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We present an exact decomposition of the complete wavefunction for a system of nuclei and electrons evolving in a time-dependent external potential. We derive formally exact equations for the nuclear and electronic wavefunctions that lead…

A covariant formalism is used in order to examine the status of Maxwell equations and to unify the concept of balances, for all chemical engineering applications in relation with electrodynamics. The resulting formal structure serves as a…

The finite basis optimized effective potential (OEP) method within density functional theory is examined as an ill-posed problem. It is shown that the generation of nonphysical potentials is a controllable manifestation of the use of…

The surface properties of solid-state materials often dictate their functionality, especially for applications where nanoscale effects become important. The relevant surface(s) and their properties are determined, in large part, by the…

The Spectral Neighbor Analysis Potential (SNAP) is a classical interatomic potential that expresses the energy of each atom as a linear function of selected bispectrum components of the neighbor atoms. An extension of the SNAP form is…

The dual continuum model serves as a powerful tool in the modeling of subsurface applications. It allows a systematic coupling of various components of the solutions. The system is of multiscale nature as it involves high heterogeneous and…

Leveraging ab initio data at scale has enabled the development of machine learning models capable of extremely accurate and fast molecular property prediction. A central paradigm of many previous works focuses on generating predictions for…

We present a method for combining proper orthogonal decomposition (POD) bases optimized with respect to different norms into a single complete basis. We produce a basis combining decompositions optimized with respect to turbulent kinetic…

We propose a computationally lean, two-stage approach that reliably predicts self-assembly behavior of complex charged molecules on a metallic surfaces under electrochemical conditions. Stage one uses ab initio simulations to provide…

The binding energy of an electron in a material is a fundamental characteristic, which determines a wealth of important chemical and physical properties. For metal-organic frameworks this quantity is hitherto unknown. We present a general…

Reduced basis approximations of Optimal Control Problems (OCPs) governed by steady partial differential equations (PDEs) with random parametric inputs are analyzed and constructed. Such approximations are based on a Reduced Order Model,…

Quadratic trapping potentials are widely used to experimentally probe biopolymers and molecular machines and drive transitions in steered molecular-dynamics simulations. Approximating energy landscapes as locally quadratic, we design…

Machine learning has become ubiquitous in materials modelling and now routinely enables large-scale atomistic simulations with quantum-mechanical accuracy. However, developing machine-learned interatomic potentials requires high-quality…

Fluid dynamics systems driven by dominant, nearly periodic large-scale dynamics are common across wakes, jets, rotating machinery, and high-speed flows. Traditional decomposition techniques such as proper orthogonal decomposition and…

The discovery and optimization of high-energy materials (HEMs) are constrained by the prohibitive computational expense and prolonged development cycles inherent in conventional approaches. In this work, we develop a general neural network…

This chapter concerns with the recent development of a new DFT methodology for accurate, reliable prediction of many-electron systems. Background, need for such a scheme, major difficulties encountered, as well as their potential remedies…

Choice of appropriate force field is one of the main concerns of any atomistic simulation that needs to be seriously considered in order to yield reliable results. Since, investigations on mechanical behavior of materials at micro/nanoscale…

The formal link between the linear combination of atomic orbitals approach to density functional theory and two-center Slater-Koster tight-binding models is used to derive an orthogonal $d$-band tight-binding model for iron with only two…

We present a physically motivated strategy for the construction of training sets for transferable machine learning interatomic potentials. It is based on a systematic exploration of all possible space groups in random crystal structures,…

We introduce, analyze, and implement a new method for parameter identification for system of ordinary differential equations that are used to model sets of biochemical reactions. Our method relies on the integral formulation of the ODE…