Tetraatomic molecules, Hamiltonian

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 ... 

We restrict ourselves again to symmetric tetraatomic molecules (ABBA) with linear eqnilibrium geometi7. After integrating over electronic spatial and spin coordinates we obtain for A elecbonic states in the lowest order (quartic) approximation the effective model Hamiltonian H — Hq+ H, which zeroth-order part is given by Eq. (A.4) and the perturbative part of it of the form... 

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 ... 

The complete vibration-rotation Hamiltonian for acetylene-like tetraatomic molecules has been derived by Handy et al. by hand [155] and using a computer algebra program [156]. (Note that in both of the mentioned papers there are some minor errors, see also [144,157,158]). Handy uses as bending coordinates... 

As an aside, we note that the n-mode representation of the potential can be made in any set of coordinates and for use in the corresponding Hamiltonian. For triatomic and tetraatomic molecules it is possible to avoid this representation because the dimensionality of the internal space is 3 or 6 and exact treatments are possible in both normal [30,31 ] and various curvilinear coordinates which have been used in exact formulations and calculations for triatomic and tetraatomic molecules [32-34]. However, for larger molecules it could prove quite useful. 

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). 

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