  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.
