A comparison of finite basis set and finite difference Hartree-Fock calculations for the InF and TlF molecules

Abstract

A comparison is made of the finite basis set approach (the algebraic approximation) and finite difference methods in calculations using the Hartree-Fock model for the ground (X¹Σ⁺) states of the heaviest Group IIIb fluorides: indium fluoride and thallium fluoride molecules. The XF molecules, X = In, Tl, are considered as a prototype for systems containing increasingly heavy atoms and a number of electrons. New finite difference Hartree-Fock calculations for the GaF ground state improve upon earlier results. The convergence of the calculations carried out within the algebraic approximation is monitored by employing systematically constructed basis sets of increasing size. The dependence of the finite difference calculations on the numerical grid employed is discussed. For the InF molecule, the total Hartree-Fock energy obtained with a grid of 595 × 595 points lies 15μΕ_h below the finite basis set energy. For the ground h state of TlF the finite basis set energy lies about 61μΕ_h above the converged finite difference result obtained on a grid of 595 × 595 points. For the TlF molecule, the matrix element required to evaluate the electric dipole moment volume interaction for the elementary particles in the Tl nucleus is evaluated from the finite difference Hartree-Fock wavefunction.