The LaF3·Arn (n = 1–21) clusters have been proposed as models to account for the matrix effects on the molecular properties of the LaF3 molecule isolated in argon solid matrix at cryogenic temperature. Because of the strong Lewis acid character of the LaF3 molecule, there is a substantial electron‐density transfer from the argon atoms to the molecule that induces important geometrical changes in the structure and vibrational frequencies. The present bottom‐up approach reveals the formation of two sets of structures close in energy having the D3h‐LaF3 and the C3v‐LaF3. The D3h‐LaF3 structures are more compact with respect to the C3v series. The largest investigated cluster of the D3h series, the LaF3·Ar21 resembles an hcp structure with the LaF3 occupying the central substitutional site that it is expected to be energetically preferred. The C3v‐LaF3 structures are more stable for lighter clusters and their high formation rates in the gas‐phase, immediately before matrix incorporation, could explain experimental IR/Raman results that point to a pyramidal shape for the molecule in argon matrix. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010