Quantum mechanical calculation of rotational constants and Franck-Condon factors of diatomic molecules

In this paper, the question of reliability of the Morse potential as a potential curve for a diatomic molecule is investigated on the basis of calculating the rotational constant. It is shown that the Morse potential describes well potential curves of X¹Σ _q ⁺ and B¹Π_u electronic states of a Na₂ molecule. Calculations of Franck-Condon factors for X¹Σ _q ⁺ ? B¹Π_u band of a Na₂ molecule using wave functions of the Morse potential confirm the known correlation between the values of Franck-Condon factors and rotational constants of combined electronic states.     

A line intensity transfer model for the rotational raman spectrum of ethylene

A new model for the spectrum of ethylene, utilizing the line-mixing concept for overlapping lines, is presented here. The Lorentzian line shape is assigned to all the lines, with the single transitions having the usual directly pressure-dependent widths, and with overlapping lines considered as a single composite feature having an inversely pressure-dependent width. This model is compared with two sets of data: interferometric data over a range of pressures, and an ad hoc model that matches experimental line spectrum data at a single pressure. Inversely pressuredependent widths are obtained for the two comparisons, and the discrepancy between the results is explained.     

Recommended conventions for defining transition moments and intensity factors in diatomic molecular spectra

Two recommendations are made that can eliminate persistent confusion in the study of diatomic spectroscopy by providing uniform and consistent definitions of the electronic transition moments and the rotational line intensity factors. First, it is recommended that the equation for the line strength of a single rotational line be adopted to specify the relationship between the electronic transition moment and the rotational line intensity factor. Second, it is recommended that the electronic transition moment operator for perpendicular transitions be defined by (1/2^1/2)(μ_x ± iμ_y). The adoption of these conventions results in a value of (2S + 1)(2J + 1) for the sum rule of the rotational line intensity factor for Σ^± ↔ Σ^± transitions and a value of 2(2S + 1)(2J + 1) for the sum rule for all other spin-allowed transitions.     

Vibration-rotational matrix elements for infrared transitions of diatomic molecules

Theoretical expressions for the vibro-rotational matrix elements corresponding to i.r. transitions vJ→v′J′ with v ⩽ v ′ ⩽ v + 6 are obtained in terms of quadratic polynomials in m, including contributions from the Dunham potential energy parameters a₁ to a₅ and from dipole-moment expansion coefficients M₀ to M₇. The formalism has been applied to vibrational transitions in the ground electronic state of CO and HCl. The Herman-Wallis coefficients have been derived for the bands 0-0 to 0-4 of CO and 0-0 to 0-6 of HCl and are compared with experimental data.     

Estimation of rotational and vibrational constants for diatomic molecules using Mattera's potential function

Summary The potential function suggested by Mattera, Salvo, Terreni and Tommasini is investigated further and the expressions for rotational constant α_e and anharmonicity constantw _e x _e are obtained. The α_e andw _e x _e values of twentyseven diatomic molecules are calculated using those expressions and they are compared with their experimental values.     

Exact analytical expressions for diatomic rotational and centrifugal distortion constants for a Kratzer-Fues oscillator

The exact closed-form expression for the vibrational-rotational eigenvalues of the Kratzer-Fues oscillator served as the starting point for a derivation of exact analytical expressions for the rotational constant B_υ, and the set D_υ to S_υ of centrifugal distortion constants up to 11th-order. The derivations employed the MAPLE symbolic algebra coprocessor. The expressions for B_υ to S_υ were then employed in the calculation of a set of constants for a Kratzer-Fues potential with specified dissociation energy and equilibrium internuclear separation for a hypothetical diatomic molecule with a reduced mass of unity. The tabulated constants serve as a benchmark against which the reliability of various existing or future numerical methods for the determination of rotational and centrifugal distortion constants may be assessed. The near-dissociation behaviour of the calculated constants was also examined and is useful in predicting the behaviour of such constants for real electronic states having pure ionic long-range form.     

On the Zeeman effect in electronic transitions of diatomic molecules

The Zeeman effect for diatomic molecules is calculated in a representation with Hund's case (a) wave functions as a basis set. The resulting expressions are simpler and easier to handle than those obtained from previous calculations on the basis of cace (b) wave functions. The calculations of intensities and polarization of Zeeman patterns is presented for transitions between doublet states with arbitrary spin-orbit (if Λ≠ 0) or spin-rotation (if Λ = 0) interaction, and for case (a)-case (a) transitions of any multiplicity. These calculations are in good agreement with observations.     

Einstein A-coefficients for pure rotational transitions in D2O

Einstein A-coefficients for the electric-dipole transitions between the rotational levels up to 785 cm⁻¹ in the ground vibrational state of D₂O are calculated. The A-values are used to compute the mean-radiative life-times of the levels.     

Subshell conversion-line intensity ratios for some pure transitions

For a number of “normal” electromagnetic transitions, either necessarily pure or judged to be essentially pure, L- and M-subshell internal conversion ratios were measured and compared with ratios obtained from the Hager and Seltzer theoretical calculations. In addition, data available in the literature were also used in these comparisons. A range of Z-values and energies and several multipole orders were included. There appears to be no real disagreement between theory and experiment. A possible source of systematic error in high-resolution internal conversion spectrometry is briefly discussed; and a simple accurate method for energy interpolation of theoretical coefficients is described.     

双原子分子电子振动光谱的转动结构分析

本文分析了双原子分子电子振动光谱的转动结构规律,说明了如何对电子振转光谱进行标识,从而获得不同电子态的转动常数、转动惯量和核间距。     

Frequency measurement of pure rotational transitions of OH

Frequencies of pure rotational transitions of OH⁻ ion were measured in the 1-5 THz region with a high-precision tunable far-infrared spectrometer. The measured frequencies were analyzed together with the data of infrared measurements to refine rotational parameters.     

Frequency measurement of pure rotational transitions of OD

Frequencies of pure rotational transitions of OD⁻ have been measured in the 1-5 THz region using a high-precision tunable far-infrared spectrometer based on difference frequency of two CO₂ lasers. The measured frequencies were analyzed together with the data in the infrared and the sub-millimeter region to refine the rotational parameters. Isotopically invariant Dunham parameters were also obtained.     

Theory of the rotational structure of resonant Raman scattering by diatomic molecules

The apparatus of irreducible tensor operators is used to calculate the rotational structure of resonant Raman light scattering by freely rotating diatomic molecules. It is shown that solution of the problem reduces to the calculation of certain special coefficients. Their relation to the Placzek-Teller factors (which are well known in the theory of polarizability) is established. The nonzero coefficients are computed for the case when resonant rotational scattering is due to the¹ terms of the diatomic molecule.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 54–58, October, 1987.The author thanks T. N. Popov for interest in the work.     

Role of electric field polarisation in rotational transitions

The molecular dynamics of polar diatomic molecule, interacting with linearly and circularly polarised laser field is studied. Non-perturbative quasi-energy technique is used to determine the rotational field surfaces. Degeneracy in different M-levels is found to be removed in the presence of circularly polarised electromagnetic radiation. In this paper, we present the calculations exhibiting the dynamics of rotational excitation of a linear molecule and characteristic features of spectra which become observable in considered fields. Received 22 March 2002 / Received in final form 15 July 2002 Published online 6 November 2002 RID="a" ID="a"e-mail: nsinghal@physics.du.ac.in RID="b" ID="b"e-mail: vnautiyal@himalaya.du.ac.in RID="c" ID="c"e-mail: manmohan@physics.du.ac.in     

Franck-condon factors for diatomic molecules and the factorization method

By means of the factorization method, recurrence relations for the matrix elementS$\text{<ψ}{}_{\mathrm{<mtext>v\text{'}</mtext>}}\text{¦r}{}^{\mathrm{N}}\text{¦ψ}{}_{\mathrm{<mtext>v</mtext>}}\text{<}$ for an arbitrary positive integer N are obtained in the framework of α-averaging for the Morse potential. The method of calculating the matrix element$\text{<ψ}{}_{\mathrm{<mtext>v\text{'}</mtext>}}\text{¦R}{}_{\mathrm{<mtext>e</mtext>}}\text{¦ψ}{}_{\mathrm{<mtext>v</mtext>}}\text{<}$ is outlined, provided a dependence of the electronic transition moment R_e on the internuclear distance r can be approximated by the polynomial R_e(r)=a₀+a₁r+a₂r²+…+ainNr^N. Recurrence relations are also obtained for the case of the exponential dependence R_e(r).     

Linestrength formulas of Hund's intermediate case multiplet transitions in diatomic molecules

Explicit expressions in fairly condensed form are obtained for the intensity distribution in the branches of quartet transitions of any type with ΔΛ = 0 and ΔΛ = ±1 where both electronic states involved in transition may belong to a coupling case intermediate between Hund's cases (a) and (b). Moreover, similar condensed expressions are given for the linestrengths already known of the doublet, triplet, and quintet transitions.     

Einstein A-coefficients for rotational transitions in the HN2O+

EinsteinA-values for the electric dipole transitions between the rotational levels up to 540 cm⁻¹ andJ=11 in the ground vibrational state of the protonated N₂O (i.e., HN₂O⁺) are calculated. The coefficients are used to compute the mean radiative lifetimes of the levels. TheseA-values can be used for analysing the spectra from astronomical objects, if observed.     

Theory of pressure-induced vibrational and rotational absorption of diatomic molecules at high temperatures

A derivation is given for the integrated absorption coefficient of pressure-induced pure rotational and vibrational transitions in binary collisions of homonuclear diatomic molecules of the same chemical species. The previously neglected effects of excited vibrational states, mechanical anharmonicity, and vibration-rotation interaction are taken into account to obtain more accurate absorption coefficients at high temperatures. In the region of the fundamental wave number the excited vibrational states make more of a contribution to the absorption than their relative population would lead one to expect.