The binding energies of selected C, N, O, and F 1s electrons in six paramagnetic molecules were measured by x-ray photoemission. A splitting of 1.934(41) eV was observed in the N(1s) line of NF2, and several other splittings were remeasured or obtained by fitting asymmetric but unresolved lines. Use of the Mg Kα12 doublet profile in fitting improved the fits markedly. A multiplet hole theory was developed to predict the final-state multiplet splitting. It uses atomic exchange integrals, INDO calculations on an ``equivalent-core'' final state to obtain spin densities, and Van Vleck's Theorem to account correctly for multiplicity. It gives results in very good agreement with experiment, and it can be used for larger molecules. During photoemission spin density migrates away from the 1s hole in most cases, and electronic charge flows toward this hole, affecting both the 1s splitting and the 1s binding energy. The lower N(1s) binding energy in di-t -butylnitroxide than in NO arises from electron flow to nitrogen from the t -butyl group during photoemission. This inductive effect is closely related to the ease of substitution of nucleophilic groups in unimolecular reactions with tertiary alkyl halides, a phenomenon that must also be understood in terms of final- (or transition-) state properties, rather than simply in terms of the initial state. Inequivalent fluorines in N2F4 were identified by an unresolved doublet structure in the F(1s) peak.