Wavefunction rovibrational

The initial wavefunction is a product of a specific rovibrational eigenfunction for the reactants and a localized translational wavepacket for R ... 

Similar to the diatom-diatom reaction, the initial wavefunction is chosen as the direct product of a localized translational wavepacket for R and a specific (JMe) state for the atom-triatom system with a specific rovibrational eigenstate (z/o, Lo,Bo) f°r the triatom ABC ... 

In the present section, we give examples of simulated vibrational bands of These bands start in the lowest inversion states 0 and end in the states V2V2 with U2<4. The rovibrational wavefunctions with 7<18 are calculated variationally as described in Ref. [1]. To make these variational calculations feasible the size of the vibrational basis set is reduced relative to that employed for the calculations of vibrational transition moments in Section 4.1. We now require that... 

The excitation of a molecule may result in a change of its electron and rotational-vibrational quantum numbers. In the adiabatic approximation," the total wavefunction of a molecule can be presented as a product of the electron wave and the rovibrational wavefunction. In those cases where the former is weakly affected by the changes in the relative position of the nuclei (this is usually the case with lower vibrational levels), we can use the Condon approximation considering the electron wavefunction only at equilibrium configuration of the nuclei. In this case the oscillator strength factorizes into an electron oscillator strength and the so-called Frank-Condon factor, which is the overlap integral of the vibrational wavefunctions of the initial and the final states of the molecule.115,116... 

Figure 9 compares transitions probabilities for zero total angular momentum J resulting from (2S-DIABATIC) and (IS-GP) calculations with initial and final states chosen to be representative of two cases (A) initial and/or final states have low rovibrational excitation, (B) initial and final states have both high rovibrational excitation. In case (A), both (2S-DIABATIC) and (IS-GP) results almost coincide, even for energies close to the three body dissociation limit. Case (A) corresponds to the kind of transitions already considered in Sect. 4.1 where it was shown that it is valid to use the single rovibrational wavefunction associated to the ground electronic state... 

These extra eigenvalues are shown as a function of energy for both Ai and A2 symmetries of the rovibronic wavefunction in Fig. 10. There are two maxima near 4.41 and 4.62 eV for Ai symmetry, 4.49 and 4.70 eV for A2 symmetry. They correspond to resonances with lifetimes close to 15 fs for Ai symmetry and 10 fs for A2 symmetry. Resonances with similar lifetimes have been computed in [60, 61] and detected experimentally in [68]. The energies of the bound rovibrational states... 

These values were, in turn, averaged over the manifold of rovibrational wavefunctions belonging to the vibrational ground state. Finally, a mean value was found on the assumption that there is a Maxwell-Boltzmann distribution of molecules in the rotational levels (for this the temperature 295K was assumed). 

The time-dependent wavefunction satisfying the Schrodinger equation (d/dr) ) = HW(t) can be expanded in terms of BF (body-fixed) rovibrational eigenfunctions defined using the reactant Jacobi coordinates as... 

The exact rovibrational function v,(J/ 0(/-) of the diatom is expanded in terms of the reference vibrational functions [Pg.254]

The main difficulty in solving (2.153) lies in the evaluation of the potential energy term (2.154). Even in the case ofH2, calculation of V from the electronic wavefunctions for different values of is no easy matter. Usually, therefore, the vibrational wave equation is solved by inserting a restricted form of the potential experimental data on the rovibrational levels are then expressed in terms of constants introduced semiempirically, as we shall show. 

Pseudomolecular Energy Level Patterns. In intrashell states, the two electrons have the same principal quantum number so are nominally at the same distance from the nucleus. The electrons hence exhibit strongly correlated, collective motions and the energy levels and wavefunctions resemble those for molecular rovi-bational states. Kellman and Herrick [92] discovered these patterns and showed that many features could be interpreted in terms of an empirical rovibrator model, e-core-e, analogous to a linear triatomic molecule. This model has since been examined and refined by anal-... 

The TD wavefunction can be expanded in the body-fixed rovibrational basis functions as [46]... 

The wavefunction, (t), composed of a linear combination of time-dependent coefficients, Cvj(t), with rovibrational state eigenvectors v7) is described by. 

---