Vibrational energy levels of CH5+

Abstract

We present a parallelized contracted basis-iterative method for calculating numerically exact vibrational energy levels of CH(5)(+) (a 12-dimensional calculation). We use Radau polyspherical coordinates and basis functions that are products of eigenfunctions of bend and stretch Hamiltonians. The bend eigenfunctions are computed in a nondirect product basis with more than 200x10(6) functions and the stretch functions are computed in a product potential optimized discrete variable basis. The basis functions have amplitude in all of the 120 equivalent minima. Many low-lying levels are well converged. We find that the energy level pattern is determined in part by the curvature and width of the valley connecting the minima and in part by the slope of the walls of this valley but does not depend on the height or shape of the barriers separating the minima.

Mathematical Methods in Quantum Molecular Dynamics

“…For molecules with five atoms, calculations of this kind are now possible [26]. One way to deal with the basis-size problem is to use basis functions that are not products of functions of a single variable [27,28,29,30,23,24,20,31,32,33,21]. Another strategy is to use product functions but only a fraction of the full product basis [34,35,36,37,38,39,40,41,42].…”

“…With a (direct or nondirect) product basis, these ideas can be applied efficiently, regardless of the form and complexity of the potential energy surface (PES), provided that a direct product quadrature is used. [16,14,17,18,19,20,21,22,23,24,25].…”

Iterative Methods for Computing Vibrational Spectra

“…The full power of the method is realized only when both stretch and bend bases are contracted [6,[59][60][61][62][63][64]. Recently, similar ideas were used for Cl − -H 2 O [65].…”

Perspective: Computing (ro-)vibrational spectra of molecules with more than four atoms

“…Both stretch and bend bases were contracted in later papers. 15,59,116,[120][121][122][123] Recently similar ideas were used for Cl -H 2 O. 124 Yu has studied several molecules using similar ideas.…”

“…However, type 2 functions obtained by setting Q B coordinates equal to values that minimize the PES at a particular Q A point are quite good, even for floppy molecules. 116 For larger molecules, the advantages of simply contracted functions are more convincing because of both the number and the size of the blocks for which one must compute eigenvectors.…”