Diatomic Potential Functions Derived from Accurate Fits to Vibrational Energy Levels Using Algebraic Theory

Abstract

Algebraic theory is used to fit the set of bound vibrational energy levels of H2 and its isotopomers, up to the dissociation limit and to an accuracy of within 1 cm-1 in each case. Coordinate space potential functions are constructed from these algebraic Hamiltonians, and the limitations of the algebraic approach are assessed.

An analytic algebraic approach to study the influence of molecular alignment and orientation on multiphoton excitation in intense laser fields

“…Quite accurate fits to the vibrational energy levels, potential functions including the zero-point energies, and the known values of dissociation energy have been obtained for theses molecules based on the algebraic Hamiltonian [see Equation 18)] according to Cooper et al [32,33]. So the molecular parameters, in atomic units, are taken …”

“…We apply the well-known results for the U(2) dynamical symmetry to describe the one-dimensional anharmonic vibrational motion of a diatomic molecule [30][31][32][33]…”

Dynamical correlation between quantum entanglement and intramolecular energy in molecular vibrations: An algebraic approach

“…In addition, the coordinate space representation of the algebraic Hamiltonian can become a power series expansion in half integral powers of the Morse Hamiltonian with a corresponding classical potential expanded in half integral powers of the Morse potential function. This algebraic model has been proven to accurately fit the vibrational energy levels of diatomic molecules, as well as potential function, including the zero-point energy, and achieve the known value of dissociation energy, [58,59] which can be represented as…”

Potential energy surface and highly excited vibrational lines of NO2 via algebraic approach

“…Levine et al treated the potential energy surfaces of triatomic molecules using U(2) algebra 8, 9. Lemus et al studied the potential energy curves in the electron‐vibron model via the algebraic approach 10, and Cooper studied the vibrational energy levels and potential energy lines of diatomic molecules 11. We constructed the potentil energy surface of triatomic molecules using U(4) algebra 12, 13.…”