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.     

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。     

q变形转动振子模型(Ⅰ)——q振子与双原子分子振动谱

我们提出具有量子群对称性的q变形转动振子模型,并采用这一模型对一类微观系统的转动振动谱给出相当精确的描述。本文集中讨论q振子模型,指出,q振子代数的表示及相应的能级结构可以准确地描述双原子分子的红外振动谱、振动喇曼谱、电子跃迁振动谱及相应的选择定则。 关键词：     

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.     

Calculation of Spectroscopic Parameters of Diatomic Molecules with an Open Electron Shell

Russian Physics Journal - The spectroscopic parameters of the BeH and CH molecules with an open electron shell are calculated in the basis of the Slater functions. An analytical expression for the...     

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.     

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.     

Analyzing the Effects of Topological Defect (TD) on the Energy Spectra and Thermal Properties of LiH,TiC and I2 Diatomic Molecules

In this study, the impacts of TD on the energy spectra and thermal properties of LiH, TiC and I₂ diatomic molecules is considered. The Schrodinger equation in cosmic string spacetime is solved with the generalized Morse potential using the well-known (NU) method. The energy spectra and eigenfunction are obtained respectively. The energy spectra is used to obtain the partition function which is then used to evaluate the thermal properties of the system is evaluated accordingly. We find that the energy spectra in the presence of the TD differ from their flat Minkowski spacetime analogue. The effects of the deformation parameter and TD on the thermal properties of the system is also analysed in detail. We observe that the specific heat capacity of the system tends to exhibit quasi-saturation as the deformation parameter and topological defect approaches unity. The results of our study can be applied in the astrophysical situation where these modifications exist in the understanding of spectroscopical data and it may be used as a probe of the presence of a cosmic string or a global monopole in the Universe.     

A New Relation Connecting Vibrationai Constant and Electronegativity in the Case of Diatomic Molecules

The electronegativity was defined by Pauling¹ as a measure of the power of an atom in the molecule to attract electrons to itself. This concept of electronegativity has undergone radical changes. Recent calculations of electronegativity show^2,3 that it is a complex quantity including an important atomic term depending on the charge and hybridization of the atom, and a molecular term depending on the length and the nature of the bonds in the molecule. In a molecular group of the type A-B, B is a halogen atom, say chlorine and A stands for different atoms of a subgroup of the periodic table. Since the nature of the bonds in the molecule AB and the electronegativity of halogen atom, B, is constant for a molecular group, the electronegativity, X, of atom A may be related to the dissociation energy and bond length which in its turn is related to the vibrational constant,ω_e, and the reduced mass, μ, of the molecule AB.     

A New Relation Free From Electronegativity For Vibrational Constant Of Diatomic Molecules

Most of the previous relations^1–3 for the calculation of vibrational constant of diatomic molecules are electronegativity dependent. Electronegativity (X) is a complex quantity containing an atomic term depending on the charge and hybridization of the atom, and a molecular term depending on the length and the nature of the bonds in the molecule and as such it is not as precise as the bond length r_e or the reduced mass μ of the molecule. Thus the formule dependent on the electronegativity are expected to yield divergent results. Though there is a relation given by Varshni and Guggenheimer⁴ which is free from electronegativity but the drawback is that it depends on too many quantities and also contains two empirical constants. Therefore it was thought to propose a new relation free from electronegativity, containing a single constant A, depending only on r_e and μ.     

普适性双原子分子解析势能函数的研究

提出了一种构造解析势能函数的新方法,由此得到了一种既适用于中性双原子分子又适用于带电双原子分子离子的解析势能函数。本文用八种基本类型的双原子分子——同核中性基态双原子分子Na₂-X1Σ+_g,同核中性激发态双原子分子C₂-A1Π_u,同核带电基态双原子分子离子He+₂-X2Σ+_u,同核带电激发态双原子分子离子N+₂-B2Σ+_u,异核中性基态双原子分子NaLi-X1Σ+_g,异核中性激发态双原子分子BH-B1Σ+,异核带电基态双原子分子离子(BC)--X3Π,异核带电激发态双原子分子离子(CS)+-A2Π等共21个算例对势能函数进行了验证并与RKR (Rydberg-Klein-Rees)实验数据进行了比较,计算结果与RKR数据符合很好。     

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.     

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.     

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.     

表面活性剂修饰多孔硅的光致发光光谱

分别利用4种不同的表面活性剂对多孔硅进行表面修饰,结果表明油酸钠溶液、CPB溶液和乳化剂OP溶液修饰的多孔硅样品发光减弱,SDS溶液修饰的多孔硅样品发光增强,不同浓度的SDS溶液的增强倍数也不同。这种现象不仅可以为研究多孔硅的发光机制提供新的依据,还为提高多孔硅的发光效率提供了一个新的有效途径。     

NMR碳谱谱峰检索系统

介绍了核磁共振(NMR)碳谱谱峰检索系统的程序设计原理、系统流程框图、检索比较算法和主要显示界面．系统数据库包含化合物核磁共振碳谱4万多张,能够根据未知物¹³C NMR波谱的谱峰个数及其化学位移值进行检索．结果得到未知化合物的有关信息及其标准波谱图．系统还允许用户将本专业的一些常用化合物的标准谱的信息以及图谱添加进数据库以供日后查询．     

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.     

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.