The authors demonstrate that the essential information about order in, and energy levels of physical systems is encapsulated in the second order reduced density matrix. They have discovered an algorithm to obtain a reasonable accurate expression for the 2-matrix of an N-particle state to make nearly all properties of matter which are of interest to chemists and physicists accessible.

The main subjects are:
- a comprehensive mathematical description of molecular systems,
- a new reaction path concept,
- an algorithm for following the reaction path.
The reaction path's tangent is determined by an excitation vector and the saddle points surrounding a minimizer can be localized without further information. A procedure appropriate to trace these reaction paths is presented.

The book contains the lectures given at the theoretical chemistry workshop in 1996 in Mariapfarr, Austria. At the first meeting Brian Sutcliffe discussed the connection of the concept of potential energy surfaces and the Born-Oppenheimer approximation, Alexander Sax gave an overview of the basic concepts and the mathematical apparatus of hypersurfaces, Ralph Jaquet discussed the fitting of calculated energy values in order to obtain analytical representations of potential energy surfaces, Philippe Hunenberger presented empirical force fields, and Markus Klein showed how the Born-Oppenheimer...