Calculation Of Energy Levels Research Articles

Manipulation and Theoretical Modeling of the Luminescence Performance of Silver Clusters in LTA Zeolites by Adjusting Extra-framework Cations.

Luminescent silver clusters that are confined inside porous zeolites have attracted great research interest due to the combined advantages of high quantum yield, tunable emission, excellent chemical stability, and desirable adoption ability of this micronano-composite. In this research, a series of Ag-exchanged R-LTA/Ag (R = Li, Na, K) zeolites were synthesized, in which the silver clusters showed blue-shifted excitation in the UV region, red-shifted emission in the visible region, and decreased emission intensity when taking Li+, Na+, and K+ as the extra-framework cations, respectively. The [Ag4(H2O)xR4-sod]6- (x = 2, 4; R = Li, Na, K) structures were constructed, and the TD-DFT method was further carried out to study the influence of extra-framework cations on the luminescence performance of [Ag4]2+ clusters, in which the substitution of Al for Si and the reasonable hydrate levels were both taken into consideration. It is estimated that the S1 and S3 levels for the [Ag4(H2O)4Li4-sod]6- cluster, the S4 level for the [Ag4(H2O)4Na4-sod]6- cluster, and the S5 level for the [Ag4(H2O)2K4-sod]6- cluster can be effectively populated through direct excitation, and the S1 → S0 transition is assumed to be responsible for the radiative emission in the visible region for the [Ag4]2+ pseudo-tetrahedrons. This calculated energy level diagram and simulated absorption spectra of [Ag4(H2O)xR4-sod]6- (x = 2, 4; R = Li, Na, K) clusters explained the modified luminescence property of silver clusters in R-LTA/Ag (R = Li, Na, K) zeolites studied in this research and reported literature.

Crystal field and microscopic spin Hamiltonians approach for V3+ ions in α-ZnAl2S4 single crystals

The optical properties of α-ZnAl2S4:V3+ single crystals were investigated by S. Angel et al. (Anghel et al., 2011) [1]. The spectra of α-ZnAl2S4:V3+ reveal electronic transitions between the energy levels of V3+ ions located at the octahedral site. A comprehensive theoretical study was performed, examining crystal field, spin-spin and other spin orbit interactions. The calculated energy level schemes significantly correspond with the experimental results of V3+ doped α-ZnAl2S4 at both low and room temperatures. A novel, consistent interpretation of the radiative properties is proposed, considering the effect of temperature on crystal field parameters. This interpretation supports the potential use of α-ZnAl2S4: V3+ single crystals, excited at λex = 532 nm, as active media in tunable lasers and amplifiers.

Machine Learning-Assisted Hartree-Fock Approach for Energy Level Calculations in the Neutral Ytterbium Atom.

Data-driven machine learning approaches with precise predictive capabilities are proposed to address the long-standing challenges in the calculation of complex many-electron atomic systems, including high computational costs and limited accuracy. In this work, we develop a general workflow for machine learning-assisted atomic structure calculations based on the Cowan code's Hartree-Fock with relativistic corrections (HFR) theory. The workflow incorporates enhanced ElasticNet and XGBoost algorithms, refined using entropy weight methodology to optimize performance. This semi-empirical framework is applied to calculate and analyze the excited state energy levels of the 4f closed-shell Yb I atom, providing insights into the applicability of different algorithms under various conditions. The reliability and advantages of this innovative approach are demonstrated through comprehensive comparisons with ab initio calculations, experimental data, and other theoretical results.

Spectrum and energy levels of the high-lying singly excited configurations of Nd III. New Nd III experimental energy levels and wavelengths, with transition probability and ionisation energy calculations

We aim to accurately determine bound-to-bound transition wavelengths and energy levels of the high-lying open-shell configurations 4f$^3$7s, 4f$^3$6d, and 4f$^3$5f of doubly ionised neodymium (Nd III, $Z=60$) through high-resolution spectroscopy and semi-empirical calculations. This study is motivated by lanthanide atomic data requirements in astronomy, such those involved in investigations of kilonova spectra. Fourier transform spectra of Nd Penning and hollow cathode discharge lamps were recorded within the region 32\,500--54\,000 and grating spectra of Nd vacuum sliding sparks were recorded within the regions 820--1159 and 1600--3250 . New energy levels were found using the observed wavelengths measured accurate to a few parts in $10^8$ in Fourier transform spectra and to a few parts in $10^7$ in grating spectra. Atomic structure and transition probability calculations of Nd III were carried out using the Cowan codes, where energy parameters were adjusted to fit all known Nd III levels. Finally, Nd-rich stellar spectra were also used to aid in the analysis. In total, 355 transitions were classified from observed spectra involving 116 previously experimentally unknown energy levels of the 4f$^3$7s, 4f$^3$6d, and 4f$^3$5f configurations of Nd III, all reported here for the first time. Three newly identified levels of the 4f$^3$5d configuration and one newly identified 4f$^4$ level are also reported. Typical level energy uncertainties are 0.01 cm$^ $ for the 4f$^3$7s and 4f$^3$6d levels and 0.3 cm$^ $ for the 4f$^3$5f levels. In addition, calculated energy levels up to 130\,936 $ are presented, including eigenvector composition and calculated level lifetimes. Calculated transition probabilities and wavelengths between 1900--50\,000 are also given. Using newly established levels of the 4f$^3$7s configuration and the recently established levels of the 4f$^3$6s configuration, the ionisation energy of Nd III has been estimated at $178\,090 $. This result offers up to twice the accuracy of the most recently published value.

Extending the functional form of the methane PES in redundant coordinates for highly excited vibrational energy levels calculation

Potential energy surfaces (PES) of methanewhich are constructed using ten symmetrised combinations of four bond length and six interbond angles are referred to as (10S) PESs. At high energy ranges, it was found that (10S) PESs permitted improving by factor of five the fit quality of ab initio electronic energies of methane versus standard nine symmetric coordinates (9S) PES representations both in internal, orthogonal or normal-mode coordinates. We extend predictions of vibrational band origins to spectral range above 10,000 cm−1 to help future analyses of experimental spectra. The accuracy at high energies is increased without notable deterioration at low-E levels (rms deviation of 0.26 cm−1). Based on a comparison between various variants of (10S) PESs we expect that new theoretical band origins should have the accuracy not worse than 1–3 cm−1 up to 13,400 cm−1.

Transition metals tailoring of phosphorus-doped gallium nitride nanotubes as sensors for N-butenyl homoserine lactone (BHL): A computational study

This investigation is focused on the impact of transition metals (Ag, Au, and Cu) encapsulations of phosphorus-doped gallium nitride nanotubes (P@GaNNTs) to achieve precise detection and sensing of N-Butenyl homoserine lactone (BHL), which is a biomarker for urinary tract infection, within the framework of density functional theory (DFT) computation at the B3LYP-D3(BJ)/def2SVP method. Adsorption studies unveil the adsorption energies for BHL detection across the systems, with BHL_Cu_P@GaNNT displaying the most favorable adsorption energy of −1.79247 eV and BSSE correction (−1.7685 eV). Additionally, sensor mechanisms are elucidated through Fermi energy level (EFL) calculations, revealing distinct values of 4.748, 4.242, 5.052, and 3.864 for BHL_Ag_P@GaNNT, BHL_Au_P@GaNNT, BHL_Cu_P@GaNNT, and BHL_P@GaNNT, respectively. These values signify variances in charge transfer dynamics upon BHL interaction. In essence, this study lays the foundation for the development of highly efficient biosensors with exceptional biomarker detection capabilities, particularly in the context of urinary tract infections (UTIs). It opens new avenues in the realm of biosensing technology, promising innovative solutions for healthcare and diagnostics.

Atomic Data for Astrophysically Important Spectral Lines of Singly Ionized Nitrogen

Nitrogen lines are widely observed in astrophysical spectra and provide important diagnostics for plasma properties. In this work, we present extended calculations for accurate energy levels, electric dipole radiative transition parameters, and lifetimes for the lowest 102 states of the 2s 22p 2, 2s2p 3, 2s2p 23s, 2s 22p{n 1 l, n 2 d, 4f}(n 1 = 3–5, l = s, p, n 2 = 3, 4), and 2p 4 configurations of N ii within the framework of the fully relativistic multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods. These data are useful for modeling astrophysical spectra, for example, for nitrogen abundance determinations in early B-type stars, and for studying the compositions and plasma properties of H ii regions and planetary nebulae. Our computed transition parameters are compared with available experimental and theoretical data. The accuracy of the calculations is also assessed via a statistical analysis of the differences between the transition rates in the Babushkin and Coulomb gauges and by consideration of cancellation factors. In this way, 201 of the 1656 transitions computed in this work are estimated to be from accurate to better than 3%, corresponding to an accuracy class of A.

Про біквадратичний ангармонічний осцилятор - підхід у рамках розкладу по осциляторному базису. I. Дослідження та розрахунок енергій основного і збуджених станів

For the quantum quartic anharmonic oscillator with the Hamiltonian H=0.5(p2+x2)+λx4 which is one of the classic traditional quantum-mechanical and quantum-field-theory models, its main physical characteristics and properties are thoroughly studied and calculated based on the system's wave function expansion in a complete set of the harmonic oscillator eigenfunctions, i.e., in the basis of eigenfunctions {φ(0)n} of the unperturbed Hamiltonian H=0.5(p2+x2). Very good convergence of the calculated energy levels of the anharmonic oscillator is demonstrated with respect to the number of basis functions included in the expansion, across a wide range of variation of the parameter λ. Thus, we have computed the energies of the ground and the first six excited states of the system for an exceptionally wide range of the oscillator coupling constant λ. In general, the proposed method provides a very good and accurate way to calculate all system characteristics.

An Investigation into Properties for (_66^156)Dy Isotope Using IBM-1 and IVBM Model

Abstract: The (_66^156)Dy isotopes in the O (6) region were investigated. The positive ground-state band of (_66^156)Dy nuclei was calculated using the interacting boson model ‎(IBM-1) and the interacting vector boson model (IVBM). The negative parity band energies of the above isotope were calculated using (IVBM) only. We plotted the ratios ((E(I+2))/(〖E(2〗_1^+)), (E(I+2))/(E(I)),r(((I+2))/I)) and the E-GOS curve as a function of the spin (I) to investigate the properties of the yrast band. Accordingly, the best-fit values of the parameters were used to construct the Hamiltonian, and the electromagnetic transition probability B(E2) of this nucleus was determined. Theoretical energy levels of dysprosium-156 isotope with a neutron number N = 90 and spin parity up to 〖30〗_1^+ were obtained using the MATLAB-20 simulation program. A comparison of these calculated energy levels with the corresponding experimentally measured ones shows a good agreement. The results also ‎draw our attention to the fact that the nucleus of interest deforms and exhibits gamma-instability ‎properties. Keywords: Dysprosium Isotopes, Even-even nuclei, Interacting Boson Model-1, Interacting Vector Boson Model, Negative parity, Yrast band. Abbreviations and Acronyms, IBM: Interacting Boson Model, IVBM: Interacting Vector Boson Model, U(5): Spherical limit, SU(3): Axially deformed shape limit O(6): γ-unstable limit, SP(12; R): the non-compact symplectic group.

Comments on the paper "Quantum defect and Rydberg energy level calculations for 85Rb and 87Rb by Weakest Bound Electron Potential Model"

The manuscript highlights some issues in the recently published paper "Quantum defect and Rydberg energy level calculations for 85Rb and 87Rb by Weakest Bound Electron Potential Model". The issues stem from fundamental and conceptual miscues. We resolved them, and new results are presented based on quantum defect theory and the weakest bound electron potential. The necessary input data to calculate the quantum defects in the 85Rb series were obtained from the NIST site. In the first step, the quantum defect theory determined the quantum defect for the series ns, np, and nd. In the second step, the calculated quantum defects were employed in the Weakest Bound Electron Potential Model theory to calculate the energy of 85Rb I levels. The quantum defects and energies of 85Rb I were determined for the series ns, np, and nd. The spectral coefficients were compared with the published work, and the energies with the NIST database showed good agreement. Our results differ significantly from the previously reported findings, highlighting key errors in methodology.

Enzymatic acylation of cyanidin-3-O-glucoside with aromatic and aliphatic acid methyl ester: Structure–stability relationships of acylated derivatives

Anthocyanins are water-soluble pigments, but they tend to be unstable in aqueous solutions. Modification of their molecular structure offers a viable approach to alter their intrinsic properties and enhance stability. Aromatic and aliphatic acid methyl esters were used as acyl donors in the enzymatic acylation of cyanidin-3-O-glucoside (C3G), and their analysis was conducted using ultraperformance liquid chromatography–mass spectrometry (UPLC-MS). The highest conversion rate achieved was 96.41 % for cyanidin-3-O-(6″-feruloyl) glucoside. Comparative evaluations of stability revealed that aromatic acyl group–conjugated C3G exhibited superior stability enhancement compared with aliphatic acyl group derivatives. The stability of aliphatic C3G decreased with increasing carbon chain length. The molecular geometries of different anthocyanins were optimized, and energy level calculations using density functional theory (DFT) identified their sites with antioxidant activities. Computational calculations aligned with the in vitro antioxidant assay results. This study provided theoretical support for stabilizing anthocyanins and broadened the application of acylated anthocyanins as food colorants and nutrient supplements.

Approaching periodic systems in ensemble density functional theory via finite one-dimensional models

Abstract Ensemble Density Functional Theory (EDFT) is a generalization of ground-state Density Functional Theory (GS DFT), which is based on an exact formal theory of finite collections of a system's ground and excited states. EDFT in various forms has been shown to improve the accuracy of calculated energy level differences in isolated model systems, atoms, and molecules, but it is not yet clear how EDFT could be used to calculate band gaps for periodic systems. We extend the application of EDFT toward periodic systems by estimating the thermodynamic limit with increasingly large finite one-dimensional "particle in a box" systems, which approach the uniform electron gas (UEG). Using ensemble-generalized Hartree and Local Spin Density Approximation (LSDA) exchange-correlation functionals, we find that corrections go to zero in the infinite limit, as expected for a metallic system. However, there is a correction to the effective mass, with results comparable to other calculations on 1D, 2D, and 3D UEGs, which indicates promise for non-trivial results from EDFT on periodic systems.

Calculation of Energy Levels B(E2) and B(M1) for 58,59Cu Isotopes by Using NushellX@MSU Code

In this study, the NushellX@MSU code was applied to compute energy levels, B(E2) and B(M1), values for 58Cu and 59Cu isotopes, using the jj44pn shell and the jun45pn effective interaction. The model space encompassed all possible nucleon configurations within the (f5/2, p3/2, p1/2, and g9/2) orbits. Overall, the computed probabilities of electromagnetic transitions and energy levels for the 58Cu and 59Cu isotopes demonstrate a reasonable consistency with available experimental data.

Biosynthesis of Pt doped Zn bimetallic nanoparticles by using Polygonum glabrum extract for colorimetric, fluorimetric (Ni2+, Hg2+ and Fe2+) ions sensing and photocatalytic degradation of organic dye with electrochemical techniques

In the present study we aimed to explore the biosynthesis and characterization of monometallic platinum nanoparticles (PtNPs), zinc oxide nanoparticles (ZnONPs) are compared to the Pt doped ZnONPs (Pt-ZnONPs) and its sensing, electrochemical, photocatalytic properties. The bimetallic Pt-ZnONPs was synthesized by using Polygonum glabrum leaves extract; it acts as reducing agent and stabilizing agent. The analysis of colorimetric and fluorimertic sensing methods to determine the highly detection of Ni2+, Hg2+ and Fe2+ ions. The optical properties were characterized by UV-visible, FT-IR, XRD, XPS, SEM-EDX and TEM-SAED analysis. The synthesized monometallic PtNPs and ZnONPs are well dispersed spherical and hexagonal particles with sizes ranging from 8 nm to 25 nm. Electrochemical analysis were carried out the synthesized monometallic and bimetallic Pt-ZnONPs oxidation with reduction potentials by using cyclic voltammetry with UV-visible absorption spectroscopy based on band gap energy to calculation of LUMO and HOMO energy levels. The photocatalytic activities with band gap energy 96% for MeB indicated that only Pt doped ZnONPs for bimetallic Pt-ZnONPs nanocatalyst as compared to monometallic PtNPs and ZnONPs for single metal nanocatalyst actions. The highly sensitivity of Ni2+, Hg2+ and Fe2+ ions are combined with synthesized NPs extended to the oxidation-reduction potential for Pt2+ by Zn2+ ions may find sensitivity for trace different metal ions of pollution level with environmental sensing and photocatalytic applications.

Nuclear structure properties and weak interaction rates of even–even Fe isotopes

Nuclear structure properties and weak interaction rates of neutron-rich even–even iron (Fe) isotopes (A = 50 – 70) are investigated using the Interacting Boson Model-1 (IBM-1) and the proton–neutron Quasiparticle Random Phase Approximation (pn-QRPA) model. The IBM-1 is used for the calculation of energy levels and the B(E2) values of neutron-rich Fe isotopes. Later their geometry was predicted within the potential energy formalism of the IBM-1 model. Weak interaction rates on neutron-rich nuclei are needed for the modeling and simulation of presupernova evolution of massive stars. In the current study, we investigate the possible effect of nuclear deformation on stellar rates of even–even Fe isotopes. The pn-QRPA model is applied to calculate the weak interaction rates of selected Fe isotopes using three different values of deformation parameter. It is noted that, in general, bigger deformation values led to smaller total strength and larger centroid values of the resulting Gamow–Teller distributions. This later translated to smaller computed weak interaction rates. The current finding warrants further investigation before it may be generalized. The reported stellar rates are up to 4 orders of magnitude smaller than previous calculations and may bear astrophysical significance.

Large-scale relativistic calculations of spectral data in Zr XXVIII, Nb XXIX and Tc XXXI of tokamak interest

Large-scale relativistic multiconfiguration Dirac–Fock calculations of energy levels and lifetimes of the 206 states arising from the 3s23p, 3p3, 3s3p3d, 3p3d2, 3s24p, 3s24f, 3s3p2, 3s23d, 3s3d2, 3s24d, 3s24s, 3s3p4s, 3s3p4d, 3p23d, 3d3, and 3s3p4p configurations of Zr XXVIII, Nb XXIX, and Tc XXXI of tokamak interest are carried out. The active space approximation is employed for the calculations. To obtain accurate and convergent results, the calculations take into account the valence and core-valence correlations within the n= 9 complex, as well as the Breit interaction, self-energy corrections, and vacuum polarization corrections. Detailed information regarding the decay properties of these ions is provided, including the transition wavelengths, line strengths, and radiative transition rates for various types (electric dipole, electric quadrupole, magnetic dipole, and magnetic quadrupole transitions) of transitions among the levels of the aforementioned configurations. The uncertainties of each dipole transition are evaluated. The present data sets are compared to previous results and a good agreement is observed, which is valuable for emission line identification and fusion modeling, especially in situations where experimental data are scarce.

ExoMol line lists – LVIII. High-temperature molecular line list of carbonyl sulphide (OCS)

ABSTRACT A new molecular line list covering wavelengths λ > 1 μm (the 0–10 000 cm−1 range) for the main isotopologue of carbonyl sulphide 16O12C32S is presented. The OCS line list, named OYT8, contains almost 2.5 billion transitions between 2.4 million rotation-vibration energy levels with the total angular momentum up to J = 223. It is suitable for high-temperature environments up to T = 2000 K. Line list calculations were performed with the variational nuclear motion code trove in conjunction with a highly accurate, empirically refined potential energy surface and a newly computed ab initio dipole moment surface of OCS. The OYT8 line list is adapted for high-resolution applications by replacing computed energy levels with empirically derived values of OCS where available. Comparisons of the OYT8 line list with other OCS line lists and spectra yields excellent agreement for both strong and weak spectroscopic bands. The increased coverage of the OYT8 line list and the many new spectral features that are available will greatly facilitate the future observation of OCS on exoplanets. Carbonyl sulphide joins a growing number of sulphur-bearing molecules available from the ExoMol database. The OYT8 line list along with the associated temperature- and pressure-dependent molecular opacities can be downloaded from www.exomol.com and the CDS astronomical database.

Relativistic calculations of energy levels, lifetimes, transition parameters, and electron impact excitation cross sections for Kr XIX

In this study, we present a detailed analysis of atomic properties for Kr XIX, specifically focusing on the lowest 128 fine-structure levels originating from the 3s23p6, 3s23p53d, 3s3p63d and 3s23p43d2 configurations. We report energy levels, lifetimes, wavelengths, weighted oscillator strengths, and transition probabilities for multipole transition types (E1, E2, M1, and M2). To achieve this, we employed the GRASP2018 code, which implements the fully relativistic multiconfigurational Dirac–Hartree–Fock method and accounts for Breit interaction and quantum electrodynamic effects. We performed another set of calculations using the many-body perturbation theory implemented in the flexible atomic code (FAC). By comparing the results obtained from GRASP2018 and FAC, we established the accuracy and consistency of our calculations. Furthermore, using the relativistic distorted wave theory, we studied electron impact excitation of all transitions to upper levels from the ground and metastable levels and reported excitation cross sections for incident electron energies up to 5 keV. To enhance the practical utility of our findings, we also provided analytical fittings of these cross sections and excitation rate coefficients for their applications in plasma modeling. This work contributes to the atomic properties and excitation cross sections of Kr XIX, addressing a marked gap in the available atomic data.

Theoretical study on Mα transition parameters of He-like to C-like cobalt ions

The multi-configuration Dirac–Hartree–Fock method is employed to investigate the Mα transitions of He-like to C-like Co ions. This study encompasses various parameters, such as energy levels, wavelengths, transition rates, oscillator strengths, and line strengths. The Breit interaction, vacuum polarization, and self-energy corrections were included in the computation of energy levels. The computed results we obtained align well with both experimental and theoretical findings. The differences for most energy levels, transition wavelengths, and oscillator strengths are all below 0.6%, 0.8%, and 20%, respectively. The uncertainty estimation method of the transitions of line strength is evaluated using quantitative and qualitative evaluation methods. The resulting accurate and consistent MCDHF data are expected to be useful for theoretical research on cobalt ions.

A dual‐responsive luminescent sensor for efficient detection of 3‐nitrotyrosine and dipicolinic acid biomarkers based on copper(II) organic framework

The trace detection of biomarkers in real samples has profound a most important significance in the early diagnosis and daily monitoring of diseases. Based on the ligand pre‐design strategy, a novel 3D CuMOF, with the formula of {[Cu4(BTPB)(μ2‐OH)2(H2O)5]·3H2O}n, was fabricated by using the hexacarboxyl ligand of 1,4‐bis(2,4,6‐tricarboxylpyrid‐5‐yl)benzene (H6BTPB) and tetranuclear {Cu4(COO)4(μ2‐OH)2} SBUs. Benefiting from the robust framework and unique luminescence performance, the prepared CuMOF displays great potential as a dual‐responsive efficient luminescent sensor in “turn‐off” detection of 3‐nitrotyrosine (3‐NT) biomarker and “turn‐on” detecting the anthrax biomarker of dipicolinic acid (DPA), with detection limits (LOD) for 3‐NT and DPA being 110.8 ng/ml and 85.2 ng/ml, respectively. Additionally, the practicality and compatibility of such developed sensors were verified by quantifying 3‐NT and DPA biomarkers in diluted serum and urine samples with satisfactory recoveries. Further, the theoretical calculations of energy levels as well as the spectral overlap between the analytes and CuMOF were conducted to elucidate the possible sensing mechanisms. This work demonstrated that MOFs‐based luminescent sensors are evolving as an efficacious and equable approach for the detection of biomarkers in real samples.