Accelerate the ePC-SAFT-DFT Calculation with the Chebyshev Pseudospectral Collocation Method

Sun, Yunhao; Lü, Xiaohua; Shen, Gulou; Ji, Xiaoyan

doi:10.1021/acs.iecr.1c01077

Cited by 8 publications

(20 citation statements)

References 75 publications

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“…Minimization of the grand potential with respect to the density profile of component i yields the following Euler–Lagrange equation:

where q i is the charge of component i , and

is the mean electric potential at position r , which can be obtained by solving the Poisson’s equation ( Li and Wu, 2006 ). The expressions of functional derivatives

are described in Rosenfeld et al (1997) , Gross (2009) , Roth (2010) , and Sun et al (2021) .…”

Section: Theorymentioning

confidence: 99%

“…The expressions of the functional derivatives

are described in Rosenfeld et al (1997) , Gross (2009) , Roth (2010) , and Sun et al (2021) . All the convolution-like integrals involved in ePC-SAFT-DFT calculation can be classified as:

where R c represents the weighting distances, which are:

…”

Section: Theorymentioning

confidence: 99%

“…For the singularities in the expression of Eq. 13b (i.e.,

), the corresponding elements can be evaluated based on the following expression ( Sun et al, 2021 ):

…”

Section: Theorymentioning

confidence: 99%

“…A general scheme for calculating the density profile of confined systems with ionic contribution was proposed in Sun et al (2021 ), as illustrated in Scheme 1 . In a loop of Scheme 1 , the Euler–Lagrange equation needs to be solved twice.…”

Section: Theorymentioning

confidence: 99%

“…Moreover, the developed ePC-SAFT has been combined with DFT (ePC-SAFT-DFT) to describe the properties of IL and CO 2 /IL confined in nanopores with acceptable results ( Shen et al, 2018 ). Recently, in order to calculate the properties of the confined ILs with ePC-SAFT-DFT efficiently, the Chebyshev pseudo-spectral collocation method ( Yatsyshin et al, 2012 ; Nold et al, 2017 ) was implemented to accelerate the ePC-SAFT-DFT calculation ( Sun et al, 2021 ). However, only the slit-shaped and cylindrical pores have been considered previously, while for the spherical cavity, the corresponding method has not been available.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Accelerate the Electrolyte Perturbed-Chain Statistical Associating Fluid Theory–Density Functional Theory Calculation With the Chebyshev Pseudo-Spectral Collocation Method. Part II. Spherical Geometry and Anderson Mixing

et al. 2022

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To improve the efficiency of electrolyte perturbed-chain statistical associating fluid theory–density functional theory (ePC-SAFT-DFT) calculation of the confined system, in this work, first, the Chebyshev pseudo-spectral collocation method was extended to the spherical pores. Second, it was combined with the Anderson mixing algorithm to accelerate the iterative process. The results show that the Anderson mixing algorithm can reduce the computation time significantly. Finally, based on the accelerated ePC-SAFT-DFT program, a systematic study of the effects of the temperature, pressure, pore size, and pore shape on the CO2 solubilities in the ionic liquids (ILs) confined inside the silica nanopores was conducted. Based on the simulation results, to obtain high CO2 solubilities in the ILs confined in silica, a better option is to use the silica material with a narrow spherical pore, and the IL-anion should be selected specifically considering that it has a more significant impact on the absorption enhancement effect.

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“…Minimization of the grand potential with respect to the density profile of component i yields the following Euler–Lagrange equation:

where q i is the charge of component i , and

is the mean electric potential at position r , which can be obtained by solving the Poisson’s equation ( Li and Wu, 2006 ). The expressions of functional derivatives

are described in Rosenfeld et al (1997) , Gross (2009) , Roth (2010) , and Sun et al (2021) .…”

Section: Theorymentioning

confidence: 99%

“…The expressions of the functional derivatives

are described in Rosenfeld et al (1997) , Gross (2009) , Roth (2010) , and Sun et al (2021) . All the convolution-like integrals involved in ePC-SAFT-DFT calculation can be classified as:

where R c represents the weighting distances, which are:

…”

Section: Theorymentioning

confidence: 99%

“…For the singularities in the expression of Eq. 13b (i.e.,

), the corresponding elements can be evaluated based on the following expression ( Sun et al, 2021 ):

…”

Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Accelerate the Electrolyte Perturbed-Chain Statistical Associating Fluid Theory–Density Functional Theory Calculation With the Chebyshev Pseudo-Spectral Collocation Method. Part II. Spherical Geometry and Anderson Mixing

et al. 2022

Self Cite

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Classical density functional theory in three dimensions with GPU-accelerated automatic differentiation: Computational performance analysis using the example of adsorption in covalent-organic frameworks

Stierle,

Bauer,

Thiele

et al. 2024

Chemical Engineering Science

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

Kanygin

Nesterova

Lomovitskiy

et al. 2022

Ind. Eng. Chem. Res.

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Density functional theory (DFT) is an efficient instrument for describing a wide range of nanoscale phenomena: wetting transition, capillary condensation, adsorption, etc. In this paper, we suggest a method for obtaining the equilibrium molecular fluid density in a nanopore using DFT without calculating the freeenergy variationVariation-Free Density Functional Theory (VF-DFT). This technique can be used to explore confined fluids with a complex type of interactions, additional constraints, and, to speed up calculations, which might be crucial in an inverse problem. The fluid density in VF-DFT approach is represented as a decomposition over a limited set of basis functions. We applied principal component analysis (PCA) to extract the basic patterns from the density function and take them into account in the construction of a set of basis functions. The decomposition coefficients of the fluid density by the basis were sought by stochastic optimization algorithms: genetic algorithm (GA) and particle swarm optimization (PSO), to minimize the free energy of the system. In this work, two different fluids were 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 optimization algorithms was compared. We also introduce the Hybrid Density Functional Theory (H-DFT) approach based on stochastic optimization methods and the classical Picard iteration method to find the equilibrium fluid density starting from the physically appropriate solution. The combination of Picard iteration and stochastic algorithms helps to significantly speed up the calculations of equilibrium density in the system without losing the quality of the solution, especially in cases with the high relative pressure and expressed layering structure.

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Accelerate the ePC-SAFT-DFT Calculation with the Chebyshev Pseudospectral Collocation Method

Cited by 8 publications

References 75 publications

Accelerate the Electrolyte Perturbed-Chain Statistical Associating Fluid Theory–Density Functional Theory Calculation With the Chebyshev Pseudo-Spectral Collocation Method. Part II. Spherical Geometry and Anderson Mixing

Accelerate the Electrolyte Perturbed-Chain Statistical Associating Fluid Theory–Density Functional Theory Calculation With the Chebyshev Pseudo-Spectral Collocation Method. Part II. Spherical Geometry and Anderson Mixing

Classical density functional theory in three dimensions with GPU-accelerated automatic differentiation: Computational performance analysis using the example of adsorption in covalent-organic frameworks

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

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