纳米多孔材料结构的快速数值密度泛函理论方法研究进展
Development of fast numerical density functional theory methods for studying the structures of nanoporous materials
摘要：
密度泛函理论（DFT）近年来得到了积极的应用和发展。密度泛函理论是一种有效的工具，用于描述广泛的纳米现象：润湿转变，毛细凝聚，吸附，和其他。本文提出了一种利用密度泛函理论（DFT）计算孔隙中平衡流体密度的方法--无变差密度泛函理论（VF-DFT）。该技术适用于探索具有复杂相互作用的流体，并加快简单流体的计算。在VF-DFT中，流体密度被表示为在有限的基函数和分解系数集合上的分解。为了构造基函数，我们应用了主成分分析（PCA）。PCA被用来提取纳米孔中流体密度的主要模式。利用遗传算法、粒子群算法等随机无梯度优化方法求解分解系数，以最小化系统的自由能。我们还提出了混合密度泛函理论（H-DFT）方法的基础上随机优化方法和经典的Piccard迭代方法来寻找平衡流体密度的孔隙。结合这些方法有助于显着加快系统中平衡密度的计算，而不会损失质量。我们考虑了两种流体：温度为T= 77.4K的氮气和温度为87.3K的氩气，在孔3.6nm处。比较了不同优化算法下的VF-DFT、H-DFT，并与经典Piccard迭代法进行了比较。此外，还讨论了纳米多孔材料孔径分布的计算问题。应用Tikhonov正则化方法对低温吸附实验数据进行PSD重构。这种方法被证明是非常敏感的吸附数据的质量。
英文摘要：
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.
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