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1. The Lieb-Oxford Lower Bounds on the Coulomb Energy, Their Importance to Electron Density Functional Theory, and a Conjectured Tight Bound on Exchange

   John P. Perdew; Jianwei Sun (July 2022, The Elliott Lieb Anniversary Volume)

   M. Lewin, Rupert L. (Ed.)

   Abstract: Lieb and Oxford (1981) derived rigorous lower bounds, in the form of local functionals of the electron density, on the indirect part of the Coulomb repulsion energy. The greatest lower bound for a given electron number N depends monotonically upon N, and the N→∞ limit is a bound for all N. These bounds have been shown to apply to the exact density functionals for the exchange- and exchange-correlation energies that must be approximated for an accurate and computationally efficient description of atoms, molecules, and solids. A tight bound on the exact exchange energy has been derived therefrom for two-electron ground states, and is conjectured to apply to all spin-unpolarized electronic ground states. Some of these and other exact constraints have been used to construct two generations of non-empirical density functionals beyond the local density approximation: the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), and the strongly constrained and appropriately normed (SCAN) meta-GGA. 

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2. Bicriteria Multidimensional Mechanism Design with Side Information

   Prasad, S; Balcan, N; Sandholm, T (December 2023, NeurIPS23)

   We develop a versatile new methodology for multidimensional mechanism design that incorporates side information about agent types to generate high social welfare and high revenue simultaneously. Prominent sources of side information in practice include predictions from a machine-learning model trained on historical agent data, advice from domain experts, and even the mechanism designer’s own gut instinct. In this paper we adopt a prior-free perspective that makes no assumptions on the correctness, accuracy, or source of the side information. First, we design a meta-mechanism that integrates input side information with an improvement of the classical VCG mechanism. The welfare, revenue, and incentive properties of our meta-mechanism are characterized by novel constructions we introduce based on the notion of a weakest competitor, which is an agent that has the smallest impact on welfare. We show that our meta-mechanism, when carefully instantiated, simultaneously achieves strong welfare and revenue guarantees parameterized by errors in the side information. When the side information is highly informative and accurate, our mechanism achieves welfare and revenue competitive with the total social surplus, and its performance decays continuously and gradually as the quality of the side information decreases. Finally, we apply our meta-mechanism to a setting where each agent’s type is determined by a constant number of parameters. Specifically, agent types lie on constant-dimensional subspaces (of the potentially high-dimensional ambient type space) that are known to the mechanism designer. We use our meta-mechanism to obtain the first known welfare and revenue guarantees in this setting. 

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3. Effects of Strong Electron Correlations and Van Der Waals Interactions in the Physical Properties of Bulk and 2d Fecl2

   López_Moreno, S; Tellez, A; Mejía_López, J; Hernández_Vázquez, EE; Romero, AH; Aguilera_del_Toro, RH (September 2024, SSRN)

   We conducted a first-principles study of FeCl2, focusing on the significance of strong electron correlations using the GGA+U approximation and van der Waals (vdW) interactions to enhance its physicochemical properties description. Our results provide an excellent characterization of both the bulk CdCl2-type structure and the 2D phase 1T crystal structure. We found that both phases were elastically and dynamically stable, showing good agreement with the experimental data from IR, Raman, inelastic neutron scattering, and magnetic measurements. The impact of the FeCl2 dimensionality is discussed in detail. Additionally, we investigated the less-explored distorted 1T phase (1T’), where structural distortions introduce anisotropies that notably affect its properties, particularly its semiconducting behavior. Moreover, our analysis of the magnon spectrum aligns with the recently characterized magnetic properties of the FM 1T phase. Simultaneously, magnetic anisotropy calculations revealed that the 1T’ configuration exhibits greater stability in the presence of an external magnetic field. 

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4. Discovering Superhard B-N-O Compounds by Iterative Machine Learning and Evolutionary Structure Predictions

   Chen, W. (November 2021, ArXivorg)

   We search for new superhard B-N-O compounds with an iterative machine learning (ML) procedure, where ML models are trained using sample crystal structures from evolutionary algorithm. We first use cohesive energy to evaluate the thermodynamic stability of varying BxNyOz compositions, and then gradually focus on compositional regions with high cohesive energy and high hardness. The results converge quickly after a few iterations. Our resulting ML models show that Bx+2NxO3 compounds with x≥3 (like B5N3O3, B6N4O3, etc.) are potentially superhard and thermodynamically favorable. Our meta-GGA density functional theory calculations indicate that these materials are also wide bandgap (≥4.4 eV) insulators, with the valence band maximum related to the p-orbitals of nitrogen atoms near vacant sites. This study demonstrates that an iterative method combining ML and ab initio simulations provides a powerful tool for discovering novel materials. 

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5. Improving the accuracy of solid-state nuclear magnetic resonance chemical shift prediction with a simple molecular correction

   https://doi.org/10.1039/C9CP01666J  

   Dracinsky, Martin; Unzueta, Pablo; Beran, Gregory J. (January 2019, Physical Chemistry Chemical Physics)

   A fast, straightforward method for computing NMR chemical shieldings of crystalline solids is proposed. The method combines the advantages of both conventional approaches: periodic calculations using plane-wave basis sets and molecular computational approaches. The periodic calculations capture the periodic nature of crystalline solids, but the computational level of the electronic structure calculation is limited to general-gradient-approximation (GGA) density functionals. It is demonstrated that a correction to the GGA result calculated on an isolated molecule at a higher level of theory significantly improves the correlations between experimental and calculated chemical shifts while adding almost no additional computational cost. Corrections calculated with a hybrid density functional improved the accuracy of 13C, 15N and 17O chemical shift predictions significantly and allowed identifying errors in previously published experimental data. Applications of the approach to crystalline isocytosine, methacrylamide, and testosterone are presented. 

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