Predictive electronic and vibrational many-body methods for molecules and macromolecules

Chemical simulations with predictive accuracy are being realized by hierarchical many-body methods for treating electrons and vibrations. Ascending these hierarchies one can reach arbitrarily high accuracy and extract reliable chemical information without conducting an experiment. Some of our methodological developments intended to make such simulations possible or more widely applicable are reviewed, including (1) a computer-aided approach to developing converging many-body methods for electrons and its application to a novel class of complex electron-correlation methods, (2) an effort to reduce the errors arising from the expansion bases of electronic wave functions, (3) an extension of mathematical techniques established in electronic many-body methods to anharmonic molecular vibrations and vibrationally averaged quantities, and (4) two approaches to extending these systematic electronic and vibrational methods to large molecules and solids.