The orthodox many-body theory of atoms, molecules and condensed phases is the electronic structure theory plus the theory of nuclear vibrations and rotations. The basic tent of this theory is the Born-Oppenheimer separation of the electronic and nuclear dynamics through deriving two Schrodinger equations, one for electrons, and the other for nuclei. The electronic Schrodinger equation, which conceives electrons as the sole quantum particles within the external field produced by clamped nuclei, yields the electronic eigenvalues, i.e. the potential energy surfaces, and the electronic eigenfunctions. On the other hand, the nuclear Schrodinger equation, which conceives nuclei as quantum particles experiencing the potential energy surfaces as the effective potentials, yields the eigenvalues and eigenstates of the collective vibrational and rotational modes. An unorthodox but more general reformulation of the many-body theory, called the multi-component quantum chemistry, dismisses the Born-Oppenheimer separation totally and the resulting many-body system is governed by a single multi-component Hamiltonian encompassing all interactions between electrons and nuclei. Theoretically, the resulting multi- component theory contains the orthodox theory as a special case thus one intuitionally expects it must be capable of reproducing the concepts and numerical results derived within the context of the orthodox many-body theory. In contrast, various theoretical arguments and computational studies, particularly in the last two decades, reveal exotic features of the multi-component quantum chemistry theory incompatible with the results derived from the orthodox many-body theory. In this talk I will introduce the basic tents of the multi-component quantum chemistry at a non-technical level as well as some of its paradoxical features by considering some illustrative examples. Some selected applications of the theory are also briefly considered including the status of nuclear quantum-superposed states in molecular systems and the newly discovered positronic bonds.


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