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.