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

The "magic" angle in the self-assembly of colloids suspended in a nematic host phase