Dynamical resonances of the deuterated CH₂⁺ complex in the electronic ground state: A quantum wavepacket study

We here investigate the effects of isotopic substituents on the vibrational energy levels of the CH₂⁺ complex, supported by the electronic ground (1 ²A') potential energy surface (PES) of the H + CH⁺ reaction. We calculate the transition state spectrum by Fourier transforming the time-autocorrelation function of the initial wavepacket (WP) chosen in the interaction region of the PES. Using the time-dependent WP approach, the dynamical resonances are identified as bound and quasibound in nature, and they are characterized in terms of the eigenfunctions and lifetimes. The present work on the isotopic variants [CHD⁺(CDH⁺) and CD₂⁺] is compared with our earlier work [P. Sundaram et al., Phys. Chem. Chem. Phys. 19, 20172 (2017)] on the parent CH₂⁺ species. The isotopic variants reveal a large number of peaks in the spectra and the eigenfunctions exhibit the systematic nodal progressions and periodic orbits, the same as in CH₂⁺. While the CD₂⁺ complex exactly mimics the resonance behaviors (local and hyperspherical modes) of the bound and quasibound CH₂⁺ complex, the CHD⁺(CDH⁺) complex reveals only the local mode behaviors at low energies and significantly less number of resonance structures at high energies. Lifetime analysis of the isotopic variants implies that the CD₂⁺ complex survives much longer than the CHD⁺(CDH⁺) complex and concludes the work by noting the following order in the decay profile of the deuterated CH₂⁺ resonances as CH₂⁺>CHD⁺(CDH⁺) >CD₂⁺.