How is the derivative discontinuity related to steps in the exact Kohn-Sham potential?

Abstract

The reliability of density-functional calculations hinges on accurately approximating the unknown exchange-correlation (xc) potential. Common (semi-)local xc approximations lack the jump experienced by the exact xc potential as the number of electrons infinitesimally surpasses an integer, and the spatial steps that form in the potential as a result of the change in the decay rate of the density. These features are important for an accurate prediction of the fundamental gap and the distribution of charge in complex systems. Although well-known concepts, the exact relationship between them remained unclear. In this Letter, we establish the common fundamental origin of these two features of the exact xc potential via an analytical derivation. We support our result with an exact numerical solution of the many-electron Schroedinger equation for a single atom and a diatomic molecule in one dimension. Furthermore, we propose a way to extract the fundamental gap from the step structures in the potential.

6 pages, 3 figures, supplementary material included

References in corpus (36)

• Restoring the density-gradient expansion for exchange in solids and surfaces
• Generalized gradient approximation for solids and their surfaces
• Perspective on density functional theory
• Localization and delocalization errors in density functional theory and implications for band-gap prediction
• Consistent set of band parameters for the group-III nitrides AlN, GaN, and InN
• Self-interaction errors in density functional calculations of electronic transport
• Kohn-Sham potential with discontinuity for band gap materials
• Combining GW calculations with exact-exchange density-functional theory: An analysis of valence-band photoemission for compound semiconductors
• The discontinuous nature of the exchange-correlation functional -- critical for strongly correlated systems
• Zero-bias molecular electronics: Exchange-correlation corrections to Landauer's formula
• Undoing static correlation: Long-range charge transfer in time-dependent density functional theory
• Piecewise Linearity of Approximate Density Functionals Revisited: Implications for Frontier Orbital Energies
• Exchange and Correlation in Open Systems of Fluctuating Electron Number
• The derivative discontinuity of the exchange-correlation functional
• The Role of the Exchange-Correlation Potential in ab initio Electron Transport Calculations
• ORBKIT - A Modular Python Toolbox for Cross-Platform Post-Processing of Quantum Chemical Wavefunction Data
• Fundamental gaps with approximate density functionals: the derivative discontinuity revealed from ensemble considerations
• Improved Semiconductor Lattice Parameters and Band Gaps from a Middle-Range Screened Hybrid Functional
• Exact Kohn-Sham potential of strongly correlated finite systems
• Discontinuities of the exchange-correlation kernel and charge-transfer excitations in time-dependent density functional theory
• Exact and approximate Kohn-Sham potentials in ensemble density-functional theory
• Exact-exchange density-functional calculations for noble-gas solids
• Kohn-Sham potentials in exact density-functional theory at non-integer electron numbers
• Restoration of the Derivative Discontinuity in Kohn-Sham Density Functional Theory: An Efficient Scheme for Energy Gap Correction
• Exact time-dependent density-functional potentials for strongly correlated tunneling electrons
• Origin of static and dynamic steps in exact Kohn-Sham potentials
• Study of the discontinuity of the exchange-correlation potential in an exactly soluble case
• A new generalized Kohn-Sham method for fundamental band-gaps in solids
• Charge-transfer in time-dependent density-functional theory via spin-symmetry-breaking
• Elimination of the asymptotic fractional dissociation problem in Kohn-Sham density functional theory using the ensemble-generalization approach
• Electric control of a $\{F{e}_4\}$ single-molecule magnet in a single-electron transistor
• Fragment-based Treatment of Delocalization and Static Correlation Errors in Density-Functional Theory
• Kohn-Sham potential for a strongly correlated finite system with fractional occupancy
• Effect of ensemble generalization on the highest-occupied Kohn-Sham eigenvalue
• The role of electron localization in density functionals
• Integer Discontinuity of Density Functional Theory

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