双原子分子电子能量损失谱的解谱方法

介绍一种双原子分子电子能量损失谱的解谱方法,在利用已知的双原子分子光谱信息及理论计算的Franck-Condon(FC)因子的基础上,通过二次函数调整整个电子态振动强度的轮廓,减少拟合过程中的待定参数个数,降低对FC因子精确性的要求,提高拟合的精度和可信度.用Mathematica语言编写基于以上方法的数据处理程序,改进算法,提高了软件的运行效率.利用该软件处理氢分子的电子能量损失谱,得到氢分子不同电子态的振动跃迁的截面信息,所得结果与以前的实验结果符合很好.     

Notations, Spectroscopic Parameters, Energy Levels and Their Relationship to Effective Hamiltonian Formalism of Diatomic Molecules

This paper presents a part of the culmination of the collective efforts in developing a cohesive and consolidated enunciation of the spectroscopic parameters and their relationship to effective molecular Hamiltonians for diatomic formalism, linear four-atomic formalism and quasi-linearity, Watson Hamiltonian and the complexities in symmetric and asymmetric top spectral structures. All these considered together present a beautiful and consistent picture of molecular spectroscopy. In this paper we deal with the diatomic formalism. This paper forms our tribute to Professor K. Narahari Rao and in the second part of the paper we convoy our gratitude to him with a summary of his more than half century of work and an obituary. We will deal with other forms of molecular species which will be connected to optical pumping and/or interstellar space.     

Photoassociation Spectroscopy: Determination of Parameters of Potentials of Diatomic Molecules

Laser-induced fluorescence studied with the help of a tunable dye laser is used to record the photoassociation spectrum of equilibrium mercury atoms in the range of 34 700–37 300 cm^–1. The so-called Franck-Condon structure, which represents periodic variations of absorption intensity on a continuous background, is observed. The structure makes it possible to determine spectroscopic parameters of the upper bound potential and the lower repulsive potential, including the potential with a shallow Van der Waals well. The Numerov-Cooley procedure is used to find the numerical solution of the boundary problem, namely, eigenfunctions and eigenvalues of the Schrödinger equation for the one-dimensional motion in a potential field, matrix elements of transitions and partial waves, and the absorption spectrum of collisional pairs of atoms are calculated. The absorption spectrum of mercury dimers was simulated taking into account 100 vibrational and 200 rotational levels. The comparison of theoretical and experimental spectra according to Tellinghuisen made it possible to determine the lower part of the potential curve for the dimer excited state.     

Dissociation Energies of Diatomic Molecules

Molecular dissociation energies of 10 electronic states of alkali molecules of KH, ^7LiD, ^7 LiH, ^6LiH, NaK, NaLi and NaRb are studied using the highest three accurate vibrational energies of each electronic state, and an improved parameter-free analytical formula which is obtained starting from the LeRoy Bernstein vibrational energy expression near the dissociation limit. The results show that as long as the highest three vibrational energies are accurate, the current analytical formula will give accurate theoretical dissociation energies De^theory, which are in excellent agreement with the experimental dissociation energies De^expt.     

The Significance of the Δkl Parameters in the Vibration-Rotational Energies of Diatomic Molecules

We discuss the physical significance of the parameters Δ_kl that arise from mostly the adiabatic and nonadiabatic effects in the vibration-rotational energles of diatomic molecules for which data from isotopic variants are available. Examples are given of the use c f these parameters to derive radial functions for HC1 and LiH. Similar to those for the U_kl coefficients, relations among the Δ_kl coefficients have been developed, but caution is urged in their use.     

Murrell-Sorbie势能参数与双原子分子光谱数据的关系研究

研究了Murrell-Sorbie势能参数与双原子分子光谱数据的关系.根据光谱数据编程计算了卤化氢分子的力常数和Murrell-Sorbie势能参数.反过来,运用ab initio和非线性最小二乘法拟合出了HF分子的Murrell-Sorbie势能函数和势能参数;并由此计算了HF分子的光谱数据,与实验光谱数据符合较好.这对难以获得实验光谱数据的双原子分子和离子的动力学研究有一定的参考价值.     

Spectroscopic Parameters of High Overtones of the Vibrations of Molecules

Based on the fundamental equation from the vibration theory of molecules and the operation of direct product of matrices and its properties for eigenvalues and eigenvectors, an equation of overtone vibrations for any high order has been obtained whose solution yields the matrices of vibration modes. Correlations determining changes in the structure parameters, just as expressions for the matrices of the coefficients of kinematic interaction and force constants, and for the parameters of vibrational-rotational interaction have been presented. Using the formulas obtained, the electro-optical parameters of water molecules H₂O and isotopes H₂ ¹⁷O and H₂ ¹⁸O have been calculated for overtones of up to the sixth order within the framework of the semiempirical quantum-chemical CNDO/2 method using the method of numerical differentiation by spline functions.     

Quantum Groups and Spectra of Diatomic Molecules

We briefly review and further investigate the quantum group theoretic approach to the spectra of the diatomic molecules presented by the authors recently. The vibration-rotational structures as well as the interactions of vibrations and rotations are described in the quantum group theoretic approach satisfactorily. When nylor expanded, the analytic formulae of the new approach reproduce the results of nonlinear vibratingrotator model. For some particular states of randomly selected molecules, the parameters of the new approach are computed to fit the phenomenological data to high accuracies. We also supply an analysis of the (pseudo-) potential implied in the new model, and compare it with the conventional model of the local potential that is applied in the explanation of the Dunham formula of energy spectra.     

Evaluation of Expansion Coefficients from Optimal Fitting Parameters for the Analysis of Spectra of Diatomic Molecules and an Application to LiH

To evaluate individual expansion coefficients composing fitting parameters of the Born-Oppenheimer corrections to Dunham's coefficients Y(ij) that have been given analytically with the Delta(B) and Delta(omega) formalism, we examined the consistency of analytic expressions for those corrections with Watson's assertion of the experimental inseparability of nonadiabatic corrections Q(a, b)(r) for a molecule AB. Derived analytic expressions in terms of optimal fitting parameters for the corrections are essential to evaluate individual expansion coefficients. These expressions also reveal redundancies between empirical correction parameters Delta(ij). A method of evaluating nonadiabatic vibrational corrections Q(a, b)(r) and adiabatic corrections S(a, b)(r) separately consistent with Watson's assertion of inseparability is presented and is applied to an analysis of spectral data of LiH. Functions Q(a, b) and S(a, b) for LiH are thus successfully evaluated; S(H, Li)(r) values agree well with those predicted simply by wobble-stretch theory. Experimental values for optimal fitting parameters r(H)(1q) and r(H)(2q) are nearly equal to those of r(Li)(1q) and r(Li)(2q), respectively, in agreement with a theoretical relation r(a)(iq)=r(b)(iq). Copyright 2001 Academic Press.     

Some Remarks on the Calculation of Standard Thermodynamic Functions of Diatomic Molecules in SF6 Plasma

Applying the Mayer's and Geppert-Mayer's method and the method of direct summation the standard thermodynamic functions of some typical diatomic molecules present in SF₆ plasma were calculated. There are given STF data in the temperature region from 100 0 to 15 000K. Some problems of the determination of the STF are discussed.     

六参数高精度双原子分子解析势能函数

提出一种构造解析势能函数的新方法,得到一种六参数解析势能函数,该势能函数适用于多种基本类型的双原子分子.用同核中性基态双原子分子Li₂-X¹Σ_g⁺、Na₂-X¹Σ_g⁺,异核带电基态双原子分子离子(BC)^--X³∏,异核中性激发态双原子分子PbS-A¹Σ⁺、BaO-A¹Σ,异核带电激发态双原子分子离子(CS)⁺-A²∏,同核中性激发态双原子分子K₂-B¹∏_u,同核带电激发态双原子分子离子N₂⁺-B²Σ_u⁺等共36个算例对该势能函数进行验证,计算结果与RKR(Rydberg-Klein-Rees)数据或振动能谱实验数据高精度符合.同时发现,在分子振动能谱计算精度方面,该势能函数总体上优于Murrell-Sorbie势能函数.     

Relationship of the Williams-Poulios and Manning-Rosen Potential Energy Models for Diatomic Molecules

By employing the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate an improved form of the Williams-Poulios potential energy model. It is found that the negative Williams-Poulios potential model is equivalent to the Manning-Rosen potential model for diatomic molecules. We observe that the Manning-Rosen potential is superior to the Morse potential in reproducing the interaction potential energy curves for the \({{a}^{3} \Sigma_{{\rm u}}^{+}}\) state of the ⁶Li₂ molecule and the \({{X}^{1} \sum^{+}}\) state of the SiF⁺ molecule.     

高浓度掺Er3+铌酸锂晶体的光谱参数计算

用提拉法成功地生长了6mol%的高浓度掺铒铌酸锂晶体。测量了晶体的两个非偏振方向(X和Z)以及两个偏振方向(π和δ)的吸收光谱。高浓度掺铒铌酸锂晶体的吸收系数高,有利于提高泵浦效率。根据所测的吸收光谱用Judd-Ofelt理论拟合出了Er3 离子的强度参数Ωλ。所得的均方差结果显示偏振拟合的误差要小于非偏振拟合。利用偏振吸收数据计算了各能级跃迁的自发辐射跃迁几率(AJJ′)、辐射寿命(τ)、荧光分支比(β)和积分发射截面(σp)等参数,对计算结果进行了讨论并与其他文献的报道结果进行了比较。     

双原子分子电子光谱的振动结构分析

从电子振转能级的光谱项出发,分析了双原子分子电子振动谱带序和电子振动谱带列的规律,并归纳出德兰德斯表(Deslandres table)及其主要性质。以C₂分子电子振动光谱的斯簧谱带系作为实例,说明了如何对电子振动光谱的测量值进行标识,并将它们按振动结构规律整理成德兰德斯表,从而获得有关分子光谱不同态的非谐性常数、振动频率等重要参数以及任意谱带的波数公式。     

Photoacoustic Spectroscopic Studies of Mono-Substituted Naphthalene Molecules

The present paper deals with the Photoacoustic (PA) studies of mono-substituted (hydroxy) naphthalene molecules, namely 1-naphthol and 2-naphthol in boric acid glass in the region 250–400 nm. The electronic transitions of these molecules observed experimentally, have been interpreted using the optimised geometries and CNDO/S-CI method. Assignments of observed electronic transitions are made on the basis of singlet-singlet and singlet-triplet transitions. The PA spectra of 1-naphthol and 2- Maphthol are compared with its parent molecule i.e. naphthalene molecule, in terms of charge transfer character of -OH group and polarization of molecules. It is observed that the non-radiative transitions in mono-substituted naphthalene molecules shift towards the higher wavelength region when compared with naphthalene molecule, which may be attributed to increase in the charge density in the substituted ring.     

Consideration of Electronic-Vibrational Interactions in Calculations of Electronic Transition Moments for Diatomic Molecules

Two different approaches to the determination of the dependence of the electronic transition moment on the internuclear distance, M_e(R), are considered. It is shown that M_e(R) dependences obtained by ab initio and semi-empirical methods take into account electronic-vibrational interactions in a various manner. In semi-empiral methods these interactions are take into account to a greater degree, than in non-empirical quantum-mechanical methods which do not include nonadiabatic corrections. A system of concepts, which allows to unite the information obtained in two different, mutually complementing ways, is considered in the paper.     

The Symmetry Properties of Linear Combination Coefficients for Molecular Orbitals of Diatomic Molecules

In this paper, the symmetry properties of linear combination coefficients for molecular orbitals of diatomicmolecules, using Slater type orbitals, are presented with the help of the symmetry operations in group theory. In order totest the presented symmetry properties, the linear combination coefficients of molecular orbitalsfor the ground electronicstate of pilot molecules F2 and CO are calculated using constructed computer programs for Hartree-Fock-Roothaanequation. It is seen that the obtained computing results satisfy the presented symmetry properties.     

The Influence of the Rotation-Vibrational Interaction on the Franck-Condon Factors for Diatomic Molecules

Using the first order perturbation theory, the analytical expressions are obtained for the dependence of the Franck-Condon factors (FCF) on the rotational quantum number J for P, Q and R-branches in the form of a polynominal expansion in J(J+1). A new quantitative criterion for estimating the influence of rotation-vibrational interactions on the FCF of diatomic molecules is obtained.