Piecewise linearity, freedom from self-interaction, and a Coulomb asymptotic potential: three related yet inequivalent properties of the exact density functional

2020 ◽  
Vol 22 (29) ◽  
pp. 16467-16481 ◽  
Author(s):  
Leeor Kronik ◽  
Stephan Kümmel
Keyword(s):  
Density Functional ◽  
Energy Functional ◽  
Piecewise Linearity ◽  
Exact Density ◽  
Exact Energy ◽  
Asymptotic Potential

Three properties of the exact energy functional of DFT are important in general and for spectroscopy in particular, but are not necessarily obeyed by approximate functionals. We explain what they are, why they are important, and how they are related yet inequivalent.

scholarly journals Multi-State Density Functional Theory for Ground and Excited States

2021 ◽  
Author(s):  
Yangyi Lu ◽  
Jiali Gao
Keyword(s):  
Density Functional Theory ◽  
Excited States ◽  
Ground State ◽  
Density Functional ◽  
Energy Functional ◽  
State Density ◽  
Hamiltonian Matrix ◽  
Functional Theory ◽  
Practical Applications ◽  
Exact Density

We report a rigorous formulation of multi-state density functional theory (MSDFT) that extends the Kohn-Sham (KS) energy functional for the ground state to a Hamiltonian matrix functional H[D] of the density matrix D in the space spanned by the lowest N adiabatic states. We establish a variational principle of MSDFT, which guarantees that the variational optimization results in a Hamiltonian matrix, whose eigenvalues are the lowest N eigen-energies of the system. We present an explicit expression of H[D] and introduce the correlation matrix functional. Akin to KS-DFT for the ground state, a universal multi-state correlation potential is derived for a two-state system as an illustrative example. This work shows that MSDFT is an exact density functional theory that treats the ground and excited states on an equal footing and provides a framework for practical applications and future developments of approximate functionals for excited states.

scholarly journals Real-time ab initio simulation of inelastic electron scattering using the exact, density functional, and alternative approaches

2020 ◽  
Vol 22 (16) ◽  
pp. 8616-8624
Author(s):  
Yeonghun Lee ◽  
Xiaolong Yao ◽  
Massimo V. Fischetti ◽  
Kyeongjae Cho
Keyword(s):  
Electron Scattering ◽  
Density Functional ◽  
Inelastic Electron ◽  
Electron Radiation ◽  
Ab Initio Simulation ◽  
Inelastic Electron Scattering ◽  
Electron Therapy ◽  
Exact Density ◽  
Alternative Approaches ◽  
Physical Materials

Inelastic electron scattering phenomena in chemical/physical/materials interests: electron radiation damage in materials; DNA damaged by electron scattering; electron therapy; electron microscope; electron-beam-induced deposition for nanofabrication.

CONSTRAINING SYMMETRY RESTORATION WITHIN THE NUCLEAR ENERGY DENSITY FUNCTIONAL METHOD

2010 ◽  
Vol 25 (21n23) ◽  
pp. 2016-2017
Author(s):  
J. SADOUDI ◽  
T. DUGUET
Keyword(s):  
Wave Function ◽  
Energy Density ◽  
Density Functional ◽  
Nuclear Energy ◽  
Density Functional Method ◽  
Energy Functional ◽  
Functional Method ◽  
Energy Density Functional ◽  
Density Functional Methods ◽  
Functional Methods

We review the notion of symmetry breaking and restoration within the frame of nuclear energy density functional methods. We focus on key differences between wave-function- and energy-functional-based methods. In particular, we point to difficulties to formulate the restoration of symmetries within the energy functional framework.

Density-Functional Thermodynamic Perturbation Theory of Lennard-Jones Solids

1992 ◽  
Vol 278 ◽  
Author(s):  
Agathagelos Kyrlidis ◽  
Robert A. Brown
Keyword(s):  
Density Functional ◽  
Interatomic Potential ◽  
Structural Information ◽  
Hard Spheres ◽  
Energy Functional ◽  
Thermodynamic Perturbation Theory ◽  
Lennard Jones ◽  
Dependent Potential ◽  
Solid Liquid ◽  
Thermodynamic Perturbation

AbstractThe thermodynamics of a fcc hard spheres solid is accurately described by recent density-functional approximations. This state is used as a reference in a thermodynamic perturbation analysis for a density-functional theory of Lennard-Jones solids. The free energy functional incorporates liquid state structural information and a density dependent potential decomposition for the Lennard-Jones interatomic potential. The computed free energies of the solids compare very well with the predictions of atonlistic simulations. Solid-liquid coexistence is predicted consistently to within 15% of results of Monte Carlo simulations, over the temperature range 0.75 ≤ kT/c ε ≤ 10.

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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