A new efficient method for density functional theory calculations of inhomogeneous fluids

The accurate computation of the effects of solvation on chemical systems can be done using density functional theories (DFT) for inhomogeneous multicomponent fluids. The DFT models of interest are non-local theories which accurately treat hard-sphere fluid mixtures; attractive inter-particle potentials (Lennard–Jones) are added as perturbations. In this paper, we develop and demonstrate a new efficient method for an accurate non-local DFT. The method described here differs from previous work in the use of fast fourier transform (FFT) methods to carry out the convolutions. As with our previous real space work (J. Comput. Phys. 159(2) (2000) 407, 425), we demonstrate that the Fourier space approach can be solved with a Newton–GMRES approach; however, we now employ a very efficient matrix-free algorithm. A simple but effective preconditioner is presented. The method is demonstrated with calculations performed for one-, two-, and three-dimensional systems, including problems with single and multicomponent fluids. Timing comparisons with previous implementations are given.