Ground-state energy of beryllium atom with parameter perturbation method

We present a perturbation study of the ground-state energy of the beryllium atom by incorporating double parameters in the atom＇s Hamiltonian. The eigenvalue of the Hamiltonian is then solved with a double-fold perturbation scheme,where the spin-spin interaction of electrons from different shells of the atom is also considered. Calculations show that the obtained ground-state energy is in satisfactory agreement with experiment. It is found that the Coulomb repulsion of the inner-shell electrons enhances the effective nuclear charge seen by the outer-shell electrons, and the shielding effect of the outer-shell electrons to the nucleus is also notable compared with that of the inner-shell electrons.

Modified Atomic Orbital Calculations of Energy of the(2s^(2)^(1)S)Ground-State,the(2p^(2)^(1)D);(3d^(2)^(1)G)and(4f^(2)^(1)I)Doubly Excited States of Helium Isoelectronic Sequence from H-to Ca^(18+)

We report in this paper the ground-state energy 2s^(2)^(1)S and total energies of doubly excited states 2p^(2)^(1)D,3d^(2)^(1)D,4f^(2)^(1)I of the Helium isoelectronic sequence from H-to Ca^(18+).Calculations are performed using the Modified Atomic Orbital Theory(MAOT)in the framework of a variational procedure.The purpose of this study required a mathematical development of the Hamiltonian applied to Slater-type wave function[1]combining with Hylleraas-type wave function[2].The study leads to analytical expressions which are carried out under special MAXIMA computational program.This first proposed MAOT variational procedure,leads to accurate results in good agreement as well as with available other theoretical results than experimental data.In the present work,a new correlated wave function is presented to express analytically the total energies for the 2s21S ground state and each doubly 2p^(2)^(1)D,3d^(2)^(1)D,4f^(2)^(1)I excited states in the He-like systems.The present accurate data may be a useful guideline for future experimental and theoretical studies in the(nI^(2))systems.

A New Method for the Atomic Ground-State Energy in the Screened Coulomb Potential

The new method proposed recently by Friedberg,Lee and Zhao is applied to the derivation of the atomic ground-state energy with the inclusion of the screening effect.The present results are compared with those obtained in the pure Coulomb potential and by the variational approach.The overall good results are obtained with this new method.

Metal-organic framework-based single-atom electro-/ photocatalysts: Synthesis, energy applications, and opportunities

Single-atom catalysts(SACs)have gained substantial attention because of their exceptional catalytic properties.However,the high surface energy limits their synthesis,thus creating significant challenges for further development.In the last few years,metal–organic frameworks(MOFs)have received significant consideration as ideal candidates for synthesizing SACs due to their tailorable chemistry,tunable morphologies,high porosity,and chemical/thermal stability.From this perspective,this review thoroughly summarizes the previously reported methods and possible future approaches for constructing MOF-based(MOF-derived-supported and MOF-supported)SACs.Then,MOF-based SAC's identification techniques are briefly assessed to understand their coordination environments,local electronic structures,spatial distributions,and catalytic/electrochemical reaction mechanisms.This review systematically highlights several photocatalytic and electrocatalytic applications of MOF-based SACs for energy conversion and storage,including hydrogen evolution reactions,oxygen evolution reactions,O_(2)/CO_(2)/N_(2) reduction reactions,fuel cells,and rechargeable batteries.Some light is also shed on the future development of this highly exciting field by highlighting the advantages and limitations of MOF-based SACs.

Structure design and electrochemical properties of carbon-based single atom catalysts in energy catalysis:A review

Single atom catalysts(SACs) possessing regulated electronic structure, high atom utilization, and superior catalytic efficiency have been studied in almost all fields in recent years. Carbon-based supporting SACs are becoming popular materials because of their low cost, high electron conductivity, and controllable surface property. At the stage of catalysts preparation, the rational design of active sites is necessary for the substantial improvement of activity of catalysts. To date, the reported design strategies are mainly about synthesis mechanism and synthetic method. The level of understanding of design strategies of carbon-based single atom catalysts is requiring deep to be paved. The design strategies about manufacturing defects and coordination modulation of catalysts are presented. The design strategies are easy to carry out in the process of drawing up preparation routes. The components of carbon-based SACs can be divided into two parts: active site and carbon skeleton. In this review, the manufacture of defects and coordination modulation of two parts are introduced, respectively. The structure features and design strategies from the active sites and carbon skeletons to the overall catalysts are deeply discussed.Then, the structural design of different nano-carbon SACs is introduced systematically. The characterization of active site and carbon skeleton and the detailed mechanism of reaction process are summarized and analyzed. Next, the applications in the field of electrocatalysis for oxygen conversion and hydrogen conversion are illustrated. The relationships between the superior performance and the structure of active sites or carbon skeletons are discussed. Finally, the conclusion of this review and prospects on the abundant space for further promotion in broader fields are depicted. This review highlights the design and preparation thoughts from the parts to the whole. The detailed and systematic discussion will provide useful guidance for design of SACs for readers.

Ground-State Energy and Entropy for One-Dimensional Heisenberg Chain with Alternating D-Term

We study the ground-state information of one-dimensional Heisenberg chain with alternating D-term. Given the ground-state phase diagram, the ground-state energy and the entanglement entropy are obtained by tensor-net work algorithm. The phase transition points are shown in the entanglement entropy figure. The results are agreed with the phase diagram.

Chemical Reaction and Energy Transfer Between Hot H Atoms and CO2 Molecules

Collisions between hot H atoms and CO2 molecules were studied experimentally by time resolved Fourier transform infrared emission spectroscopy. H atoms with three translational energies, 174.7, 241.0 and 306.2 k J/mol respectively, were generated by UV laser photolysis to initiate a chemical reaction of H＋CO2→OH＋CO. Vibrationally excited CO （v≤2） was observed in the spectrum, where CO was the product of the reaction. The highly efficient T-V energy transfer fro,n the hot H atoms to the CO2 was verified too. The highest vibrational level of v=4 in CO2 （va） was found. Rate ratio of the chemical reaction to the energy transfer was estimated as 10.

Effects of atomic number Z on the energy distribution of hot electrons generated by femtosecond laser interaction with metallic targets

The effects of atomic number Z on the energy distribution of hot electrons generated by the interaction of 60fs, 130mJ, 800nm, and 7×10^17W/cm^2 laser pulses with metallic targets have been studied experimentally. The results show that the number and the effective temperature of hot electrons increase with the atomic number Z of metallic targets, and the temperature of hot electrons are in the range of 190-230keV, which is consistent with a scaling law of hot electrons temperature.

Wavefunction and energy of the 1s^2 2sns configuration in a beryllium atom

A new set of trial functions for 1s^22sns configurations in a beryllium atom is suggested. A Mathematica program based on the variational method is developed to calculate the wavefunctions and energies of 1s^22sns （n = 3 - 6） configurations in a beryllium atom. Non-relativistic energy, polarization correction and relativistic correction which include mass correction, one- and two-body Darwin corrections, spin-spin contact interaction and orbit-orbit interaction, are calculated respectively. The results are in good agreement with experimental data.

Solution of the Energy Level of Hydrogen-Like Atom for the Debye Shielding Potential

The first-order revision and the approximation analytical formula of the energy levels for hydrogen-like atoms under the condition of Debye shielding potential are achieved by means of the Rayleigh–Schr?dinger perturbation theory; meanwhile, the corresponding recurrence relations are obtained from the use of the solution of power series. Based on the above solutions and with the use of energy consistent method the equivalent value of second-order reversion under the condition of Debye shielding potential is produced as well and the result is compared with the data obtained by the numerical method. Besides, the critical bond-state and corresponding cut-off conditions are discussed.

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.

Solution of the Energy Level of Hydrogen-Like Atom for the Debye Shielding Potential

The first-order revision and the approximation analytical formula of the energy levels for hydrogen-likeatoms under the condition of Debye shielding potential are achieved by means of the Rayleigh-Schrodinger perturbationtheory; meanwhile, the corresponding recurrence relations are obtained from the use of the solution of power series. Basedon the above solutions and with the use of energy consistent method the equivalent value of second-order reversion underthe condition of Debye shielding potential is produced as well and the result is compared with the data obtained by thenumerical method. Besides, the critical bond-state and corresponding cut-off conditions are discussed.

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.

The fabrication of atomically thin-MoS_(2) based photoanodes for photoelectrochemical energy conversion and environment remediation:A review

Photoelectrochemical(PEC) technology has been proved a promising approach to solve the problems of energy shortages and environmental pollution damages.It can convert unlimited solar energy resources into energy forms needed by mankind.The development of highly efficient photoanodes is a key step in realizing the large-scale practical application of PEC systems.However,the development of PEC photoanodes has been severely hindered by the issues of easy recombination of photo-generated charge carriers,low photon-to-electron conversion efficiency,poor photo-corrosion resistance,and low catalytic activity.Therefore,constructing high-performance and stable photoanodes is an urgent research field to promote the progress of PEC technology.The atomically thin molybdenum disulfide(AT-MoS_(2)) with unique physical and chemical properties has been widely applied in the fabrication of PEC photoanodes.The AT-MoS_(2) based photoanodes have exhibited excellent PEC performance,which providing promising candidates for ideal PEC application.Here,we summarize the fundamental natures of MoS_(2) and present the research efforts in the preparation of AT-MoS_(2) based photoanodes.Strategies for the fabrication of high-efficient AT-MoS_(2) based photoanodes are emphasized to provide guidelines to advance emerging PEC photoanodes.Besides,perspectives for the development of more efficient AT-MoS_(2) based photoanodes are proposed.

Low-energy atomic displacement model of SRIM simulations

Radiation-induced atomic displacement damage is a pressing issue for materials.The present work investigates the number of atomic displacements using the Primary Knock-on Atom (PKA) energy E_(PKA)and threshold displacement energy E_(d)as two major parameters via lowenergy SRIM Binary Collision Approximation (BCA) full cascade simulations.It is found that the number of atomic displacements cannot be uniquely determined by E_(PKA)/E_(d )or E_(D) /E_(d)(E_(D) refers to the damage energy) when the energy is comparable with E_(d).The effective energy E_(D,eff)proposed in the present work allows to describing the number of atomic displacements for most presently studied monatomic materials by the unique variable E_(D,eff)/E_(d).Nevertheless,it is noteworthy that the BCA simulation damage energy depends on E_(d),whereas the currently used analytical method is independent of E_(d).A more accurate analytical damage energy function should be determined by including the dependence on E_(d).

DETERMINATION OF THE SURFACE BINDING ENERGY OF A Cu/Li ALLOY BY MEASUREMENTS OF ANGULAR DISTRIBUTION OF SPUTTERED ATOMS

A copper based binary alloy containing 16.9 at % lithium has been bombarded with deuterium ions in energy range of 400 eV to 2 keV at the incidence angles of 70° and 80° away from the surface normal. The sputtered flux was condensed on Al- strips arranged arround the target in a cylindrical cup. 1.5 MeV proton backscattering and nuclear reaction 7Li(p, α)4He were used to detect the collected atoms of Cu and Li simultaneously. The angular distribution of sputtered atoms has been shown to be different for two components and strongly anisotropic for the grazing incidence. According to direct knock-on sputtering model and the experimental results the angle for the maximum differential sputtering yield is dependent on the incidence angle α, the bombarding energy E, the energy transfer factor γ= 4M1M2/(M1+ M2)2 and the surface binding energy U. With the assumption that the sputtered particles are diffracted by a planar barrier the surface binding energies of 2.3 eV for the Li component and 3.0 eV for the Cu component have been determined by fitting the measured angles of preferred ejection to the direct knock-on sputtering model, and the results agree well with a pair-binding model.

Molecular Dynamics Study on Interfacial Energy and Atomic Structure of Ag/Ni and Cu/Ni Heterophase System

The results of molecular dynamics calculations on the interfacial energies and atomic structures of Ag/Ni and Cu/Ni interfaces are presented. Calculation on Ag/Ni interfaces with low-index planes shows that those containing the (111) plane have the lowest energies, which is in agreement with the experiments. Comparing surface energy with interfacial energy, it is found the order of the interfacial energies of Ag/Ni and Cu/Ni containing the planes fall in the same order as solid-vapor surface energies of Ag, Cu and Ni. In this MD simulation, the relaxed atomic structure and dislocation network of (110)_Ag||(110)Ni interface are coincident to HREM observations.

THE ENERGY CRITERION OF MINIMUM EQUIVALENT DIAMETER IN GAS ATOMIZATION

Gas atomization has been studied by using energy method in this paper. It shows that the capillary potential energy of the atomization droplets is supplied by the impingement of the gas on the liquid. The energy criterion of the minimum equivalent diameter of the atomization droplets is obtained. The result is comparable to the empirical formulae.[HJ*2/3]

Effective Atomic Number Measurement with Energy-Resolved Computed Tomography Using Two-Dimensional “transXend” Detector

Introduction: We have previously developed an effective atomic number (Zeff) measurement method using linear attenuation coefficients (LACs) obtained by energy-resolved computed tomography (CT) with one-dimensional (1D) detector. The energy-resolved CT was performed with a “transXend” detector, which measured X-rays as electric current and then gave X-ray energy distribution with unfolding analysis using pre-estimated response function (RF). The purpose of this study is to measure Zeff by the energy-resolved CT using a flat panel detector (FPD). Methods: To demonstrate a 2D transXend detector, we developed the stripe absorbers for the FPD. Eleven human tissue-equivalent material rods which were grouped into four material categories were measured by X-rays with 120 kVp tube voltage, 2.3 mA tube current, and 1.0 s exposure time. Zeff is measured by the ratio of LACs with two different pseudo-monochromatic X-ray energies. RFs of each rod material were estimated by numerical calculation. First, we employed the RF estimated for the same rod material (self-RF scenario). Second, we employed the RF estimated for the different rod materials in the same material category (cross-RF scenario). The purpose of the cross-RF scenario was to find representative rod materials in each material category. Results: Upon the self-RF scenario, measured Zeffs were systematically underestimated. Median relative error to theoretical Zeff was -6.92% (range: -7.89% - -4.60%). After normalizing measured Zeffs to the theoretical one for Breast, median relative error improved to -0.75% (range: -1.79% - +1.73%). Upon the cross-RF scenario, the representative rod materials were found in two material categories. Conclusion: Zeff measurements were performed by energy-resolved CT using 2D transXend detector with numerically-estimated RF data. Normalized Zeffs for all rod materials in the self-RF scenario were in good agreement with the theoretical ones.

A Graph Theoretical Interpretation of Different Types of Energies of Elementary Particles, Atoms and Molecules

The present work illustrates a predictive method, based on graph theory, for different types of energy of subatomic particles, atoms and molecules, to be specific, the mass defect of the first thirteen elements of the periodic table, the rotational and vibrational energies of simple molecules (such as , H2, FH and CO) as well as the electronic energy of both atoms and molecules (conjugated alkenes). It is shown that such a diverse group of energies can be expressed as a function of few simple graph-theoretical descriptors, resulting from assigning graphs to every wave function. Since these descriptors are closely related to the topology of the graph, it makes sense to wonder about the meaning of such relation between energy and topology and suggests points of view helping to formulate novel hypotheses about this relation.