  Various explicitly correlated Gaussian (ECG) basis sets are considered for
the solution of the molecular Schr\"odinger equation with particular attention
to the simplest polyatomic system, H$_3^+$. Shortcomings and advantages are
discussed for plain ECGs, ECGs with the global vector representation, floating
ECGs and their numerical projection, and ECGs with complex parameters. The
discussion is accompanied with particle density plots to visualize the
observations. In order to be able to use large complex ECG basis sets in
molecular calculations, a numerically stable algorithm is developed, the
efficiency of which is demonstrated for the lowest rotationally and
vibrationally excited states of H$_2$ and H$_3^+$.
