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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…
Deep learning methods for electronic-structure Hamiltonian prediction has offered significant computational efficiency advantages over traditional DFT methods, yet the diversity of atomic types, structural patterns, and the high-dimensional…
Density functional theory (DFT) serves as the basis for computational discovery in materials science and chemistry, yet each calculation demands extensive human effort: adjusting algorithms when convergence stalls, revising plans when…
We propose a framework to learn the time-dependent Hartree-Fock (TDHF) inter-electronic potential of a molecule from its electron density dynamics. Though the entire TDHF Hamiltonian, including the inter-electronic potential, can be…
Density Functional Theory (DFT) stands as a widely used and efficient approach for addressing the many-electron Schr\"odinger equation across various domains such as physics, chemistry, and biology. However, a core challenge that persists…
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 theorems of density functional theory (DFT) and reduced density matrix functional theory (RDMFT) establish a bijective map between the external potential of a many-body system and its electron density or one-particle reduced density…
In the near future, material and drug design may be aided by quantum computer assisted simulations. These have the potential to target chemical systems intractable by the most powerful classical computers. However, the resources offered by…
In order to obtain a reasonably accurate and easily implemented approach to many-electron calculations, we will develop a new Density Functional Theory (DFT). Specifically, we derive an approximation to electron density, the first term of…
We survey approaches to nonrelativistic density functional theory (DFT) for nuclei using progress toward ab initio DFT for Coulomb systems as a guide. Ab initio DFT starts with a microscopic Hamiltonian and is naturally formulated using…
Density-corrected density functional theory (DC-DFT) is enjoying substantial success in improving semilocal DFT calculations in a wide variety of chemical problems. This paper provides the formal theoretical framework and assumptions for…
High-entropy materials (HEMs) have recently emerged as a significant category of materials, offering highly tunable properties. However, the scarcity of HEM data in existing density functional theory (DFT) databases, primarily due to…
Predicting interfacial thermodynamics across molecular and continuum scales remains a central challenge in computational science. Classical density functional theory (cDFT) provides a first-principles route to connect microscopic…
Density Functional Theory calculations traditionally suffer from an inherent cubic scaling with respect to the size of the system, making big calculations extremely expensive. This cubic scaling can be avoided by the use of so-called linear…
Melting is a high temperature process that requires extensive sampling of configuration space, thus making melting temperature prediction computationally very expensive and challenging. Over the past few years, I have built two methods to…
In this paper we consider Sparse Fourier Transform (SFT) algorithms for approximately computing the best $s$-term approximation of the Discrete Fourier Transform (DFT) $\mathbf{\hat{f}} \in \mathbb{C}^N$ of any given input vector…
Imaginary-time time-dependent Density functional theory (it-TDDFT) has been proposed as an alternative method for obtaining the ground state within density functional theory (DFT) which avoids some of the difficulties with convergence…
Over this past decade, we combined the idea of stochastic resolution of identity with a variety of electronic structure methods. In our stochastic Kohn-Sham DFT method, the density is an average over multiple stochastic samples, with…
A formulation of the density functional theory is constructed on the foundations of entropic inference. The theory is introduced as an application of maximum entropy for inhomogeneous fluids in thermal equilibrium. It is shown that entropic…
Most of the FFT methods available for homogenization of the mechanical response use the strain/deformation gradient as unknown, imposing their compatibility using Green's functions or projection operators. This implies the allocation of…