  We present an accurate ab initio tight-binding model, capable of describing
the dynamics of Dirac points in tunable honeycomb optical lattices following a
recent experimental realization [L. Tarruell et al., Nature 483, 302 (2012)].
Our scheme is based on first-principle maximally localized Wannier functions
for composite bands. The tunneling coefficients are calculated for different
lattice configurations, and the spectrum properties are well reproduced with
high accuracy. In particular, we show which tight binding description is needed
in order to accurately reproduce the position of Dirac points and the
dispersion law close to their merging, for different laser intensities.
