Effect of vibrational pre-excitation on sub-femtosecond structural evolution of water cation in ²A₁ state

We study the effects of vibrational excitation of neutral water molecule on sub-femtosecond nuclear dynamics of the ²A₁ electronic state of cationic water and its isotopomers that are induced by high-harmonic generation (HHG) process. Both the photoelectron spectra and the autocorrelation functions of electronically excited states of M₂O⁺ (M = H, D, and T) that are produced by Franck-Condon ionization of vibrationally pre-excited M₂O to its ²A₁ electronic state are calculated. HHG signals are also calculated from the square of the absolute value of autocorrelation functions. In addition, the ratio of the HHG signal of D₂O⁺ to that of H₂O⁺ and that between T₂O⁺ and H₂O⁺ are calculated with respect to time, for varying initially prepared vibrational state of the corresponding neutral molecule. Vibrational dynamics are notably strong on the ²A₁ state of the cationic species, as the initial vibrational quantum number increases. The HHG signal of a heavier isotopomer is larger than that of water when the initial vibrational state is on its ground state. The expectation values of the bond length and bond angle show quasiperiodic oscillations with respect to time, which are ascribed to the observed overall rise in the HHG signals. Exceptionally strong vibrational dynamics observed on the ²A₁ state potential energy surface of the cationic water molecule can be attributed to the excitation of water bending mode upon Franck-Condon ionization of the corresponding neutral molecule. Here, the observed peaks in the ratios of the HHG signals are theoretically explained in terms of time-evolving molecular structures at two different turning points of the ²A₁ surface. We anticipate that the present computational method of solving time-dependent Schrödinger equation would be of use to provide explanations on both ultrafast and chiroptical HHG spectroscopy of polyatomic molecules with certain handedness.