Scattering resonances are quantum phenomena arising from the decay of metastable collision complexes trapped by a centrifugal barrier or supported by a closed channel that is coupled to a scattering state. As such, resonances can provide significant insights into the scattering process and serve as a sensitive probe of the interaction potential. In this article, we present a detailed analysis of a cluster of shape resonances associated with the orbital angular momentum L = 5 in the j = 2 → j' = 0 rotational transition in Ne + D2 collisions for vibrational levels v = 0, 1, and 4. The energies and lifetimes of the resonances arising from different values of the total angular momentum quantum number J were analyzed through numerical fitting of the scattering matrix and employing a one-dimensional model based on an effective potential. We further investigated the sensitivity of the resonances to changes in the alignment of the D2 internuclear axis with respect to the initial relative velocity. Our results show that resonances can be exquisitely controlled by carefully selecting the initial alignment of the D2 molecule. In particular, not only the intensity of the resonance can be modulated but also the shape of the overall resonance profile can be altered, depending on the stereodynamical preferences of the individual resonances that contribute to the cluster.

How good is the time-dependent DFT method for simulating anionic shape resonances of DNA nucleobases?

We have studied the effect of microhydration on the anionic shape resonance states of uracil nucleobase. The resonance parameters were determined using the resonance via Padé approach along with the efficient wave function-based EA-EOM-DLPNO-CCSD method. Our results showed that the uracil resonances get stabilized with an increase in the extent of microsolvation. The energy of the resonances decreased, and the lifetime increased as the number of water molecules surrounding uracil was increased. Our calculation shows that ten water molecules are sufficient to make the lowest shape resonance of uracil a bound radical anionic state. It indicates that the lowest energy resonance state may become a bound state under bulk solvation.

Although the concept of resonance is a key element of any organic chemistry course, its modulation by supramolecular stabilization remains poorly explored. This article seeks to address this issue with the use of natural resonance theory and other computational tools such as ab initio methods (DF-MP2, coupled-cluster singles and doubles, and SAPT2 + 3(CCD)δMP2), interaction region indicator, and charge-transfer analysis. A set of structurally straightforward noncovalently bonded systems with general formula X/H2O where X = CO2, SO2, HCONH2, C4H4O, and C6H5NH2 is subjected to investigation. The findings indicate that the complexation can have significant impact on the relative weights of the resonance structures observed for isolated X by up to 32%. Furthermore, formation of X/H2O complex is found to introduce new resonance structures with water's outer-valence electrons participating in the resonance. These findings broaden understanding of how supramolecular interactions shape resonance, a fundamental concept in chemistry, and can improve predictions of molecular behavior in complex systems.

The complex absorbing potential (CAP) formalism has been successfully employed in various wave function-based methods to study electronic resonance states. In contrast, Green's function-based methods are widely used to compute ionization potentials and electron affinities but, despite a few influential contributions, have seen only limited application to resonances. We integrate the CAP formalism within the GW approximation, enabling the description of electronic resonances in a Green's function framework. This approach entails a fully complex treatment of orbitals and quasiparticle energies in a non-Hermitian setting. We validate our CAP-GW implementation by applying it to the prototypical shape resonances of N2-, CO-, CO2-, C2H2-, C2H4-, and CH2O-. It offers a fast and practical route to approximate both the lifetimes and positions of resonance states, achieving an accuracy comparable to that of state-of-the-art wave function-based methods.

This review presents a comprehensive examination of how second-order linear differential equations serve as a foundational tool for analyzing the dynamic behavior of electrical circuits, with a primary focus on series RLC networks. Beginning with the derivation of the governing equation from Kirchhoff’s voltage law, the discussion explores the natural, forced, and total responses that describe transient and steady-state phenomena. Key concepts such as natural frequency, damping ratio, and quality factor are highlighted to show how resistance, inductance, and capacitance shape oscillations, resonance, and energy dissipation. Analytical solution methods including characteristic-root analysis, variation of parameters, and Laplace transforms are compared with modern numerical approaches like Runge–Kutta and finite-difference techniques, emphasizing their respective strengths for both theoretical study and practical design. Applications extend from filter design and oscillatory circuits in communication systems to transient surge analysis and modern power electronics. By integrating classical mathematics with contemporary simulation and control strategies, this review underscores the enduring importance of second-order differential-equation methods in both electrical engineering practice and applied mathematics education.

We present a microwave-frequency method for measuring the polar Kerr effect and spontaneous time-reversal symmetry breaking (TRSB) in unconventional superconductors. While this experiment is motivated by work performed in the near infrared using zero-loop-area Sagnac interferometers, the microwave implementation is quite different and is based on the doubly degenerate modes of a TE111 cavity resonator, which act as polarization states analogous to those of light. The resonator system has in situ actuators that allow quadrupolar distortions of the resonator shape to be controllably tuned, as these compete with the much smaller perturbations that arise from TRSB. The most reliable way to detect the TRSB signal is by interrogating the two-mode resonator system with circularly polarized microwaves, in which case the presence of TRSB shows up unambiguously as a difference between the forward and reverse transmission responses of the resonator-i.e., as a breaking of reciprocity. We illustrate and characterize a coupler system that generates and detects circularly polarized microwaves and then show how these are integrated with the TE111 resonator, resulting in a dilution refrigerator implementation with a base temperature of 20 mK. We show test data on yttrium-iron-garnet ferrite and the van der Waals ferromagnet CrGeTe3 as an illustration of how the system operates. We then present data showing system performance under realistic conditions at millikelvin temperatures, achieving a Kerr-angle resolution δθK = 810 nrad for a 2 × 2mm2 sample, approaching the resolution of an optical Sagnac interferometer.

We report on the observation of highly excited ( ν ∼ 100 ) vibrational states of a trilobite ultralong-range Rydberg molecule in Rb 87 . These states manifest spectroscopically in a regularly spaced series of peaks red-detuned from the 25 f 7 / 2 dissociation threshold. The existence and observed stability of these states require the almost complete suppression of the adiabatic decay pathway induced by the P -wave shape resonance of Rb. This stabilization is predicted to occur only for certain Rydberg levels where the avoided crossing between trilobite and P -wave-dominated butterfly potential energy curves nearly vanishes, allowing the vibrational states to diabatically traverse the crossing with almost unit probability. This is the first direct measurement of beyond-Born-Oppenheimer physics in long-range Rydberg molecules, and paves the way for future experiments to access and manipulate wave packets formed from high-lying vibrational states.

In this work, we investigate the effect of an amino acid environment on nucleobase-centered anion radical shape resonances, using uracil as a model system for pyrimidine bases in RNA. Anionic uracil-glycine complexes were used to model the RNA-protein interactions. The resonance positions and widths of these complexes were simulated using the equation of motion coupled cluster method coupled with resonance via the Padé approach. Our results show that in the transient negative ion (TNI, i.e., the anion radical of glycine:uracil complex), glycine stabilizes nucleobase-centered resonances through hydrogen bonding, thereby increasing the lifetime of TNI. Simultaneously, a glycine-centered resonance demonstrates the ability of amino acids to capture the electron density and divert it away from the uracil nucleobase. At the micro-solvation level, this modeling indicates that amino acids would have more influence on nucleobase-centered resonances in the TNI than that displayed by the corresponding aqueous environment.

Radiation-induced processes in the aromatic cyano compound benzonitrile have attracted renewed interest since its detection in the interstellar medium in 2018, and recent studies have elucidated dissociative ionization pathways leading to species such as CN• and HCN, which can play important roles in interstellar chemistry. This work explores negative ion formation from benzonitrile upon electron attachment with mass spectrometry experiments and the most extensive theoretical study to date of the underlying negative ion states and their respective dissociative relaxation pathways. The measurements confirm the previously reported CN- formation at a collision energy of 3.0 eV as well as formation of the dehydrogenated parent anion and phenyl anion and CN- formation in the 7-10 eV energy range. Threshold energies for these dissociation channels are reported at the G4(MP2) level of theory for the first time. Furthermore, by using both scattering calculations and bound state techniques, CN- formation at around 3.0 eV may proceed from a 2B1, π4* shape resonance through nonadiabatic coupling with the σ*, CCN state. In the 7-10 eV range, complete active space plus second-order perturbation (CASPT2) calculations suggest strong contributions from core excited π4* and σ* resonances.

Spontaneous symmetry breaking, driven by nonadiabatic electron-nuclear coupling, can lead to geometric complexity in molecules and solids. While structural distortion from symmetry breaking occurs in femtoseconds, the timescale to lift electronic state degeneracy has remained elusive. We use the vibrationally resolved attosecond chronoscope to capture the electronic symmetry breaking induced by the Renner-Teller effect in bent CO2 molecules after photoionization by an extreme ultraviolet photon by measuring attosecond ionization delays. Relative photoionization delays between the four cation states are observed, with vibrational state–dependent delays, we analyze the evolution of the degenerate state to the nondegenerate A′ and A″ states due to molecular bending. With the help of theoretical analysis, we show that the relative photoionization delays of up to 72 as between the vibrational levels originate from the symmetry breaking–induced shape resonance. This study offers fundamental insights by resolving the coupled electron and structural dynamics simultaneously.

Metamaterial absorbers (MMAs) have appeared as innovative structures capable of effectively manipulating electromagnetic (EM) waves beyond the capabilities of natural materials. This review provides a comprehensive summary of narrowband and wideband MMAs, discussing their design strategies, working principles, and application-specific configurations. This study intends to point out current growths that enable high absorption performance, polarization insensitivity, angular stability, and frequency selectivity. A variety of unit cell structures, resonator shapes, and material selections are explored to realize their roles in achieving desired absorption features. The review categorizes MMAs based on their absorption bandwidth, structural parameters and performance metrics such as quality factor, sensitivity and frequency tunability. Methods like impedance matching, resonant mode coupling and equivalent circuit modeling are investigated to enlighten the physical mechanism of absorption. Crucial applications in wireless communication, radar cross-section reduction, energy harvesting, biomedical and environmental sensing are also discussed. Meanwhile, comparisons among current designs are presented in tabular form to back future designers in choosing ultimate MMA configurations. The paper concludes by summarizing the design challenges and providing visions into emerging trends and potential future guidelines in MMA technology. IUBAT Review—A Multidisciplinary Academic Journal, 8(1): 145-175

Abstract Isoflurane is a halogenated anaesthetic gas adopted in modern clinical practice due its efficacy and safety profile. However, its atmospheric persistence contributes to global warming potential that influences its overall environmental burden. In this study, we employed a crossed electron-molecular beam technique to investigate dissociative electron attachment (DEA) processes in order to investigate isoflurane fragmentation induced by electron impact. The DEA process results in the formation of twelve anionic fragments, including halogenated anions (Cl− and F−), complex fluoro-chloro containing species (e.g., [C2F3Cl]−, [C2HFCl]−), and oxygen-containing anions such as [CHF2O]− and [CFO]−. The most intense signal corresponds to Cl−, which exhibits a sharp resonance near 0.1 eV, can be attributed to a shape resonance or due high dipole moment of isoflurane (2.47 D) to a vibrational Feshbach resonance (VFR). In contrast, F− formation is observed in a high-energy domain (4–7 eV) and proceeds via core-excited resonance. Remarkably, the [FHF]− anion was detected with unexpectedly high intensity at low energies, suggesting the occurrence of complex multi-bond dissociation and electron-induced molecular rearrangement. These findings provide important insights into the electron-induced chemistry of halogenated anaesthetics. Graphic abstract

Photodissociation dynamics of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>X</mml:mi><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:math> ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>X</mml:mi></mml:math> = Na, K, Rb, Cs): Rovibrationally resolved shape resonances driven by potential barriers in the ultraviolet spectrum

Abstract Low-energy electron scattering calculations on the open-shell CN radical are performed using the fixed-nucleus R-matrix method for several internuclear separations (R). The elastic, momentum transfer, differential and electronic excitation cross section are presented at various target and scattering models. We report five CN− core-excited shape resonances lying above the first electronic excitation threshold, namely 3Σ+, 1 3Π, 2 3Π, 3Σ- and 1Σ-. The CN− resonance curves are analyzed as a function of R, confirming that the resonances become narrower with increasing R and in general their energies drop; the 3Σ+ resonance becomes bound for R &gt; 1.3918 Å. The designation of these resonances are discussed. By the analysis of changing R, the difference on the magnitude of cross sections is prominent happening at the peak positions. The results obtained here provide a starting point for studies of electron-impact resonant vibration excitation and other CN− resonance-driven phenomena in plasma.

Amid the accelerating processes of modernization and commercialization, traditional rural public spaces are increasingly losing their cultural value and social functions. This study investigates the transformative role of art intervention in enhancing the quality and cultural significance of rural public spaces, with a focus on Machang Village in Tengchong, China. The study first develops a conceptual model to explore the causal relationships and pathways between these influencing factors. Drawing on this framework, the research then uses Structural Equation Modeling (SEM) to empirically test a multi-dimensional resident satisfaction model that incorporates spatial aesthetics, functional suitability, historical-cultural identity, and emotional cognition. Through field surveys and data collected from 224 residents, the study reveals that cultural emotions and functional completeness are the most influential factors in driving overall satisfaction. Artistic innovation and aesthetics contribute moderately, indicating that visual creativity alone is insufficient without deeper cultural integration and functional coherence. The findings suggest a dual-pathway satisfaction mechanism, where both symbolic emotional resonance and practical usability shape residents’ perceptions of public space quality. The study offers theoretical and practical insights into optimizing rural public space design, advocating for art-led, community-engaged, and culturally embedded approaches to rural revitalization.

Prior investigations into the photodissociation dynamics of the hydrogen molecular ion (H_ ) have frequently neglected the impact of shape resonances, which could potentially lead to inaccuracies in astrophysical modeling. This study systematically explores the photodissociation cross sections of H_ with a rigorous consideration of shape resonances. We aim to elucidate comprehensively the photodissociation mechanisms by accurately accounting for transitions from the electronic ground state $1^2Σ_ g $ to multiple electronically excited states. Our results provide updated, precise cross-sectional data essential for refining chemical evolution models of interstellar environments and for rectifying previous methodological oversights. We employed high-level ab initio calculations based on the multireference single- and double-excitation configuration interaction (MRDCI) method to determine the electronic structure of the H_ ion accurately. The photodissociation cross sections were calculated under the assumption of local thermodynamic equilibrium (LTE) across photon wavelengths ranging from $25$ nm to the dissociation threshold, incorporating contributions from the majority of rovibrational states of the ground electronic state. Particular attention was given to analyzing the effects of shape resonances, especially the significant role played by the 1^2Π_ state near the spectral region of the Lyman α line. Our computed cross sections clearly demonstrate that shape resonances substantially influence the photodissociation dynamics of H_ near the Lyman α line. The contribution from the 1^2Π_ excited state prominently shapes the spectral absorption features around the Lyman α region. These refined theoretical results offer substantial improvements over previous datasets, delivering the precise spectral information necessary for astrophysical simulations, modeling ultraviolet-driven chemical processes in interstellar media, and enhancing our understanding of photochemical dynamics in the early universe.

Abstract Van der Waals (vdW) materials have garnered growing interest for use as nanophotonic building blocks that offer precise control over light‐matter interaction at the nanoscale, such as optical metasurfaces hosting sharp quasi‐bound states in the continuum resonances. However, traditional fabrication strategies often rely on lift‐off processes, which inherently introduce imperfections in resonator shape and size distribution, ultimately limiting the resonance performance. Here, an optimized fabrication approach for vdW‐metasurfaces is presented that implements inverse patterning of the etching mask, resulting in increased resonator quality solely limited by the resolution of the electron beam lithography resist and etching. Applying this inverse fabrication technique on hexagonal boron nitride (hBN), quality (Q) factors exceeding 103 in the visible spectral range are demonstrated, significantly surpassing previous results shown by lift‐off fabricated structures. Additionally, the platform's potential as a biosensor is displayed, achieving remarkable sensitivity and figure of merit of 220 in a refractive index sensing experiment. The inverse technique is applied to create chiral metasurfaces from hBN, using a two‐height resonator geometry to achieve up to 50% transmittance selectivity. This inverse lithography technique paves the way toward high‐performances vdW‐devices with high‐Q resonances, establishing hBN as a cornerstone for next‐generation nanophotonic and optoelectronic devices.

Abstract The most abundant nuclides in the cosmos have equal numbers of protons and neutrons. These include He 2 4 , C 6 12 , N 7 14 , O 8 16 , Ne 10 20 , Mg 12 24 , Si 14 28 , and S 16 32 , which together comprise 99.5% of ordinary polynucleonic matter. These are the most kinetically resilient (stable) nuclides within the highly exothermic reaction conditions of cosmic nucleosynthesis. This paper analyzes the relationship between the composition and relative cosmic abundance of light, stable nuclides. Structural symmetry emerges as a sensitive and specific predictor of superabundance within a proposed alternating nucleon model. The model derives ab initio from the proton’s radius (r =0.8414 fm), the hadron’s prolate shape (from the transition to the proton’s first excited state, the ∆+(1232) resonance), and the separation distance between a pair of bound nucleons (≈ 0.8 fm, from the nucleon-nucleon potential). Various nucleon geometries were considered for each nuclide, with preference given to structures having optimal numbers of stable proton-neutron short-range interactions and whose model radii (derived from the regular polygon radius formula) best correlate with experimental charge radii (r(31)=.98, p&lt;.001). Remarkably, the best-fit solutions for the eight superabundant Z=N nuclides categorically demonstrate bilateral structural symmetry, in which neutrons reflect protons on opposite sides of a bisecting chiral plane. Conversely, when an element’s stable isotopes are compared, the best-fit structures in which nucleon symmetry is not possible (generally because proton and neutron numbers are unequal) are less abundant by ≈ 2 orders of magnitude. Symmetry is ubiquitous in nature, and the proposed alternating nucleon model is consistent with the axiom that structural symmetry confers structural stability.

Abstract The photodetachment cross sections of positronium negative ions are calculated using the complex coordinate rotation method for photon energies below 6 eV. The calculated photodetachment cross sections are in good agreement with those obtained using the hyperspherical close-coupling method [Igarashi et al. 2000, New J. Phys. 2 17]. Good agreement is also observed above the detachment threshold of Ps (n = 2) + e− where multiple detachment channels are open. We report that the peak structure corresponding to the shape resonance around 5.44 eV is consistent with experimental observations. The proposed method can be applied to more complicated systems containing positrons to provide predictions for future photodetachment experiments and to reveal their dynamics.