Ab initio calculation on accurate analytic potential energy functions and harmonic frequencies of c^3∑g^＋ and B^1-Пu states of dimer 7Li2

The comparison between single-point energy scanning （SPES） and geometry optimization （OPT） in determining the equilibrium geometries of c^3∑g^＋ and B^1-Пu states of dimer 7Li2 is made at numerous basis sets by using a symmetryadapted-cluster configuration-interaztion （SAC-CI） method in the Gaussian 03 program package. In this paper the difference of the equilibrium geometries obtained by SPES and by OPT is reported. The results obtained by SPES are found to be more reasonable than those obtained by OPT in full active space at the present SAC-CI level of theory. And the conclusion is attained that the cc-PVTZ is a most suitable basis set for these states. The calculated dissociation energies and equilibrium geometries are 0.8818 eV and 0.3090 nm for c^3∑g^＋ state, and 0.3668 eV and 0.2932 nm for B^1-Пu state respectively. The potential energy curves are calculated over a wide internuclear distance range from about 2.5α0 to 37α0 and have a least-squares fit into the Murrell-Sorbie function. According to the calculated analytic potential energy functions, the harmonic frequencies （We） and other spectroscopic data （ωeXe, Be and αe） are calculated. Comparison of the theoretical determinations at present work with the experiments and other theories clearly shows that the present work is the most complete effort and thus represents an improvement over previous theoretical results.

Abnormal transition of the electron energy distribution with excitation of the second harmonic in low-pressure radio-frequency capacitively coupled plasmas

The self-excited second harmonic in radio-frequency capacitively coupled plasma was significantly enhanced by adjusting the external variable capacitor.At a lower pressure of 3 Pa,the excitation of the second harmonic caused an abnormal transition of the electron energy probability function,resulting in abrupt changes in the electron density and temperature.Such changes in the electron energy probability function as well as the electron density and temperature were not observed at the higher pressure of 16 Pa under similar harmonic changes.The phenomena are related to the influence of the second harmonic on stochastic heating,which is determined by both amplitude and the relative phase of the harmonics.The results suggest that the self-excited high-order harmonics must be considered in practical applications of lowpressure radio-frequency capacitively coupled plasmas.

Analysis of the Energy and Environmental Sustainability of a Built Space System: The Case of Patte d’Oie University Campus in Ouagadougou

The aim of this study was to carry out a dynamic simulation of the energy and environmental performance of a built space system, with a view to assessing its energy and environmental class. The use of a simulation and modeling tool, supported by various methodological references, formed the basis of our approach. Adopting a systemic perspective, we described the structural and functional aspects of the systems making up built spaces, as well as the associated energy flows. Our approach was also based on a typology, taking into account typical days, structural and functional configurations at different scales and angles of observation. The analysis tool we developed in Java was applied to the built space system of the Patte d’Oie university campus in Ouagadougou. Annual electricity consumption was measured at 124387.34 kWh, closely aligned with the average annual electricity bill (125224.31 kWh), with a maximum relative deviation of 1%, followed by a carbon emission balance of 58337.66 kg eq CO2 per year. This validation confirmed the effectiveness of our tool. In addition, following the analysis of electricity consumption using our tool, the university campus was classified in energy class B and environmental class C. These results will be based on the emission factors of the energy mix of the West African Economic and Monetary Union (WAEMU) territory, with particular emphasis on Burkina Faso.

MRCI potential energy curves and analytical potential energy functions for the X^2Σ^+ and ~2Π states of BO molecule

The potential energy curves （PECs） of BO molecule, including ∑^＋and ∏ symmetries with doublet spin multiplicities, are obtained employing multi-reference configuration interaction （MRCI） method and Dunning＇s correlation consistent basis sets. The analytical potential energy functions （APEFs） are fitted using the Murrell-Sorbie （MS） function and the least square method. Based on the PECs, the spectroscopic constants of the states have been determined and compared with the theoretical and experimental results available to affirm the accuracy and liability of the calculations. The root-mean-square （RMS） errors between the fitted results and the ab initio values are too little in comparison with the chemical accuracy （349.755 cm^-1）. It is shown that the present APEFs are accurate and can display the interaction between the atoms well. The present APEFs can be used to construct more complicated APEF or do some dynamic investigations.

On the State-dependent Switched Energy Functions of DFIG-based Wind Power Generation Systems

This paper proposes a novel state-dependent switched energy function(SdSEF)for general nonlinear autonomous systems,and constructs an SdSEF for doubly-fed induction generator(DFIG)-based wind power generation systems(WPGSs).Different from the conventional energy function,SdSEF is a piece-wise continuous function,and it satisfies the conditions of conventional energy functions on each of its continuous segments.SdSEF is designed to bridge the gap between the well-developed energy function theory and the description of system energy of complex nonlinear systems,such as power electronics converter systems.The stability criterion of nonlinear autonomous systems is investigated with SdSEF,and mathematical proof is presented.The SdSEF of a typical DFIGbased WPGS is simulated in the whole processes of a grid fault and fault recovery.Simulation results verify the negativeness of the derivative of each continuous segment of the SdSEF.

Potential energy curves and analytical potential energy functions of the metastable states of B2^＋＋

The multi-reference configuration interaction method and aug-cc-pvqz （AVQZ） have been used to calculate potential energy curves （PECs） of the singlet and triplet states of the riu and rig symmetry of B2＋＋. All of the four states （^l∏u, ^1∏g, ^3∏u and ^3∏g） are found to be metastable states, though the potential well of ^3∏u symmetry is very shallow. Based on the PECs, the analytical potential energy functions （APEFs） of these states have been fitted using the least square fitting method and two models of function. The spectroscopic parameters of each state are also calculated, and are compared with other investigations in the literature. The credibility and veracity of the two functions are evaluated. Some ideas to improve the fitting accuracy are presented. Also the vibrational levels for each state are predicted by solving the SchrSdinger equation of nuclear motion.

Effect of parallel resonance on the electron energy distribution function in a 60 MHz capacitively coupled plasma

In general,as the radio frequency(RF)power increases in a capacitively coupled plasma(CCP),the power transfer efficiency decreases because the resistance of the CCP decreases.In this work,a parallel resonance circuit is applied to improve the power transfer efficiency at high RF power,and the effect of the parallel resonance on the electron energy distribution function(EEDF)is investigated in a 60 MHz CCP.The CCP consists of a power feed line,the electrodes,and plasma.The reactance of the CCP is positive at 60 MHz and acts like an inductive load.A vacuum variable capacitor(VVC)is connected in parallel with the inductive load,and then the parallel resonance between the VVC and the inductive load can be achieved.As the capacitance of the VVC approaches the parallel resonance condition,the equivalent resistance of the parallel circuit is considerably larger than that without the VVC,and the current flowing through the matching network is greatly reduced.Therefore,the power transfer efficiency of the discharge is improved from 76%,70%,and 68%to 81%,77%,and 76%at RF powers of 100 W,150 W,and 200 W,respectively.At parallel resonance conditions,the electron heating in bulk plasma is enhanced,which cannot be achieved without the VVC even at the higher RF powers.This enhancement of electron heating results in the evolution of the shape of the EEDF from a biMaxwellian distribution to a distribution with the smaller temperature difference between high-energy electrons and low-energy electrons.Due to the parallel resonance effect,the electron density increases by approximately 4%,18%,and 21%at RF powers of 100 W,150 W,and 200 W,respectively.

ENERGY-LOSS FUNCTIONS DERIVED FROM REELS SPECTRA FOR ALUMINUM

The effective energy loss functions for Al have been derived from differential i nverse inelastic mean free path based on the extended Landau approach. It has be en revealed that the effective energy loss function is very close in value to th e theoretical surface energy loss function in the lower energy loss region but g radually approaches the theoretical bulk energy loss function in the higher ener gy loss region. Moreover, the intensity corresponding to surface excitation in e ffective energy loss functions decreases with the increase of primary electron e nergy. These facts show that the present effective energy loss function describe s not only surface excitation but also bulk excitation. At last, REELS spectra s imulated by Monte Carlo method based on use of the effective energy loss functio ns has reproduced the experimental REELS spectra with considerable success.

Alloy gene Gibbs energy partition function and equilibrium holographic network phase diagrams of Au_3Cu-type sublattice system

Taking Au3Cu-type sublattice system as an example, three discoveries have been presented. First, the fourth barrier to hinder the progress of metal materials science is that today’s researchers do not understand that the Gibbs energy function of an alloy phase should be derived from Gibbs energy partition function constructed of alloy gene sequence and their Gibbs energy sequence. Second, the six rules for establishing alloy gene Gibbs energy partition function have been discovered, and it has been specially proved that the probabilities of structure units occupied at the Gibbs energy levels in the degeneracy factor for calculating configuration entropy should be degenerated as ones of component atoms occupied at the lattice points. Third, the main characteristics unexpected by today’s researchers are as follows. There exists a single-phase boundary curve without two-phase region coexisting by the ordered and disordered phases. The composition and temperature of the top point on the phase-boundary curve are far away from those of the critical point of the Au3Cu compound; At 0 K, the composition of the lowest point on the composition-dependent Gibbs energy curve is notably deviated from that of the Au3Cu compounds. The theoretical limit composition range of long range ordered Au3Cu-type alloys is determined by the first jumping order degree.

Alloy gene Gibbs energy partition function and equilibrium holographic network phase diagrams of AuCu_3-type sublattice system

Taking AuCu3-type sublattice system as an example, three discoveries have been presented: First, the third barrier hindering the progress in metal materials science is that researchers have got used to recognizing experimental phenomena of alloy phase transitions during extremely slow variation in temperature by equilibrium thinking mode and then taking erroneous knowledge of experimental phenomena as selected information for establishing Gibbs energy function and so-called equilibrium phase diagram. Second, the equilibrium holographic network phase diagrams of AuCu3-type sublattice system may be used to describe systematic correlativity of the composition?temperature-dependent alloy gene arranging structures and complete thermodynamic properties, and to be a standard for studying experimental subequilibrium order-disorder transition. Third, the equilibrium transition of each alloy is a homogeneous single-phase rather than a heterogeneous two-phase, and there exists a single-phase boundary curve without two-phase region of the ordered and disordered phases; the composition and temperature of the top point on the phase-boundary curve are far away from the ones of the critical point of the AuCu3 compound.

Accurate ab initio-based analytical potential energy function for S_2(~1△_g) via extrapolation to the complete basis set limit

The potential energy curves（PECs） of the first electronic excited state of S2（a^1△g） are calculated employing a multi-reference configuration interaction method with the Davidson correction in combination with a series of correlationconsistent basis sets from Dunning： aug-cc-p VX Z（X = T, Q, 5, 6）. In order to obtain PECs with high accuracy, PECs calculated with aug-cc-p V（Q, 5）Z basis sets are extrapolated to the complete basis set limit. The resulting PECs are then fitted to the analytical potential energy function（APEF） using the extended Hartree–Fock approximate correlation energy method. By utilizing the fitted APEF, accurate and reliable spectroscopic parameters are obtained, which are consistent with both experimental and theoretical results. By solving the Schr o¨dinger equation numerically with the APEFs obtained at the AV6 Z and the extrapolated AV（Q, 5）Z level of theory, we calculate the complete set of vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants.

Determination of Material Parameters of EVA Foam under Uniaxial Compressive Testing Using Hyperelastic Models

The objective of this research was to determine the mechanical parameter from EVA foam and also investigate its behavior by using Blatz-Ko,Neo-Hookean,Mooney model and experimental test.The physical characteristic of EVA foam was also evaluated by scanning electron microscopy(SEM).The results show that Blatz-Ko and Neo-Hookean model can fit the curve at 5%and 8%strain,respectively.The Mooney model can fit the curve at 50%strain.The modulus of rigidity evaluated from Mooney model is 0.0814±0.0027 MPa.The structure of EVA foam from SEM image shows that EVA structure is a closed cell with homogeneous porous structure.From the result,it is found that Mooney model can adjust the data better than other models.This model can be applied for mechanical response prediction of EVA foam and also for reference value in engineering application.

THE NONLINEAR STABILITY OF PLANE PARALLEL SHEAR FLOWS WITH RESPECT TO TILTED PERTURBATIONS

The nonlinear stability of plane parallel shear flows with respect to tilted perturbations is studied by energy methods.Tilted perturbation refers to the fact that perturbations form an angleθ∈(0,π/2)with the direction of the basic flows.By defining an energy functional,it is proven that plane parallel shear flows are unconditionally nonlinearly exponentially stable for tilted streamwise perturbation when the Reynolds number is below a certain critical value and the boundary conditions are either rigid or stress-free.In the case of stress-free boundaries,by taking advantage of the poloidal-toroidal decomposition of a solenoidal field to define energy functionals,it can be even shown that plane parallel shear flows are unconditionally nonlinearly exponentially stable for all Reynolds numbers,where the tilted perturbation can be either spanwise or streamwise.

Effects of power on ion behaviors in radio-frequency magnetron sputtering of indium tin oxide(ITO)

This study delves into ion behavior at the substrate position within RF magnetron discharges utilizing an indium tin oxide(ITO)target.The positive ion energies exhibit an upward trajectory with increasing RF power,attributed to heightened plasma potential and initial emergent energy.Simultaneously,the positive ion flux escalates owing to amplified sputtering rates and electron density.Conversely,negative ions exhibit broad ion energy distribution functions(IEDFs)characterized by multiple peaks.These patterns are clarified by a combination of radiofrequency oscillation of cathode voltage and plasma potential,alongside ion transport time.This elucidation finds validation in a one-dimensional model encompassing the initial ion energy.At higher RF power,negative ions surpassing 100 e V escalate in both flux and energy,posing a potential risk of sputtering damages to ITO layers.

Experimental studies of H_(2)/Ar plasma in a cylindrical inductive discharge with an expansion region

The electrical parameters of H_(2)/Ar plasma in a cylindrical inductive discharge with an expansion region are investigated by a Langmuir probe,where Ar fractions range from 0%to 100%.The influence of gas composition and pressure on electron density,the effective electron temperature and the electron energy probability functions(EEPFs)at different spatial positions are present.In driver region,with the introduction of a small amount of Ar at 0.3 Pa,there is a rapid increase in electron density accompanied by a decrease in the effective electron temperature.Additionally,the shape of the EEPF transitions from a three-temperature distribution to a bi-Maxwellian distribution due to an increase in electron-electron collision.However,this phenomenon resulting from the changes in gas composition vanishes at 5 Pa due to the prior depletion of energetic electrons caused by the increase in pressure during hydrogen discharge.The EEPFs for the total energy in expansion region is coincident to these in the driver region at 0.3 Pa,as do the patterns of electron density variation between these two regions for differing Ar fractions.At 5 Pa,as the discharge transitions from H_(2)to Ar,the EEPFs evolved from a bi-Maxwellian distribution with pronounced low energy electrons to a Maxwellian distribution in expansion region.This evolve may be attributed to a reduction in molecular vibrational excitation reactions of electrons during transport and the transition from localized electron dynamics in hydrogen discharge to non-localized electron dynamics in argon discharge.In order to validate the experimental results,we use the COMSOL simulation software to calculate electrical parameters under the same conditions.The evolution and spatial distribution of the electrical parameters of the simulation results agree well with the trend of the experimental results.

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.

Potential energy curves and spectroscopic properties of X^2Σ^+ and A^2Π states of ^(13)C^(14)N

The potential energy curves （PECs） of X2∑ and A2П states of the CN molecule have been calculated with the multi- reference configuration interaction method and the aug-cc-pwCVSZ basis set. Based on the PECs, all of the vibrational and rotational levels of the 13C14N molecule are obtained by solving the Schrrdinger equation of the molecular nuclear motion. The spectroscopic parameters are determined by fitting the Dunham coefficients with the levels. Both the levels and the spectroscopic parameters are in good qualitative agreement with the experimental data available. The analytical potential energy functions are also deduced from the calculated PECs. The present results can provide a helpful reference for future spectroscopy experiments or dynamical calculations of the molecule.

A UNIVERSAL ANALYTIC POTENTIAL-ENERGY FUNCTION BASED ON A PHASE FACTOR

Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are obtained adjusting the phase factors. The linear thermal expansion coefficients and Young's moduli of eleven kinds of face-centered cubic (fcc) metals - Al, Cu, Ag, etc. are calculated using the potential-energy function; the computational results are quite consistent with experimental values. Moreover, an analytic relation between the linear thermal expansion coefficients and Young's moduli of fcc metals is given using the potential-energy function. Finally, the force constants of fifty-five kinds of diatomic moleculars with low excitation state are computed using this theory, and they are quite consistent with RKR (Rydberg-Klein-Rees) experimental values.

Structure and analytical potential energy function for the ground state of the BC^x （x=0, -1）

In this paper, the electronic states of the ground states and dissociation limits of BC and BC- are correctly determined based on group theory and atomic and molecular reaction statics. The equilibrium geometries, harmonic frequencies and dissociation energies of the ground state of BC and BC- are calculated by using density function theory and quadratic CI method including single and double substitutions. The analytical potential energy functions of these states have been fitted with Murrell-Sorbie potential energy function from our ab initio calculation results. The spectroscopic data （αe, ωe and ωeχe） of each state is calculated via the relation between analytical potential energy function and spectroscopic data. All the calculations are in good agreement with the experimental data.

Ab initio calculations of accurate dissociation energy and analytic potential energy function for the second excited state B^1∏ of ^7LiH

The reasonable dissociation limit of the second excited singlet state B1∏ of ^7LiH molecule is obtained. The accurate dissociation energy and equilibrium geometry of the B^∏ state are calculated using a symmetry-adaptedcluster configuration interaction method in full active space. The whole potential energy curve for the B1H state is obtained over the internuclear distance ranging from about 0.10 nm to 0,54 nm, and has a least-square fit to the analytic Murrell-Sorbie function form. The vertical excitation energy is calculated from the ground state to the B^1∏ state and compared with previous theoretical results. The equilibrium internuclear distance obtained by geometry optimization is found to be quite different from that obtained by single-point energy scanning under the same calculation condition. Based on the analytic potential energy function, the harmonic frequency value of the B^1∏ state is estimated. A comparison of the theoretical calculations of dissociation energies, equilibrium interatomic distances and the analytic potential energy function with those obtained by previous theoretical results clearly shows that the present work is more comprehensive and in better agreement with experiments than previous theories, thus it is an improvement on previous theories.