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Numerical methods for the inverse problem of density functional theory

Journal Article · · International Journal of Quantum Chemistry
DOI:https://doi.org/10.1002/qua.25425· OSTI ID:1421863
 [1];  [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Purdue Univ., West Lafayette, IN (United States)
+ Show Author Affiliations

Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one-dimensional finite and periodic model systems.

Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
NSF Funded from Graduate School; USDOE
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1421863
Report Number(s):
SAND-2017-7018J; 655000
Journal Information:
International Journal of Quantum Chemistry, Vol. 118, Issue 1; ISSN 0020-7608
Publisher:
WileyCopyright Statement
Country of Publication:
United States
Language:
English

References (42)

Libxc: A library of exchange and correlation functionals for density functional theory journal October 2012
PDE-constrained optimization with error estimation and control journal April 2014
Density-Based Partitioning Methods for Ground-State Molecular Calculations journal July 2014
Generation of finite difference formulas on arbitrarily spaced grids journal January 1988
The Morse oscillator in position space, momentum space, and phase space journal April 1988
Exchange-correlation potential with correct asymptotic behavior journal April 1994
Boundaryless beam propagation journal January 1996
ImprovedSCF convergence acceleration journal January 1982
Reference electronic structure calculations in one dimension journal January 2012
Determination of Kohn–Sham effective potentials from electron densities using the differential virial theorem journal October 2012
Variational finite-difference representation of the kinetic energy operator journal October 2001
Kohn-Sham calculations with the exact functional journal July 2014
Dual consistency and functional accuracy: a finite-difference perspective journal January 2014
octopus: a tool for the application of time-dependent density functional theory journal September 2006
Numerical Methods for Evaluating the Derivatives of Eigenvalues and Eigenvectors journal June 1975
DFT in a nutshell journal July 2012
An efficient method for finding the minimum of a function of several variables without calculating derivatives journal February 1964
Controlling the Dynamics of Many-Electron Systems from First Principles: A Combination of Optimal Control and Time-Dependent Density-Functional Theory journal October 2012
A direct optimization method for calculating density functionals and exchange–correlation potentials from electron densities journal January 2003
One-dimensional mimicking of electronic structure: The case for exponentials journal June 2015
Fragment-based treatment of delocalization and static correlation errors in density-functional theory journal December 2015
Electronic Structure book January 2004
A survey of the parallel performance and accuracy of Poisson solvers for electronic structure calculations journal November 2013
Newton-Type Minimization via the Lanczos Method journal August 1984
Demonstration of initial-state dependence in time-dependent density-functional theory journal March 2001
An Introduction to the Adjoint Approach to Design journal December 2000
Computational chemistry from the perspective of numerical analysis journal April 2005
Computational Methods for Inverse Problems book January 2002
Optimized effective potentials from electron densities in finite basis sets journal November 2007
Gradient Type Optimization Methods For Electronic Structure Calculations journal January 2014
Density functional approach to quantum lattice systems journal February 1985
Smoothing and Differentiation of Data by Simplified Least Squares Procedures. journal July 1964
Numerical density-to-potential inversions in time-dependent density functional theory journal January 2016
Analysis of Costate Discretizations in Parameter Estimation for Linear Evolution Equations journal January 1995
On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming journal April 2005
PDE-constrained optimization with error estimation and control conference November 2012
Electronic Structure book September 2020
A survey of the parallel performance and the accuracy of Poisson solvers for electronic structure calculations preprint January 2012
Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems text January 2015
One Dimensional Mimicking of Electronic Structure: The Case for Exponentials text January 2015
Real-Space Mesh Techniques in Density Functional Theory text January 2000
Variational finite-difference representation of the kinetic energy operator text January 2001

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Accurate embedding through potential reconstruction: A comparison of different strategies journal August 2018
Constructing a non-additive non-interacting kinetic energy functional approximation for covalent bonds from exact conditions journal October 2018
Adiabatic connection in density functional theory in two-dimensions: A semi-analytic wavefunction based study for two-electron atomic systems journal November 2019
Description of intermolecular charge transfer with subsystem density-functional theory journal October 2019
Universal nature of different methods of obtaining the exact Kohn–Sham exchange-correlation potential for a given density journal March 2019
Improvement of functionals in density functional theory by the inverse Kohn–Sham method and density functional perturbation theory journal November 2019
Exchange-correlation magnetic fields in spin-density-functional theory journal September 2019
First step in the nuclear inverse Kohn-Sham problem: From densities to potentials journal February 2020
Numerical construction of the density-potential mapping journal October 2018
Non-additive Non-interacting Kinetic Energy of Rare Gas Dimers text January 2017
Constructing a Non-additive Non-interacting Kinetic Energy Functional Approximation for Covalent Bonds from Exact Conditions text January 2018
Exchange-correlation magnetic fields in spin-density-functional theory text January 2019
Kinetic-Energy Density-Functional Theory on a Lattice journal June 2018
Self-Consistent Density-Functional Embedding: A Novel Approach for Density-Functional Approximations journal September 2019

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97 MATHEMATICS AND COMPUTING
density functional theory
inverse problems
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