Variation-Free Approach for Density Functional Theory: Data-Driven Stochastic Optimization

Yuriy Kanygin

doi:10.1021/acs.iecr.2c00547

2022-05-18

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DOI：10.1021/acs.iecr.2c00547

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摘要

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Density functional theory (DFT) is an efficientinstrument for describing a wide range of nanoscale phenomena:wetting transition, capillary condensation, adsorption, etc. In thispaper, we suggest a method for obtaining the equilibrium molecularfluid density in a nanopore using DFT without calculating the free-energy variation???Variation-Free Density Functional Theory (VF-DFT). This technique can be used to explore confinedfluids with acomplex type of interactions, additional constraints, and, to speed upcalculations, which might be crucial in an inverse problem. Thefluiddensity in VF-DFT approach is represented as a decomposition overa limited set of basis functions. We applied principal componentanalysis (PCA) to extract the basic patterns from the density functionand take them into account in the construction of a set of basisfunctions. The decomposition coefficients of thefluid density by the basis were sought by stochastic optimization algorithms: geneticalgorithm (GA) and particle swarm optimization (PSO), to minimize the free energy of the system. In this work, two differentfluidswere studied: nitrogen at a temperature of 77.4 K and argon 87.3 K, at a pore size of 3.6 nm, and the performance of optimizationalgorithms was compared. We also introduce the Hybrid Density Functional Theory (H-DFT) approach based on stochasticoptimization methods and the classical Picard iteration method tofind the equilibriumfluid density starting from the physicallyappropriate solution. The combination of Picard iteration and stochastic algorithms helps to significantly speed up the calculations ofequilibrium density in the system without losing the quality of the solution, especially in cases with the high relative pressure andexpressed layering structure.

Keyword:

PORE-SIZE ANALYSIS

GENETIC ALGORITHM

STATISTICAL-MECHANICS

MODEL

NETWORK

FORCES

FLUIDS