Low State Research Articles

Electric dipole polarizability of low-lying excited states in atomic nuclei

New equations for the electric dipole polarizability α E1 of low-lying excited states in atomic nuclei—and the related (−2) moment of the total photo-absorption cross section, σ −2—are inferred in terms of electric dipole and quadrupole matrix elements. These equations are valid for arbitrary angular momenta of the initial/ground and final/excited states and have been exploited in fully converged 1ℏ ω shell-model (SM) calculations of selected p- and sd-shell nuclei that consider configuration mixing; advancing previous knowledge from 17O to 36Ar, where thousands of electric dipole matrix elements are computed from isovector excitations which include the giant dipole resonance (GDR) region. Our results are in reasonable agreement with previous SM calculations and follow—except for 6,7Li and 17,18O—Migdal’s global trend provided by the combination of the hydrodynamic model and second-order non-degenerate perturbation theory. Discrepancies in 6,7Li and 17O arise as a result of the presence of α-cluster configurations in odd-mass nuclei, whereas the disagreement in 18O comes from the mixing of intruder states, which is lacking in the SM interactions. More advanced ab initio calculations of the dipole polarizability for low-lying excited states covering all the isovector states within the GDR region are missing and could be very valuable to benchmark the results presented here and shed further light on how atomic nuclei polarize away from the ground state

Primary processes of the archetypal model complex azido(porphinato)iron(III) from ultrafast vibrational-electronic spectroscopy.

Azidoiron complexes serve as valuable photochemical precursors for catalytically active species containing high-valent iron. In bioinorganic chemistry, azido(tetraphenylporphinato)iron(III), i.e., [FeIII(tpp)(N3)] with tpp = 5, 10, 15, 20-tetraphenylporphyrin-21, 23-diido, constitutes the archetypal model system that was used to access for the first time the terminal nitridoiron core, FeV ≡ N, in the biomimetic redox-non-innocent ligand environment. So far, the light-induced dynamics leading to the oxidation of the metal and the release of dinitrogen from the N3-ligand have only been studied for precursors featuring redox-innocent auxiliary ligands that simplify the electronic structure change accompanying the photo-transformation. Here, we monitored the primary events of the above paradigmatic complex, following its optical excitation in the ultraviolet-to-visible spectral range using femtosecond spectroscopy with probing in both the UV-vis and mid-infrared regions. Following ultrafast Soret-excitation at 400nm, the complex relaxes to the lowest excited sextet state by a first internal conversion in less than 200fs. The excited state then undergoes vibrational relaxation on a time scale of roughly 2ps before internally converting yet again to recover the sextet electronic ground state within 19.5ps. Spectroscopic evidence is obtained neither for a transient occupation of the energetically lowest metal-centered state, 41A1, nor for vibrational relaxation in the ground-state. The primary processes seen here are thus in contrast to those previously derived from ultrafast UV-pump/vis-probe and UV-pump/XANES-probe spectroscopies for the halide congener [FeIII(tpp)(Cl)]. Any photochemical transformation of the complex arises from two-photon-induced dynamics.

Long-Range Gating in Single-Molecule One-Dimensional Topological Insulators.

Single-molecule one-dimensional topological insulator (1D TI) is a class of molecular wires that exhibit increasing conductance with wire length. This unique trend is due to the coupling between the two low-lying topological edge states of 1D TIs described by the Su-Schrieffer-Heeger model. In principle, this quantum phenomenon within 1D TIs can be utilized to achieve long-range gating in molecular conductors. Here, we study electron transport through a single-edge state of doubly oxidized oligophenylene bis(triarylamine) to understand the effect of the edge state coupling on conductance. We find that conductance is elevated by approximately 1 order of magnitude compared to a control molecule with the same conductance pathway. Density function theory calculations further support that the increase in conductance is due to the interaction between the edge states of 1D TIs. This work demonstrates a new gating paradigm in molecular electronics, while also providing a deeper understanding of how edge states interact and affect electron transport within 1D TIs.

Axial Coordinated Manganese(III) Porphyrin/Tetraazaporphyrin - 4-(10-phenylanthracen-9-yl)Pyridine Dyads: Self-Assembly, Structure and Spectral Properties in Ground and Excited States.

Self-assembly of new donor-acceptor systems based on (5,10,15,20-tetraphenylporphinato)manganese(III)/(5,10,15,20-tetra-4-tert-butylphenylporphinato)manganese(III)/(octakis(4-tert-butylphenyl)tetraazaporphinato)manganese(III) acetate ((AcO)MnTPP/(AcO)MnTBPP/(AcO)MnTAP) and 4-(10-phenylanthracen-9-yl)pyridine (PyAn) was studied using fluorescence spectroscopy and mass spectrometry. It was found that the coordination complexes of 1 : 1 composition (dyads) are formed in toluene. The spectral properties, the chemical structures and redox behavior of the dyads were described using 1H NMR, IR, ESR spectroscopy and cyclic voltammetry, respectively. The dynamic processes and the characteristics in the excited state of the dyads were obtained using the femtosecond transient absorption spectroscopy method. Density functional theory (DFT), time-dependent DFT methods were used to elucidate the dyad electronic structures and to establish the differences in their frontier molecular orbitals. The analysis of the lambda parameter and the distance of hole-pair interaction was indicated more favorable charge transfer between the macrocycle and the axial PyAn fragment in (AcO)(PyAn)MnTAP. The calculated values of the zero-field splitting parameters D and E/D, together with the g tensors of the lowest spin-orbit state for (AcO)MnTPP and (AcO)(PyAn)MnTPP were obtained using the combination of DFT and Multireference Perturbation Theory (CASSCF/NEVPT2) simulations. The data obtained develop the fundamental basis in the field of photovoltaics and show the prospects for the study of molecular systems of this class.

Direct probing of low-energy intra d-band transitions in gas-phase cobalt clusters

The interplay between constituent localized and itinerant electrons of metal clusters defines their physical and chemical properties. In turn, the electronic and geometrical structures are strongly entwined and exhibit strong size-dependent variations. Current understanding of low-energy excited states of metal clusters relies on stand-alone theoretical investigations and few comparisons with measured properties, since direct identification of low-lying states is lacking hitherto. Here, we report on the measurement of low-lying electronic transitions in cationic cobalt clusters using infrared photofragmentation spectroscopy. Broad and size-dependent absorption features were observed within 0.056 – 0.446 eV, well above the energies of the sharp absorption bands caused by cluster vibrations. Complementary time-dependent density functional theory calculations reproduce the main observed absorption features, providing direct evidence that they correspond to transitions between electronic states of mainly d-character, arising from the open d-shells of the Co atoms and the high spin multiplicity of the clusters.

Jet-cooled ethylene cavity ring-down spectroscopy between 5880 and 6200 cm−1

Absorption spectra of jet-cooled ethylene (ethene, C2H4) are recorded at three different rotational temperatures (6/8 K, 12 K, 38 K) using cavity ring-down spectroscopy (CRDS) in the 5880–6200 cm−1 spectral region. Rotational cooling is used to determine the various vibrational band centers by simplifying drastically the rotational band structure. A line-by-line assignment, based on a direct comparison with the TheoReTS variational line list and a systematic use of lower state combination difference (LSCD), is performed. Experimental line lists including line position and line integrated absorption cross sections are drawn up. The 6/8 K, 12 K and 38 K spectra contain 668, 1553 and 1679 absorption lines respectively. Overall, 320 rovibrational lines are assigned across 20 interacting vibrational bands. Among the 20 vibrational cold bands identified in this work, 14 had never been observed before. Line intensities are in the range of 10−24 - 10−20 cm/molecule. A direct comparison between our work and the TheoReTS and ExoMol theoretical line lists, as well as with the recent experimental work of Ben Fathallah et al. (2024) is provided.

An inverted singlet-triplet excited state in a pentaazaphenalene derivative (5AP-N(C12)2)

The characteristic of inverted singlet-triplet excited states, in which the lowest singlet excited state (S1) is lower than the lowest triplet state (T1) in energy, was observed in a dialkylamine-substituted pentaazaphenalene derivative, 5AP-N(C12)2. The transient photoluminescence measurements showed that the reverse intersystem crossing has virtually zero activation energy, whereas the intersystem crossing is proceeded by a thermal activation process. T1 was located energetically above S1 with a negative energy gap between S1 and T1 (ΔE ST) of −37 meV. Fluorescence and phosphorescence spectra also confirmed the negative ΔE ST of −46 to −32 meV.

Simulation studies of tungsten impurity behaviors in helium plasma in comparison with deuterium plasma via SOLPS-ITER

The sputtering and transport of tungsten (W) impurities in helium (He) and deuterium (D) plasma discharges are compared using the SOLPS-ITER code. To reduce the computational resources of modeling, W ions are treated using the bundled charge state model. The results show that the W erosion flux of He plasma is almost a factor of two higher than that of D plasma under the same upstream electron density and heating power due to the higher W sputtering yield in He plasma. Moreover, the W self-sputtering flux is significantly higher than the W flux sputtered by the main ions. The leakage and retention of W impurities in the divertor region is also analyzed. W ions mainly escape from the near scrape-off layer (SOL) region through the divertor entrance as the stagnation point of the average W impurity poloidal velocity is considerably closer to the target plates in the near SOL region. Furthermore, the leakage flux of W ions in He plasma is higher than that in D plasma, mainly because of the higher W sputtering level in He plasma, which results in a larger W density. W ions with low-lying charge states, mostly comprising the charge state of W10–12+, easily escape from the divertor through the near SOL flux tubes in both D and He plasmas. In addition, the effects of upstream electron density on W sputtering and retention in He and D plasma discharges are presented.

Supramolecular Polymerization as a Tool to Reveal the Magnetic Transition Dipole Moment of Heptazines.

Heptazine derivatives have attracted significant interest due to their small S1-T1 gap, which contributes to their unique electronic and optical properties. However, the nature of the lowest excited state remains ambiguous. In the present study, we characterize the lowest optical transition of heptazine by its magnetic transition dipole moment. To measure the magnetic transition dipole moment, the flat heptazine must be chiroptically active, which is difficult to achieve for single heptazine molecules. Therefore, we used supramolecular polymerization as an approach to make homochiral stacks of heptazine derivatives. Upon formation of the supramolecular polymers, the preferred helical stacking of heptazine introduces circular polarization of absorption and fluorescence. The magnetic transition dipole moments for the S1 ← S0 and S1 → S0 are determined to be 0.35 and 0.36 Bohr magneton, respectively. These high values of magnetic transition dipole moments support the intramolecular charge transfer nature of the lowest excited state from nitrogen to carbon in heptazine and further confirm the degeneracy of S1 and T1.

Spectroscopic Quantification of the Inverted Singlet-Triplet Gap in Pentaazaphenalene.

We report the direct and accurate spectroscopic quantification of the inverted singlet-triplet gap in 1,3,4,6,9b-pentaazaphenalene. This measurement is achieved by directly probing the lowest singlet and triplet states via high-resolution cryogenic anion photoelectron spectroscopy. The assignment of the first excited singlet state is confirmed by visible absorption spectroscopy in an argon matrix at 20 K. Our measurements yield an inverted singlet-triplet gap with ΔEST= -0.047(7) eV. The accurate quantification of the singlet-triplet gap presented here allows for direct evaluation of various computational electronic structure methods and highlights the critical importance of the proper description of the double excitation character of these electronic states. Overall, this study validates the idea that despite Hund's multiplicity rule, useful organic chromophores can have inherently inverted singlet-triplet gaps.

Quantum mechanical treatment of nuclear friction in coupled-channels heavy-ion fusion

Nuclear friction causes energy dissipation in heavy-ion collisions. Its understanding and inclusion in quantum mechanical reaction models are crucial for advancing the physics of heavy-ion reactions forming heavy elements. The effects of nuclear friction on heavy-ion fusion reactions are investigated using the coupled-channels density-matrix method. In this open-quantum-system description, a phenomenological nuclear friction form factor is introduced along with coherent coupled-channels effects. The key nucleus was the 92Zr target, due to its high density of low-lying non-collective excited states, which was recently theorised to be cause of nuclear friction. The calculations using the 16O + 92Zr collision showed that the inclusion of nuclear friction effects increased the fusion probability significantly, and that the agreement between the theoretical and experimental fusion barrier distributions was improved when nuclear friction effects were included.

Exploring the photochemistry of OAlOH: Photodissociation pathways and electronic spectra.

This study was focused on the photochemistry of OAlOH and three possible pathways, which were studied with high-level multireference configuration interaction abinitio calculations. We computed cuts of the six-dimensional potential energy surfaces for the ground, the lowest singlet and triplet excited states, and probed the photodissociation mechanisms and the stabilities. The OAlOH electronic spectrum, with an energy reaching 7.15eV, contained four prominent peaks. Photodissociation to AlO, OH, and AlOH constituted a plausible mechanism within the deep-UV range (λ = 250.4nm). Our data indicated the photostability of OAlOH in the near-UV‒Vis region, so detection with laser-induced fluorescence is possible. Fluorescence and phosphorescence may occur upon excitation at 363.5nm. The roles of OAlOH in the photochemical reactions of Al-bearing molecules in the upper atmosphere and VY Canis Majoris are discussed.

Chelate Complexes of 3d Transition Metal Ions─A Challenge for Electronic-Structure Methods?

Different electronic-structure methods were assessed for their ability to predict two important properties of the industrially relevant chelating agent nitrilotriacetic acid (NTA): its selectivity with respect to six different first-row transition metal ions and the spin-state energetics of its complex with Fe(III). The investigated methods encompassed density functional theory (DFT), the random phase approximation (RPA), coupled cluster (CC) theory, and the auxiliary-field quantum Monte Carlo (AFQMC) method, as well as the complete active space self-consistent field (CASSCF) method and the respective on-top methods: second-order N-electron valence state perturbation theory (NEVPT2) and multiconfiguration pair-density functional theory (MC-PDFT). Different strategies for selecting active spaces were explored, and the density matrix renormalization group (DMRG) approach was used to solve the largest active spaces. Despite somewhat ambiguous multi-reference diagnostics, most methods gave relatively good agreement with experimental data for the chemical reactions connected to the selectivity, which only involved transition-metal complexes in their high-spin state. CC methods yielded the highest accuracy followed by range-separated DFT and AFQMC. We discussed in detail that even higher accuracies can be obtained with NEVPT2, under the prerequisite that consistent active spaces along the entire chemical reaction can be selected, which was not the case for reactions involving Fe(III). A bigger challenge for electronic-structure methods was the prediction of the spin-state energetics, which additionally involved lower spin states that exhibited larger multi-reference diagnostics. Conceptually different, typically accurate methods ranging from CC theory via DMRG-NEVPT2 in combination with large active spaces to AFQMC agreed well that the high-spin state is energetically significantly favored over the other spin states. This was in contrast to most DFT functionals and RPA which yielded a smaller stabilization and some common DFT functionals and MC-PDFT even predicting the low-spin state to be energetically most favorable.

Loading or Unloading? This Is the Question! A Multi-Season Study in Professional Football Players.

This study examined the impact of training load periodization on neuromuscular readiness in elite football players using the Locomotor Efficiency Index (LEI) as a measure of performance optimization. Throughout the 2021/22 and 2022/23 seasons, 106 elite male players (age: 19.5 ± 3.9 years) from an Italian professional football club were monitored using Global Positioning Systems (GPS) external load data. The LEI was derived from a machine learning model, specifically random forest regression, which compared predicted and actual PlayerLoad™ values to evaluate neuromuscular efficiency. Players were categorized by weekly LEI into three readiness states: bad, normal, and good. Analysis focused on the variation in weekly LEI relative to weekly load percentage variation (large decrease, moderate decrease, no variation, moderate increase, large increase), which included total distance, high-speed distance (above 25.2 km/h), and mechanical load, defined as the sum of accelerations and decelerations. Statistical analysis showed significant differences only with variations in total distance and mechanical load. Specifically, reducing weekly loads improved LEI in players in lower readiness states, while maintaining or slightly increasing loads promoted optimal readiness. This approach enables coaches to tailor training prescriptions more effectively, optimizing workload and recovery to sustain player performance throughout a demanding season.

BaCoO2 with Tetrahedral Cobalt Coordination: The Missing Element to Understand Energy Storage and Conversion Applications in BaCoO3-δ-Based Materials.

Barium-cobaltate-based perovskite (BaCoO3-δ) and barium-cobaltate-based nanocomposites have been intensively studied in energy storage and conversion devices mainly due to flexible oxygen stoichiometry and tunable nonprecious transition metal oxidation states. Although a rich and complex family of structural polymorphs has already been reported for these perovskites in the literature, the potential structural evolution that may occur during the oxygen reduction reaction and the oxygen evolution reaction has not been investigated so far. In this study, we synthesized and characterized the lowest Co-oxidation state possible in the compound, BaCoO2, which exhibits a quartz-derived, trigonal structure with a helicoidally corner-sharing, CoO4-tetrahedral-framework as already proposed by Spitsbergen et al. Oxygen can reversibly be inserted in such a crystal structure to form BaCoO3-δ, i.e., with 0 ≤ δ ≤ 1, based on the results of an in situ coupled thermogravimetric - neutron diffraction study and which presents therefore giant oxygen capacity storage due to the extreme tunability of the electronic configuration of the cobalt cations which defines the fundamental origins of the materials performance. The reversible conversion of BaCoO2 to BaCoO3-δ associated with a similar electronic conductivity above 900 K permits to clarify the high potential of BaCoO3-δ-based energy storage and conversion devices.

The n,π* States of Heteroaromatics: When are They the Lowest Excited States and in What Way Can They Be Aromatic or Antiaromatic?

Heteroaromatic molecules are found in areas ranging from biochemistry to photovoltaics. We analyze the n,π* excited states of 6π-electron heteroaromatics with in-plane lone pairs (nσ, herein n) and use qualitative theory and quantum chemical computations, starting at Mandado's 2n + 1 rule for aromaticity of separate spins. After excitation of an electron from n to π*, a (4n + 2)π-electron species has 2n + 2 πα-electrons and 2n + 1 πβ-electrons (or vice versa) and becomes πα-antiaromatic and πβ-aromatic. Yet, the antiaromatic πα- and aromatic πβ-components seldom cancel, leading to residuals with aromatic or antiaromatic character. We explore vertically excited triplet n,π* states (3n,π*), which are most readily analyzed, but also singlet n,π* states (1n,π*), and explain which compounds have n,π* states with aromatic residuals as their lowest excited states (e.g., pyrazine and the phenyl anion). If the πβ-electron population becomes more (less) uniformly distributed upon excitation, the system will have an (anti)aromatic residual. Among isomers, the one that has the most aromatic residual in 3n,π* is often of the lowest energy in this state. Five-membered ring heteroaromatics with one or two N, O, and/or S atoms never have n,π* states as their first excited states (T1 and S1), while this is nearly always the case for six-membered ring heteroaromatics with electropositive heteroatoms and/or highly symmetric (D2h) diheteroaromatics. For the complete compound set, there is a modest correlation between the (anti)aromatic character of the n,π* state and the energy gap between the lowest n,π* and π,π* states (R2 = 0.42), while it is stronger for monosubstituted pyrazines (R2 = 0.84).

Superconformal indices and localization in N = 2B quantum mechanics

Superconformal ‘type B’ quantum mechanical sigma models arise in a variety of interesting contexts, such as the description of D-brane bound states in an AdS2 decoupling limit. Focusing on N = 2B models, we study superconformal indices which count short multiplets and provide an alternative to the standard Witten index, as the latter suffers from infrared issues. We show that the basic index receives contributions from lowest Landau level states in an effective magnetic field and that, due to the noncompactness of the target space, it is typically divergent. Fortunately, the models of interest possess an additional target space isometry which allows for the definition of a well-behaved refined index. We compute this index using localization of the functional integral and find that the result agrees with a naive application of the Atiyah-Bott fixed point formula outside of it’s starting assumptions. In the simplest examples, this formula can also be directly verified by explicitly computing the short multiplet spectrum.

Coupling structural, chemical composition and stress fluctuations with relaxation dynamics in metallic glasses

Understanding the atomistic mechanisms of relaxation dynamics in metallic glasses remains a longstanding challenge. Here, using microsecond time scale molecular dynamics simulations, three main relaxation stages in metallic glasses are identified. At about 0.6Tg, chemical composition plays a dominant role in the relaxation, manifested by stress accumulation and only minimal variations in structure. As Tg approaches, the confluence of structural heterogeneity and chemical composition leads to the decoupling of relaxation mechanisms. At this temperature, the relaxation results in a structure with a lower energy state and a lower level of stress. In the supercooled liquid regime, an extensive increase in the number of closed-packed icosahedral clusters is responsible for accelerated structural relaxation while their packing frustration leads to the accumulation of intrinsic residual stresses in the glass. The atomistic origin of these dynamic relaxation modes is discussed in terms of structural, chemical composition and stress variations.

Assessment of Iron-Based Spin-Orbit Coupling Effects in Pt-Fe Heterobimetallic Lantern Complexes via 57Fe Mössbauer Spectroscopy.

A series of heterobimetallic lantern complexes, [PtFe(SOCR)4(pyX)] where R = Me, X = H (1), X = NH2 (2), X = SMe (3); R = Ph, X = H (4), X = NH2 (5), X = SMe (6), have been prepared and characterized spectroscopically. Compounds 1, 4, and 5 are reported herein for the first time. The high-spin iron(II) sites of 1-6 have been investigated using 57Fe Mössbauer spectroscopy. Although the isomer shift of these species is nearly identical, their quadrupole splitting exhibits a much larger variation. Moreover, the zero-field Mössbauer spectra of 3-5 show surprising changes over time which are likely indicative of small structural distortions. The field dependent Mössbauer study of 1 and 6 revealed a zero field splitting (ZFS) characterized by a relatively large and positive D value. The combined Density Functional Theory (DFT) and ab initio Complete Active Space Self-Consistent Field (CASSCF) investigation of 1-6 indicates that their ground state is best described using a linear combination of {|xz⟩, |yz⟩} states. Our theoretical analysis suggests that the ZFSs and magnitude of the quadrupole splitting of 1-6 are determined by the spin-orbit coupling of the three lowest orbital states which have a T2g parentage.

Multistate Dynamics and Kinetics of CO2 Activation by Ta+ in the Gas Phase: Insights into Single-Atom Catalysis.

The activation of carbon dioxide (CO2) by a transition-metal cation in the gas phase is a unique model system for understanding single-atom catalysis. The mechanism of such reactions is often attributed to a "two-state reactivity" model in which the high-energy barrier of a spin state correlating with ground-state reactants is avoided by intersystem crossing (ISC) to a different spin state with a lower barrier. However, such a "spin-forbidden" mechanism, along with the corresponding dynamics, has seldom been rigorously examined theoretically, due to the lack of global potential energy surfaces (PESs). In this work, we report full-dimensional PESs of the lowest-lying quintet, triplet, and singlet states of the TaCO2+ system, machine-learned from first-principles data. These PESs and the corresponding spin-orbit couplings enable us to provide an extensive theoretical characterization of the dynamics and kinetics of the reaction between the tantalum cation (Ta+) and CO2, which have recently been investigated experimentally at high collision energies using crossed beams and velocity map imaging, as well as at thermal energies using a selected-ion flow tube apparatus. The multistate quasi-classical trajectory simulations with surface hopping reproduce most of the measured product translational and angular distributions, shedding valuable light on the nonadiabatic reaction dynamics. The calculated rate coefficients from 200 to 600 K are also in good agreement with the latest experimental measurements. More importantly, these calculations revealed that the reaction is controlled by intersystem crossing, rather than potential barriers.