A novel technique to obtain analytical direct correlation functions for use in classical density functional theory

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The excess interaction term of classical density functional theory (cDFT) represents the effect of the neighboring atoms through the two-body direct correlation function (DCF). The DCF plays a crucial role in cDFT and the first peak of DCF is important in the phase field crystal (PFC) model. Unlike the reciprocal-space formulation, the real-space formulation of cDFT would not be restricted to only periodic systems, and thus, it has considerable potential for exploring non-periodic complex phenomena at the atomic scale. An accurate representation of the DCF is very important for the accurate and efficient implementation of cDFT. In this work, we propose a two-step process for systematically deriving the real-space DCF for any crystal structure. In the first step, we fit a set of rational functions to the experimental or molecular simulation data in reciprocal space, as shown in a previous study (Pisutha-Arnond et al., 2013). Then, in the second step, we obtain the analytical expression for the DCF in real space using an inverse Fourier–Bessel transform. One advantage of this method is that the functional fit to the DCF in reciprocal space is accomplished automatically. The proposed analytical technique is validated by comparing against numerically obtained DCF for bcc iron. This technique can be used to obtain a real-space DCF for any material. Finally, the domain of influence for DCF is investigated by integrating the DCF over a 3D domain.

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© 2017 Elsevier B.V. All rights reserved. Publisher's version of record: https://doi.org/10.1016/j.commatsci.2017.07.001

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Computational Materials Science