Inhomogeneous Electron Gas

By A. Rajagopal, J. Callaway. 1973

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Neural Message Passing for Quantum Chemistry (2017, neutral): “…a hierarchy of approximations to quantum mechanics with varying tradeoffs of speed and accuracy, such as Density Functional Theory (DFT) with a variety of functionals (Becke, 1993; Hohenberg & Kohn, 1964), the GW approximation (Hedin, 1965), and Quantum Monte-Carlo (Ceperley & Alder, 1986).”
Theory-Guided Data Science: A New Paradigm for Scientific Discovery from Data (2016, methodology): “To address this, a new class of quantum chemical modeling approaches was developed by Hohenberg and Kohn in 1964 [57], which uses the electron density nðrÞ as”
Cormorant: Covariant Molecular Neural Networks (2019, background): “Even Density Functional Theory (DFT) [Hohenberg and Kohn, 1964], a widely used approximation to the equations of quantum mechanics, has trouble scaling to more than a few hundred atoms.”
Machine learning of molecular electronic properties in chemical compound space (2013, background): “nuclear charges Z I and positions RI ,9 and that are mapped to the corresponding total potential energy, H({Z I ,RI }) 9 7−→ E [11, 12].”
N-body Networks: a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentials (2018, background): “Even Density Functional Theory (DFT) (Hohenberg & Kohn, 1964), a widely used approximation in quantum chemistry, has trouble scaling to more than about a hundred atoms.”
Wavelet Scattering Regression of Quantum Chemical Energies (2016, background): “In the Kohn-Sham approach to density functional theory [29], the total energy of the system is expressed as such a functional of the charge density: Ehk(ρ) = T (ρ)︸︷︷︸ Kinetic energy − K∑ k=1 ∫ R3 zkρ(u) |u− rk| du︸︷︷︸ External energy (electron-nucleus) + 1 2 ∫ R3 ∫ R3 ρ(u)ρ(v) |u− v| du dv︸︷︷︸ ”
Phonons and Anomalous Thermal Expansion Behaviour in Crystalline Solids (2017, methodology): “Density functional theory is based on two pillars namely Hohenberg-Kohn theorem[158] and”
Optical excitations in electron microscopy (2009, background): “The inverse relation is less direct, although one can extend the equivalent of the Hohenberg and Kohn (1964) theorem to light, thus asserting that there is a univocal correspondence between dielectric functions and LDOS, with both quantities defined within a finite frequency range above ω = 0…”