Normal and hyperspherical mode analysis of NO-doped Kr crystals upon Rydberg excitation of the impurity

Molecular dynamics simulations and both normal mode and hyperspherical mode analyses of NO-doped Kr solid are carried out in order to get insights into the structural relaxation of the medium upon electronic excitation of the NO molecule. A combined study is reported on the time evolution of the cage radius and on the density of vibrational states, according to the hyperspherical and normal mode analyses. For the hyperspherical modes, hyper-radial and grand angular contributions are considered. For the normal modes, radial and tangential contributions are examined. Results show that the first shell radius dynamics is driven by modes with frequencies at $∼47$ and $∼15cm−1$⁠. The first one is related to the ultrafast regime where a large part of the energy is transmitted to the lattice and the second one to relaxation and slow redistribution of the energy. The density of vibrational states $γ(ω)$ is characterized by a broad distribution of bands peaking around the frequencies of $∼13$⁠, $∼19$⁠, $∼25$⁠, $∼31$⁠, $∼37$⁠, $∼47$⁠, and $∼103cm−1$ (very small band). The dominant modes in the relaxation process were at 14.89, 23.49, and $53.78cm−1$⁠; they present the largest amplitudes and the greatest energy contributions. The mode at $14.89cm−1$ is present in both the fit of the first shell radius and in the hyper-radial kinetic energy spectrum and resulted the one with the largest amplitude, although could not be revealed by the total kinetic energy power spectrum.