Largeorder dimensional perturbation theory for diatomic molecules within the BornOppenheimer approximation
Abstract
A renormalization of the Ddimensional Hamiltonian is developed to ensure that the largeD limit corresponds to a single well at any value of the internuclear distance R. This avoids convergence problems caused by a symmetrybreaking transition that is otherwise expected to occur when R is approximately equal to the equilibrium bond distance R_{eq}, with larger R giving a double well. This symmetry breaking has restricted the applicability of largeorder perturbation theory in 1/D to cases where R is significantly less than R_{eq}. The renormalization greatly extends the range of R for which the largeorder expansion can be summed. A numerical demonstration is presented for H^{ +}_{2}. The 1/D expansions are summed using PadéBorel approximants with modifications that explicitly model known singularity structure.
 Publication:

Physical Review A
 Pub Date:
 July 1998
 DOI:
 10.1103/PhysRevA.58.250
 Bibcode:
 1998PhRvA..58..250H
 Keywords:

 31.15.Md;
 02.30.Lt;
 Perturbation theory;
 Sequences series and summability