Orientational order parameter estimated from molecular polarizabilities – an optical study

An optical study of N-(p-n-alkyloxybenzylidene)-p-n-butyloxyanilines, nO.O4 compounds with the alkoxy chain number n?=?1, 3, 6, 7, and 10 has been carried out by measuring the refractive indices using modified spectrometer and direct measurement of birefringence employing the Newton's rings method. Further, the molecular polarizability anisotropies are evaluated using Lippincott δ-function model, the molecular vibration method, Haller's extrapolation method, and scaling factor method. The molecular polarizabilities α _e and α ₀ are calculated using Vuk's isotropic and Neugebauer anisotropic local field models. The order parameter S is estimated by employing the molecular polarizability values determined from experimental refractive indices and density data and the polarizability anisotropy values. Further, the order parameter S is also obtained directly from the birefringence data. A comparison has been carried out among the order parameter obtained from different ways and the results are compared with the body of the data available in the literature.     

Bound states and critical behavior of the Yukawa potential

We investigate the bound states of the Yukawa potential V (r)=−λexp(−αr)/r, using different algorithms: solving the Schr?dinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical α = α_C, above which no bound state exists. We study the relation between α_C and λ for various angular momentum quantum number l, and find in atomic units, α_C(l) = λ[A ₁ exp(−l/B ₁) + A ₂ exp(−l/B ₂)], with A ₁ = 1.020(18), B ₁ = 0.443(14), A ₂ = 0.170(17), and B ₂ = 2.490(180).     

7Li2分子23Πu激发态的解析势能函数、振动能级及其转动惯量

使用Gaussian 03程序包中的“对称性匹配簇-组态相互作用”方法、在0.13—2.0nm的核间距范围内利用6-311+〖KG-*3〗+G(d,p)基组对⁷Li₂(2³Π_u)分子的势能曲线进行了计算, 同时使用最小二乘法将计算结果拟合成了解析势能函数. 利用拟合出的解析势能函数并结合Rydberg-Klein-Rees方法, 计算了该态的谐振频率, 进而计算了该态的其他光谱常数, 分别为T关键词： 解析势能函数 谐振频率 振动能级 转动惯量     

The analytical potential energy function of flue gas SO2（X1A1）

The equilibrium structure of flue gas SO2 is optimized using the density functional theory （DFT）/B3P86 method and CC-PV5Z basis. The result shows that it has a bent （C2v, X1A1） ground state structure with an angle of 119.1184°. The vibronic frequencies and the force constants are also calculated. Based on the principles of atomic and molecular reaction statics （AMIIS）, the possible electronic states and reasonable dissociation limits for the ground state of SO2 molecule are determined. The potential functions of SO and 02 are fitted by the modified Murrell-Sorbie＋c6 （M-S＋c6） potential function and the fitted parameters, the force constants and the spectroscopic constants are obtained, which are all close to the experimental values. The analytic potential energy function of the SO2 （X1A1） molecule is derived using the many-body expansion theory. The contour liues are constructed, which show the static properties of SO2 （XIA1）, such as the equilibrium structure, the lowest energies, the most possible reaction channel, etc.     

High Pressure effect on fluorescence lifetime τ for magnetic dipole 5D0→5F1 transitions in YAG:Eu3+

The fluorescence lifetime for magnetic dipole ⁵D₀→⁷F₁ transition in yttrium aluminum garnet doped with Eu³⁺ (YAG:Eu³⁺) crystal was studied under the pressure of up to 10.4?GPa at room temperature. The fluorescence lifetime τ (⁵D₀→⁷F₁ transition) slowly decreased with pressure. The pressure effect on τ (⁵D₀→⁷F₁ transition) was explained with a model which considered pressure effect on line position: inter-ionic distance, ion volume, molecular volume, ion polarizability, molecular polarizability, sample refractive index, and surrounding hydrostatic medium refractive index. The fluorescence lifetime τ calculated by the presented model was in close correspondence with the experimental values.     

B2C(1A1)和BC2(2A′)的结构与解析势能函数

采用单双取代的二次组态相互作用方法，分别选用6-311++G(d,p)和6-311G(df,pd)基组，对B₂C和BC₂分子的结构进行了优化，得到这两个分子的基态结构为C_2v和C_s，基态电子状态为¹A₁和²A′，同时还得到了它们的平衡几何结构、离解能、谐振频率和力常数. 关键词： 碳化硼 Murrell-Sorbie函数 谐振频率 势能函数     

利用WBEPM模型和稳定变分法计算氦原子的极化率和色散系数

以最弱受约束电子势模型(WBEPM)理论为基础,建立了计算氦原子多极动态极化率和相互作用色散系数的稳定变分方法.导出了该方法中所涉及的矩阵元和线性方程组的解析表达式.作为应用,具体计算了基态氦原子的极化率和两体色散系数,将计算结果与用其他方法所得到的结果进行了比较, 数据基本一致.     

利用WBEPM模型和稳定变分法计算氦原子的极化率和色散系数

以最弱受约束电子势模型(WBEPM)理论为基础,建立了计算氦原子多极动态极化率和相互作用色散系数的稳定变分方法 .导出了该方法中所涉及的矩阵元和线性方程组的解析表达式.作为应用,具体计算了基态氦原子的极化率和两体色散系数,将计算结果与用其他方法所得到的结果进行了比较,数据基本一致.     

Ab initio potential energy curves for the CO+ ion and a study of the photoelectron spectra of CO

The potential energy curves for the low-lying electronic states of CO⁺ are calculated by using the ab initio full valence configuration interaction method with minimal STOs. Calculated spectroscopic parameters are given for twenty five bound states, and the compared with the experimental values for four observed bound states. The band systems, observed in the 22 eV and 27 eV region of He II photoelectron spectra of CO, are analysed by using calculated potential energy curves and spectral intensities. New assignment for the fourth band system at 22 eV ～ 23 eV is proposed.     

Accurate potential energy function and spectroscopic study of the X^2∑＋, A^2П and B^2∑＋ states of the CP radical

This paper calculates the equilibrium internuclear separations, the harmonic frequencies and the potential energy curves of the X^2∑＋, A^2П and B^2∑＋ states of the CP radical by the highly accurate valence internally contracted multireference configuration interaction method with correlation-consistent basis sets （aug-cc-pV6Z for C atom and aug-cc-pVQZ for P atom）. The potential energy curves are all fitted with the analytic potential energy function by the least-square fitting. Employing the analytic potential energy function, we determine the spectroscopic constants （Be, αe and ωeχe） of these states. For the X2∑＋ state, the obtained values of De, Be, αe, ωeχe, Re and ωe are 5.4831 eV, 0.792119 cm-1, 0.005521 cm-1, 6.89653 cm-1, 0.15683 nm, 12535.11 cm-1, respectively. For the A2H state, the present values of De, Be,αe, ωeχe, Re and We are 4.586 eV, 0.703333 cm-1, 0.005458 cm-1, 6.03398 cm-1, 0.16613 nm, 1057.89 cm-1, respectively. For the B2E＋ state, the present values of De, Be, αe, ωeχe, Re and We are 3.506 eV, 0.677561 cm-1, 0.00603298 cm-1, 5.68809 cm-1, 0.1696 nm, 822.554 cm-1, respectively. For these states, the vibrational states with the rotational quantum number J equals zero （J = 0） are studied by solving the radial nuclear Schr6dinger equation using the Numerov method. For each vibrational state, the vibrational level, the classical turning points, the rotational inertial and the centrifugal distortion constants are calculated. Comparison is made with recent theoretical and experimental results.     

The influence of intermolecular interactions on the Kerr effect in gases

Expressions are derived for the second and third Kerr virial coefficients, B _K and C _K, of spherical top molecules in terms of irreducible cluster polarizabilities, and values are calculated using the dipole-induced dipole model for argon, krypton, xenon, methane, tetrafluoromethane, neopentane and sulphur hexafluoride. For mixtures of rare gases it is shown that the collision-induced dipole moment makes a negligible contribution to B _K. The effect of the choice of intermolecular potential function on the calculated second Kerr virial coefficients is also demonstrated. It is found that the predominant contributions to C _K arise from the pair polarizability, and that the triplet polarizability is only of minor importance.     

CALCULATION OF THE FINE STRUCTURE OF OXYGEN-LIKE IONS USING THE POLARIZATION POTENTIAL FUNCTION

We have calculated the forbidden transition energies and magnetic dipole transition probabilities of 2s²2p⁴(³P₁－³P₂) and 2s²2p⁴ (³P₀－³P₁) of oxygen-like isoelectronic sequences (Z=10－32) by a method of polarization potential correction. The transition energies show good agreement with experiment and are much better than the calculations in the literature. These results also illustrate that it is feasible to use the dipole expansion of the polarization potential to deal with some dynamic and non-dynamic effects in the central field approach. The relation of polarizability and cut-off radius with atomic number is discussed. We also give the fitted formula between the polarizability α₁ and atomic number Z as α₁=0.73429-9.56644×10^-4Z+7.43016×10^-5Z^{2-2.53298×10-6Z3+2.08306×10-8Z4.}     

Temperature-dependent ionization potential of sodium clusters

The ionization potential of sodium clusters () at a finite temperature is studied using density functional theory and ab initio molecular dynamics. The threshold regions of the photoionization efficiency curves are deduced from the integrated IP distributions, which are obtained from the energy eigenvalues of the highest occupied Kohn-Sham states during molecular dynamics by applying a theoretically well-defined shift. The calculated ionization potentials are directly compared to the experimental values. The energetically best geometry of Na₅₅ is found to be a slightly distorted icosahedron. Received 16 April 1999 and Received in final form 6 July 1999     

密度泛函方法对SiO分子基态（X 1Σ+）势能函数的研究

利用密度泛函B3P86方法,分别选用STO-3G,D95^**,6-311G,6-311++G,6-311++G^**,cc-PVTZ基组对SiO分子基态(X¹Σ⁺)进行结构优化计算.通过比较得出,cc-PVTZ基组为对SiO分子基态(X¹Σ⁺)进行结构优化最优基组的结论.使用密度泛函B3P86方法,选用cc-PVTZ基组进 关键词： B3P86 SiO 势能函数 光谱常数     

Ab initio potential energy surface and intermolecular vibrational frequency of C3-He complex

The intermolecular potential energy surface for C₃–He complex has been constructed using supermolecular CCSD(T) and MP4 methods. The potential surfaces have been calculated for 27 values of R ranging from 2.8 to 8.0 Å and 19 values of θ equally spaced between 0° and 180°. Both CCSD(T) and MP4 potentials have similar global behaviors. The global minimum in each of the potentials corresponds to the slightly distorted T-shaped geometry. On the basis of these two potentials, the intermolecular vibrational energies and wavefunctions were calculated. The energy level pattern of the vdW vibrational states was predicted for C₃–He complex. The zero point bending motion of this complex has a range of 180°. The calculated fundamental frequency of vdW bending is 3.16 cm^?1 at CCSD(T) level, and 5.38 cm^?1 at the MP4 level. In addition, we have also constructed the intermolecular potential energy surface with C₃ bending coordinate of 160° by using supermolecular CCSD(T) method. Two local minima including arrow-shaped and Y-shaped configurations were determined. The rotational constants of three C₃–He structures including T-shaped, arrow-shaped and Y-shaped configurations at CCSD(T) level were also reported.     

XY(H,Li, Na)分子基态的结构与势能函数

运用群论及原子分子反应静力学方法，推导了XY(H，Li，Na)分子基态的电子态及相应的离解极限.并采用密度泛函方法(B3LYP)和二次组态相互作用方法(QCISD)优化计算了XY(H，Li，Na)分子基态的平衡结构、振动频率和离解能.使用QCISD/6-311++G(3df,3pd)方法，对XY(H，Li，Na)分子基态进行了单点能扫描计算，采用最小二乘法拟合Murrell-Sorbie函数得到了相应的势能函数和与该基态相对应的光谱常数(B_e,α_e,ω_e和ω_eχ_e)，计算结果与实验数据符合得相当好. 关键词： 组态相关方法 基态 势能函数     

TiO基态 (X 3 Δr) 的势能函数与光谱常数

应用群论及原子分子反应静力学方法推导了TiO分子基态(X³Δ_r)的离解极限.采用不同的计算方法,包括密度泛函B3LYP,B3P86,BP86,B3PW91和MP2,MP4方法,结合不同基组计算了TiO分子基态的平衡核间距、能量和振动频率.研究表明,使用B3LYP方法,对O原子使用6-311+G基组,Ti原子使用6-311+ +G^**基组时计算得到的平衡几何结构、分子离解能和谐振频率与实验值符合得最好.使用优选出的方法和基组对T 关键词： TiO 势能函数 光谱常数 密度泛函理论     

α-particle preformation of heavy nuclei using proximity potential

The half lives for α decay have been calculated using four different versions of the proximity potential for the even even isotopes of all known α-emitters. Using the experimental half lives, the preformation probability (P₀) of α particle before emission is calculated. Also the assault frequency (ν₀) is calculated through a modified formula. Half-lives obtained from the potential Prox 76 are minimum, and these values are used for calculating the preformation probability (P₀). Use of the potential Prox 76 in calculating P₀ is justified as it can best reproduce experimental Coulomb barriers among the four potentials. The trend of the values of P₀ versus the neutron number, N, and the proton number, Z, are in agreement with the shell model. The values of P₀ are also fitted using a four-parameter formula.     

High-pressure optical studies on R-line fluorescence lifetime in Al2O3:V2+

The effect of high hydrostatic pressure (up to 10.3?GPa) at room temperature on fluorescence lifetime τ for R line (²E→⁴A₂ transition) in ruby Al₂O₃:V²⁺ was studied. The performed studies show the linear increase of τ with increasing pressure. At 10.3?GPa, τ is about 1.36 times higher than at ambient pressure. The obtained trend was explained by a model which considered the effect of pressure on τ through an induced change of line position, inter-ionic distance, compressibility, and molecular polarizability. A good agreement between the calculated and experimental values for τ was obtained.