  An interesting class of tetrahedrally coordinated ternary compounds have
attracted considerable interest because of their potential as good
thermoelectrics. These compounds, denoted as I$_3$-V-VI$_4$, contain three
monovalent-I (Cu, Ag), one nominally pentavalent-V (P, As, Sb, Bi), and four
hexavalent-VI (S, Se, Te) atoms; and can be visualized as ternary derivatives
of the II-VI zincblende or wurtzite semiconductors, obtained by starting from
four unit cells of (II-VI) and replacing four type II atoms by three type I and
one type V atoms. In trying to understand their electronic structures and
transport properties, some fundamental questions arise: whether V atoms are
indeed pentavalent and if not how do these compounds become semiconductors,
what is the role of V lone pair electrons in the origin of band gaps, and what
are the general characteristics of states near the valence band maxima and the
conduction band minima. We answer some of these questions using ab initio
calculations (density functional methods with both local and nonlocal
exchange-correlation potential).
