Development of fast numerical density functional theory methods for studying the structures of nanoporous materials

Abstract: Density functional theory (DFT) has been actively used and developed recently. DFT is an efficient instrument for describing a wide range of nanoscale phenomena: wetting transition, capillary condensation, adsorption, and others. In this work, we suggest a method for obtaining the equilibrium fluid density in a pore using DFT without calculating the free energy variation - Variation Free Density Functional Theory (VF-DFT). This technique is applicable to explore fluids with complex interactions and speed up calculations for simple fluids. In VF-DFT the fluid density is represented as a decomposition over a limited set of basis functions and decomposition coefficients. To construct basis functions, we applied principal component analysis (PCA). PCA is used to extract the main patterns of the fluid densities in the nanopore. Decomposition coefficients are sought with stochastic gradient-free optimization methods, such as genetic algorithm (GA), particle swarm optimization (PSO) to minimize the free energy of the system. We also suggest the Hybrid Density Functional Theory (H-DFT) approach based on stochastic optimization methods and the classical Piccard iteration method to find the equilibrium fluid density in the pore. Combining these methods helps to significantly speed up the calculations of equilibrium density in the system without losing quality. We considered two fluids: nitrogen at the temperature of T=77.4 K and argon 87.3 K, at the pore 3.6 nm. VF-DFT, H-DFT with different optimization algorithms were compared with each other and with classical Piccard iteration technique. Furthermore, the problem of calculation pore size distribution (PSD) for nanoporous materials is discussed. The Tikhonov regularization method was applied to reconstruct of PSD from experimental data on low-temperature adsorption. This method is proved to be very sensitive to the quality of adsorption data.