Could some physics guru here please help ? I have recently written and tested some C and Python code to compute the energy band structure for common semiconductor materials as Si, Ge, InP(FCC conventional lattice) and GaN(
both FCC and HCP conventional lattices) using the empirical pseudopotential method(EPM). The point that I am not very sure about is how to compute the reciprocal lattice k vectors, for both of these
conventional lattices. Specifically, given a reciprocal lattice Hamiltonian
H = sum(KE_constant*|k + G|^2*del_Kr + FF_SYM(G-G')*cos((G-G').tau) +
j FF_ASYM(G-G')*sin((G-G').tau)
where KE_constant = hbar^2/2*m_prime ...
del_Kr is the Kronecker delta function
FF_ASYM, FF_SYM are the asymmetric|symmetric form factors
tau is the mid-point interatomic distance
Questions are:
1. How to compute the k vectors, given the reciprocal lattice's
symmetry points
2. For the Wurtzite isotope of GaN, what is tau, as there are two
conventional lattice interatomic distances - 5.186 A and 3.186 A
All hints, suggestions will be gratefully accepted. Thanks in
advance.

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