Group-theoretical formulation of an Eckart-frame kinetic energy operator in curvilinear coordinates for polyatomic molecules

Abstract

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

New Ab Initio Potential Energy Surfaces for NH3 Constructed from Explicitly Correlated Coupled-Cluster Methods

“…Concerning the nuclear motion calculations, our variational computer code TENSOR − has been adapted to molecules exhibiting one large-amplitude motion . This code was initially designed for the treatment of rigid molecules, which was applied with success to the construction of accurate spectroscopic line lists (see, e.g.…”

Vibrational levels of formaldehyde: Calculations from new high precision potential energy surfaces and comparison with experimental band origins

“…In order to calculate energy levels in normal coordinates the energy values generated from the analytical form of the PES in orthogonal coordinates were computed on our G (R) grid of geometries (see paragraph 2) and then re-fitted in internal coordinates with the torsion function of (τ -π). The TENSOR code [83] [84] [85] [86] was then used to calculate the energy levels in normal coordinates using the Watson-Eckart KEO. Most likely, the accuracy of the levels computed from empirically optimized PES for doubly and triply excited quanta is higher than the accuracy of the levels obtained using the pure ab initio PES.…”

Derivation of ρ-dependent coordinate transformations for nonrigid molecules in the Hougen–Bunker–Johns formalism

“…• A polynomial expansion in Q and ρ in appropriate elementary functions for both KEO and PES may lead to an efficient algebraic solution of Schrödinger equation with the HBJ Hamiltonian, making thus possible the use of our reduction-compression tools [36][37][38] initially designed for variational nuclear motion calculations of semirigid molecules. A full account of symmetry via the use of irreducible tensor operators 36,39,40 can be also implemented.…”

“…This strategy closely follows the "linearisation" procedure proposed in Ref. 40 to invert the set of nonlinear equations S = S(Q). This leads to…”