Improved Calculation of Vibrational Energy Levels in F2 Molecule using the RKR Method

The potential energy curves of the ground state X2∑＋g of the fluorine molecule have been accurately reconstructed employing the Ryderg-Klein-Rees （RKR） method extrapolated by a Hulburt and Hirschfeler potential function for longer internuclear distances. Solving the corresponding radial one-dimensional Schr？dinger equation of nuclear motion yields 22 bound vibrational levels above v=0. The comparison of these theoretical levels with the experimental data yields a mean absolute deviation of about 7.6 cm^-1 over the 23 levels. The highest vibrational level energy obtained using this method is 13308.16 cm？1 and the relative deviation compared with the experimental datum of 13408.49 cm^-1 is only 0.74%. The value from our method is much closer and more accurate than the value obtained by the quantum mechanical ab initio method by Bytautas. The reported agreement of the vibrational levels and dissociation energy with experiment is contingent upon the potential energy curve of the F2 ground state.

Dietary energy sources and levels shift the multi-kingdom microbiota and functions in the rumen of lactating dairy cows

Background: Dietary energy source and level in lactation diets can profoundly affect milk yield and composition.Such dietary effects on lactation performance are underpinned by alteration of the rumen microbiota, of which bacteria, archaea, fungi, and protozoa may vary differently. However, few studies have examined all the four groups of rumen microbes. This study investigated the effect of both the level and source of dietary energy on rumen bacteria, archaea, fungi, and protozoa in the rumen of lactating dairy cows. A 2 × 2 factorial design resulted in four dietary treatments: low and high dietary energy levels(LE: 1.52–1.53;and HE: 1.71–1.72 Mcal/kg dry matter) and two dietary energy sources(GC: finely ground corn;and SFC: steam-flaked corn). We used a replicated 4 × 4 Latin square design using eight primiparous Chinese Holstein cows with each period lasting for 21 d. The rumen microbiota was analyzed using metataxonomics based on kingdom-specific phylogenetic markers [16 S r RNA gene for bacteria and archaea, 18 S r RNA gene for protozoa, and internally transcribed spacer 1(ITS1) for fungi] followed with subsequent functional prediction using PICRUSt2.Results: The GC resulted in a higher prokaryotic(bacterial and archaeal) species richness and Faith's phylogenetic diversity than SFC. For the eukaryotic(fungi and protozoa) microbiota, the LE diets led to significantly higher values of the above measurements than the HE diets. Among the major classified taxa, 23 genera across all the kingdoms differed in relative abundance between the two dietary energy levels, while only six genera(none being protozoal)were differentially abundant between the two energy sources. Based on prokaryotic amplicon sequence variants(ASVs) from all the samples, overall functional profiles predicted using PICRUSt2 differed significantly between LE and HE but not between the two energy sources. Fish Taco analysis identified Ruminococcus and Coprococcus as the taxa potentially contributing to the enriched KEGG pathways for biosynthesis of amino acids and to the metabolisms of pyruvate, glycerophospholipid, and nicotinate and nicotinamide in the rumen of HE-fed cows. The co-occurrence networks were also affected by the dietary treatments, especially the LE and GC diets, resulting in distinct co-occurrence networks. Several microbial genera appeared to be strongly correlated with one or more lactation traits.Conclusions: Dietary energy level affected the overall rumen multi-kingdom microbiota while little difference was noted between ground corn and steam-flaked corn. Some genera were also affected differently by the four dietary treatments, including genera that had been shown to be correlated with lactation performance or feed efficiency.The co-occurrence patterns among the genera exclusively found for each dietary treatment may suggest possible metabolic interactions specifically affected by the dietary treatment. Some of the major taxa were positively correlated to milk properties and may potentially serve as biomarkers of one or more lactation traits.

Solving Energy Levels for SSH Hamiltonian Describing Peierls Phase Transition by Virtue of Invariant Eigen-operator Method

We show that the recently proposed invariant eigen-operator （IEO） method can be successfully applied to solving energy levels for SSH Hamiltonian describing Peierls phase transition. The electronic energy band of compound lattice is also studied by IEO method.

Analytical Potential Energy Function,Spectroscopic Constants and Vibrational Levels for A^1E_u^+ State of Dimer ~7Li_2

The symmetry-adapted-duster configuration-interaction method is used to investigate the spectroscopicproperties of ~7Li_2(A^1∑_u^+) over the internuclear distance ranging from 2.4ao to 37ao.The complete potential energycurves are calculated at numbers of basis sets.All the ab initio calculated points are fitted to the analytic MurrellSorbie function and then employed to compute the spectroscopic constants.By comparison,the spectroscopic constantsreproduced by the potential attained at D95(3df,3pd) are found to be very close to the experiments,a^d the values (T_e,D_e,R_e,ω_e,ω_eχ_e,α_e and B_e) are of 1.732 93 eV,1.161 36 eV,0.313 27 nm,251.95 cm^(-1),1.623 cm^(-1),0.005 35 cm^(-1),and0.490 cm^(-1),respectively.With the potential obtained at D95(3df,3pd),the totally 75 vibrational states are found whenJ=0.The vibrational levels,the classical turning points and the inertial rotation constants of the first 68 vibrationalstates are calculated for the first time and compared with the available measurements.Good agreement is obtained.The centrifugal distortion constants of the first 32 vibrational states are also reported for the first time.The reasonabledissociation limit for ~7Li_2(A^1∑_u^+) is deduced using the calculated results at present.

Energy levels and states of parabolic cylindrical lens shaped quantum dots

The parabolic cylindrical lens shaped quantum dot is investigated theoretically. The Schrǒdinger equation for an electron confined in this structure is solved in the parabolic cylindrical coordinate system. The wavefunctions for the electron are presented in terms of confluent hypergeometric functions, and the electron energy spectra are also obtained.

Effects of Different Dietary Energy and Protein Levels on Meat Performance and Meat Quality of Jinghai Yellow Chickens

To investigate the effect of different dietary energy and protein levels on meat performance and meat quality of Jinghai yellow chickens, 480 43-day old Jinghai yellow chickens with similar weight were randomly divided into four experimental groups： experimental group 1 （protein 15%, metabolic energy 9.95 MJ/kg）, experimental group 2 （protein 16%, metabolic energy 10.95 MJ/kg）, experimental group 3 （protein 17%, metabolic energy 12.65 MJ/kg） and experimental group 4 （ protein 18%, metabolic energy 13.95 MJ/kg）, respectively. All chickens were slaughtered at 112-day old. The breast and leg muscles of Jinghai yellow chickens were collected, to determine the slaughter performance, conventional meat quality and muscle chemical indicators. The results indicated that dressing-out percentage and eviscerated yield percentage in four experimental groups were above 87.27% and 67.00%, respectively; other slaughter performance indicators exhibited no significant differences among various groups （P 〉 0.05 ） ; breast muscle color of hens in experimental group 4 varied significantly from that in other three groups （ P 〈 0.05 ） ; leg muscle color of hens in experimental group 2 varied extremely significantly from that in other three groups （ P 〈 0.01 ） ; water-holding capacity of breast muscles of hens in experimental group 3 was significantly higher than that in experimental group 4 （P 〈 0.05 ） ; thiamine content of breast muscles of cocks in experimental group 3 was significandy higher than that in experimental group 2 （ P 〈 0.05 ） ; however, other properties exhibited no significant differenees among various groups （P 〉 0.05 ）.

Distribution of Vibrational Energy Levels of Protein Molecular Chains

The distributions of the quantum vibrational energy levels of the protein molecular chain are found by the discretely nonlinear Schr?dinger equation appropriate to protein obtained from the Davydov theory. The results calculated by this method are basically consistent with the experimental values. Furthermore, the energy spectra at high excited states have also been obtained for the molecular chain which is helpful in researching the properties of infrared absorption and Raman scattering of the protein molecules.

Calculation of Rydberg energy levels for the francium atom

Based on the weakest bound electron potential model theory, the Rydberg energy levels and quantum defects of the nP^2P^o1/2 （n=7-50） and np^2P^o3/2 （n=7-50） spectrum series for the francium atom are calculated. The calculated results are in excellent agreement with the 48 measured levels, and 40 energy levels for highly excited states are predicted.

The Quantum Condition That Should Have Been Assumed by Bohr When Deriving the Energy Levels of a Hydrogen Atom

Bohr assumed a quantum condition when deriving the energy levels of a hydrogen atom. This famous quantum condition was not derived logically, but it beautifully explained the energy levels of the hydrogen atom. Therefore, Bohr’s quantum condition was accepted by physicists. However, the energy levels predicted by the eventually completed quantum mechanics do not match perfectly with the predictions of Bohr. For this reason, it cannot be said that Bohr’s quantum condition is a perfectly correct assumption. Since the mass of an electron which moves inside a hydrogen atom varies, Bohr’s quantum condition must be revised. However, the newly derived relativistic quantum condition is too complex to be assumed at the beginning. The velocity of an electron in a hydrogen atom is known as the Bohr velocity. This velocity can be derived from the formula for energy levels derived by Bohr. The velocity v of an electron including the principal quantum number n is given by αc/n. This paper elucidates the fact that this formula is built into Bohr’s quantum condition. It is also concluded in this paper that it is precisely this velocity formula that is the quantum condition that should have been assumed in the first place by Bohr. From Bohr’s quantum condition, it is impossible to derive the relativistic energy levels of a hydrogen atom, but they can be derived from the new quantum condition. This paper proposes raising the status of the previously-known Bohr velocity formula.

Measurement and Strategy Research on the Green Development Level for the New Energy Vehicle Industry in Chongqing City

This article takes 2016-2022 as the inspection period to construct an evaluation index system for the green development level of the new energy vehicle industry.The entropy method and comprehensive index are used to measure the green development level of the new energy vehicle industry in Chongqing,and compared with neighboring provinces such as Yunnan,Guizhou,and Sichuan.Policy recommendations are proposed to promote the development of the new energy vehicle industry in Chongqing City.

Variation of the Observed Widths of La I Lines with the Energy of the Upper Excited Levels, Demonstrated on Previously Unknown Energy Levels

We performed systematic laser spectroscopic investigations of La I spectral lines, using optogalvanic detection. Sixteen previously unknown even parity levels, having energies between 40,300 and 44,300 cm-1, are reported. These levels classify altogether 67 lines, not listed in spectral tables. The new levels were found due to the observation of the depopulation of the lower levels of the excited transitions. We found a remarkable variation of the observed widths of single hyperfine structure components dependent on the energy of the upper excited levels. Some levels having energies higher than 43,000 cm-1 appear to have a very high ionization probability.

Theoretical study on the potential energy surface and vibrational energy levels of HXeI

The potential energy surface for the electronic ground state of the HXeI molecule is constructed by using the internally contracted multi-reference configuration interaction with the Davidson correction（icMRCI＋Q）method and large basis sets. The stabilities and dissociation barriers are identified from the potential energy surfaces.The three-body dissociation channel is found to be the dominate dissociation channel for HXeI.Based on the obtained potentials,vibrational energy levels of HXeI are calculated using the Lanczos algorithm.Our theoretical results are in excellent agreement with the available observed values.

An ab initio potential energy surface and vibrational energy levels of HXeBr

A three-dimensional global potential energy surface for the electronic ground state of HXeBr molecule is constructed from more than 4200 ab initio points. These points are generated using an internally contracted multi-reference configuration interaction method with the Davidson correction （icMRCI ＋ Q） and large basis sets. The stabilities and dissociation barriers are identified from the potential energy surfaces. The three-body dissociation channel is found to be the dominate dissociation channel for HXeBr. Based on the obtained potentials, low-lying vibrational energy levels of HXeBr calculated using the Lanczos algorithm is found to be in good agreement with the available experimental band origins.

Theoretical Studies on the Potential Energy Surface and Vibrational Energy Levels of HXeBr

The potential energy surface for the electronic ground state of the HXeBr molecule is constructed from more than 4200 ab initio points calculated using the internally contracted multi-reference configuration interaction method with the Davidson correction （icMRCI ＋ Q）. The stabilities and dissociation barriers are identified from the potential energy surface. The three-body dissociation channel is found to be the dominant dissociation channel for HXeBr. Low-lying vibrational energy levels of HXeBr calculated using the Lanczos algorithm are found to be in good agreement with the available experimental band origins.

Saturable Absorption Enchantment of Au Nanorods Based on Energy Transfer between Longitudinal and Transverse Energy Levels

Four kinds of Au nanorods（NRs）with different aspect ratios are designed to adjust the relationship between resonance energy level of longitudinal（L）and transverse（T）modes.During the femto-second Z-scan experiments,huge saturable absorption phenomena are observed while the energy level T is located between one to two times of the energylevel L.This means that the energy may transfer between longitudinal and transverse energylevels in the same and/or different Au NRs.It effectively depresses the production of revised saturated absorption and increases the saturable absorption efficiency.This method is significant for the preparation of high-efficiency saturable absorption devices.

Investigation of analytical harmonic frequency and potential energy function, vibrational levels for the X^2∑^＋ and A^2Л states of CN radical

This paper calculates the equilibrium structure and the potential energy functions of the ground state （X^2∑^＋） and the low lying excited electronic state （A^2Л） of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell-Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency （ωe） and other spectroscopic constants （ωeχe, βe and αe） are calculated by employing the Rydberg-Klei-Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional SchrSdinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.

Red Organic Light-Emitting Diodes Based on Energy Levels Matching of Dopant with the Host Materials

By doping red dye 4 dicyanomethylene 2 ( tert butyl) 6 methyl 4H pyran(DCJTB) in the tris (8 hydroxyquinolinato) metal Mq 3(where M = Al, Ga, In) chelate complexes, a series of red dopant organic light emitting diodes with different doping concentrations have been fabricated. The electroluminescence efficiency of these red diodes with a DCJTB doped Mq 3 emitting layer is found to be decreased markedly with the increasing of doping concentration. Electroluminescence characteristics of these devices are studied in terms of energy levels matching of red dopant with the host materials and carrier transporting layers.

Relativistic calculations of fine-structure energy levels of He-like Ar in dense plasmas

The fine-structure energy levels of 1 s2s and 1 s2p atomic states for the He-like Ar ion immersed in dense plasmas are calculated. The ion sphere model is used to describe the plasma screening effect on the tested ion. The influences of the hard sphere confinement and plasma screening on the fine-structure energy levels are investigated respectively. The calculated results show that the confined effect of the hard sphere on the fine-structure energy levels increases with decreasing hard sphere radius, and the plasma screening effect on the fine-structure energy levels increases with the increase of free electron density. In dense plasmas, the confined effect of the hard generally, compared with the contribution from free electron crossing is found among 1 s2s （1 So） and 1 s2p （3P0,1） atomic plasma diagnostics. sphere on the fine-structure energy levels can be neglected screening. An interesting phenomenon about the energy level states. The results reported at the present work are useful for

The Relationship Between the Energy Levels of Shock Waves and the Degree of Renal Damage After ESWL:A Prospective Clinical Matching Trail

In an attempt to understand the effects of high energy shock wave (HESW)on renal function, we studied prospectively 40 patients with nephrolithiasis in 4 groups,using same voltage with different numbers of shock wave therapy to identify the difference of effects on renal function. Stone burdens and posit ion were similar in these groups. Each group received 1500, 2000, 2500 or 3000 puises at 12. 5 KV on JT-3lithotripotor respectively. All the groups had significantly increased the levels of urinary NAG, β2MG, ALB and serum β2MG, which reached the highest values on 1-3days after ESWL (P<0. 001), and then decreased to the pre-ESWL levels except urinary NAG in group Cand D and serum β2MG which were still significantly higher (P<0.05) than those before-ESWL on the 7th day after ESWL. There was significant correlation between either urinary NAG (γ=0. 977, P<0. 05) or β2MG (γ=0. 933, P<0. 001) with the number of shock wave. In addition, urinary NAG and β2MG increased significantly when the number of shock waves was over 2500 shots.These above findings suggest that shock wave had induced acute changes in renal functions and transient renal tubular damages, although these functional changes recovered within one week, and the tubular damage might last longer than 7 days , In order to avoid serious renal damage, it’s necessary to limit the energy level of shock waves under 12. 5 KV×2500 shots by using JT-3 lithotriptor.

Energy Levels of Coupled Plasmonic Cavities

We demonstrate the hybridization of the plasmonic modes in directly coupled whispering gallery cavities fabricated on silver films and present the mode patterns and energy levels using cathodoluminescence spectroscopy. Although the energy of the most antisymmetrically coupled modes is higher than that of the corresponding symmetrically coupled ones, the contrary cases happen for small quantum number modes. We attribute the phenomenon to the different surface plasmon polariton paths between the symmetrically and antisymmetrically coupled modes; These results provide an understanding of the resonant properties in coupled plasmonic cavities, which have potential applications in nanophotonic devices.