Isotope Effects on Ground and Excited States of Ethyl Cation, H⁺(C₂H₄)

The structure and spectra of ethyl cation, H⁺(C₂H₄), and its deuterated analogues are investigated using diffusion Monte Carlo (DMC). These calculations all show that the ground state wave function for H⁺(C₂H₄) is localized near the minimum energy configuration in which the excess proton is in a bridging configuration, although the amplitude of the vibrational motions of the bridging proton is large. Deuteration of the bridging proton reduces the amplitude of this motion, while deuteration of only the ethylenic hydrogen atoms in H⁺(C₂D₄) has little effect on the amplitude of the motion of the bridging proton. Excited states that are accessed by spectroscopically observed transitions in H⁺(C₂H₄) are calculated using fixed-node DMC. The calculated and measured frequencies for the states with one quantum of excitation in the ethylenic CH stretching vibrations show good agreement. We also explore the excited state with one quantum of excitation in the proton transfer vibration of the bridging proton and obtain a frequency of 616 cm^-1 for H⁺(C₂H₄). This frequency increases to 629 cm^-1 in H⁺(C₂D₄). Deuteration decreases this frequency to 491 and 495 cm^-1 in D⁺(C₂H₄) and D⁺(C₂D₄), respectively. The effects of partial deuteration on the frequencies of the CH stretching vibrations, and the corresponding probability amplitudes are also explored. Finally, we report the vibrationally averaged rotational constants for the four isotopologues of ethyl cation considered in this study.