  In pre-Born-Oppenheimer (pre-BO) theory a molecule is considered as a quantum
system as a whole, including the electrons and the atomic nuclei on the same
footing. This approach is fundamentally different from the traditional quantum
chemistry treatment, which relies on the separation of the motion of the
electrons and the atomic nuclei. A fully quantum mechanical treatment of
molecules has a great promise for future developments and applications. Its
most accurate versions may contribute to the definition of new schemes for
metrology and testing fundamental physical theories; its approximate versions
can provide an efficient theoretical description for molecule-positron
interactions and, in general, it would circumvent the tedious computation and
fitting of potential energy surfaces and non-adiabatic coupling vectors. To
achieve these goals, the review points out important technical and fundamental
open questions. Most interestingly, the reconciliation of pre-BO theory with
the classical chemistry knowledge touches upon fundamental problems related to
the measurement problem of quantum mechanics.
