In recent high-resolution and sophisticated soft X-ray molecular spectroscopies, small exchange interaction (EX) involving the core electron has been revealed. Interatomic core-core EX is generally small; therefore, it is considered that even the core electron described as 1ssigma(g) and 1ssigma(u) in homonuclear systems is localized on an atom. However, small but appreciable interatomic core-valence EX in N-2 and C2H2 results in observable g-u splittings in the core ionization, which are experimentally evaluated from extrapolation of the 1ssigma(g)(local) --> npsigma(u), nppi(u) and 1ssigma(u)(local) --> nsdsigma(g), ndpi(g) Rydberg series. Due to intermolecular Rydberg-valence EX, blue shifts in low-lying core-to-Rydberg excitations in N-2 and Ar are experimentally identified from gas phase to surface, from surface to bulk, and from large to small cage size of rare gas matrixes. EX involving the 2p core electron is anisotropic, depending on the relation between the 2p orbital direction and molecular structure. In some sulfur containing molecules, it is experimentally revealed that the S 2p and excited electrons have EX compatible to the 2p spin-orbit interaction (SO) for parallel 2ppi --> pi* transitions and EX smaller than SO for perpendicular 2psigma --> pi* transitions. In other words, the jj coupling scheme is not applicable to the parallel transitions. Furthermore, it is revealed that, in resonant photoelectron and soft X-ray emissions on the S 2p excitation of CS2 and SF6, spin-forbidden shake-up valence ionizations with quartet spin couplings and spin-forbidden valence excitations with triplet spin couplings are observable via triplet components mixed in intermediate core-excited states. (C) 2004 Elsevier B.V. All rights reserved.