Dependence of the Diatomic Rotational Constant Bν on the Long-Range Internuclear Potential

A simple expression is derived which explicitly relates the rotational constant Bν for vibrational levels near the dissociation limit D of a diatomic molecule, to the nature of the long-range interatomic potential. Assuming a long-range potential of the form V(R) = D – Cn/Rn, the expression Bν = Qn(νD – ν)[4/(n−2)] is obtained, where νD is the effective vibrational index at the dissociation limit, and Qn is a constant depending only on n, Cn, and the reduced mass. This result is slightly less accurate than an analogous recently developed relation for the vibrational level distribution near D. Its utility and accuracy are demonstrated by application to experimental data for the [Formula: see text] states of Cl2, Br2, and I2.

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THE LYMAN BANDS OF MOLECULAR HYDROGEN

Canadian Journal of Physics ◽

10.1139/p59-070 ◽

1959 ◽

Vol 37 (5) ◽

pp. 636-659 ◽

Cited By ~ 269

Author(s):

G. Herzberg ◽

L. L. Howe

Keyword(s):

High Resolution ◽

Vibrational Level ◽

Ground State ◽

Molecular Hydrogen ◽

Equilibrium Constants ◽

Dissociation Limit ◽

Vibrational Levels ◽

State Formula ◽

Single Formula ◽

Vibrational Constants

The Lyman bands of H2 have been investigated under high resolution with a view to improving the rotational and vibrational constants of H2 in its ground state. Precise Bv and ΔG values have been obtained for all vibrational levels of the ground state. One or two of the highest rotational levels of the last vibrational level (v = 14) lie above the dissociation limit. Both the [Formula: see text] and ΔG″ curves have a point of inflection at about v″ = 3. This makes it difficult to represent the whole course of each of these curves by a single formula and therefore makes the resulting equilibrium constants somewhat uncertain. This uncertainty is not very great for the rotational constants for which we find[Formula: see text]but is considerable for the vibrational constants ωe and ωexe for which three-, four-, five-, and six-term formulae give results diverging by ± 1 cm−1. The rotational and vibrational constants for the upper state [Formula: see text] of the Lyman bands are also determined. An appreciable correction to the position of the upper state is found.

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Ground State D2 Dissociation Energy from the Near-dissociation Behavior of Rotational Level Spacings

Canadian Journal of Physics ◽

10.1139/p75-248 ◽

1975 ◽

Vol 53 (19) ◽

pp. 1983-1990 ◽

Cited By ~ 37

Author(s):

Robert J. Le Roy ◽

Margaret G. Barwell

Keyword(s):

Long Range ◽

Diatomic Molecule ◽

Dissociation Energy ◽

Vibrational Level ◽

Ground State ◽

Potential Application ◽

Rotational Level ◽

Intermolecular Potential ◽

Continuum Absorption ◽

Exact Agreement

A method of determining the dissociation energy of a diatomic molecule from the rotational term value(s)of a single vibrational level lying near dissociation is derived and tested. It is based on expressions relating the characteristic near-dissociation behavior of the rotational constants Bv, Dv, Hv,… etc., to the asymptotically dominant inverse power contribution to the long range intermolecular potential. Application of this procedure to data for ground state D2 yields a dissociation energy of D0 = 36 748.88(±0.3)cm−1, in essentially exact agreement with the value Herzberg determined from the onset of continuum absorption in the vacuum u.v., 36 748.9(±0.4) cm−1. This agreement between results obtained from completely different observables appears to confirm the existence of a small discrepancy between experiment and the most recent theoretical nonadiabatic dissociation energy of Kolos and Wolniewicz, 36 748.2 cm−1.

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Population Distribution of Vibrational Levels of the 2\(^1\Pi\) State of NaLi

Communications in Physics ◽

10.15625/0868-3166/27/3/10567 ◽

2017 ◽

Vol 27 (3) ◽

pp. 215

Author(s):

Nguyen Tien Dung

Keyword(s):

Long Range ◽

Turning Point ◽

Population Distribution ◽

Excited Level ◽

Dissociation Limit ◽

Dynamical Processes ◽

Radial Schrödinger Equation ◽

Vibrational Levels ◽

Experimental Parameters ◽

The Right

We studied population distribution of vibrational levels for the 2\(^1\Pi\) of NaLi molecule from \(v'=0\) to \(v'=16\). The population of the levels was calculated numerically by solving the radial Schrodinger equation with an experimental potential extrapolated to the dissociation limit via a long range potential. We found that, for each highly excited level its population distribution is favorable around the right turning-point. The results provide important information for choosing convenient experimental parameters and explaining dynamical processes in the molecule

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The Lyman and Werner Bands of Deuterium

Canadian Journal of Physics ◽

10.1139/p73-119 ◽

1973 ◽

Vol 51 (9) ◽

pp. 867-887 ◽

Cited By ~ 63

Author(s):

H. Bredohl ◽

G. Herzberg

Keyword(s):

High Resolution ◽

Ab Initio Calculations ◽

Vibrational Level ◽

Ground State ◽

Electronic Excitation ◽

Theoretical Calculations ◽

Dissociation Limit ◽

Excitation Energies ◽

Vibrational Levels ◽

Theory And Experiment

The Lyman and Werner bands of D2 have been measured under high resolution and their analysis has been extended. From this analysis the rotational and vibrational levels of the ground state of D2 have been evaluated up to the last vibrational level ν = 21 which lies only 2 cm−1 below the dissociation limit. The deviations of the observed ΔG(ν + 1/2) and Bv values from theoretical values given by Kolos and Wolniewicz on the basis of ab initio calculations are very small but systematic and are probably due to the neglect of nonadiabatic corrections in the theoretical calculations. Similar comparisons have been made for the lower vibrational levels of the B1Σu+ and C1Πu− states. Here the differences between theory and experiment are somewhat larger. The observed electronic excitation energies agree with the theoretical ones within 15 cm−1 for 1Σu+ and 8 cm−1 for 1Πu−.

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Bichromatic Photoassociation Spectroscopy for the Determination of Rotational Constants of Cs2 0 u + Long-Range State below the 6S1/2 + 6P1/2 Asymptote

Molecules ◽

10.3390/molecules25173963 ◽

2020 ◽

Vol 25 (17) ◽

pp. 3963

Author(s):

Jizhou Wu ◽

Jie Ma ◽

Yuqing Li ◽

Wenliang Liu ◽

Peng Li ◽

...

Keyword(s):

Long Range ◽

Spectroscopic Technique ◽

Rigid Rotor ◽

Simple Analysis ◽

Rotational Constants ◽

Vibrational Levels ◽

Photoassociation Spectroscopy ◽

Rotor Model ◽

Good Agreement

This article demonstrates new observation of the high-resolution ro-vibrational bichromatic photoassociation spectra (BPAS) of Cs2 in the 0u+ long-range state below the asymptotes 6S1/2 + 6P1/2. By combining with a modulation spectroscopic technique, precise references of the frequency differences have been engineered through the BPAS, with which the rotational constants of low-lying vibrational levels of the Cs20u+ long-range state have been accurately determined by fitting the frequency differences to the non-rigid-rotor model. The rotational constants for the newly observed seven ro-vibrational levels are summarized and disagreement for the level ῦ = 498 is clarified. The rotational constants of different vibrational levels demonstrate strong perturbations of the related energy structures. A simple analysis is performed and shows good agreement with experimental results.

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Analysis for RKR long-range potential of the B 3Π0+u state of I2

Chemical Physics Letters ◽

10.1016/0009-2614(73)80149-6 ◽

1973 ◽

Vol 21 (2) ◽

pp. 334-337 ◽

Cited By ~ 5

Author(s):

K.K. Yee

Keyword(s):

Long Range ◽

Range Potential

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The number of bound vibrational levels in a diatomic molecule

Journal of Molecular Spectroscopy ◽

10.1016/j.jms.2013.02.006 ◽

2013 ◽

Vol 286-287 ◽

pp. 1-4 ◽

Cited By ~ 5

Author(s):

Photos G. Hajigeorgiou

Keyword(s):

Diatomic Molecule ◽

Vibrational Levels

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3D-Atom Probe Investigation of Vacancy Induced Interdiffusion during High Pressure Torsion Deformation

Materials Science Forum ◽

10.4028/www.scientific.net/msf.503-504.433 ◽

2006 ◽

Vol 503-504 ◽

pp. 433-438 ◽

Cited By ~ 7

Author(s):

Xavier Sauvage

Keyword(s):

Experimental Data ◽

High Pressure ◽

Long Range ◽

High Pressure Torsion ◽

Pearlitic Steel ◽

Atom Probe ◽

Concentration Gradients ◽

Deformed State ◽

Torsion Deformation ◽

Probe Investigation

Concentration gradients resulting from long range diffusion during Severe Plastic Deformation (SPD) have been investigated with the 3D Atom Probe technique (3D-AP). First, in a pearlitic steel where alloying elements (Mn, Si and Cr) are partitioned between the ferrite and carbides in the non-deformed state. After processing by High Pressure Torsion (HPT), they are homogeneously distributed in the nanostructure, indicating that long range diffusion occurred along with the dissolution of carbides. 3D-AP data of a Cu-Fe composite processed by HPT show as well a significant interdiffusion of Cu and Fe, probably promoted by additional vacancies. On the basis of these experimental data, and using the theory described for irradiated materials, vacancy fluxes and vacancy production rates were estimated assuming that new vacancies are continuously produced and eliminated on grain boundaries.

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