Transition Moment Research Articles

A theoretical investigation of spectroscopy properties and transition properties of TlBr+ cation

The potential energy curves, dipole moments and transition dipole moments of the 14 Λ–S states and 30 Ω states of TlBr+ cation were performed using the multi-reference configuration interaction method. The Davidson correction and spin–orbit coupling effects were also considered. The spectroscopic properties and transition properties of TlBr+ cation were reported at the first time. The results show that the X2Π is the ground state and the A2Σ+ is the first excited state, which are both weakly bound states. 14 Λ–S states are all electronically bound except for the 24Π state, which is repulsive. The phenomenon of avoided crossing in the Ω states occurs in the energy region between 30,000 and 50,000 cm−1. The Franck–Condon factors, radiative lifetimes and emission coefficients between the and transitions are both calculated. The results indicated that the radiative lifetimes of the and states are too large to laser cooling TlBr+ cation, laser cooling of TlBr+ cation is not feasible. These results provide a theoretical basis to explore the spectroscopic properties of TlBr+ cation.

Line List for the A2Π−X2Σ+ and the B2Σ+−X2Σ+ Band Systems of CaF

Abstract The spectral analysis of molecule-rich asymptotic giant branch (AGB) stars is challenging. Although other calcium and fluorine bearing molecules are observed in the microwave and in the visible spectrum of AGB stars, CaF has never been detected, despite favorable chemical equilibrium predictions. Yet, measuring the CaF abundance could give more insight into the fluorine budget of AGB stars and allow better simulation of stellar spectra. In this work, we present an analysis of the visible spectrum of CaF obtained with a Fourier transform spectrometer. CaF A 2Π−X 2Σ+ and B 2Σ+−X 2Σ+ band systems were excited with a hollow cathode discharge. Using previous fluorescence spectroscopy measurements, highly accurate ground state constants, and reasonable extrapolation schemes, the strongest features of CaF in the visible spectrum can be accurately modeled for both band systems. Spectroscopic constants are determined for A 2 Π with v ≤ 16 and for B 2Σ+ with v ≤ 20. Ab initio transition dipole moment curves of both transitions were calculated and scaled, and we provide a line list with Einstein A coefficients and oscillator strengths. This line list can be used to simulate spectra of CaF at temperatures and pressures relevant to astrophysical environments.

The Properties of the Low-Lying Electronic States and Avoided Crossings of the SbP Molecule: A Theoretical Investigation Includes Spin-Orbit Coupling.

High-level multireference configuration interaction plus Davidson correction (MRCI + Q) calculation method was employed to determine the potential energy curves (PECs) of 10 Λ-S states, which come from the first and second dissociation channels of the SbP molecule, as well as 34 Ω states considering the spin-orbit coupling (SOC) effect. By solving the Schrödinger equation for nuclear motion, spectroscopic constants for the ground state X1Σ+ and low-lying excited states were obtained and compared with experimental data. The excellent agreement indicates the reliability of our calculations. Additionally, the calculated spin-orbit (SO) matrix elements of the 13Π and 15Π states with other Λ-S states were analyzed, and the majority of the values in the Franck-Condon region exceed 200 cm-1, indicating strong interactions between these states. What's more, the joint effects of spin-orbit coupling and avoided crossing were discussed in detail, leading to the complex potential energy curves and double-well phenomena observed in the Ω states. Taking forbidden transitions into account, transition dipole moments with the SOC effect are considered. The Franck-Condon factors, Einstein coefficients, and radiative lifetimes for the 13Σ+1 ↔ X1Σ+0+ transition were obtained. Analysis indicates that direct laser cooling of SbP is inappropriate.

A computational study on the effect of structural isomerism on the excited state lifetime and redox energetics of archetype iridium photoredox catalyst platforms [Ir(ppy)2(bpy)]+ and Ir(ppy)3.

This study investigates the impact of structural isomerism on the excited state lifetime and redox energetics of heteroleptic [Ir(ppy)2(bpy)]+ and homoleptic Ir(ppy)3 photoredox catalysts using ground-state and time-dependent density functional theory methods. While the ground- and excited-state reduction potentials differ only slightly among the isomers of these complexes, our findings reveal significant variations in the radiative and non-radiative decay rates of the reactivity-controlling triplet 3MLCT states of these closely related species. The observed differences in radiative decay rates could be traced back to variations in the transition dipole moment, vertical energy gaps, and spin-orbit coupling of the isomers. In [Ir(ppy)2(bpy)]+, transition dipole moment differences play a significant role in controlling the relative lifetime of the triplet states, which we rationalized by a vectorial analysis of permanent dipole moments of the ground and excited states. Regarding the two isomers of Ir(ppy)3, changes in radiative decay rates were primarily attributed to variations in vertical energy gaps and intensity borrowing from other singlet-singlet transitions driven by spin-orbit coupling. Non-radiative decay variations were assessed in terms of differences in reorganization energies, adiabatic energy gap, and spin-orbit coupling. For both complexes, reorganization energies associated with low-energy molecular vibrations and metal-ligand bond length changes following the de-excitation process were major contributors. These insights provide a deeper understanding of how molecular design can be leveraged to optimize the performance of iridium-based photoredox catalysts, potentially guiding the development of more efficient catalytic systems for future applications.

A sense of belonging and cultism in public universities in Kenya: An analysis of Christian Union students’ perceptions

The purpose of the study was to determine Christian Union students’ perceptions of a sense of belonging as a factor influencing cultism in public universities in Kenya. Numerous research indicates that cultism is prevalent and increasing among university students, resulting in several social ills. The study employed a mixed-method research design and was guided by Bounded Choice Theory. The study was carried out in six public universities in Kenya. The total population for the study was 55,600 CU students, and the accessible population was 10,900, out of which a sample of 220 CU students was selected through simple random and stratified sampling methods. The study also included 60 small group Bible study leaders and 6 CU Patrons, one from each selected university through purposive sampling. The study established that a Sense of Belonging (β=0.222; p<0.05) significantly influences cultism. The study concludes that CU students perceived that students were recruited into cults due to the urge to fit into a social group with a promise of social identity and acceptance, especially for fragile learners who are emotionally vulnerable and likely to succumb to recruitment into cultism. The study recommends training of freshers during orientation on critical thinking and discernment to prevent cult recruitment. This study further recommends that universities and CU develop policy frameworks to mitigate cultism. The CU should create an inclusive socio-psychological environment and programs that attract and retain members by addressing members’ needs during vulnerable moments of loneliness, transition, grief, pain and loss.

Challenging excited states from adaptive quantum eigensolvers: subspace expansions vs. state-averaged strategies

Abstract The prediction of electronic structure for strongly correlated molecules represents a promising application for near-term quantum computers. Significant attention has been paid to ground state wavefunctions, but excited states of molecules are relatively unexplored. In this work, we consider the ADAPT-VQE algorithm, a single-reference approach for obtaining ground states, and its state-averaged generalization for computing multiple states at once. We demonstrate for both rectangular and linear H2 as well as for BeH2, that this approach, which we call MORE-ADAPT-VQE, can make better use of small excitation manifolds than an analagous method based on a single-reference ADAPT-VQE calculation, q-sc-EOM. In particular, MORE-ADAPT-VQE is able to accurately describe both avoided crossings and crossings between states of different symmetries. In addition to more accurate excited state energies, MORE-ADAPT-VQE can recover accurate transition dipole moments in situations where traditional ADAPT-VQE and q-sc-EOM struggle. These improvements suggest a promising direction toward the use of quantum computers for difficult excited state problems.

SHARC meets TEQUILA: mixed quantum-classical dynamics on a quantum computer using a hybrid quantum-classical algorithm.

Recent developments in quantum computing are highly promising, particularly in the realm of quantum chemistry. Due to the noisy nature of currently available quantum hardware, hybrid quantum-classical algorithms have emerged as a reliable option for near-term simulations. Mixed quantum-classical dynamics methods effectively capture nonadiabatic effects by integrating classical nuclear dynamics with quantum chemical computations of the electronic properties. However, these methods face challenges due to the high computational cost of the quantum chemistry part. To mitigate the computational demand, we propose a method where the required electronic properties are computed through a hybrid quantum-classical approach that combines classical and quantum hardware. This framework employs the variational quantum eigensolver and variational quantum deflation algorithms to obtain ground and excited state energies, gradients, nonadiabatic coupling vectors, and transition dipole moments. These quantities are used to propagate the nonadiabatic molecular dynamics using the Tully's fewest switches surface hopping method, although the implementation is also compatible with other molecular dynamics approaches. The approach, implemented by integrating the molecular dynamics program package SHARC with the TEQUILA quantum computing framework, is validated by studying the cis-trans photoisomerization of methanimine and the electronic relaxation of ethylene. The results show qualitatively accurate molecular dynamics that align with experimental findings and other computational studies. This work is expected to mark a significant step towards achieving a "quantum advantage" for realistic chemical simulations.

Deciphering nonlinear optical properties in functionalized hexaphyrins via explainable machine learning.

Over the years, several studies have aimed to elucidate why certain molecules show more enhanced nonlinear optical (NLO) properties than others. This knowledge is particularly valuable in the design of new NLO switches, where the ON and OFF states of the switch display markedly different NLO behaviors. In the literature, orbital contributions, aromaticity, planarity, and intramolecular charge transfer have been put forward as key factors in this regard. Based on our previous work on functionalized hexaphyrin-based redox switches, we aim at identifying through explainable machine learning the driving forces of the first hyperpolarizability related to the hyper-Rayleigh scattering (βHRS) of meso-substituted and/or core-modified [26]- and [30]hexaphyrins. The significant correlation between βHRS and the HOMO-LUMO energy gap can be further improved by including other orbitals as well as charge-transfer features in a 6-fold cross-validated kernel-ridge-regression model. Our Shapley additive explanations (SHAP) analysis shows that the charge transfer excitation length is more important for 30R systems, whereas the transition dipole moment between the ground and first excited state is one of the main contributors for 26R systems. We also demonstrate that, besides various hexaphyrin-based redox states, the ML model can describe to a large degree the βHRS response of other hexaphyrins, differing in substitution pattern and topology (26D and 28M).

Inversion of circularly polarized luminescence by electric current flow during transition.

The development of chiral compounds exhibiting circularly polarized luminescence (CPL) has advanced remarkably in recent years. Designing CPL-active compounds requires an understanding of the electric transition dipole moment (μ) and the magnetic transition dipole moment (m) in the excited state. However, while the direction and magnitude of μ can, to some extent, be visually inferred from chemical structures, m remains elusive, posing challenges for direct predictions based on structural information. This study utilized binaphthol, a prominent chiral scaffold, and achieved CPL-sign inversion by strategically varying the substitution positions of phenylethynyl (PE) groups on the binaphthyl backbone, while maintaining consistent axial chirality. Theoretical investigation revealed that the substitution position of PE groups significantly affects the orientation of m in the excited state, leading to CPL-sign inversion. Furthermore, we propose that this CPL-sign inversion results from a reversal in the rotation of instantaneous current flow during the S1 → S0 transition, which in turn alters the orientation of m. The current flow can be predicted from the chemical structure, allowing anticipation of the properties of m and, consequently, the characteristics of CPL. This insight provides a new perspective in designing CPL-active compounds, particularly for C2-symmetric molecules where the S1 → S0 transition predominantly involves LUMO → HOMO transitions. If μ represents the directionality of electron movement during transitions, i.e., the "difference" in electron locations before and after transitions, then m could be represented as the "path" of electron movement based on the current flow during the transition.

Charge-transfer mediated J-aggregation in red emitting ultra-small-single-benzenic meta-fluorophore crystals.

Red emission in crystals has been observed with an ultra-small-single-benzenic meta-fluorophore (MF) with a molecular weight (MW) of only 197 Da, bettering the literature report of fluorophores with the lowest MW = 252 Da. Supramolecular extensive hydrogen-bonding and J-aggregate type centrosymmetric discrete-dimers or a 1D chain of MFs led to red emission (λ max em = 610-636 nm) in MF crystals. Unlike in the solution phase showing one absorption band, in thin films and in crystals the transition from the S0 state to both the S1 - state and S1 + state becomes feasible. The angle between the transition dipole moments has been obtained to be 66.99° and the exciton splitting energy has been obtained to be (-) 55.7 meV. Significant overlap have been observed and the extent of overlaps integrals between the HOMOs and the LUMOs were assessed to be 0.0068 and (-) 0.00024, respectively. Planar molecules are shown to be involved in anti-parallel stacking with a slip-angle of 44.05° and an inter-planar longitudinal distance of 3.40 Å. A large magnitude of ΔE ES (energy difference between the S1 - state and S1 + state) (0.83 eV) has been obtained. A much higher magnitude of the CT coupling constant (-0.708 for MF2) has been noted in comparison to the coulombic coupling constant (0.016 for MF2). The excited-state-lifetime has been shown to increase from 5.98 ns (in hexane) to 30.90 ns in the crystal. All these extra-ordinary optical properties point to the existence of a charge-transfer mediated J-aggregation phenomenon in these MF crystals. Based on these fascinating observations, highly stable, bright and colour pure white LEDs could be generated.

Analysis of entropy on the European markets of energy and energy commodities prices.

The paper analyzes the problem of entropy in the moments of transition from a normal economic situation (2015-2019) to the Pandemic period (2020-2021) and the period of Russia's attack on Ukraine (2022-2023). The research in the article is based on the analysis of electricity, oil, coal, and gas prices in 27 countries of the European Union and Norway. The daily data cover the period from January 1, 2015, to March 30, 2023, and were analyzed using two-dimensional sets of electricity and commodity prices. The work uses the time dependent James-Stein estimator of the Shannon informational entropy.

Absorption spectra of PS in the ultraviolet and infrared region.

The line list is essential for accurately modeling various astrophysical phenomena, such as stellar photospheres and atmospheres of extrasolar planets. This paper introduces a new line database for the PS molecule spanning from the ultraviolet to the infrared regions, covering wavenumbers up to 45000cm-1 and containing over ten million transitions between 150,458 states with total angular momentum J<160. Accurate line intensities for rotational, vibrational and electronic transitions are generated by using the general purpose variational code DUO. Before applying the DUO program, the potential energy curves (PECs), the electric dipole transition moments (EDTMs) and the spin-orbit coupling (SOC) matrix need to be provided, which are computed by an ab initio method at the icMRCI level. The DUO program is executed to generate two files - a state file and a transition file, which are provided to the ExoCross program which supply cross sections, intensities, partition functions, lifetimes and quantum number assignments. The cross-sections and intensities for the observed transitions are necessary for the correct modeling of the spectra. Tests of the line lists show that our predictions not only provide a favorable comparison with the experimental spectrum but also a cornerstone for various astronomical observations.

Theoretical investigation of the A1Π-X1Σ+, B1Σ+-X1Σ+, C1Σ+-X1Σ+, and E1Π-X1Σ+ transitions of the CO molecule.

The spectrum of carbon monoxide is important for astrophysical media, such as planetary atmospheres, interstellar space, exoplanetary and stellar atmospheres; it also important in plasma physics, laser physics and combustion. Interpreting its spectral signature requires a deep and thorough understanding of its absorption and emission properties. A new accurate spectroscopic model for the ground and electronically-excited states of the CO molecule computed at the aug-cc-pV5Z ab initio CASSCF/MRCI+Q level is reported. Detailed investigation of the A1Π-X1Σ+, B1Σ+-X1Σ+, C1Σ+-X1Σ+, and E1Π-X1Σ+ band systems is presented consisting of calculated potential energy curves as well as permanent and transition dipole moment curves. The B1Σ+ and C1Σ+ states are characterized by having multiple avoided crossings which are diabatized to obtain an accurate electronic structure model. The results are validated by comparing our computed spectra with various high-resolution spectroscopy experiments. To the best of our knowledge, this is the first systematic theoretical spectroscopic study of highly excited states of the CO molecule.

Reassessing the role and lifetime of Q x in the energy transfer dynamics of chlorophyll a.

Chlorophylls are photoactive molecular building blocks essential to most photosynthetic systems. They have comparatively simple optical spectra defined by states with near-orthogonal transition dipole moments, referred to as B x and B y in the blue/green spectral region, and Q x and Q y in the red. Underlying these spectra is a surprisingly complex electronic structure, where strong electronic-vibrational interactions are crucial to the description of state characters. Following photoexcitation, energy-relaxation between these states is extremely fast and connected to only modest changes in spectral shapes. This has pushed conventional theoretical and experimental methods to their limits and left the energy transfer pathway under debate. In this work, we address the electronic structure and photodynamics of chlorophyll a using polarization-controlled static - and ultrafast - optical spectroscopies. We support the experimental data analysis with quantum dynamical simulations and effective heat dissipation models. We find clear evidence for B → Q transfer on a timescale of ∼100 fs and identify Q x signatures within fluorescence excitation and transient spectra. However, Q x is populated only fleetingly, with a lifetime well below our ∼30 fs experimental time resolution. Outside of these timescales, the kinetics are determined by vibrational relaxation and cooling. Despite its ultrashort lifetime, our theoretical analysis suggests that Q x plays a crucial role as a bridging state in B → Q energy transfer. In summary, our findings present a unified and consistent picture of chlorophyll relaxation dynamics based on ultrafast and polarization-resolved spectroscopic techniques supported by extensive theoretical models; they clarify the role of Q x in the energy deactivation network of chlorophyll a.

Electronic states of the N2+ ion dissociating to the four lowest dissociation limits: Energies, transition dipole moments, and Einstein coefficients.

This study presents Born-Oppenheimer energies and transition dipole moments of the 36 lowest electronic states of the N2+ ion as a function of internuclear distance in the interval between 1.5 and 10 bohrs obtained in first-principles calculations. The electronic states are of the total electronic spin S = 1/2, 3/2, and 5/2, dissociating toward to the lowest four N(4S0) + N+(3P), N(2P0) + N+(3P), N(2D0) + N+(3P), and N(4S0) + N+(1D) dissociation limits. Energies of the lowest states, dissociating toward to the N(4S0) + N+(3P) limit, are computed accounting for relativistic corrections. The obtained potential energy curves and the transition dipole moments are employed to compute vibrational energies in these states, vibronic transition dipole moments, and the Einstein coefficients for radiative transitions between the vibronic levels.

"Consciousness of machines" (1957, 1963) by Gotthard Günter and the new technocratic paradigm in Germany

This article introduces the main philosophical work of the German-American philosopher and cyberneticist Gotthard Günther (1900–1984), The Consciousness of Machines, and considers its second edition as a transitional moment in the debate on technology in Germany. The article presents Günther’s philosophy of technology, which is based on the concept of transclassical cybernetics and reflects the relevance of the technocratic agenda in the USA and the USSR in the 1950s and, with a lag of one decade, in Western Europe and, in particular, in the Federal Republic of Germany in the 1960s. Günther’s view of technology differs from the post-war techno-pessimistic views of German philosophers and sociologists in that it attempts to overcome the classical dichotomies of spirit and nature, subject and object, consciousness and matter. Günther also goes beyond A. Gehlen’s interpretation of technology as a consequence of the compensation for the defects of the human being. According to Günther, technology acquires a completely new function, becoming “another technology”. It is no longer a compensation for organic shortcomings, its purpose is no longer a mastery of nature or even an intermediary between man and nature, limited by the possibilities of engineering science, but a general theory of all systems, physical and spiritual, a “mirror” of the otherness and diversity of people, their autonomy and sovereignty.

Transnational Television Caricature: The Global Spread of Spitting Image 1984–1994

This article examines the transnational journeys of the popular puppet caricature sketch programme Spitting Image (1984-1996) at a moment of change in the global television industry. Satirical programming, which tends to be rooted in a specific time and place, is not an obvious candidate for the global television trade. Nevertheless, Spitting Image travelled, both in the sense of direct export of the series and as a television format, franchised across the globe. The article explores the origins of the series at a transitional moment in UK broadcasting, as a rare case of an independent co-production within the ITV network in the early 1980s. It traces the difficulties faced by its producers when attempting to export the series to the US market, with content deemed too ‘parochial’ for the American audience. It examines the series as a (qualified) television ‘format’, via the cases of the official Italian remake Teste di gomma (1987-88) and the French Les Guignols de l’info (1988 – 2018), informally inspired by Spitting Image. Finally, it details a failed attempt to remake the show in Post-Soviet Russia, and the political problems encountered by the puppet satire Kukly (1994-2002).

ExoMol line lists – LXI. A trihybrid line list for rovibronic transitions of the hydroxyl radical (OH)

Abstract The hydroxyl radical (OH) is a species of high importance in exoplanetary studies, the interstellar medium, and in stellar spectra. Terrestrially it is a significant component of combustion chemistry, an oxidizer in the upper atmosphere, and a source of telluric bands. Internally contracted multi-reference configuration interaction potential energy curves (PECs), spin-orbit couplings, electronic angular momentum couplings, and (transition) dipole moments for eight electronic states of OH are computed and refined against empirical energy levels to produce an OH spectroscopic model. A line list consisting of rovibronic term values, allowed electronic dipole transitions, Einstein-A coefficients, and partition functions for varying temperature and a continuum absorption data set are then produced by variational solution of the coupled-channel Schrödinger equations using the nuclear motion code Duo. Marvel energy levels substitute equivalent levels in the OH line list, with estimated uncertainties in experimentally dark regions, following an established hybridization procedure. Predissociation lifetimes of the A 2Σ+ state are calculated using a stabilization method and convoluted with natural lifetimes to include predissociative effects. Continuum absorption cross sections for T ∈ [100, 200, ..., 8000] K and zero pressure are provided in the range of 0 → 80 000 cm−1 with a step size of 0.01 cm−1. Comparison with available literature cross sections exhibits strong agreement. The line list is suitable for high-resolution studies up to 8000 K. The OH MYTHOS dataset is available for download via www.exomol.com.

β‐Sheets Orientation in Physisorbed Protein Layers

AbstractPhysisorption of antibodies onto surfaces is a low‐cost, rapid, and effective approach for immobilizing bioreceptors in applications such as bioelectronic sensors. However, there is a prevailing notion that physisorbed protein layers lack structural order, thus potentially compromising their stability and sensitivity compared to antibody films that are covalently attached to the substrate surface. This study demonstrates the preferential orientation of β‐sheets within the secondary structure of protein layers, specifically anti‐immunoglobulin G (anti‐IgG) and bovine serum albumin (BSA), when physisorbed onto gold (Au) thin films. Using polarization modulation infrared reflection‐absorption spectroscopy (PM‐IRRAS) and infrared attenuated total reflection (IR‐ATR) spectroscopy, it has been confirmed that the β‐strands in these protein layers are tilted relative to the surface normal by average angles of 75.3° ± 0.4° for anti‐IgG and of 79.3 ± 0.2° for BSA. These results are obtained by analyzing the orientation of the transition dipole moments (TDMs) associated with the amide I molecular vibrations derived from a comparison between experimental and simulated mid‐infrared spectra assuming isotropically oriented TDMs. The simulations incorporate refractive and absorption index dispersions obtained from the IR‐ATR spectra. Thus obtained findings offer valuable molecular‐level insights facilitating the design and optimization of biofunctionalized interfaces in advanced biomedical and biosensing applications.

Strategies for Controlling Emission Anisotropy in Lead Halide Perovskite Emitters for LED Outcoupling Enhancement.

In the last decade, momentous progress in lead halide perovskite (LHP) light-emitting diodes (LEDs) is witnessed as their external quantum efficiency (ηext) has increased from 0.1 to more than 30%. Indeed, perovskite LEDs (PeLEDs), which can in principle reach 100% internal quantum efficiency as they are not limited by the spin-statistics, are reaching their full potential and approaching the theoretical limit in terms of device efficiency. However, ≈70% to 85% of total generated photons are trapped within the devices through the dissipation pathways of the substrate, waveguide, and evanescent modes. To this end, numerous extrinsic and intrinsic light-outcoupling strategies are studied to enhance light-outcoupling efficiency (ηout). At the outset, various external and internal light outcoupling techniques are reviewed with specific emphasis on emission anisotropy and its role on ηout. In particular, the device ηext can be enhanced by up to 50%, taking advantage of the increased probability for photons outcoupled to air by effectively inducing horizontally oriented emission transition dipole moments (TDM) in the perovskite emitters. The role of the TDM orientation in PeLED performance and the factors allowing its rational manipulation are reviewed extensively. Furthermore, this account presents an in-depth discussion about the effects of the self-assembly of LHP colloidal nanocrystals (NCs) into superlattices on the NC emission anisotropy and optical properties.