Statistically representative databases for density functional theory via data science

2019 ◽  
Vol 21 (35) ◽  
pp. 19092-19103 ◽  
Author(s):  
Pierpaolo Morgante ◽  
Roberto Peverati
Keyword(s):  
Density Functional Theory ◽  
Cluster Analysis ◽  
Quantum Chemistry ◽  
Density Functional ◽  
Data Science ◽  
Computational Cost ◽  
Chemical Properties ◽  
Functional Theory

Cluster analysis applied to quantum chemistry: a new broad database of chemical properties with a reasonable computational cost.

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?

Theoretical Methods

1992 ◽  
Author(s):  
John A. Tossell ◽  
David J. Vaughan
Keyword(s):  
Density Functional Theory ◽  
Quantum Chemistry ◽  
Density Functional ◽  
Point Group ◽  
Theoretical Background ◽  
Wave Functions ◽  
General Reference ◽  
Functional Theory ◽  
Hartree Fock ◽  
Self Consistent Field

In this chapter, the most important quantum-mechanical methods that can be applied to geological materials are described briefly. The approach used follows that of modern quantum-chemistry textbooks rather than being a historical account of the development of quantum theory and the derivation of the Schrödinger equation from the classical wave equation. The latter approach may serve as a better introduction to the field for those readers with a more limited theoretical background and has recently been well presented in a chapter by McMillan and Hess (1988), which such readers are advised to study initially. Computational aspects of quantum chemistry are also well treated by Hinchliffe (1988). In the section that follows this introduction, the fundamentals of the quantum mechanics of molecules are presented first; that is, the “localized” side of Fig. 1.1 is examined, basing the discussion on that of Levine (1983), a standard quantum-chemistry text. Details of the calculation of molecular wave functions using the standard Hartree-Fock methods are then discussed, drawing upon Schaefer (1972), Szabo and Ostlund (1989), and Hehre et al. (1986), particularly in the discussion of the agreement between calculated versus experimental properties as a function of the size of the expansion basis set. Improvements on the Hartree-Fock wave function using configuration-interaction (CI) or many-body perturbation theory (MBPT), evaluation of properties from Hartree-Fock wave functions, and approximate Hartree-Fock methods are then discussed. The focus then shifts to the “delocalized” side of Fig. 1.1, first discussing Hartree-Fock band-structure studies, that is, calculations in which the full translational symmetry of a solid is exploited rather than the point-group symmetry of a molecule. A good general reference for such studies is Ashcroft and Mermin (1976). Density-functional theory is then discussed, based on a review by von Barth (1986), and including both the multiple-scattering self-consistent-field Xα method (MS-SCF-Xα) and more accurate basis-function-density-functional approaches. We then describe the success of these methods in calculations on molecules and molecular clusters. Advances in density-functional band theory are then considered, with a presentation based on Srivastava and Weaire (1987). A discussion of the purely theoretical modified electron-gas ionic models is followed by discussion of empirical simulation, and we conclude by mentioning a recent approach incorporating density-functional theory and molecular dynamics (Car and Parrinello, 1985).

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.

scholarly journals Multiresolution quantum chemistry in multiwavelet bases: Analytic derivatives for Hartree–Fock and density functional theory

2004 ◽  
Vol 121 (7) ◽  
pp. 2866-2876 ◽  
Author(s):  
Takeshi Yanai ◽  
George I. Fann ◽  
Zhengting Gan ◽  
Robert J. Harrison ◽  
Gregory Beylkin
Keyword(s):  
Density Functional Theory ◽  
Quantum Chemistry ◽  
Density Functional ◽  
Functional Theory ◽  
Hartree Fock

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.

scholarly journals Density functional theory across chemistry, physics and biology

2014 ◽  
Vol 372 (2011) ◽  
pp. 20120488 ◽  
Author(s):  
Tanja van Mourik ◽  
Michael Bühl ◽  
Marie-Pierre Gaigeot
Keyword(s):  
Density Functional Theory ◽  
Quantum Chemistry ◽  
Density Functional ◽  
Theme Issue ◽  
Functional Theory ◽  
The Past ◽  
Computational Quantum Chemistry ◽  
Computational Quantum

The past decades have seen density functional theory (DFT) evolve from a rising star in computational quantum chemistry to one of its major players. This Theme Issue, which comes half a century after the publication of the Hohenberg–Kohn theorems that laid the foundations of modern DFT, reviews progress and challenges in present-day DFT research. Rather than trying to be comprehensive, this Theme Issue attempts to give a flavour of selected aspects of DFT.

Differences in chemical properties and reactivity patterns of mono- and dioxomanganese(V) porphyrins as revealed by density functional theory

2013 ◽  
Vol 17 (10) ◽  
pp. 954-963 ◽  
Author(s):  
Sam P. de Visser
Keyword(s):  
Density Functional Theory ◽  
Ligand Exchange ◽  
Density Functional ◽  
Experimental Studies ◽  
Chemical Properties ◽  
Hydrogen Atom Abstraction ◽  
Functional Theory ◽  
Orbital Interactions ◽  
Catalytic Potential ◽  
Unique Mechanism

Recent experimental studies of Liu and Groves (J. Am. Chem. Soc. 2010; 132: 12847) on dioxomanganese(V) porphyrin complexes implicated substrate halogenation in good yield. Currently, little is known of this unique mechanism, therefore to gain understanding on the halogenation mechanism and the chemical features of this oxidant we decided to do a computational (density functional theory) study. We show that the dioxomanganese(V) complex has considerably different molecular (valence) orbitals as compared to monooxomanganese(V) porphyrin due to mixing of the metal 3d orbitals with 2p orbitals on both oxygen atoms. This results in a set of three pairs of orbitals of which the bonding and nonbonding pairs are doubly occupied and the antibonding orbitals are vacant. As a consequence, the bonding character along the Mn–O bond is less in dioxomanganese(V) as compared to monooxomanganese(V) complexes and therefore this bond can formally be described as a double bond rather than a triple bond. The differences in orbital interactions and orbital energies also affect the intrinsic chemical properties of the oxidants, such as the electron affinity and pKa values, which result in enhanced catalytic potential for dioxomanganese(V) porphyrin. Our calculations predict a halogenation mechanism in line with that proposed by experiment with an initial hydrogen atom abstraction followed by ligand exchange and halogen transfer.

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