Soft X-ray emission spectra of the molecules CO, N 2, NO and O 2 are examined for the purpose of deriving information on their core hole energy curves. Molecular force constant and equilibrium bond lengths are determined for the core hole species C*O and N 2*, and a qualitative analysis is made for CO*, N*O, NO* and O 2*. The results show that differences of equilibrium geometries between the core hole states and the ground states are very well reproduced (better than 1 pm) by SCF calculations within the Hartree-Fock formalism. Inclusion of anharmonicity in the Franck-Condon analysis gives a small but significant effect on the best fitted value for the core hole state bond lengths (about 0.5 pm). Oxygen is binding energies determined from the X-ray spectra are shown to agree with ESCA data, in most cases within a few tenths of an eV. Calculated ΔSCF transition energies reproduce the experimental data within a few eV.