An Accurate Theoretical Prediction of the Zero Point Vibrational Energy of CH5+

A recently developed signal processing method has been applied to a time evolved Gaussian wave packet roughly corresponding to the ground vibrational state of protonated methane at time zero. The time evolution of the wave packet was described by semiclassical initial value representation theory where classical trajectories are used to evaluate the quantum mechanical propagator, exp[−i Ĥt /ℏ]. We show that only about 25 000 relatively short time trajectories are necessary to yield a well converged eigenvalue of the ground vibrational state. The calculations reveal an unusually large red shift of 448 cm -1 from the harmonic zero point level placing the ground state at 10 973 cm -1, with a statistical error of ±30 cm -1 . These results agree remarkably well with full-dimensionality quantum mechanical calculations.