Atomic and Molecular Complexities: Their Physical and Chemical Interpretations -- Uncertainty relations related to the Renyi entropy -- Entropy and complexity analyses of D-dimensional quantum systems -- Analyzing the atomic shape function with information theory and complexity measures -- Statistical indicators of complexity and its applications -- Renyi and Fisher information as complexity measures -- Statistical complexity in quantum many-body systems -- Structural entropy and its applications.

“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.