An efficient algorithm for classical density functional theory in three dimensions: ionic solutions.

Area of Science:

• Computational physics
• Statistical mechanics
• Physical chemistry

Background:

• Classical density functional theory (DFT) is crucial for analyzing inhomogeneous fluids.
• Limited numerical solution algorithms exist for 3D DFT systems.
• Efficient computation is vital for large-scale simulations.

Purpose of the Study:

• To develop an efficient numerical scheme for 3D DFT of charged, hard sphere fluids.
• To enable analysis of complex inhomogeneous fluid systems.
• To compare different numerical approaches for DFT solvers.

Main Methods:

• Developed an O(N log N) operation and O(N) memory algorithm using fast Fourier transforms (FFTs).
• Employed Picard (iterative substitution) iteration with line search to solve DFT Euler-Lagrange equations.
• Utilized fundamental measure theory for hard-sphere DFT and two electrostatic DFT functionals (bulk-fluid and RFD).

Main Results:

• The FFT/Picard method achieves efficient O(N log N) scaling for 3D systems.
• A bulk-fluid electrostatic DFT functional algorithm with O(N log N) operations was implemented.
• A more accurate reference fluid density (RFD) functional algorithm was developed, requiring O(N^2) operations.

Conclusions:

• The presented FFT/Picard scheme significantly enhances the computational feasibility of 3D DFT for charged hard sphere fluids.
• The choice between bulk-fluid and RFD functionals involves a trade-off between accuracy and computational cost.
• This work provides a valuable tool for studying complex fluid systems with unprecedented efficiency.