Bent triatomic molecules Hamiltonian

For bent triatomic molecules one can easily construct a local mode Hamiltonian whose eigenvalues reproduce the spectrum ... 

The normal-mode Hamiltonians for bent triatomic molecules... 

Calculations of vibrational spectra of bent triatomic molecules with second order Hamiltonians produce results with accuracies of the order of 1-5 cm-1. An example is shown in Table 4.9. These results should again be compared with those of a Dunham expansion with cubic terms [Eq. (0.1)]. An example of such an expansion for the bent S02 molecule is given in Table 0.1. Note that because the Hamiltonian (4.96) has fewer parameters, it establishes definite numerical relations between the many Dunham coefficients similar to the so-called x — K relations (Mills and Robiette, 1985). For example, to the lowest order in l/N one has for the symmetric XY2 case the energies E(vu v2, V3) given by... 

We have discussed up to now vibrational spectra of linear and bent triatomic molecules. We address here the problem of rotational spectra and rotation-vibration interactions.3 At the level of Hamiltonians discussed up to this point we only have two contributions to rotational energies, coming from the operators C(0(3]2)) and IC(0(412))I2. The eigenvalues of these operators are... 

The anharmonic potential energy is usually easier to represent in internal coordinates than in normal mode coordinates. However, what restricts the use of internal coordinates is the complicated expression for the vibrational/rotational kinetic energy in these coordinates (Pickett, 1972). It is difficult to write a general expression for the vibrational/rotational kinetic energy in internal coordinates and, instead, one usually considers Hamiltonians for specific molecules. For a bent triatomic molecule confined to rotate in a plane, the internal coordinate Hamiltonian is (Blais and Bunker, 1962) ... 

In this section we study in detail the Hamiltonian operator (4.23) with the aim of describing the rovibrational spectrum of an either symmetric or nonsymmetric bent triatomic molecule. Therefore, we need to complete the conversion from algebraic to rovibrational quantum numbers [Eq. (4.30)]. It is possible to show [69] that the desired relations for the bending-rotation part are given by... 

When the bent triatomic molecule is initially nonrotating (/=0) and the diatom is assumed to be bound for all energies considered, the nuclear Hamiltonian for motion of the nonlinear triatomic molecule YiXY2 on the final state of H2O + can be written as [263-266]... 

Beswick and Gelbart (55) published an interesting paper concerned with the bending contribution to rotational distribution. They considered the photodissociation of a triatomic molecule ABC + hv A + BC applicable to both linear and bent molecules. The Hamiltonian is expressed in terms of so-called dis-... 

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