The energy band structures of the Bi12SiO20 and Bi12GeO20 single cryst
als were calculated using a local pseudopotential method. An iteration
procedure was carried out by use of increasing number of plane waves
(up to 1500) until the required energy eigenvalue stability was less t
han 0.02 Ry. An agreement between the calculated reflection coefficien
t and the experimental optical reflection data was obtained. Moreover,
a striking similarity of the Bi12SiO20 and Bi12GeO20 energy band stru
ctures was found. The local pseudopotential approach is suggested to b
e more effective than any nonlocal one in order to describe other comp
lex single crystals.