On the Quantum Theory of Vibration-Rotation Bands

1926 ◽  
Vol 23 (3) ◽  
pp. 327-335 ◽  
Author(s):  
J. R. Oppenheimer
Keyword(s):  
Quantum Theory ◽  
Diatomic Molecule ◽  
Central Line ◽  
Rotational Energy ◽  
Dynamical Problem ◽  
Corresponding States ◽  
Main Term ◽  
Fundamental Band ◽  
Vibration Rotation

The dynamical problem of the “diatomic molecule” is solved on the new mechanics. The terms of the rotational energy are , where ; the weights of the corresponding states are 2m; the frequencies differ a little from the classical ones. Finally the intensities are slightly different from those computed by Kemble; the main term agrees with that of Fowler, but the positive branch is only slightly stronger than the negative. The central line vanishes. The intensities are valid only for the fundamental band.

RKR-type inversion of the diatomic energy shifts due to breakdown of the Born–Oppenheimer approximation

2004 ◽  
Vol 82 (6) ◽  
pp. 820-825 ◽  
Author(s):  
James KG Watson
Keyword(s):  
Diatomic Molecule ◽  
Internuclear Distance ◽  
Diatomic Molecules ◽  
Isotope Effects ◽  
Electron Mass ◽  
Effective Hamiltonian ◽  
Expectation Values ◽  
Oppenheimer Approximation ◽  
Vibration Rotation

The principal effects of the breakdown of the Born–Oppenheimer approximation on the vibration–rotation energies of a diatomic molecule can be represented by the expectation values of terms to order (me/Mi) in the effective Hamiltonian, where me is the electron mass and Mi is the mass of atom i. This paper examines the possibility of inverting these expectation values to obtain the correction functions as functions of the internuclear distance r, using a generalization of the semiclassical Rydberg–Klein–Rees method. It is shown that the correction functions are not completely determinable from the inversion, and the form of the determinable combinations is obtained.Key words: diatomic molecules, vibration–rotation energies, isotope effects, Born–Oppenheimer breakdown, Rydberg–Klein–Rees method.

Vibration–Rotation Interaction in the Fundamental Band of HF†

1964 ◽  
Vol 54 (5) ◽  
pp. 715_1 ◽  
Author(s):  
L. F. Eldreth ◽  
W. F. Herget ◽  
R. J. Lovell
Keyword(s):  
Fundamental Band ◽  
Vibration Rotation

scholarly journals Infra-red investigations of molecular structure. Part II.—The molecule of nitric oxide

1929 ◽  
Vol 124 (794) ◽  
pp. 453-464 ◽  
Keyword(s):  
Electronic State ◽  
Diatomic Molecule ◽  
Band Spectrum ◽  
Electric Moment ◽  
Electronic Band ◽  
Hydrogen Halides ◽  
Direct Measurements ◽  
Infra Red ◽  
Band Spectra ◽  
Vibration Rotation

There have been few attempts at the resolution of the vibration-rotation bands of a diatomic molecule. In 1919 Imes was successful with the bands of three of the hydrogen halides, work which was later extended by Colby and Meyer; Czerny proved the existence of a doublet due to HI, but the weakness of the absorption prevented more detailed study; E. F. Lowry in 1924 failed to analyse the structureless doublets of carbon monoxide, although his apparatus was similar to that used by Imes. It does not seem possible that the fine-structure would reveal itself if a lower pressure of the gas were used (E. F. Lowry worked at one atmosphere pressure). The molecule of CO, like those of the hydrogen halides, has a permanent electric moment, and its bands must be similar in kind. Apart from HF, HCI, HBr, HI and CO, NO is the only other diatomic molecule with a permanent electric moment, and its choice as the subject of this research was natural. It is more definitely homopolar than the hydrogen halides, although the distinction is almost certainly one of degree; there was the interest of establishing the self-evident proposition that there is no fundamental difference in the bands of No and the bands HCI. There was also the advantage of knowledge of the electronic band spectrum of the molecule acquired by Guillery, Jenkins, Barton and Mulliken, and summarised by Mulliken. The thoroughness of this work makes NO one of the best-known of molecules to the spectroscopist. It has been mentioned in the introduction to Part I that throughout this series of papers there will be maintained the deal of correlation between infra-red and electronic band spectra. Accordingly, it became our aim to compare the constants of the molecule in the normal state as derived from electronic band spectra and as obtained from the direct measurements of the infra-red. The unexcited electronic state of the molecule measurements of the infra-red. The unexcited electronic state of the molecule is, of course, the only one with which infra-red observations are concerned.

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