  We present a formal expression for Wannier functions of composite bands of
1-D Bloch electrons in terms of parallel-transported Bloch functions and their
non-Abelian geometric phases. Spatial decay properties of these Wannier
functions are studied in the case of simple bands of 1-D model insulator and
metal. Within first-principles density functional theory, we illustrate the
formalism through the construction of Wannier functions of polyethylene and
polyacetylene.
