density functional theory modeling (9 résultats)

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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - Density functional theory (DFT) provides the most widely used models for simulating molecules and materials based on the fundamental laws of quantum mechanics. It plays a central role in a huge spectrum of applications in chemistry, physics, and materials science.Quantum mechanics describes a system of N interacting particles in the physical 3-dimensional space by a partial differential equation in 3N spatial variables. The standard numerical methods thus incur an exponential increase of computational effort with N, a phenomenon known as the curse of dimensionality; in practice these methods already fail beyond N=2.DFT overcomes this problem by1) reformulating the N-body problem involving functions of 3N variables in terms of the density, a function of 3 variables,2) approximating it by a pioneering hybrid approach which keeps important ab initio contributions and re-models the remainder in a data-driven way.This book intends to be an accessible, yet state-of-art text on DFT for graduate students and researchers in applied and computational mathematics, physics, chemistry, and materials science. It introduces and reviews the main models of DFT, covering their derivation and mathematical properties, numerical treatment, and applications.

Buch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - Density functional theory (DFT) provides the most widely used models for simulating molecules and materials based on the fundamental laws of quantum mechanics. It plays a central role in a huge spectrum of applications in chemistry, physics, and materials science.Quantum mechanics describes a system of N interacting particles in the physical 3-dimensional space by a partial differential equation in 3N spatial variables. The standard numerical methods thus incur an exponential increase of computational effort with N, a phenomenon known as the curse of dimensionality; in practice these methods already fail beyond N=2.DFT overcomes this problem by1) reformulating the N-body problem involving functions of 3N variables in terms of the density, a function of 3 variables,2) approximating it by a pioneering hybrid approach which keeps important ab initio contributions and re-models the remainder in a data-driven way.This book intends to be an accessible, yet state-of-art text on DFT for graduate students and researchers in applied and computational mathematics, physics, chemistry, and materials science. It introduces and reviews the main models of DFT, covering their derivation and mathematical properties, numerical treatment, and applications.

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Taschenbuch. Etat : Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Fullerenes, hollow carbon cages on the order of 1 nm in diameter, are future building blocks in many areas of applied and fundamental nanoscience. Fullerenes show potential for applications in nanotechnology due to the possibility of tuning their properties by doping and/or functionlization. In particular, the endohedral doping of the hollow carbon cage with metal atoms and clusters allows changing of the electronic and magnetic properties of the molecule without significant distortion of the geometry of the outer shell. Despite their outstanding applications in technology and in bio-medical sciences the limited availability of endohedral metallofullerenes has hindered studies that describe their electronic and structural properties, the knowledge of which are essential prerequisites for many nanotechnological applications. In this book, we present our results on the characterization (structural, electronic and vibrational) of cerium endohedral fullerenes and provide precious clues about the formation mechanism of these species at the nanoscale.

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