A quantum hindsight on density functional theory for computation of materials properties
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roduction For 55 years, density functional theory (DFT), founded by the fundamental Hohenberg–Kohn (HK) theorem1 and the practical Kohn–Sham (KS) equation,2 has flourished, due to advances in computation methods and applications to materials properties. Advances in computation have been fueled by tremendous innovations in formulating the exchange and correlation functional potentials in the KS equation empirically for large classes of systems and open computation program apps in the free spirit of the internet in its pioneering days. Further development of the theory and applications does not seem to be flattening. In the early 1960s, single-electron-band structure computations had become reliable3 and the interacting electron gas treated by field-theoretic methods went beyond the Hartree– Fock approximation to include correlation effects by, for example, the random phase approximation4 or the ring diagrams.5 There was the dichotomy of the former looking for a reliable effective potential for the single electron and the latter being limited to the jellium (a uniform background of positive charges) extended somewhat to simple metals. DFT then built a bridge to bring the exchange and correlation effects to the band calculation.
The DFT field has become too vast to review in a single article. I will use a thread of what I have been involved in to examine the field from a quantum perspective. This spans from the old quantum criterion of state coherence to the quantum information era requirement of entanglement. The former drives, for example, density oscillations due to an impurity in a metal or the electron density shell structure in atoms, while the latter is concerned with what phenomena entanglement can drive. We examine how DFT elucidates such quantum phenomena in various systems.
Hohenberg–Kohn theorem and the state topography The HK theorem1 forms the foundation of DFT. It allows the ground-state energy of a many-electron state to be determined by the knowledge of the electron-density distribution as a function of electron position instead of its potential. The use of the variational principle of the ground-state energy as a function of the density allows it to be determined for a given single-electron potential. This work reaches the pinnacle of the improvement of the Thomas–Fermi theory. The important point is the introduction of the Legendre transformation from the potential v(r) to the density n(r). The
Lu J. Sham, University of California, San Diego, USA; [email protected] doi:10.1557/mrs.2020.192 • VOLUME © 2020 Materials Research Society Carleton University Library, on 26 Aug 2020 at 15:52:20, subject to the MRS BULLETINCore AUGUST 2020at• Downloaded from https://www.cambridge.org/core. Cambridge terms45 of •use, available https://www.cambridge.org/core/terms. https://doi.org/10.1557/mrs.2020.192
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A quantum hindsight on density functional theory for computation of materials properties
transformation has the convenience for computation that can be extended to other duality
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