Simple one-centre calculation of breathing force constants and equilibrium internuclear distances for NH3, H2O and HF

Total molecular energies, breathing force constants and equilibrium internuclear distances are determined for the NH₃, H₂O and HF molecules using a single determinant wave function of the simplified one-centre form s ² s′² p _x ² p _y ² p _z ², where each of the five Slater orbitals, s, s′, p _x , p _y , p _z , is characterized by an effective orbital exponent ζ and an effective principal quantum number n. Five different calculations are performed for each molecule: in (a) the orbitals are centred on the heavy atom, the parameters n are taken to be integral, and the orbitals p _x , p _y and p _z are given the same ζ values (the spherical approximation); in (b) the orbitals p _x , p _y and p _z are allowed to have different ζ values (the ellipsoidal approximation); (c) and (d) are the same as (a) and (b) except that non-integral n values are allowed; (e) is the same as (d) except that the orbital centre also is taken to be a variational parameter. The values obtained are compared with experimental values (the agreement is surprisingly good) and with values from previous one-centre wave functions. The electronic densities for the various spherical approximations are tabulated.