  Through the introduction of a class of trial wave functions portraying
combined rotations and vibrations of molecules formed through particle
localization in concentric polygonal rings, a correlated basis is constructed
that spans the translationally invariant part of the lower-Landau-level (LLL)
spectra. These trial functions, referred to as rovibrational molecular (RVM)
functions, generalize our previous work which focused exclusively on electronic
cusp states, describing them as pure vibrationless rotations. From a
computational viewpoint, the RVM correlated basis enables controlled and
systematic improvements of the original strongly-correlated variational wave
function. Conceptually, it provides the basis for the development of a quantal
molecular description for the full LLL spectra. This quantal molecular
description is universal, being valid for both bosons and fermions, for both
the yrast and excited states of the LLL spectra, and for both low and high
angular momenta. Furthermore, it follows that all other translationally
invariant trial functions (e.g., the Jastrow-Laughlin, compact
composite-fermion, or Moore-Read functions) are reducible to a description in
terms of an excited rotating/vibrating quantal molecule.
