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 Density Functional Theory of Material Design: Fundamentals and Applications - I

2021 ◽  
Author(s):  
Prashant Singh ◽  
Manoj K Harbola
Keyword(s):  
Density Functional Theory ◽  
Schrödinger Equation ◽  
Local Density Approximation ◽  
Schrodinger Equation ◽  
Density Functional ◽  
Local Density ◽  
Density Approximation ◽  
Dft Methods ◽  
Electronic Density ◽  
Functional Theory

Abstract This article is part-I of a review of density-functional theory (DFT) that is the most widely used method for calculating electronic structure of materials. The accuracy and ease of numerical implementation of DFT methods has resulted in its extensive use for materials design and discovery and has thus ushered in the new field of computational material science. In this article we start with an introduction to Schrödinger equation and methods of its solutions. After presenting exact results for some well-known systems, difficulties encountered in solving the equation for interacting electrons are described. How these difficulties are handled using the variational principle for the energy to obtain approximate solutions of the Schrödinger equation is discussed. The resulting Hartree and Hartree-Fock theories are presented along with results they give for atomic and solid-state systems. We then describe Thomas-Fermi theory and its extensions which were the initial attempts to formulate many-electron problem in terms of electronic density of a system. Having described these theories, we introduce modern density functional theory by discussing Hohenberg-Kohn theorems that form its foundations. We then go on to discuss Kohn-Sham formulation of density-functional theory in its exact form. Next, local density approximation is introduced and solutions of Kohn-Sham equation for some representative systems, obtained using the local density approximation, are presented. We end part-I of the review describing the contents of part-II.

Quasicontinuum-Like Reduction of Density Functional Theory Calculations of Nanostructures

2008 ◽  
Vol 8 (7) ◽  
pp. 3729-3740
Author(s):  
Dan Negrut ◽  
Mihai Anitescu ◽  
Anter El-Azab ◽  
Peter Zapol
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Computational Cost ◽  
Density Functional Theory Calculations ◽  
Optimization Techniques ◽  
Electronic Density ◽  
Functional Theory ◽  
Cross Domain ◽  
Explicit Consideration ◽  
Orbital Free

Density functional theory can accurately predict chemical and mechanical properties of nanostructures, although at a high computational cost. A quasicontinuum-like framework is proposed to substantially increase the size of the nanostructures accessible to simulation. It takes advantage of the near periodicity of the atomic positions in some regions of nanocrystalline materials to establish an interpolation scheme for the electronic density in the system. The electronic problem embeds interpolation and coupled cross-domain optimization techniques through a process called electronic reconstruction. For the optimization of nuclei positions, computational gains result from explicit consideration of a reduced number of representative nuclei and interpolating the positions of the rest of nuclei following the quasicontinuum paradigm. Numerical tests using the Thomas-Fermi-Dirac functional demonstrate the validity of the proposed framework within the orbital-free density functional theory.

Density Functional Theory Study on the Absorption of CO2 by the Ionic Liquid of 1-butyl-3-methylimidazolium Acetate

2013 ◽  
Vol 807-809 ◽  
pp. 543-548 ◽  
Author(s):  
Yan Fei Chen ◽  
Yan Hong Cui ◽  
Dong Shun Deng ◽  
Ning Ai
Keyword(s):  
Density Functional Theory ◽  
Ionic Liquid ◽  
Ionic Liquids ◽  
Density Functional ◽  
Ion Pairs ◽  
Ion Pair ◽  
Frontier Molecular Orbitals ◽  
Density Functional Theory Study ◽  
Electronic Density ◽  
Functional Theory

The absorptions of CO2on the 1-butyl-3-methylimidazolium acetate ([Bmi [Ac]) with different substituents are calculated systematically at GGA/PW91 level. Three hydrogen bonds are formed between [A and cations of 1-n-[Bmi [A ([NBmi+) and 1-tert-[Bmi [A ([TBmi+). The interaction between CO2and the [NBmi [A by a C-O bond is much weaker than that with the [TBmi [A by forming a O...O...C...C four member-ring. The chemisorption of CO2on the ion pairs of [NBmi [A is much weaker than that on the [TBmi [A, resulted from the absorption energies analysis. The frontier molecular orbitals shows the electronic density overlap between absorbed CO2and the [A in CO2-[NBmi [A is much weaker than that in [TBmi [A. Therefore, the chemisorption of CO2on the ion pair of [NBmi [A is much weaker than that on the [TBmi [A. The ionic liquids based [NBmi+can be used repetitively, and the adsorbed CO2would be easier desorbed.

Density Functional Theory and Quantum Theory of Atoms in Molecules Analysis: Influence of Intramolecular Interactions on Pirouetting Movement in Tetraalkylsuccinamide[2]rotaxanes

2017 ◽  
Vol 17 (11) ◽  
pp. 5845-5857 ◽  
Author(s):  
Marcos A. P. Martins ◽  
Leticia V. Rodrigues ◽  
Alexandre R. Meyer ◽  
Clarissa P. Frizzo ◽  
Manfredo Hörner ◽  
...  
Keyword(s):  
Density Functional Theory ◽  
Quantum Theory ◽  
Density Functional ◽  
Intramolecular Interactions ◽  
Atoms In Molecules ◽  
Functional Theory

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.

Sign in / Sign up

Export Citation Format

Share Document