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The systematic underestimation of band gaps is one of the most fundamental challenges in semilocal density functional theory (DFT). In addition to hindering the application of DFT to predicting electronic properties, the band gap problem is…

Density functional theory has become the world's favorite electronic structure method, and is routinely applied to both materials and molecules. Here, we review recent attempts to use modern machine-learning to improve density functional…

Meta-materials are an important emerging class of engineered materials in which complex macroscopic behaviour--whether electromagnetic, thermal, or mechanical--arises from modular substructure. Simulation and optimization of these materials…

One of the ultimate goals of computational modeling in condensed matter is to be able to accurately compute materials properties with minimal empirical information. First-principles approaches such as the density functional theory (DFT)…

Quantum computers open up new avenues for modelling the physical properties of materials and molecules. Density Functional Theory (DFT) is the gold standard classical algorithm for predicting these properties, but relies on approximations…

Density functional theory underlies the most successful and widely used numerical methods for electronic structure prediction of solids. However, it has the fundamental shortcoming that the universal density functional is unknown. In…

The marriage of density functional theory (DFT) and deep learning methods has the potential to revolutionize modern computational materials science. Here we develop a deep neural network approach to represent DFT Hamiltonian (DeepH) of…

Ab initio study of magnetic superstructures (e.g., magnetic skyrmion) is indispensable to the research of novel materials but bottlenecked by its formidable computational cost. For solving the bottleneck problem, we develop a deep…

A new electronic structure model is developed in which the ground state energy of a molecular system is given by a Hartree-Fock-like expression with parametrized one- and two-electron integrals over an extended (minimal + polarization) set…

Density Functional Theory (DFT) is widely used for atomistic simulations. However, its reach stays limited due to several limitations such as lack of accurate exchange-correlation functional, requirement of costly O(N 3) diagonalization…

The swift progression of machine learning (ML) has not gone unnoticed in the realm of statistical mechanics. ML techniques have attracted attention by the classical density-functional theory (DFT) community, as they enable discovery of…

The extension of the density functional theory (DFT) to include pairing correlations without formal violation of the particle-number conservation condition is described. This version of the theory can be considered as a foundation of the…

The electronic and magnetic properties of many strongly-correlated systems are controlled by a limited number of states, located near the Fermi level and well isolated from the rest of the spectrum. This opens a formal way for combining the…

Nuclear Density Functional Theory (DFT) plays a prominent role in the understanding of nuclear structure, being the approach with the widest range of applications. Hohenberg and Kohn theorems warrant the existence of a nuclear Energy…

We present an extension of reverse engineered Kohn-Sham potentials from a density matrix renormalization group calculation towards the construction of a density functional theory functional via deep learning. Instead of applying machine…

A hybrid Kohn-Sham Density Functional Theory (KS-DFT) and 1-electron Reduced Density Matrix Functional Theory (1-RDMFT) has recently been developed to describe strongly correlated systems at mean-field computational cost. This approach…

Accelerated discovery with machine learning (ML) has begun to provide the advances in efficiency needed to overcome the combinatorial challenge of computational materials design. Nevertheless, ML-accelerated discovery both inherits the…

Density functional theory (DFT) can run into serious difficulties with localized states in elements such as transition metals with occupied-d states and oxygen. In contrast, Hartree-Fock (HF) method can be a better approach for such…

A mathematical framework for reduced density matrix functional theory (RDMFT) is proposed. The work is inspired by and generalizes the work by E.H.~Lieb [E.H. Lieb, Int. J. Quant. Chem. 24(1983), pp.243--277] on density-functional theory…

Understanding the properties of warm dense hydrogen is of key importance for the modeling of compact astrophysical objects and to understand and further optimize inertial confinement fusion (ICF) applications. The work horse of warm dense…