Journal
JOURNAL OF CHEMICAL PHYSICS
Volume 132, Issue 12, Pages -Publisher
AMER INST PHYSICS
DOI: 10.1063/1.3357981
Keywords
density functional theory; ionic conductivity; liquids
Funding
- U.S. Army Research Laboratory
- U.S. Army Research Office [W911NF-09-1-0488]
- NIH [GM076013]
- U.S. Department of Energy [DE-AC01-06CH11357]
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Classical density functional theory (DFT) of fluids is a valuable tool to analyze inhomogeneous fluids. However, few numerical solution algorithms for three-dimensional systems exist. Here we present an efficient numerical scheme for fluids of charged, hard spheres that uses O(N log N) operations and O(N) memory, where N is the number of grid points. This system-size scaling is significant because of the very large N required for three-dimensional systems. The algorithm uses fast Fourier transforms (FFTs) to evaluate the convolutions of the DFT Euler-Lagrange equations and Picard (iterative substitution) iteration with line search to solve the equations. The pros and cons of this FFT/Picard technique are compared to those of alternative solution methods that use real-space integration of the convolutions instead of FFTs and Newton iteration instead of Picard. For the hard-sphere DFT, we use fundamental measure theory. For the electrostatic DFT, we present two algorithms. One is for the bulk-fluid functional of Rosenfeld [Y. Rosenfeld, J. Chem. Phys. 98, 8126 (1993)] that uses O(N log N) operations. The other is for the reference fluid density (RFD) functional [D. Gillespie , J. Phys.: Condens. Matter 14, 12129 (2002)]. This functional is significantly more accurate than the bulk-fluid functional, but the RFD algorithm requires O(N(2)) operations.
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