Density Distribution in Soft Matter Crystals and Quasicrystals

TL;DR

This paper proposes representing the logarithm of density distributions in soft matter crystals and quasicrystals via Fourier sums, demonstrating improved accuracy and enabling phase diagram calculations with non-local density functional theory.

Contribution

It introduces a novel Fourier-based method for density representation, especially effective for soft matter crystals and useful for quasicrystals.

Findings

Fourier sum of the logarithm of density converges rapidly for soft matter crystals.

The method allows accurate phase diagram calculations for quasicrystals.

Truncation after few terms yields high accuracy in density representation.

Abstract

The density distribution in solids is often represented as a sum of Gaussian peaks (or similar functions) centred on lattice sites or via a Fourier sum. Here, we argue that representing instead the $\mathit{logarithm}$ of the density distribution via a Fourier sum is better. We show that truncating such a representation after only a few terms can be highly accurate for soft matter crystals. For quasicrystals, this sum does not truncate so easily, nonetheless, representing the density profile in this way is still of great use, enabling us to calculate the phase diagram for a 3-dimensional quasicrystal forming system using an accurate non-local density functional theory.