The calculation of the ground state energy of weakly bound van der waals trimers using the method of hyperspherical harmonics I. The Born—Oppenheimer and adiabatic approximations

Abstract

Abstract The method of hyperspherical harmonics is applied to the calculation of the vibrational energy levels of the three-particle weakly bound van der Waals complexes. (H 2 ) 3− (D 2 ) 3 and Ne 3 . Hyperspherical coordinates and the properties of the associated hyperspherical harmonic functions are discussed. These functions are used as an angular basis in which to expand the wavefunction for the three-particle system. A Born—Oppenheimer-type separation of the angular and hyper-radial motion is made. permitting a lower bound (Born—Oppenheimer approximation) and an upper bound (adiabatic approximation) to the energy of the clusters to be calculated.