Anharmonic vibrational levels and photoelectron spectra of linear trinitrogen from wavepacket propagation

The assignment of the asymmetric stretch frequency of the linear N₃ molecule has been controversial due to the associated large anharmonicity. Also, there is no consensus on the interpretation of the photoelectron spectra.

The Franck-Condon factors for photoelectron spectra can be computed from: (1) the overlap between the initial and the final vibrational wave functions; or (2) the Fourier transform of a wave packet time autocorrelation function. We implemented both models.

Gaussian wavepacket propagation on the ab-initio potential of the asymmetric stretch

Linear N₃ vibrational levels in the harmonic approximation (in orange) and on the one dimensional anharmonic ab initio potential (in grey).

The potential is strongly anharmonic along the asymmetric stretch, which results in the failure of the harmonic approximation. The full Shrodinger equation should be solved to obtain correct vibrational wavefunctions.

Sample photoelectron spectra from the Gaussian wavefunction propagation

The wavepacket approach can be employed in a multidimensional case. For example, the cartoon below shows a Gaussian wave packet propagating on a 2D Morse potential. When the X and Y axes of the plot are R(AB) and R(BC) inter-atomic distances of a linear triatomic molecule, the movie represents the symmetric stretch vibration, or more precisely, the first period of the stretched A--B--C molecule relaxation.