scholarly journals Pure non-local machine-learned density functional theory for electron correlation

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Johannes T. Margraf ◽  
Karsten Reuter
Keyword(s):  
Density Functional Theory ◽  
Electron Correlation ◽  
Density Functional ◽  
Local Treatment ◽  
Computational Cost ◽  
Mean Field ◽  
Water Dimer ◽  
Free Energy Surface ◽  
Functional Theory ◽  
Non Local

AbstractDensity-functional theory (DFT) is a rigorous and (in principle) exact framework for the description of the ground state properties of atoms, molecules and solids based on their electron density. While computationally efficient density-functional approximations (DFAs) have become essential tools in computational chemistry, their (semi-)local treatment of electron correlation has a number of well-known pathologies, e.g. related to electron self-interaction. Here, we present a type of machine-learning (ML) based DFA (termed Kernel Density Functional Approximation, KDFA) that is pure, non-local and transferable, and can be efficiently trained with fully quantitative reference methods. The functionals retain the mean-field computational cost of common DFAs and are shown to be applicable to non-covalent, ionic and covalent interactions, as well as across different system sizes. We demonstrate their remarkable possibilities by computing the free energy surface for the protonated water dimer at hitherto unfeasible gold-standard coupled cluster quality on a single commodity workstation.

scholarly journals Charge radii of potassium isotopes in the RMF(BCS)* approach

2022 ◽  
Author(s):  
Rong An ◽  
Shisheng Zhang ◽  
Li-Sheng Geng ◽  
Feng-Shou 张丰收 Zhang
Keyword(s):  
Experimental Data ◽  
Density Functional Theory ◽  
Density Functional ◽  
Mean Field ◽  
Field Studies ◽  
Nuclear Density ◽  
Isotopic Chain ◽  
Functional Theory ◽  
Charge Radii ◽  
Nuclear Density Functional Theory

Abstract We apply the recently proposed RMF(BCS)* ansatz to study the charge radii of the potassium isotopic chain up to $^{52}$K. It is shown that the experimental data can be reproduced rather well, qualitatively similar to the Fayans nuclear density functional theory, but with a slightly better description of the odd-even staggerings (OES). Nonetheless, both methods fail for $^{50}$K and to a lesser extent for $^{48,52}$K. It is shown that if these nuclei are deformed with a $\beta_{20}\approx-0.2$, then one can obtain results consistent with experiments for both charge radii and spin-parities. We argue that beyond mean field studies are needed to properly describe the charge radii of these three nuclei, particularly for $^{50}$K.

scholarly journals Towards a density functional theory of molecular fragments. What is the shape of atoms in molecules?

2020 ◽  
Vol 44 (170) ◽  
pp. 269-279
Author(s):  
Victor H. Chávez ◽  
Adam Wasserman
Keyword(s):  
Density Functional Theory ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Density Functional ◽  
Computational Cost ◽  
Atoms In Molecules ◽  
Electronic Density ◽  
Functional Theory ◽  
New Methods ◽  
The Cost

In some sense, quantum mechanics solves all the problems in chemistry: The only thing one has to do is solve the Schrödinger equation for the molecules of interest. Unfortunately, the computational cost of solving this equation grows exponentially with the number of electrons and for more than ~100 electrons, it is impossible to solve it with chemical accuracy (~ 2 kcal/mol). The Kohn-Sham (KS) equations of density functional theory (DFT) allow us to reformulate the Schrödinger equation using the electronic probability density as the central variable without having to calculate the Schrödinger wave functions. The cost of solving the Kohn-Sham equations grows only as N3, where N is the number of electrons, which has led to the immense popularity of DFT in chemistry. Despite this popularity, even the most sophisticated approximations in KS-DFT result in errors that limit the use of methods based exclusively on the electronic density. By using fragment densities (as opposed to total densities) as the main variables, we discuss here how new methods can be developed that scale linearly with N while providing an appealing answer to the subtitle of the article: What is the shape of atoms in molecules?

scholarly journals Double-well potential energy surface in the interaction between h-BN and Ni(111)

2019 ◽  
Vol 21 (21) ◽  
pp. 10888-10894
Author(s):  
Jorge Ontaneda ◽  
Francesc Viñes ◽  
Francesc Illas ◽  
Ricardo Grau-Crespo
Keyword(s):  
Density Functional Theory ◽  
Potential Energy ◽  
Density Functional ◽  
Energy Surface ◽  
Density Functional Theory Calculations ◽  
Dispersion Forces ◽  
Local Correlation ◽  
Functional Theory ◽  
Non Local ◽  
Double Well Potential

Density functional theory calculations with non-local correlation functionals, properly accounting for dispersion forces, predict the presence of two minima in the interaction energy between h-BN and Ni(111).

scholarly journals Including dispersion interactions in the ONETEP program for linear-scaling density functional theory calculations

2008 ◽  
Vol 465 (2103) ◽  
pp. 669-683 ◽  
Author(s):  
Quintin Hill ◽  
Chris-Kriton Skylaris
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Computational Cost ◽  
Density Functional Theory Calculations ◽  
Binding Energies ◽  
Molecular Structures ◽  
Dispersion Interactions ◽  
Biomolecular Systems ◽  
Functional Theory ◽  
High Level

While density functional theory (DFT) allows accurate quantum mechanical simulations from first principles in molecules and solids, commonly used exchange-correlation density functionals provide a very incomplete description of dispersion interactions. One way to include such interactions is to augment the DFT energy expression by damped London energy expressions. Several variants of this have been developed for this task, which we discuss and compare in this paper. We have implemented these schemes in the ONETEP program, which is capable of DFT calculations with computational cost that increases linearly with the number of atoms. We have optimized all the parameters involved in our implementation of the dispersion correction, with the aim of simulating biomolecular systems. Our tests show that in cases where dispersion interactions are important this approach produces binding energies and molecular structures of a quality comparable with high-level wavefunction-based approaches.

Demixing and ordering in Ni(Ti,Zr)(Sb,Sn) half-Heusler materials

2017 ◽  
Vol 19 (45) ◽  
pp. 30695-30702 ◽  
Author(s):  
Joaquin Miranda Mena ◽  
Thomas Gruhn
Keyword(s):  
Density Functional Theory ◽  
Monte Carlo ◽  
Phase Separation ◽  
Monte Carlo Simulations ◽  
Density Functional ◽  
Field Model ◽  
Mean Field ◽  
Study Phase ◽  
Mean Field Model ◽  
Functional Theory

We employed density functional theory, Monte Carlo simulations and a mean field model to study phase separation in thermoelectric Ni(Ti,Zr)(Sb,Sn) half-Heusler materials, simultaneously alloyed in the (Ti,Zr)- and (Sb,Sn) sublattices.

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