<P>This book provides a detailed description of the modern variational methods available for solving the nuclear motion Schr¿dinger equation to enable accurate theoretical spectroscopy of polyatomic molecules. These methods are currently used to provide important molecular data for spectroscopic studies of atmospheres of astronomical objects including solar and extrasolar planets as well as cool stars. This book has collected descriptions of quantum mechanical methods into one cohesive text, making the information more accessible to the scientific community, especially for young researchers, who would like to devote their scientific career to the field of computational molecular physics. </P><P></P><P>The book addresses key aspects of the high-accuracy computational spectroscopy of the medium size polyatomic molecules. It aims to describe numerical algorithms for the construction and solution of the nuclear motion Schr¿dinger equations with the central idea of the modern computational
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