Bound states and time-dependent dynamics of the N₂H⁺ molecular ion in its ground electronic state. I. 2D treatment

Abstract

The ground-state potential energy surface (PES) for linear arrangements of the N₂H⁺ molecular ion is numerically computed by the multireference single- and double-excitation configuration interaction (MRD-CI) technique. An analytical representation of the potential energy function is obtained by fitting a power series in the Simons–Parr–Finlan coordinates to the numerical data. For investigating the intramolecular dynamics we describe the nuclear motion by a Gaussian wave packet located initially in the strong interaction region of the PES. The vibrational eigenvalue spectrum is calculated by Fourier transforming the time autocorrelation function. The spectrum is then analyzed statistically in the light of random matrix theory (RMT) to understand the nature of the intramolecular dynamics. We examine the short-range correlation in the spectrum through the nearest neighbor level spacing distribution P(s) and the long-range correlation through Δ₃ and Σ² statistics. The spectrum in the time domain is analyzed by computing the ensemble averaged survival probability ⟨⟨P(t)⟩⟩. The above four quantities obtained from the spectrum are compared with the distribution predicted for regular, irregular, and mixed (intermediate) spectra by the RMT. We find the system is of mixed type and the fractional irregularity is 0.7±0.05. In order to reveal a possible correspondence to the classical dynamics, we have carried out the spectral analysis of the dynamical variables for classical trajectories over a wide range of internal energies. In addition the classical dynamics of proton collisions with N₂ molecules has also been preliminarily studied on the same PES, in particular the dependence of the final vibrational action n_f on the initial vibrational phase φ_i of N₂ and, furthermore, the Poincare surface-of-section superimposed with the zero-order separatrix; we find a large number of trapped trajectories.