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.

The influence of vibration-rotation interaction on intensities in the electronic spectra of diatomic molecules I. The hydroxyl radical

1962 ◽  
Vol 269 (1338) ◽  
pp. 311-326 ◽  
Keyword(s):  
Hydroxyl Radical ◽  
Internuclear Distance ◽  
Electronic Spectra ◽  
Rotational Temperature ◽  
Diatomic Molecules ◽  
Transition Probability ◽  
Transition Moment ◽  
Vibration Rotation

The effect of vibration-rotation interaction on transition probability is examined in detail for the 2 E + - 2 lI i transition of the hydroxyl radical, using a Morse-Pekeris model. It is shown to have a significant effect on the rotational temperature (of the order of 200° at 3000 °K) for the (0, 0) b and and to be especially important for the (0, 1) band. The variation of transition moment with internuclear distance is examined and an expression of the form R e ( r ) = constant x e -2.5r where r is the internuclear distance in angstroms is recommended. With this value, corrections are obtained to rotational temperatures and the f value for the Q 1 (6) line of th e (0, 0) band is altered to 1.0 ±0.5 x 10 -3 . Calculations for the OD radical are also presented.

INFLUENCE OF VIBRATION–ROTATION INTERACTION ON THE INTENSITIES OF PURE ROTATION LINES OF DIATOMIC MOLECULES

1956 ◽  
Vol 34 (11) ◽  
pp. 1119-1125 ◽  
Author(s):  
Robert Herman ◽  
Robert J. Rubin
Keyword(s):  
Line Intensity ◽  
Anharmonic Oscillator ◽  
Diatomic Molecules ◽  
Potential Energy Function ◽  
Complete Agreement ◽  
Contact Transformation ◽  
First Order ◽  
Pure Rotation ◽  
Rotation Line ◽  
Vibration Rotation

The magnitude of the effect of the vibration–rotation interaction on the intensities of pure rotation lines of diatomic molecules has been calculated for two different molecular models, the anharmonic oscillator and the rotating Morse or Pekeris oscillator. The intensity correction for the anharmonic oscillator has been obtained by adapting the contact transformation formalism for calculating second-order corrections to the energy to the calculation of first-order corrections to the matrix elements of the electric moment as suggested by H. H. Nielsen. The correction to the line intensity for vibrationless transitions of the anharmonic oscillator is found to be[Formula: see text]The results obtained here are also in complete agreement, to first order, with the results obtained earlier by Herman and Wallis for the 1–0 and 2–0 vibration–rotation line intensities. In the case of the Pekeris or rotating Morse oscillator the correction to the pure rotation line intensity is of the same form as above, namely,[Formula: see text]but exhibits minor differences which can be explained in terms of the difference in the vibrational potential energy function in the two cases.

Exact formula for the dipole moment of a one-electron diatomic molecule

1985 ◽  
Vol 401 (1821) ◽  
pp. 373-392 ◽  
Keyword(s):  
Dipole Moment ◽  
Electronic State ◽  
Diatomic Molecule ◽  
Recursion Relation ◽  
Energy Eigenvalue ◽  
Exact Formula ◽  
Electronic Energy ◽  
Moment Function ◽  
Expectation Values ◽  
Feynman Theorem

It is shown that the dipole moment function, μ ( R , Z a , Z b ), for an arbitrary bound electronic state of a one-electron diatomic molecule, with inter-nuclear distance R and atomic numbers Z a , Z b may be expressed exactly in terms of the separation eigenconstant C and the electronic energy eigenvalue W of the Schrödinger equation by means of the Hellmann-Feynman theorem and a new recursion relation. The formula is used to investigate the behaviour of μ in the vicinity of the united atom and when the nuclei are far apart. The generalization required to extend the relation to other expectation values is derived in an appendix.

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