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This chapter starts with a summary of the atomistic processes that occur during epitaxy. We then introduce density functional theory (DFT) and describe its implementation into state-of-the-art computations of complex processes in condensed…

Despite the wide availability of density functional theory (DFT) codes, their adoption by the broader materials science community remains limited due to challenges such as software installation, input preparation, high-performance computing…

Diffusion transformers (DiTs) combine transformer architectures with diffusion models. However, their computational complexity imposes significant limitations on real-time applications and sustainability of AI systems. In this study, we aim…

Progress towards the energy breakthroughs needed to combat climate change can be significantly accelerated through the efficient simulation of atomic systems. Simulation techniques based on first principles, such as Density Functional…

Density functional theory (DFT) exploits an independent-particle-system construction to replicate the densities and current of an interacting system. This construction is used here to access the exact effective potential and bias of…

One of the most promising techniques used for studying the electronic properties of materials is based on Density Functional Theory (DFT) approach and its extensions. DFT has been widely applied in traditional solid state physics problems…

Modern applications of Covariant Density Functional Theory (CDFT) are discussed. First we show a systematic investigation of fission barriers in actinide nuclei within constraint relativistic mean field theory allowing for triaxial…

Nowdays, modern microscopic approaches for fission are generally based on the framework of nuclear density functional theory (DFT), which has enabled a self-consistent treatment of both static and dynamic aspects of fission. The key issue…

We report on the GPU port of the Abinit high-performance simulation code for plane-wave DFT calculations. Large-scale electronic structure calculations require computing the electronic wave function by solving the Kohn-Sham equations…

The nonuniform fast Fourier transform (NUFFT) enables spectral methods for problems with irregularly spaced samples, with applications in medical imaging, molecular dynamics, and kinetic plasma simulations. Existing implementations are…

A novel addition to the family of integral transforms, the quadratic phase Fourier transform (QPFT) embodies a variety of signal processing tools, including the Fourier transform (FT), fractional Fourier transform (FRFT), linear canonical…

Interoperability and cross-validation remains a significant challenge in the computational materials discovery community. In this context, we introduce a common input/output standard designed for internal translation by various workflow…

We present an efficient and systematically convergent approach to all-electron real-time time-dependent density functional theory (TDDFT) calculations using a mixed basis, termed as enriched finite element (EFE) basis. The EFE basis…

We present a new library for parallel distributed Fast Fourier Transforms (FFT). The importance of FFT in science and engineering and the advances in high performance computing necessitate further improvements. AccFFT extends existing FFT…

Density functional theory (DFT), one of the most widely utilized methods available to computational chemistry, fails to describe systems with statically correlated electrons. To address this shortcoming, in previous work we transformed DFT…

Recently, large language models (LLMs) have shown surprising performance in task-specific workloads as well as general tasks with the given prompts. However, to achieve unprecedented performance, recent LLMs use billions to trillions of…

Density functional theory (DFT) provides a theoretical framework for efficient and fairly accurate calculations of the electronic structure of molecules and crystals. The main features of density functional theory are described and DFT…

The Fast Fourier Transform (FFT) is a fundamental numerical technique with widespread application in a range of scientific problems. As scientific simulations attempt to exploit exascale systems, there has been a growing demand for…

For studying the group theoretical classification of the solutions of the density functional theory in relativistic framework, we propose quantum electrodynamical density-matrix functional theory (QED-DMFT). QED-DMFT gives the energy as a…

With the advent of new synthesis and large-scale production technologies, nanostructured gas-adsorbent materials (GAM) like carbon nanocomposites and metal-organic frameworks are becoming increasingly more influential in our everyday lives.…