Density-Functional Thermodynamic Perturbation Theory of Lennard-Jones Solids

1992 ◽  
Vol 278 ◽  
Author(s):  
Agathagelos Kyrlidis ◽  
Robert A. Brown
Keyword(s):  
Density Functional ◽  
Interatomic Potential ◽  
Structural Information ◽  
Hard Spheres ◽  
Energy Functional ◽  
Thermodynamic Perturbation Theory ◽  
Lennard Jones ◽  
Dependent Potential ◽  
Solid Liquid ◽  
Thermodynamic Perturbation

AbstractThe thermodynamics of a fcc hard spheres solid is accurately described by recent density-functional approximations. This state is used as a reference in a thermodynamic perturbation analysis for a density-functional theory of Lennard-Jones solids. The free energy functional incorporates liquid state structural information and a density dependent potential decomposition for the Lennard-Jones interatomic potential. The computed free energies of the solids compare very well with the predictions of atonlistic simulations. Solid-liquid coexistence is predicted consistently to within 15% of results of Monte Carlo simulations, over the temperature range 0.75 ≤ kT/c ε ≤ 10.

Density profiles of fluids in some special symmetries

1995 ◽  
Vol 73 (7-8) ◽  
pp. 432-439 ◽  
Author(s):  
Seong-Chan Lee ◽  
Zi-Hong Yoon ◽  
Soon-Chul Kim
Keyword(s):  
Free Energy ◽  
Computer Simulations ◽  
Hard Sphere ◽  
Density Functional ◽  
Energy Functional ◽  
Empirical Method ◽  
Density Profiles ◽  
Functional Approximation ◽  
Free Energy Functional ◽  
Lennard Jones

A free-energy-functional approximation based on a semi-empirical method is proposed. The main advantage of the free-energy-functional approximation is its accuracy compared with other models and its relative simplicity compared with other well-known weighted-density approximations. The free-energy-functional approximation is applied to predict the density profiles of the hard-sphere fluids and the Lennard–Jones fluids in some special symmetries. For the density profiles near a hard flat wall, the results reproduced the hard-sphere oscillatory structures qualitatively and quantitatively. For the density profiles of hard-sphere fluids confined in a spherical cage, the results are also in a fair agreement with the computer simulations. For Lennard–Jones fluids, two kinds of density-functional perturbation theories, the density-functional mean-field theory (DFMFT) and the density-functional perturbation theory (DFPT), examined. The results show that at higher temperature the DFPT compares well with computer simulations. However, the agreement deteriorates slightly as the temperature of the Lennard–Jones fluids is reduced. These results demonstrate that both the free-energy-functional approximation and the DFPT succesfully describe the inhomogeneous properties of classical fluids.

scholarly journals Methanol Carbonylation over Acid Mordenite: Insights from Ab Initio Molecular Dynamics and Machine Learning Thermodynamic Perturbation Theory

2021 ◽  
Author(s):  
Monika Gešvandtnerová ◽  
Dario Rocca ◽  
Tomas Bucko
Keyword(s):  
Machine Learning ◽  
Molecular Dynamics ◽  
Perturbation Theory ◽  
Ab Initio ◽  
Molecular Dynamics Simulations ◽  
Density Functional ◽  
Ab Initio Molecular Dynamics ◽  
Thermodynamic Perturbation Theory ◽  
Dynamics Simulations ◽  
Thermodynamic Perturbation

<div>In this work we present a detailed \textit{ab initio} study of the carbonylation reaction of methoxy groups in the zeolite mordenite, as it is the rate determining step in a series of elementary reactions leading to ethanol. </div><div>For the first time we employ full molecular dynamics simulations to evaluate free energies of activation for the reactions in side pockets and main channels. Results show that the reaction in the side pocket is preferred and, when dispersion interactions are taken into account, this preference becomes even stronger. This conclusion is confirmed using multiple levels of density functional theory approximations with (PBE-D2, PBE-MBD, and vdW-DF2-B86R) or without (PBE, HSE06) dispersion corrections. These calculations, that in principle would require several demanding molecular dynamics simulations, were made possible at a minimal computational cost by using a newly developed approach that combines thermodynamic perturbation theory with machine learning.</div>

Classical density functional approach to depletion interaction of Lennard-Jones binary mixtures

2021 ◽  
Author(s):  
Yue Chen ◽  
Wei Chen ◽  
Xiaosong Chen
Keyword(s):  
Bulk Density ◽  
Density Functional ◽  
Binary Systems ◽  
Hard Spheres ◽  
Distribution Functions ◽  
Functional Formalism ◽  
Depletion Interaction ◽  
Lennard Jones ◽  
Depletion Force ◽  
Binary Fluid Mixtures

Abstract In this article, we apply classical density functional theory to investigate the characteristics of depletion interaction in Lennard-Jones (LJ) binary fluid mixtures. First of all, in order to confirm the validity of our adopted density functional formalism, we calculate the radial distribution functions with theoretical approach and compare them with results obtained by molecular dynamics simu- lation. Then this approach is applied to the case of two colloids immersed in LJ solvent systems. We investigate the variation of depletion interaction with respect to the distance of two colloids in LJ binary systems. We find that depletion interaction may be attractive or repulsive, mostly depending on the bulk density of solvent and the temperature of binary system. For high bulk densities, the repulsive barrier of depletion force is remarkable when the total excluded volume of colloids touches each other and reaches a maximum. The height of repulsive barrier is related to the parameters of LJ potential and bulk density. Moreover, depletion force may exhibit attractive wells if the bulk density of solvent is low. The attractive well tends to appear when the surface-surface distance of colloids is half of the size of polymer and deepen with temperature lowering in a fixed bulk density. In contrast with the hard-spheres system, no oscillation of depletion potential around zero is observed.

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