Dr. Hoffmann's research interests are in the electronic structure of stable and unstable molecules across the periodic table, and of transition states in reactions. He applies a variety of quantum chemical computational methods as well as qualitative arguments to problems of structure and reactivity of both organic and inorganic molecules of medium size and to extended systems in one-, two-, and three dimensions.

His first major contribution was the development of the extended Hückel method (in collaboration with the Lipscomb group), a molecular orbital scheme which allowed the calculation of the approximate electronic structure of molecules, and which gave reasonable predictions of molecular conformations and simple potential surfaces. These calculations were instrumental in a renaissance of interest in σ electrons and their properties.

Roald Hoffmann’s second major contribution was a two-pronged exploration of the electronic structure of transition states and intermediates in organic reactions. In a fruitful collaboration with R. B. Woodward of Harvard University, he applied simple but powerful arguments of symmetry and bonding to the analysis of concerted reactions. These considerations have been of remarkable predictive value and have stimulated much productive experimental work. In the second approach Dr. Hoffmann analyzed with the aid of various semiempirical methods the molecular orbitals of most types of reactive intermediates in organic chemistry — carbonium ions, diradicals, methylenes, benzynes, etc. Important concepts such as through-bond coupling, and hyperconjugative orbital interaction came out of this work, as well as the general concept of frontier orbital control.