- The Debye-Hückel theory of electrolytic solutions
- The Hückel method of approximate molecular orbital (MO) calculations on pi electron systems.

On receiving his doctorate, he became an assistant at Göttingen, but soon became an assistant to Peter Debye at Zürich. It was there that he and Debye developed their theory (the *Debye-Hückel theory*, in 1923) of electrolytic solutions, elucidating the behavior of strong electrolytes to account for their conductivity by considering interionic forces.

In 1928 and 1929 he spent time in England and Denmark, working briefly with Niels Bohr. Then he became a faculty member at the Technische Hochschule in Stuttgart, serving until 1935, when he went to Phillips University in Marburg, where he remained until 1961.

Eventually his interests moved to the use of quantum mechanics to deal with organic molecules. In 1931 he formulated the "Hückel rule" for determining whether ring molecules would show aromatic properties, and in 1937 developed his approximate MO theory for unsaturated organic molecules. This is still used as an approximation, though the more precise Pariser-Parr-Pople method succeeded it after its publication separately by Pariser and Parr and by Pople in 1953, for more accurate calculations. An extension of the Hückel MO theory was also developed by Roald Hoffmann for nonplanar molecules in 1963.