turns out that the mixed electric-magnetic responses can be of the same order of magnitude as the pure electric-dipole counterpart when there is no donor/acceptor (D/A) substituent or these D/A pairs are weak, i.e., when the pure electric-dipole response is small. When adding strong D/A substituents, the pure electric-dipole response increases substantially and much more than its mixed electric-magnetic counterpart. Consequently, the ratio between the mixed electric-magnetic and pure electric responses decreases. Although there is no general rule, the mixed responses evolve as a function of substitution quasi similarly to the pure electric contribution. This study confirms therefore the possibility of tuning the mixed electric-magnetic response by employing appropriate chiral molecules. [ABSTRACT FROM AUTHOR]