  Using extensive Monte Carlo (MC) simulations of colloids immersed in a
nematic liquid crystal we compute an effective interaction potential via the
local nematic director field and its associated order parameter. The effective
potential consists of a local Landau-de Gennes (LdG) and a Frank elastic
contribution. Molecular expressions for the LdG expansion coefficients are
obtained via classical density functional theory (DFT). The DFT result for the
LdG parameter $A$ is improved by locating the phase transition through
finite-size scaling theory. We consider effective interactions between a pair
of homogeneous colloids with Boojum defect topology. In particular, colloids
attract each other if the angle between their center-of-mass distance vector
and the far-field nematic director is about $30^{\circ}$ which settles a
long-standing discrepancy between theory and experiment. Using the effective
potential in two-dimensional MC simulations we show that self-assembled
structures formed by the colloids are in excellent agreement with experimental
data.
