  We apply the diabatic formalism, first introduced in molecular physics, to
the description of heavy-quark mesons. In this formalism the dynamics is
completely described by a diabatic potential matrix whose elements can be
derived from unquenched lattice QCD studies of string breaking. For energies
far below the lowest open flavor meson-meson threshold, the resulting diabatic
approach reduces to the well-known Born-Oppenheimer approximation where
heavy-quark meson masses correspond to energy levels in an effective
quark-antiquark potential. For energies close below or above that threshold,
where the Born-Oppenheimer approximation fails, this approach provides a set of
coupled Schr\"{o}dinger equations incorporating meson-meson components
nonperturbatively, i.e. beyond loop corrections. A spectral study of heavy
mesons containing $c\overline{c}$ with masses below $4.1$ GeV is carried out
within this framework. From it a unified description of conventional as well as
unconventional resonances comes out.
