Theoretical investigations of spectroscopic parameters and molecular constants for electronic ground state of Cl_2 and its isotopes

The potential energy curve of the C12 （X1∑g＋） is investigated by the highly accurate valence internally contracted multireference configuration interaction （MRCI） approach in combination with the largest correlation-consistent basis set, aug-cc-pV6Z, in the valence range. The theoretical spectroscopic parameters and the molecular constants of three isotopes, 35Cl2, 35Cl37Cl and 37Cl2, are studied. For the 35Cl2（X1∑g＋）, the values of Do, De, Re, We, we）we, ae and Be are obtained to be 2.3921 eV, 2.4264 eV, 0.19939 nm, 555.13 cm-1, 2.6772 cm-1, 0.001481 cm-1 and 0.24225 cm-1, respectively. For the 356137Cl（X1∑g＋）, the values of Do, De, Re, We, WeXe, ae and Be are calculated to be 2.3918 eV, 2.4257 eV, 0.19939 nm, 547.68 cm-1, 2.6234 cm-1, 0.00140 cm^1 and 0.23572 cm-1, respectively. And for the 37Cl2（X1∑g＋）, the values of Do, De, Re, We, WeXe, ae and Be are obtained to be 2.3923 eV, 2.4257 eV, 0.19939 nm, 540.06 cm-1, 2.5556 cm-1, 0.00139 cm-1 and 0.22919 cm-1, respectively. These spectroscopic results are in good agreement with the available experimental data. With the potential of Cl2 molecule determined at the MRCI/aug-cc-pV6Z level of theory, the total of 59 vibrational states is predicted for each isotope when the rotational quantum number J equals zero （J = 0）. The theoretical vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are determined when J = 0, which are in excellent accordance with the available experimental findings.

Enhanced Circular Dichroism of Z-Shaped Nanorod in Rectangular Nanohole Arrays

Chiral nanostructures have attracted much attention due to the valuable applications in biochemistry, medicine industries, and photonic devices. In this study, we propose an ease-of-fabrication planar nanostructure that consists of rectangular nanohole arrays in which the Z-shaped nanorod is arranged. Theoretically, such chiral nanostructure supports significant absorption circular dichroism (CD) compared with the Z-shaped nanorod because charge distributions are tuned after the introduction of the rectangular frame. Meanwhile, the Z-shaped nanorod directs the flow of current on the rectangular frame, thereby generating the effective quadruple electron oscillation in the Z-shaped nanorod. A novel mode also emerges when an identical Z-shaped nanorod is added into the rectangular hole. The studies will provide a novel approach to enhance the CD effect of planar structures. .

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.

Investigations on molecular constants of the CD(X^2Π) radical and elastic collisions between ground-state C and D atoms at low temperatures

The potential energy curve of the CD（X2∏） radical is obtained using the coupled-cluster singles-doublesapproximate-triples [CCSD（T）] theory in combination with the correlation-consistent quintuple basis set augmented with diffuse functions, aug-cc-pV5Z. The potential energy curve is fitted to the Murrell-Sorbie function, which is used to determine the spectroscopic parameters. The obtained Do, De, Re, ωe, ωeXe, αe and Be values are 3.4971 eV, 3.6261 eV, 0.11197 nm, 2097.661 cm^-1, 34.6963 cm^-1, 0.2083 cm^-1 and 7.7962 cm^-1, respectively, which conform almost perfectly to the available measurements. With the potential obtained at the UCCSD（T）/aug-cc-pV5Z level of theory, a total of 24 vibrational states have been predicted for the first time when J = 0 by solving the radial Schrodinger equation of nuclear motion. The complete vibrational levels, the classical turning points, the inertial rotation constants and centrifugal distortion constants are reproduced from the CD（X2∏） potential when J = 0, and are in excellent agreement with the available measurements. The total and the various partial-wave cross sections are calculated for the elastic collisions between the ground-state C and D atoms at energies from 1.0×10^-11 to 1.0 × 10^-4 a.u. when the two atoms approach each other along the CD（X2∏） potential energy curve. Only one shape resonance is found in the total elastic cross sections, and the resonant energy is 8.36×10^-6 a.u. The results show that the shape of the total elastic cross section is mainly dominated by the s partial wave at very low temperatures. Because of the weak shape resonances coming from higher partial waves, most of them are passed into oblivion by the strong total elastic cross sections.

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.

Synchrotron-Based Data-Constrained Modeling Analysis of Microscopic Mineral Distributions in Limestone

Three dimensional (3D) microscopic distributions of dolomite and calcite in a limestone sample have been analyzed with a data-constrained modeling (DCM) technique using synchrotron radiation-based multi-energy X-ray computed tomography (CT) data as constraints. In order to optimize the experimental parameters, X-ray CT simulations and DCM analysis of a numerical phantom consisting of calcite (CaCO3) and dolomite (CaMg(CO3)2) have been used to investigate the effects on the predicted results in relation to noise, X-ray energy and sample-to-detector distance (SDD). The simulation results indicate that the optimal X-ray energies are 25 and 35 keVs, and the SDD is 10 mm. The high resolution 3D distributions of mineral phases of a natural limestone have been obtained. The results are useful for quantitative understanding of mineral, porosity, and physical property distributions in relation to oil and gas reservoirs hosted in carbonate rocks, which account for more than half of the world’s conventional hydrocarbon resources. The case studied is also instructive for the applicability of the DCM methods for other types of composite materials with modest atomic number contrasts between the mineral phases.

Elastic scattering of two H(~2S_g) and N(~4S_u) atoms at low temperatures and accurate spectroscopic parameters of NH (X^3Σ^-) radical

This paper reports that the interaction potential for the X3Z- state of NH radical is constructed at the CCSD（T）/ cc-PV6Z level of theory. Using this potential, this paper calculates the spectroscopic parameters （De, Re, ωe, ωeχe, αe and Be） and their values are of 3.578eV, 0.10368nm, 3286.833cm^-1, 78.433cm^-1, 0.6469cm^-1 and 16.6735cm^-1 respectively, which are in excellent agreement with the experiments. Then the total of 14 vibrational states has been found when J=0 by solving the radial Schrodinger equation of nuclear motion. For each vibrational state, the vibrational manifolds are reported for the first time. And last, the total cross sections, s-wave, p-wave and d-wave cross sections are computed for the elastic collisions between two ground-state atoms （hydrogen and nitrogen） at low temperatures. It finds that the total elastic cross sections are dominated by s-wave scattering when the collision energy is below 10^-6a.u. The pronounced shape resonance is found at energy of 6.1 × 10^-6a.u. Calculations have shown that the shape resonance comes from the p-wave contributions.

Elastic collisions of sulfur and hydrogen in their ground states at low temperatures and spectroscopic parameters of SH(X^2Π ) radical

This paper constructs the interaction potential of the SH（X^2∏） radical by using the coupled-cluster singlesdoubles-approximate-triples theory combining the correlation-consistent quintuple basis set augmented with the diffuse functions, aug-cc-pV5Z, in the valence range. Employing the potential, it accurately determines the spectroscopic parameters. The present De, Re, ωe, ωeχe, ae and Be values are of 3.7767eV, 0.13424nm, 2699.846 cm^-1, 47.7055 cm^-1, 0.2639cm^-1 and 9.4414 cm^-1, respectively, which are in excellent agreement with those obtained from the measure- ments. A total of 19 vibrational states has been found when J = 0 by solving the radial SchrSdinger equation of nuclear motion. The complete vibrational levels, classical turning points, initial rotation and centrifugal distortion constants when J = 0 are reported for the first time, which are in good accord with the experimental results. The total and various partial-wave cross sections are computed for the elastic collisions of sulfur and hydrogen in their ground states at low temperatures when two atoms approach each other along the SH（X^2∏） potential energy curve. Over the impact energy range from 1.0×10^-11 to 1.0×10^-4 a.u., eight shape resonances have been found in the total elastic cross sections. For each shape resonance, the resonant energy is accurately calculated. Careful investigations have pointed out that these resonances result from the 1 = 0, 1, 2, 3, 4, 6, 7, 8 partial-wave contributions.

Ab initio calculation of accurate dissociation energy, potential energy curve and dipole moment function for the A^1∑＋ state ^7LiH molecule

The reasonable dissociation limit of the A^1∑＋ state ^7LiH molecule is obtained. The accurate dissociation energy and the equilibrium geometry of this state are calculated using a symmetry-adapted-cluster configuration-interaction method in complete active space for the first time, The whole potential energy curve and the dipole moment function for the A^1∑＋ state are calculated over a wide internuclear separation range from about 0.1 to 1.4 nm. The calculated equilibrium geometry and dissociation energy of this potential energy curve are of Re=0.2487 nm and De=1.064eV, respectively. The unusual negative values of the anharmonicity constant and the vibration-rotational coupling constant are of ωeXe=-4.7158cm^-1 and αe=0.08649cm^-1, respectively. The vertical excitation energy from the ground to the A^1∑＋ state is calculated and the value is of 3.613eV at 0.15875nm （the equilibrium position of the ground state）. The highly anomalous shape of this potential energy curve, which is exceptionally flat over a wide radial range around the equilibrium position, is discussed in detail. The harmonic frequency value of 502.47cm^-1 about this state is approximately estimated. Careful comparison of the theoretical determinations with those obtained by previous theories about the A^1∑＋ state dissociation energy clearly shows that the present calculations are much closer to the experiments than previous theories, thus represents an improvement.

Ab initio calculations on the α^3∑u^＋ state properties of dimer ^7Li2

The comparison between single-point energy scanning （SPES） and geometry optimization （OPT） in determining the equilibrium geometry of the α^3∑u^＋ state for ^7Li2 is made at numerous basis sets such as 6-311＋＋G（2df）, cc-PVTZ, 6-311＋＋G（2df, p）, 6-311G（3df,3pd）, 6-311＋＋G（2df,2pd）, D95（3df,3pd）, 6-311＋＋G, DGDZVP, 6-311＋＋G（3df,2pd）, 6-311G（2df,2pd）, D95V＋＋, CEP-121G, 6-311＋＋G（d,p）, 6-311＋＋G（2df, pd） and 6-311＋＋G（3df,3pd） in full active space using a symmetry-adapted-cluster/ symmetry-adapted-cluster configuration-interaction （SAC/SAC=CI） method presented in Gaussian03 program package. The difference of the equilibrium geometries obtained by SPES and by OPT is reported. Analyses show that the results obtained by SPES are more reasonable than those obtained by OPT. We have calculated the complete potential energy curves at those sets over a wide internuclear distance range from about 3.0α0 to 37.0α0, and the conclusion is that the basis set cc-PVTZ is the most suitable one. With the potential obtained at ccopVTZ, the spectroscopic data （Te, De, D0, ωe,ωeХe, αe and Be） are computed and they are 1.006 eV, 338.71 cm^-1, 307.12 cm^-1, 64.88 cm^-1, 3.41 cm^-1, 0.0187 cm^-1 and 0.279 cm^-1, respectively, which are in good agreement with recent measurements. The total 11 vibrational states are found at J=0. Their corresponding vibrational levels and classical turning points are computed and compared with available RKR data, and good agreement is found. One inertial rotation constant （By） and six centrifugal distortion constants （Dr Hv, Lv, My, Nv, and Ov） are calculated. The scattering length is calculated to be -27.138α0, which is in good accord with the experimental data.

A theoretical study of the stereodynamics on the abstraction reactions H/D+HS/DS

The quasi-classical trajectory （QCT） method is employed to calculate the stereodynamics of the abstraction reactions H/D ＋ HS/DS based on an accurate potential energy surface [Lti S J, Zhang P Y, Han K L and He G Z 2012 J. Chem. Phys. 136 094308]. The reaction cross sections of the title reaction are computed, and the vector correlations for different collision energies and different initial vibrational states are presented. The influences of the collision energy and reagent vibration on the product polarization are studied, and the product polarizations of the title reactions are found to be distinctly different, which arises from the different mass factors, collision energies, and reagent vibrational states.

Elastic collisions between Si and D atoms at low temperatures and accurate analytic potential energy function and molecular constants of the SiD(X^2Π) radical

Interaction potential of the SiD（χ^2П） radical is constructed by using the CCSD（T） theory in combination with the largest correlation-consistent quintuple basis set augmented with the diffuse functions in the wlence range. Using the interaction potential, the spectroscopic parameters are accurately determined. The present Do, De, Re, ωe, αe and Be values are of 3.0956 eV, 3.1863 eV, 0.15223 nm, 1472.894 cm^-1, 0.07799 cm^-1 and 3.8717 cm^-1, respectively, which are in excellent agreement with the measurements. A total of 26 vibrational states is predicted when J = 0 by solving the radial Schroedinger equation of nuclear motion. The complete vibrational levels, classical turning points, initial rotation and centrifugal distortion constants when J = 0 are reported for the first time, which are in good accord with the available experiments. The total and various partial-wave cross sections are calculated for the elastic collisions between Si and D atoms in their ground states at 1.0× 10^-11-1.0×10^-3 a.u. when the two atoms approach each other along the SiD（χ^2П） potential energy curve. Four shape resonances are found in the total elastic cross sections, and their resonant energies are of 1.73×10^-5, 4.0×10^-5, 6.45×10^-5 and 5.5×10^-4 a.u., respectively. Each shape resonance in the total elastic cross sections is carefully investigated. The results show that the shape of the total elastic cross sections is mainly dominated by the s partial wave at very low temperatures. Because of the weakness of the shape resonances coming from the higher partial waves, most of them are passed into oblivion by the strong s partial-wave elastic cross sections.

Investigations on analytic potential energy function, spectroscopic parameters and vibrational manifolds (J = 0) of the SD + (X^3 Σ^- ) ion

This paper investigates the spectroscopic properties of the SD^＋（X^3∑^-） ion by employing the coupled-cluster singles-doubles-approximate-triples [CCSD（T）] theory combining with the quintuple correlation-consistent basis set augmented with diffuse functions （aug-cc-pV5Z） of Dunning and co-workers. The accurate adiabatic potential energy function is obtained by the least-squares fitting method with the 100 ab initio points, which are calculated at the unrestricted CCSD（T）/aug-cc-pV5Z level of theory over the internuclear separation range from 0.09 to 2.46 nm. Using the potential, it accurately determines the spectroscopic parameters （De, ωeХe, αe and Be）. The present De, Re, We, ωeХe, αe and Be results are of 3.69119 eV, 0.13644 nm, 1834.949 cm^-1, 25.6208 cm^-1, 0.1068 cm^-1 and 4.7778 cm^-1, respectively, which are in remarkably good agreement with the experimental findings. A total of 29 vibrational states has been predicted by numerically solving the radial Schrodinger equation of nuclear motion when the rotational quantum number J equals zero. The complete vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are reported when J = 0 for the first time, which are in good accord with the measurements wherever available.

Elastic scattering of two ground-state N atoms

An interaction potential for an N2（X^1∑g^＋） molecule is constructed by using the highly accurate valence internally contracted multireference configuration interaction method and the largest basis set, aug-cc-pV6Z, in the valence range. The potential is used to investigate the elastic scattering of two N atoms at energies from 1.0×10^-11 to 1.0 × 10^-4 a.u. The derived total elastic cross sections are very large and almost constant at ultralow temperatures, and the shape of total elastic cross section curve is mainly dominated by the s-partial wave at very low collision energies. Three shape resonances are found in the total elastic cross sections. Concretely, the first one is very sharp and strong. It results from the g-partial-wave contribution and the resonant energy is 3.645 × 10^-6 a.u. The second one is contributed by the h-partial wave and the resonant energy is 1.752 × 10^-5 a.u. This resonance is broadened by those from the d- and f-partial waves. The third one comes from the l = 6 partial wave contribution and the resonant energy is 3.522 × 10^-5 a.u. This resonance is broadened by those from the g- and h-partial waves. The N2（X1∑g＋） molecular parameters, which are determined at the current theoretical level, achieve very high accuracy due to the employment of the largest correlation-consistent basis set in the valence range.

Quantitative Analysis of Composition Change in AZ31 Magnesium Alloy Using CF-LIBS After Laser Material Processing

The concentration of elements in molten metal of AZ31 magnesium alloy after long pulsed Nd：YAG laser processing was quantitatively analyzed by using calibration-free laser-induced breakdown spectroscopy （CF-LIBS）. The composition change in AZ31 magnesium alloy under different laser pulse width was also investigated. The experimental results showed that CF-LIBS can obtain satisfactory quantitative or semi-quantitative results for matrix or major elements, while only qualitative analysis was possible for minor or trace elements. Moreover, it is found that the chemical composition of molten metal will change after laser processing. The concentration of magnesium in molten metal is lower than that present in the base metal. The Mg loss increases with an increase of pulse width in the laser processing. This result shows that the selective vaporization of different elements is affected by the pulse width during laser processing.

A Bio-Physical Analysis of Extracellular Ion Mobility and Electric Field Stress

The electric field stress applied to the cell in the electric field will cause the biological effects of the cell on electromagnetic field. In this paper, the single-shell spherical cell is equated to dielectric spheres, and a biophysical method is used to solve the boundary value problem, and then Maxwell tensor analysis is used to discuss the electric field stresses affecting the applied electric field applied to the cells. The results of numerical analysis show that the ion mobility decreases nonlinearly with increasing frequency in the lower region of the applied electric field frequency, and increases with increasing equivalent dielectric constant at a certain frequency, and the magnitude of the electric field stress is almost independent of the frequency;as the frequency increases, the ion mobility tends to a minimum value and is almost independent of the equivalent dielectric constant, while the applied electric field frequency and the cell dielectric constant both affect the cell normal and the tangential stresses. Therefore, the frequency applied electric field and cell dielectric constant affect the extracellular ion mobility, electric field stress applied to the cell membrane by the electric field;the extracellular ion mobility caused by the electric field in the low frequency range is more pronounced than that in the high frequency, and electric field stress is the basic cause of cell deformation.

Tunable acoustic radiation pattern assisted by effective impedance boundary

The acoustic wave propagation from a two-dimensional subwavelength slit surrounded by metal plates decorated with Helmholtz resonators （HRs） is investigated both numerically and experimentally in this work. Owing to the presence of HRs, the effective impedance of metal surface boundary can be manipulated. By optimizing the distribution of HRs, the asymmetric effective impedance boundary will be obtained, which contributes to generating tunable acoustic radiation pattern such as directional acoustic beaming. These dipole-like radiation patterns have high radiation efficiency, no finger- print of sidelobes, and a wide tunable range of the radiation pattern directivity angle which can be steered by the spatial displacements of HRs.

Elastic Collisions Between two Ground-State P and D Atoms at Low and Ultralow Temperatures

PD (X3 ?) 相互作用潜力用 CCSD (T) 理论和基础集合被构造， aug-cc-pV5Z。用这个潜力，分光镜的参数是精确地坚定的。礼品， De ， Re ， e ， ee ， e ，并且具有 3.056 99 eV ， 3.161 75 eV ， 0.142 39 nm ， 1701.558 厘米? 1 ， 23.6583 厘米? 1 ， 0.085 99 厘米? 1 ，和 4.3963 厘米? 1 ，分别地它几乎完美地符合大小。当时， 26 个震动的状态的一个总数被预言 J = 0 由解决光线的 Schr ? 原子运动的 dinger 方程。完全的震动的层次，古典拐弯处点，起始的旋转和离心的失真常数什么时候 J = 0 第一次被报导，它有利地同意实验。全部、各种各样的部分波浪的生气的节在 1.0 魄为在二个地面状态 P 和 D 原子之间的有弹性的影响被计算吗？？

Using Helmholtz resonator arrays to improve dipole transmission efficiency in waveguide

It is well known that the radiation efficiency of an acoustic dipole is very low, increasing the radiation efficiency of an acoustic dipole is a difficult task, especially in an ordinary waveguide.In addition, current acoustic superlenses all utilize in-phase sources to do the super-resolution imaging, it is almost impossible to realize super-resolution imaging of an acoustic dipole.In this paper, after using the Helmholtz resonator arrays(HRAs) which are placed at the upper and lower surfaces of the waveguide, we observe a large dipole radiation efficiency at the certain frequency, which gives a method to observe an acoustic dipole in the far field and offers a novel model which is promising to realize the superlens with a source of an acoustic dipole.We discuss how the arrangement of HRAs affects the transmission of the acoustic dipole.

Consensus for second-order multi-agent systems with position sampled data

In this paper, the consensus problem with position sampled data for second-order multi-agent systems is investigated.The interaction topology among the agents is depicted by a directed graph. The full-order and reduced-order observers with position sampled data are proposed, by which two kinds of sampled data-based consensus protocols are constructed. With the provided sampled protocols, the consensus convergence analysis of a continuous-time multi-agent system is equivalently transformed into that of a discrete-time system. Then, by using matrix theory and a sampled control analysis method, some sufficient and necessary consensus conditions based on the coupling parameters, spectrum of the Laplacian matrix and sampling period are obtained. While the sampling period tends to zero, our established necessary and sufficient conditions are degenerated to the continuous-time protocol case, which are consistent with the existing result for the continuous-time case. Finally, the effectiveness of our established results is illustrated by a simple simulation example.