Ab initio calculation of accurate dissociation energy, potential energy curve and dipole moment function for the A1∑ + state 7LiH molecule

The reasonable dissociation limit of the A¹∑⁺ state $^{7}$LiH 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 theA¹∑⁺ 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 R_{\e}=0.2487\,nm and D_{\e}=1.064\,eV, respectively. The unusual negative values of the anharmonicity constant and the vibration-rotational coupling constant are of \textit{\omega }_{\e}\textit{\chi }_{\e}=--4.7158cm^{ - 1} and \textit{\alpha }_{\e}=--0.08649cm^{ -1}, respectively. The vertical excitation energy from the ground to the A¹∑⁺ state is calculated and the value is of 3.613\,eV 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 502.47cm¹ about this state is approximately estimated. Careful comparison of the theoretical determinations with those obtained by previous theories about the A¹∑⁺ state dissociation energy clearly shows that the present calculations are much closer to the experiments than previous theories, thus represents an improvement.     

Spectroscopic investigations on NO+(x1∑+,a3∑+,A1Ⅱ) ion using multi-reference configuration interaction method and correlation-consistent sextuple b

Three low-lying electronic states (x¹∑⁺,a³∑⁺,and A¹Ⅱ) of NO⁺ ion are studied using the complete active space self-consistent-field (CASSCF) method followed by highly accurate valence internally contracted multi-reference configuration interaction (MRCI) approach in combination of the correlation-consistent sextuple basis set augmented with diffuse functions, aug-cc-pV6Z. The potential energy curves (PECs) of the NO⁺(x¹∑⁺,a³∑⁺,A¹Ⅱ) are calculated. Based on the PECs, the spectroscopic parameters R_e, D_e, ω_e, ω_eχ_e, α _e, B_e, and D₀ are reproduced, which are in excellent agreement with the available measurements. By numerically solving the radial Schrödinger equation of nuclear motion using the Numerov method, the first 20 vibrational levels, inertial rotation and centrifugal distortion constants of NO⁺(x¹∑⁺,a³∑⁺,A¹Ⅱ) ion are derived when the rotational quantum number J is equal to zero (J = 0) for the first time, which accord well with the available measurements. Finally, the analytical potential energy functions of these states are fitted, which are used to accurately derive the first 20 classical turning points when J = 0. These results are compared in detail with those of previous investigations reported in the literature.     

高能电子对原子核C12的弹性散射

In this paper, we have calculated the elastic scattering of high energy electrons with nuclei C¹² by phase shift calculation.We take the charge distribution of the nucleus C¹² as following:(1) exponential distribution:ρ(x)=ρ₀θ^-x/a, (2) gaussian distribution:ρ(x)=ρ₀e^(-x2/a2),(3) uniform distribution: ρ(x) ={ρ₀ when 0kR, where a and b are the parameters, and the constant R is the radius of the nucleus C¹². The energy of the electrons is 187 Mev.The result of the calculation shows that the gaussian distribution confirms the experimental result better than the other two kinds of distributions, and gives R=(12)^1/3r₀, where r₀=1.35×10^-13 cm.     

Intense up-conversion emissions of Yb3+/Dy3+ co-doped Al2O3 nanopowders prepared by non-aqueous sol—gel method

Yb³⁺/Dy³⁺ co-doped Al₂O₃ nanopowders have been prepared by the non-aqueous sol-gel method and their up- conversion photoluminescence spectra are measured under excitation by 980-nm semiconductor laser. The results show that there are comparatively abundant spectra of up-conversion emissions centered at 378, 408, 527 and 543, and 663 nm, corresponding to ⁴G_9/2 → ⁶H_13/2, ⁴G_9/2 → ⁶H_11/2, ⁴I_15/2 → ⁶H_13/2, and ⁴F_9/2 → ⁶H_11/2 transitions of Dy³⁺, respectively. Two-photon and three-photon processes are involved in ultraviolet, violet, green, and red up-conversion emissions. The energy transition between Yb³⁺ and Dy³⁺ is discussed.     

On long-time limit behavior of the solution of atom's master equation

We study long-time limit behavior of the solution of atom's master equation, for the first time we derive that the probability of the atom being in the α-th (α =j+1-j_z, j is the angular momentum quantum number, j_z is the z-component of angular momentum) state is {(1-K/G)/[1-(K/G)^2j+1]}(K/G)^α-1 as t→+∞, which coincides with the fact that when K/G > 1, the larger the α is, the larger probability of the atom being in the α-th state (the lower excited state). We also consider the case for some possible generalizations of the atomic master equation.     

Theoretical study of structure and analytic potential energy function for the ground state of PO2 molecule

In this paper, the energy, the equilibrium geometry, and the harmonic frequency of the ground electronic state of PO₂ are computed using B3LYP, B3P86, CCSD(T), and QCISD(T) methods in conjunction with 6-311++G(3df, 3pd) and cc-pVTZ basis sets. A comparison between the computational results and the experimental values indicates that the B3P86/6-311++G(3df, 3pd) method can give better energy calculation results for the PO₂ molecule. It is shown that the ground state of the PO₂ molecule has C_2v symmetry and its ground electronic state is X²A₁. The equilibrium parameters of the structure are R_P-O=0.1465 nm, d=19.218 eV. The bent vibrational frequency ν₁=386 cm^-1, the symmetric stretching frequency ν₂=1095 cm^-1, and the asymmetric stretching frequency ν₃=1333 cm^-1 are obtained. On the basis of atomic and molecular reaction statics, the reasonable dissociation limit for the ground state of the PO₂ molecule is determined. Then the analytic potential energy function of the PO₂ molecule is first derived by using the many-body expansion theory. The potential curves correctly reproduce the configurations and the dissociation energy for the PO₂ molecule.     

CuH分子A1∑+态的寿命和预解离研究

A combined cavity ringdown (CRD) and laser induced fluorescence (LIF) spectroscopic study on the A¹∑⁺-X¹∑⁺ transition of CuH has been presented.The CuH molecule,as well as its deuterated isotopologue CuD,are produced in a supersonic jet expansion by discharging H₂(or D₂) and Ar gas mixtures using two copper needles.Different profiles of relative line intensities are observed between the measured LIF and CRD spectra,providing an experimental evidence for the predissociation behavior in the A¹∑⁺ state of CuH.The lifetimes of individual upper rotational levels are measured by LIF,in which the J''-dependent predissociation rates are obtained.Based on the previous theoretical calculations,a predissociation mechanism is concluded due to the strong spin-orbit coupling between the A¹∑⁺ state and the lowest-lying triplet ³∑⁺ state,and a tunneling effect may also be involved in the predissociation.Similar experiments are also performed for CuD,showing that the A¹∑⁺ state of CuD does not undergo a predissociation process.     

异氰酸分子NH(a1Δ)+CO(X1Σ+)通道在193nm的离子成像光解动力学研究

The photodissociation dynamics of isocyanic acid (HNCO) has been studied by the timesliced velocity map ion imaging technique at 193 nm. The NH(a¹Δ) products were measured via (2+1) resonance enhanced multiphoton ionization. Images have been accumulated for the NH(a¹Δ) rotational states in the ground and vibrational excited state (v=0 and 1). The center-of-mass translational energy distribution derived from the NH(a¹Δ) images implies that the CO vibrational distributions are inverted for most of the measured ¹NH(v|j) internal states. The anisotropic product angular distribution observed indicates a rapid dissociation process for the N-C bond cleavage. A bimodal rotational state distribution of CO(v) has been observed, this result implies that isocyanic acid dissociates in the S₁ state in two different pathways.     

Investigations of spectroscopic parameters and molecular constants for X1Σg+, w3Δu, and W1Δu electronic states of P2 molecule

The potential energy curves (PECs) of three low-lying electronic states (X¹Σ_g⁺, w³Δ_u, and W¹Δ_u)of P₂ molecule are investigated using the full valence complete active space self-consistent field (CASSCF) method followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach in conjunction with the correlation-consistent basis set in the valence range. The PECs of the electronic states involved are modified by the Davidson correction and extrapolated to the complete basis set (CBS) limit. With these PECs, the spectroscopic parameters of the three electronic states are determined and compared in detail with the experimental data. The comparison shows that excellent agreement exists between the present results and the available experimental data. The complete vibrational states are computed for the w³Δ_u, and W¹Δ_u electronic states when the rotational quantum number J equals zero and the vibrational level G(v), the inertial rotation constant B_v, and the centrifugal distortion constant D_v of the first 30 vibrational states are reported, which accord well with the experimental data. The present results show that the two-point extrapolation scheme can obviously improve the quality of spectroscopic parameters and molecular constants.     

Investigation of the A2Σ- state of CuO by laser-induced fluorescence

The laser-induced fluorescence excitation spectrum of the A²Σ^－X²Π_3/2 transition of CuO in the 540－620nm region has been studied, where the CuO molecule was produced by using the technique of dc discharge reaction under a supersonic condition. We have recorded and rotationally analysed the 0－0, 1－0, 2－0 and 3－0 bands. The rotational constants of the upper state A²Σ^- were determined and vibrational constants improved. In addition, the lifetime measurement for the A²Σ^- state was carried out under the collision-free condition, and the lifetimes obtained are 469±2, 456±2, 488±3 and 490±4ns for v'=0, v'=1, v'=2 and v'=3 levels, respectively.     

Ab initio calculations of accurate dissociation energy and analytic potential energy function for the second excited state B1∏ 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 B¹\Pi state are calculated using a symmetry-adapted-cluster configuration--interaction method in full active space. The whole potential energy curve for the B¹∏ state is obtained over the internuclear distance ranging from about 0.10nm to 0.54nm, 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 B¹∏ 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 B¹∏ 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.     

OPTICAL-OPTICAL DOUBLE-RESONANCE EXCITATION SPECTRA OF THE (6d)1Πg, (7d)1Πg HIGH-LYING RYDBERG STATES IN Na2

Two ¹Π_g states of Na₂ for v≤13 have been observed by using optical-optical double resonance (OODR) fluorescence excitation spectroscopy. The intermediate levels in B¹Π_u state are identified by the numerical calculations with the molec-ular constants for B¹Π_u←X¹Σ_g⁺ transitions and confirmed by the complemen-tary A¹Σ_g⁺←X¹Σ_g⁺ polarization spectra. Absolute vibrational numberings of the (6d)¹Π_g and (7d)¹Π_g states are determined by comparing the experimental OODR excitation intensities with the simulated Franck-Condon factors. The Dnnham coef-ficients and the Rydberg-Klein-Rees (RKR) potential energy curves of the (6d)¹Π_g, (7d)¹Π_g states are reported.     

双力程核子力的讨论

The binding energies of nuclei H³. He³, He⁴, the low energy n-p scattering length and effective range are calculated by using the standard variational methods. A two-range central Yukawa potential is considered in the first two sections. The longer range corresponds to the π meson mass. The smaller range corresponds either to the heavier meson or to the higher order field interactions. No repulsive core appears, when the force parameters are chosen to fit the low energy scattering and deuteron data. The calculated binding energies of nuclei H³, He³ and He⁴ are too high. This result is in agreement with most of the previous calculations. Tensor force of the Schwinger mixed type is considered in the third and fourth sections. The force parameters are chosen to fit the low energy two body data. They are not uniquely determined and are given for a set of possible D-percentage values. The adding of the tensor force reduces considerably the calculated binding energies of nuclei H³, He³, He⁴. But still, the calculated values increase too fast with the mass number. It does not fit the triton and helium binding energies simultaneously. The possibility of adding many body forces is discussed at the end of the paper.     

丙烷与O(3P)反应机理和动力学的理论研究

The reaction of C₃H₈+O(³P)→C₃H₇+OH is investigated using ab initio calculation and dynamical methods. Electronic structure calculations for all stationary points are obtained using a dual-level strategy. The geometry optimization is performed using the unrestricted second-order Møller-Plesset perturbation method and the single-point energy is computed using the coupled-cluster singles and doubles augmented by a perturbative treatment of triple excitations method. Results indicate that the main reaction channel is C₃H₈+O(³P)→i-C₃H₇+OH. Based upon the ab initio data, thermal rate constants are calculated using the variational transition state theory method with the temperature ranging from 298 K to 1000 K. These calculated rate constants are in better agreement with experiments than those reported in previous theoretical studies, and the branching ratios of the reaction are also calculated in the present work. Furthermore, the isotope effects of the title reaction are calculated and discussed. The present work reveals the reaction mechanism of hydrogen-abstraction from propane involving reaction channel competitions is helpful for the under-standing of propane combustion.     

GROUP-CHAIN SCHEME ANALYSIS OF THE ENERGY LEVELS AND MAGNETIC PROPERTIES OF Nd3+ IN LiYF4 CRYSTAL

Based on the analysis of group-chain scheme, the crystal-field-level fitting of Nd³⁺: LiYF₄ has been carried out, in which the Nd³⁺ inos occupy positions with site symmetry S₄. The RMS deviation of energy-level fitting is 12.8cm^-1. Using the obtained wave functions, g-factors of the fround state are calculated,which are g_∥=2.067 and g_⊥=2.631, in good agreement with the experimental values(g_∥=1.978 and g_⊥=2.554). The method proposed turns out to be effective in the study of spectral properties of localized centres in laser crystals.     

TWO PHOTONS EXCITED 4d RYDBERG STATE OF AsH3

In this paper, by using resonance enhanced (2+1) multiphoton ionization (REMPI) of AsH₃ and detecting the daughter molecular ions AsH⁺ and As⁺, a long progression discrete structure was obtained from 267 to 291 nm, which obeys the formula ν₀(cm^-1)=68875.3+504.1v′₂+5.26v′²₂. Analysis of the spectrum has revealed that it belongs to 4d Rydberg state transition. Our assignment yields the 4d Rydberg state parameters T_e′=67881.1 cm^-1, ω_e′=495.1 cm^-1 and δ=0.962. Finally the 4d Rydberg state structure of AsH₃ was discussed.     

UPCONVERSION FLUORESCENCE DYNAMICS OF Tm3+ IONS IN LiYF4 CRYSTAL

According to Judd-Ofelt parameter calculation and energy transfer theory, the cross-relaxation process of the Tm³⁺ ions is investigated. A four-level system of coupled rate equations is established to study the fluorescence dynamics of Tm³⁺ in LiYF₄ crystal. Attentions are focused on the upconversion luminescence ¹G₄→³H₆ (483.0 nm) in Tm³⁺:LiYF₄. The relationship between the avalanche properties (critical pump rate, fluorescence intensity and buildup time) originated by resonant excited state absorption and the doped Tm³⁺ concentration is discussed, and some useful conclusions are drawn.     

boldmath B3Σu-–X3Σg- transition in selenium dimer: ab initio multireference configuration interaction calculations

Theoretical investigation of low-lying electronic states and B³Σ_u^-–X³Σ_g^- transition properties of selenium dimer using size-extensivity singly and doubly excitation multireference configuration interaction theory with nonrelativistic all-electron basis set and relativistic effective core potential plus its split valence basis set is presented in this paper. The spectroscopic constants of ten low-lying Λ-S bound states have been obtained and compared with experiments. Spin-orbit calculations for coupling between B³Σ_u^- sates and repulsive ¹Π_u, ⁵Π_u states have been made to interpret the predissociation mechanisms of the B³Σ_u^- state. The lifetimes of B³Σ_u^- (v=0～6) have been calculated with scalar relativistic effects included or excluded, respectively, and reasonably agree with experimental values.     

Effective ionization coefficients and electron drift velocities in gasmixtures of CF3I with N2 and CO2 obtained from Boltzmannequation analysis

The electron swarm parameters including the density-normalized effective ionization coefficients (α-η)/N and the electron drift velocities V_e are calculated for the gas mixture of CF₃I with N₂ and CO₂ by solving the Boltzmann equation in the condition of steady-state Townsend (SST) experiment. The overall density-reduced electric field strength is from 100 Td to 1000 Td (1 Td=10^-17 V·cm²), while the CF₃I content k in the gas mixture can be varied over the range from 0% to 100%. From the variation of (α-η)/N with the CF₃I mixture ratio k, the limiting field strength (E/N)_lim for each CF₃I concentration is derived. It is found that for the mixtures with 70% CF₃I, the values of (E/N)_lim are essentially the same as that for pure SF₆. Additionally, the global warming potential (GWP) and the liquefaction temperature of the gas mixtures are also taken into account to evaluate the possibility of applying in the gas insulation of power equipment.     

Ar原子偶宇称3p5(2P1/2)nl''[K'']J(l''=1,3)自电离态激发谱线形研究

The even-parity autoionizing resonance series 3p⁵np''[3/2]_1,2, 3p⁵np''[1/2]₁, and 3p⁵nf''[5/2]₃ of Ar have been investigated exciting from the two metastable states 3p⁵4s[3/2]₂ and 3p⁵4s''[1/2]₀ in the photon energy range of 32500-35600 cm^-1 with an experimental bandwidth of ~0.1 cm^-1. The excitation spectra of the even-parity autoionizing resonance series show typical asymmetric line shapes. New level energies, quantum defects, line profile index and resonance widths, resonance lifetime and reduced widths of the autoionizing resonances are derived by a Fano-type line-shape analysis. The line profile index q and the resonance widths Γ are shown to be approximately proportional to the effective principal quantum number n^*. The line separation of the 3p⁵np'' autoionizing resonances is discussed.