A new method is presented for calculating optical properties within th
e framework of the self-consistent linear muffin-tin orbital (LMTO) ba
nd-structure theory. We show how Green's second identity along with th
e commutation relation between the position and Hamiltonian operators
may be used to calculate, independently of the gauge, the velocity mat
rix elements required for optical properties. The method has been appl
ied to calculate the imaginary part of the dielectric function epsilon
(2)(E) for FeSi and Si. Notably, the new expressions for matrix elemen
ts are also valid for Hamiltonians in which non-local potentials are i
ncluded.