Density functional theory of freezing: Analysis of crystal density

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Abstract
The density functional theory of freezing is used to study the liquid to crystal phase transition in the hardsphere and Lennard-Jones systems. An important step in the calculation is the parametrization of the solid phase average single particle density ρ(r). In this work two popular parametrizations are compared. The first method is a general Fourier decomposition of the periodic solid density in which the amplitude of each (non-symmetry-related) Fourier component is treated as an independent parameter. The second parametrization, which is more restrictive but easier to implement, approximates the solid density as a sum of Gaussian peaks centered at the sites of a periodic lattice. The two methods give essentially identical results for the phase diagrams for the two systems studied, but the crystal density predicted by the Fourier method exhibits significant anisotropies which are excluded from the Gaussian representation by construction.