Assignment and simplified Hamiltonian for molecular vibrations obtained by an improved diabatic correlation method

Assigning the low lying vibronic states of CH3O and CD3O

The assignment of lines in vibrational spectra in strongly mixing systems is considered. Several low lying vibrational states of the ground electronic X∼²E state of the CH₃O and CD₃O radicals are assigned. Jahn-Teller, spin-orbit, and Fermi couplings mix the normal mode states. The mixing complicates the assignment of the infrared spectra using a zero-order normal mode representation. Alternative zero-order representations, which include specific Jahn-Teller couplings, are explored. These representations allow for definitive assignments. In many instances it is possible to plot the wavefunctions on which the assignments are based. The plots, which are shown in the adiabatic representation, allow one to visualize the effects of various higher order couplings. The plots also enable one to visualize the conical seam and its effect on the wavefunctions. The first and the second order Jahn-Teller couplings in the rocking motion dominate the spectral features in CH₃O, while first order and modulated first order couplings dominate the spectral features in CD₃O. The methods described here are general and can be applied to other Jahn-Teller systems.

Demixing and cleaning of wave functions by projection, application to the assignment of molecular vibrations

It is shown how the projection of a quantum mechanical state into an appropriate subspace of the Hilbert space can be useful for the classification and the assignment of states. The projection cleans the wave function and decomposes mixtures caused by near-accidental degeneracy. The idea is applied to vibrational states of the molecule CF(3)CHFI obtained from an algebraic Hamiltonian.