scholarly journals An Entropic Approach to Classical Density Functional Theory

2021 ◽  
Vol 3 (1) ◽  
pp. 13
Author(s):  
Ahmad Yousefi ◽  
Ariel Caticha
Keyword(s):  
Density Functional Theory ◽  
Variational Principle ◽  
Maximum Entropy ◽  
Thermal Equilibrium ◽  
Density Functional ◽  
Approximation Scheme ◽  
Probability Distributions ◽  
Functional Theory ◽  
Dft Model ◽  
Expected Density

The classical Density Functional Theory (DFT) is introduced as an application of entropic inference for inhomogeneous fluids in thermal equilibrium. It is shown that entropic inference reproduces the variational principle of DFT when information about the expected density of particles is imposed. This process introduces a family of trial density-parametrized probability distributions and, consequently, a trial entropy from which the preferred one is found using the method of Maximum Entropy (MaxEnt). As an application, the DFT model for slowly varying density is provided, and its approximation scheme is discussed.

Study of the BaTiO3electronic structure using the maximum entropy method and density functional theory calculations

2016 ◽  
Vol 174 (1) ◽  
pp. 104-110 ◽  
Author(s):  
I. B. Catellani ◽  
G. M. Santos ◽  
J. C. Pastoril ◽  
B. F. Oliveira ◽  
I. A. Santos ◽  
...  
Keyword(s):  
Density Functional Theory ◽  
Maximum Entropy ◽  
Density Functional ◽  
Maximum Entropy Method ◽  
Density Functional Theory Calculations ◽  
Entropy Method ◽  
Functional Theory

Charge density of 4-methyl-3-[(tetrahydro-2H-pyran-2-yl)oxy]thiazole-2(3H)-thione. A comprehensive multipole refinement, maximum entropy method and density functional theory study

2020 ◽  
Vol 76 (3) ◽  
pp. 450-468
Author(s):  
Barbora Vénosová ◽  
Julia Koziskova ◽  
Jozef Kožíšek ◽  
Peter Herich ◽  
Karol Lušpai ◽  
...  
Keyword(s):  
Density Functional Theory ◽  
Charge Density ◽  
Maximum Entropy ◽  
Density Functional ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Experimental Results ◽  
Basis Set ◽  
Functional Theory ◽  
Radial Functions

The structure of 4-methyl-3-[(tetrahydro-2H-pyran-2-yl)oxy]thiazole-2(3H)-thione (MTTOTHP) was investigated using X-ray diffraction and computational chemistry methods for determining properties of the nitrogen—oxygen bond, which is the least stable entity upon photochemical excitation. Experimentally measured structure factors have been used to determine and characterize charge density via the multipole model (MM) and the maximum entropy method (MEM). Theoretical investigation of the electron density and the electronic structure has been performed in the finite basis set density functional theory (DFT) framework. Quantum Theory of Atoms In Molecules (QTAIM), deformation densities and Laplacians maps have been used to compare theoretical and experimental results. MM experimental results and predictions from theory differ with respect to the sign and/or magnitude of the Laplacian at the N—O bond critical point (BCP), depending on the treatment of n values of the MM radial functions. Such Laplacian differences in the N—O bond case are discussed with respect to a lack of flexibility in the MM radial functions also reported by Rykounov et al. [Acta Cryst. (2011), B67, 425–436]. BCP Hessian eigenvalues show qualitatively matching results between MM and DFT. In addition, the theoretical analysis used domain-averaged fermi holes (DAFH), natural bond orbital (NBO) analysis and localized (LOC) orbitals to characterize the N—O bond as a single σ bond with marginal π character. Hirshfeld atom refinement (HAR) has been employed to compare to the MM refinement results and/or neutron dataset C—H bond lengths and to crystal or single molecule geometry optimizations, including considerations of anisotropy of H atoms. Our findings help to understand properties of molecules like MTTOTHP as progenitors of free oxygen radicals.

scholarly journals Modeling nuclear resonance vibrational spectroscopic data of binuclear nonheme iron enzymes using density functional theory

2014 ◽  
Vol 92 (10) ◽  
pp. 975-978 ◽  
Author(s):  
Kiyoung Park ◽  
Edward I. Solomon
Keyword(s):  
Density Functional Theory ◽  
Active Sites ◽  
Density Functional ◽  
Structural Information ◽  
Nonheme Iron ◽  
Nuclear Resonance ◽  
Functional Theory ◽  
Nonheme Iron Enzymes ◽  
Iron Enzymes ◽  
Dft Model

Nuclear resonance vibrational spectroscopy (NRVS) is a powerful technique that can provide geometric structural information on key reaction intermediates of Fe-containing systems when utilized in combination with density functional theory (DFT). However, in the case of binuclear nonheme iron enzymes, DFT-predicted NRVS spectra have been found to be sensitive to the truncation method used to model the active sites of the enzymes. Therefore, in this study various-level truncation schemes have been tested to predict the NRVS spectrum of a binuclear nonheme iron enzyme, and a reasonably sized DFT model that is suitable for employing the NRVS/DFT combined methodology to characterize binuclear nonheme iron enzymes has been developed.

scholarly journals Polyelectrolyte chain at thermal equilibrium: A comparison between the density functional theory framework (DFT) and the molecular dynamic simulations (MD)

2021 ◽  
Author(s):  
Mike J. Edwards
Keyword(s):  
Density Functional Theory ◽  
Molecular Dynamic ◽  
Thermal Equilibrium ◽  
Density Functional ◽  
Molecular Dynamic Simulations ◽  
Dynamic Simulations ◽  
Functional Theory ◽  
The Density Functional Theory ◽  
Bjerrum Length ◽  
Theory Framework

ABSTRACTBy means of the density functional theory framework (DFT) as well as the molecular dynamic simulations (MD), a polyelectrolyte chain (PE) in the good solvent conditions at thermal equilibrium is studied. The strength of the electrostatic interactions is varied by the Bjerrum length of the solvent. It turns out that average extension of a PE scales with the degree of polymerization, very much similar to a neutral polymer chain in good solvent. Remarkably, the difference between a PE and a neutral chain appears to be solely in the correlations among monomers which are stored in the Virial coefficients. Interestingly, upon increasing the Bjerrum length of solvent, the chain shrinks. This outcome is confirmed by the DFT framework as well as the MD simulations.SIGNIFICANCEThe significance of this study is that it strongly criticizes the idea (already mentioned in T. Kreer, Soft Matter, 12, 3479 (2016)) that the PEs behave similar to a neutral ideal chain. This study could be useful in our understanding of biopolymers.

scholarly journals Density Functional Theory of Coulombic Excited States Based on Nodal Variational Principle

Computation ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 93
Author(s):  
Ágnes Nagy
Keyword(s):  
Density Functional Theory ◽  
Variational Principle ◽  
Excited States ◽  
Density Functional ◽  
Functional Theory ◽  
Correct Number ◽  
The Density Functional Theory

The density functional theory developed earlier for Coulombic excited states is reconsidered using the nodal variational principle. It is much easier to solve the Kohn–Sham equations, because only the correct number of nodes of the orbitals should be insured instead of the orthogonality.

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