A finite basis-discrete variable representation calculation of vibrational levels of planar acetylene

Abstract

A methodology for the calculation of high energy vibrational eigenstates of S0 acetylene is described. Acetylene is modeled as a 5D planar molecule. The discrete variable representation (DVR) is employed for radial coordinates with a finite basis representation (FBR) for the angular coordinates. Symmetry adaptation of the primitive basis (dimension 2.7 × 106) coupled with a two level diagonalization/truncation scheme maintains relatively small basis sets (< 2500 functions) in all diagonalizations. Eigenvalues up to nearly 3700 cm−1 above the ground state are reported.

Reduced dimension discrete variable representation study of cis–trans isomerization in the S1 state of C2H2

“…Ours is not the first such calculation, even on acetylene 20,21 , but our approach differs from those of previous authors. We specify significant departures from earlier reduced dimension DVR calculations on acetylene where appropriate.…”

“…The problem of separating vibration and rotation is exacerbated when large amplitude motions are possible 22 , and even remaining in the center of mass frame may not be trivial 20,21 for molecules larger than triatomics. For acetylene, several different coordinate systems have been used in the literature for various types of calculations 23,24 .…”

“…The form of the Laplacian in the chosen coordinate system must be determined, which can be very tricky 20,21,24 , especially since singularities in the kinetic energy are possible. Furthermore, expressing the Laplacian in a DVR basis can lead to a non-Hermitian H. The kinetic energy operator matrix elements are more complicated than those of V , but we merely need to add matrix representations of differential operators to the trivial matrix representations of functions of coordinates already in our repertoire.…”

“…We therefore replace R CC with the normal coordinate for v 2 from the harmonic frequency calculation, which provides a prescription for varying the CH distances as the CC bond length changes. 33 We did also consider vibrational adiabatic potentials, which are commonly used in the literature 20,21 . However, given the limited return and the enormous computational cost of minimizing the energy at every point on the entire three dimensional grid, we elected not to pursue this option.…”

Theoretical Elucidation of the Unusually High [HNC]/[HCN] Abundance Ratio in Interstellar Space: Two‐dimensional and Two‐State Quantum Wave Packet Dynamics Study on the Branching Ratio of the Dissociative Recombination Reaction HCNH++e−→ HNC/HCN + H

“…The kinetic energy operator T, the effective potential V eff , and the reduced mass are derived from the Hamiltonian for acetylene (Bentley et al 1992). It is noted that rotational degrees of freedom of nuclear motions were ignored in the present simulation.…”