Improving on the conventional presentation of molecular vibrations: Advantages of the pseudoharmonic potential and the direct construction of potential energy curves

Abstract

Articles you may be interested inGround-and excited-state diatomic bond lengths, vibrational levels, and potential-energy curves from conventional and localized Hartree-Fock-based density-functional theory

Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential

“…The potential in (12) solved for the limiting case of β = 0 by using the orthogonal polynomial solution method [32] and by the Rydberg-Klein-Rees (RKR) procedures [20,21]. In fact the energy spectrum for the potential in (12) can be obtained directly since the potential is classified amongst the separable non-central potentials discussed previously in [65].…”

“…Due to importance of the pseudoharmonic potential in chemical physics, the quantum systems with this potential in 3D [20,21,[24][25][26][27][28], in 2D [29] and D-dimensions [30,31] were also investigated. Recently, the solution was also carried out by using an orthogonal polynomial solution method and also by performing a proper transformation procedure [32].…”

“…The pseudoharmonic potential, which, while more realistic than the harmonic, maintains some of the advantages, such as the availability of explicit solutions. Also, the pseudoharmonic and Mie-type potentials [16][17][18][19][20][21][22][23] are two exactly solvable potentials other than the Coulombic and the anharmonic oscillator [13][14][15].…”

Cat-states in the framework of Wigner–Heisenberg algebra

“…Recently, Sage has studied the vibrations and rotations of the pseudo-gaussian oscillator in order to describe the diatomic molecule [57], in which he briefly reinvestigated some properties of the PHO to study the pseudo-gaussian oscillator. Advantages of the pseudo-harmonic potential have been considered for improvements in the conventional presentation of molecular vibrations [58]. Hurley found that this kind of PHO interaction between the particles can be exactly solved by separation of variables when he studied the three-body problem in one dimension [59].…”

“…This model was first proposed by Post in 1956 when he studied the one-dimensional many identical particles problem in the case of the pair-force interaction between particles [46]. Since 1961 such a quantum system has been studied by many authors [46][47][48][49][50][51][52][53][54][55][56][57][58]. For example, Landau and Lifshitz studied its exact solutions in three dimensions [48].…”