Statistical complexity : applications in electronic structure

“I think the next century will be the century of complexity” Prof. Stephen W. Hawking (DAMPT, University of Cambridge, UK), San Jose Mercury News, Morning Final Edition, January 23 (2000) Several different measures defining complexity have been recently proposed within the scientific disciplines of physics, biology, mathematics and computer science. Such measures of complexity are generally context dependent. In chemical physics, a set of statistical complexity measures have been introduced using the information theoretical tools centering around the electron probability density of an N-electron system and its additional characteristics. The current monograph presents a detailed description of such measures of complexity. Starting with the information theoretical foundations, this monograph discusses at length their applications in the electronic structure of atoms and molecules including reactivity. The subject matter of the title is covered by the leading research scientists in the field who present an up-to-date account of their contributions, including future projections. __Statistical Complexity: Applications in Electronic Structure__ is intended for practicing physical, theoretical and computational chemists, material scientists, bio physicists and mathematical physicists. "(BI think the next century will be the century of complexity" Prof. Stephen W. Hawking (DAMPT, University of Cambridge, UK), San Jose Mercury News, Morning Final Edition, January 23 (2000)Several different measures defining complexity have been recently proposed within the scientific disciplines of physics, biology, mathematics and computer science. Such measures of complexity are generally context dependent. In chemical physics, a set of statistical complexity measures have been introduced using the information theoretical tools centering around the electron probability density of an N-electron system and its additional characteristics. The current monograph presents a detailed description of such measures of complexity. Starting with the information theoretical foundations, this monograph discusses at length their applications in the electronic structure of atoms and molecules including reactivity. The subject matter of the title is covered by the leading research scientists in the field who present an up-to-date account of their contributions, including future projections. Statistical Complexity: Applications in Electronic Structure is intended for practicing physical, theoretical and computational chemists, material scientists, bio physicists and mathematical physicists Front Matter....Pages I-XVI Entropic Uncertainty Relations in Quantum Physics....Pages 1-34 Derivation of Generalized von Weizsäcker Kinetic Energies from Quasiprobability Distribution Functions....Pages 35-48 Atomic Statistical Complexity....Pages 49-64 Statistical Complexity and Fisher-Shannon Information: Applications....Pages 65-127 Entropy and Complexity Analyses of D -dimensional Quantum Systems....Pages 129-166 Atomic and Molecular Complexities: Their Physical and Chemical Interpretations....Pages 167-213 Rényi Entropy and Complexity....Pages 215-235 Scaling Properties of Net Information Measures for Bound States of Spherical Model Potentials....Pages 237-249 Chemical Information from Information Discrimination and Relative Complexity....Pages 251-291 Back Matter....Pages 293-297 The understanding of electron density as the carrier of all the information of a multielectronic system is implicit in the theorems of density functional theory. Information theoretical based measures giving a quantitative understanding of statistical complexity of such systems is shaping up as a new area of research in chemical physics. This book is the first monograph of its kind covering the aspects of complexity measure in atoms and molecules.