The Renner effect in triatomic molecules with application to CH\u2082\u207a, MgNC and NH\u2082

We have developed a computational procedure, based on the variational method, for the calculation of the rovibronic energies of a triatomic molecule in an electronic state that become degenerate at the linear nuclear configuration. In such an electronic state the coupling caused by the electronic orbital angular momentum is very significant and it is called the Renner effect. We include it, and the effect of spin-orbit coupling, in our program. We have developed the procedure to the point where spectral line intensities can be calculated so that absorption and emission spectra can be simulated. In order to gain insight into the nature of the eigenfunctions, we have introduced and calculated the overall bending probability density function f(& rho;) of the states. By projecting the eigenfunctions onto the Born-Oppenheimer basis, we have determined the probability density functions f\u208a(& rho;) and f\u208b(& rho;) associated with the individual Born-Oppenheimer states & Phi;elec\u207d\u207b\u207e and & Phi;elec\u207d\u207a\u207e. At a given temperature the Boltzmann averaged value of the f(& rho;) over all the eigenstates gives the bending probability distribution function F(& rho;), and this can be related to the result of a Coulomb Explosion Imaging (CEI) experiment. We review our work and apply it to the molecules CH\u2082\u207a, MgNC and NH\u2082, all of which are of astrophysical interest.NRC publication: Ye