Triatomic molecules effective Hamiltonians

Hamiltonian equations, 627-628 perturbative handling, 641-646 II electronic states, 631-633 vibronic coupling, 630-631 ABC bond angle, Renner-Teller effect, triatomic molecules, 611-615 ABCD bond angle, Renner-Teller effect, tetraatomic molecules, 626-628 perturbative handling, 641-646 II electronic states, 634-640 vibronic coupling, 630-631 Abelian theory, molecular systems, Yang-Mills fields ... 

Floquet theory principles, 35—36 single-surface nuclear dynamics, vibronic multiplet ordering, 24—25 Barrow, Dixon, and Duxbury (BDD) method, Renner-Teller effect tetraatomic molecules, Hamiltonian equations, 626-628 triatomic molecules, 618-621 Basis functions ... 

EWW Hamiltonian, Renner-Teller effect, triatomic molecules, 610—615 Expanding potential, molecular systems,... 

II electronic states, 638-640 vibronic coupling, 628-631 triatomic molecules, 594-598 Hamiltonian equations, 612-615 pragmatic models, 620-621 Kramers doublets, geometric phase theory linear Jahn-Teller effect, 20-22 spin-orbit coupling, 20-22 Kramers-Kronig reciprocity, wave function analycity, 201 -205 Kramers theorem ... 

In a paper in 1979, Carl Ballhausen [1] expressed the belief that today we realize that the whole of chemistry is one huge manifestation of quantum phenomena, but he was perfectly well aware of the care that had to be taken to express the relevant quantum theory appropriately. So in an earlier review [2] that he had undertaken with Aage Hansen, he scorned the usual habit of chemists in naming an experimental observation as if it was caused by the theory that was used to account for it. Thus in the review they remark that a particular phenomenon observed in molecular vibration spectra is presently refered to as the Duchinsky effect. The effect is, of course, just as fictitious as the Jahn-Teller effect. Their aim in the review was to make a start towards rationalization of the nomenclature and to specify the form of the molecular Hamiltonian implicit in any nomenclature. In an article that Jonathan Tennyson and I published in the festschrift to celebrate his sixtieth birthday in 1987 [3], we tried to present a clear account of a molecular Hamiltonian suitable for treating the vibration rotation spectrum of a triatomic molecule. In an article that I wrote that appeared in 1990 [4], I discussed the difficulty of deciding just how far the basic chemical idea of molecular structure could really be fitted into quantum mechanics. 

There are many different forms that the transformed Hamiltonian K may take (43). A particularly convenient form is one where the Hamiltonian is block-diagonal. We have found this form to be an efficient approach for describing the triatomic molecules C02, HCN, H20, D20, and S02. It has also proven effective for the tetraatomics HCCH, DCCD, H2CO and D2CO and well as for the pentaatomic CHD3 (43,45-47,49). This structure is also the basis of the construction of the polyad phase spheres of Kellman and co-workers (69-71). 

Let us consider the explicit effect of the Majorana operator on a symmetric triatomic molecule. In light of the symmetry under bond exchange, the Hamiltonian operator (4.23) can be written as... 

Bunker, P.R., Moss, R.E. Effect of the breakdown of the Born-Oppenheimer approximation on the rotation-vibration Hamiltonian of a triatomic molecule, J. Mol. Spectry. 1980, 80,217-28. 

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