Toward chemical accuracy at low computational cost: Density-functional theory with σ-functionals for the correlation energy

2021 ◽  
Vol 154 (1) ◽  
pp. 014104
Author(s):  
Egor Trushin ◽  
Adrian Thierbach ◽  
Andreas Görling
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Correlation Energy ◽  
Computational Cost ◽  
Functional Theory ◽  
Low Computational Cost

Exchange-Correlation Energy Densities and Response Potentials: Connection Between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

2019 ◽  
Author(s):  
S. Giarrusso ◽  
Paola Gori-Giorgi
Keyword(s):  
Density Functional Theory ◽  
Strong Coupling ◽  
Density Functional ◽  
Correlation Energy ◽  
Order Term ◽  
Strong Coupling Limit ◽  
Local Form ◽  
Coupling Constant ◽  
Functional Theory ◽  
Exchange Correlation

We analyze in depth two widely used definitions (from the theory of conditional probablity amplitudes and from the adiabatic connection formalism) of the exchange-correlation energy density and of the response potential of Kohn-Sham density functional theory. We introduce a local form of the coupling-constant-dependent Hohenberg-Kohn functional, showing that the difference between the two definitions is due to a corresponding local first-order term in the coupling constant, which disappears globally (when integrated over all space), but not locally. We also design an analytic representation for the response potential in the strong-coupling limit of density functional theory for a model single stretched bond.<br>

scholarly journals Simple and Efficient Truncation of Virtual Spaces in Embedded Wave Functions via Concentric Localization

2019 ◽  
Author(s):  
Daniel Claudino ◽  
Nicholas Mayhall
Keyword(s):  
Density Functional ◽  
Correlation Energy ◽  
Accuracy Assessment ◽  
Computational Cost ◽  
Virtual Space ◽  
Functional Theory ◽  
Energy Diagram ◽  
Torsional Potential ◽  
Starting Point ◽  
Retinal Chromophore

<p>We present a strategy to generate “concentrically local orbitals” for the purpose of decreasing the computational cost of wave function-in-density functional theory (WF-in-DFT) embedding. The concentric localization is performed for the virtual orbitals by first projecting the virtual space onto atomic orbitals centered on the embedded atoms. Using a one-particle operator, these projected orbitals are then used as starting point to iteratively span the virtual space, recursively creating virtual orbital “shells” with consecutively decreasing correlation energy recovery at each iteration. This process can be repeated to convergence, allowing for tunable accuracy. Assessment of the proposed scheme is performed by application to the potential energy diagram of the Menshutkin reaction of chloromethane and ammonia inside a segment of a carbon nanotube and the torsional potential of a simplified version of the retinal chromophore.</p>

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 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.

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 BEYOND DENSITY FUNCTIONAL THEORY: THE DOMESTICATION OF NONLOCAL POTENTIALS

2004 ◽  
Vol 18 (02n03) ◽  
pp. 73-82 ◽  
Author(s):  
ROBERT K. NESBET
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Correlation Energy ◽  
Mean Field Theory ◽  
Mean Field ◽  
Energy Functional ◽  
Functional Theory ◽  
Large Molecules ◽  
Cellular Method ◽  
Nonlocal Potentials

Due to efficient scaling with electron number N, density functional theory (DFT) is widely used for studies of large molecules and solids. Restriction of an exact mean-field theory to local potential functions has recently been questioned. This review summarizes motivation for extending current DFT to include nonlocal one-electron potentials, and proposes methodology for implementation of the theory. The theoretical model, orbital functional theory (OFT), is shown to be exact in principle for the general N-electron problem. In practice it must depend on a parametrized correlation energy functional. Functionals are proposed suitable for short-range Coulomb-cusp correlation and for long-range polarization response correlation. A linearized variational cellular method (LVCM) is proposed as a common formalism for molecules and solids. Implementation of nonlocal potentials is reduced to independent calculations for each inequivalent atomic cell.

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