Theoretical methods for the rotation–vibration spectra of triatomic molecules: distributed Gaussian functions compared with hyperspherical coordinates

Abstract

An approximate variational method based in the use of distributed Gaussian functions (DGF) and bond-length coordinates has been applied to study the rotation-vibration spectra of different triatomic molecules. In addition, an approach which employs hyperspherical coordinates (HC) and a basis set of hyperspherical harmonics constitutes a valid benchmark to test its capabilities. This work describes the technical details of both methods to provide the energies and symmetry of the corresponding rovibrational states and reviews their application to three different systems: For Ar 3 and Ne 3 the DGF technique exhibits a particularly good performance, but some limitations are observed for a more demanding scenario such as the H + 3 ion. The possible origin of these deficiencies are also discussed in detail.

The Challenge of ab Initio Calculations in Small Neon Clusters

“…The first calculations were performed using hyperspherical harmonics and quantum monte carlo methods. [24,25] Later on, several authors [26][27][28][29] have studied the structural properties and the energy of the ground state of Ne 3 , with a potential using Distributed Gaussian Functions, and have analyzed its rotationvibration spectrum. These authors suggest a predominant equilateral structure with an expectation value for the atomatom distance of 6.274 bohr.…”

Molecular spectra calculations using an optimized quasi-regular Gaussian basis and the collocation method

“…Likewise, a generalized eigenvalue problem is obtained if the basis is not orthogonal. There are a number of strategies to approach this problem with their pros and cons, long histories, and long citation lists [1][2][3][4][5][6] . Each strategy has its own set of sub-challenges.…”