Cecilia Coletti

TL;DR: In this paper, Sturmian basis sets in configuration (or direct) space are introduced as alternatives to the ordinary ones in spherical coordinates: extensions of Fock stereographic projections allow us to establish the relationships between the corresponding momentum (or reciprocal) space orbitals and the alternative forms of hyperspherical harmonics.

TL;DR: In this article, rate coefficients for the relaxation of vibrational excited oxygen molecules, including both vibrationtovibration (V-V) and vibration-to-translation energy exchange, have been calculated using a semiclassical method and a new potential energy surface for a large interval of initial vibrational quantum numbers (1⩽ v ⩽29) in the temperature range between 50 and 1000 K.

TL;DR: In this article, Fock projection into momentum space for the hydrogen atom is extended to the mathematical d-dimensional case, higher than the physical case d = 3 for a system of N particles interacting through Coulomb forces, this method allows us to work both in a 3 n - 1 dimensional configuration space (on eigenfunctions expanded on a Sturmian basis) and in momentum space (using a ( d + 1)-dimensional hyperspherical harmonics basis set) Numerical examples for three-body problems are presented.

TL;DR: The current model is able to reproduce remarkably well the main features of the potential energy surface for the heavier X(-)-C( 6)H(6) systems, whereas for fluoride-benzene, the binding energies are underestimated as a consequence of the failure of the semiempirical method to describe the electrostatic interaction between a diffuse anion and a benzene at short range by means of a simple point charge model.

TL;DR: In this article, the relationship between alternative separable solutions of the Coulomb problem both in configuration and in momentum space is exploited in order to obtain Sturmian orbitals of use as expansion basis sets in atomic and molecular problems.