Hund in 1926 speculated on the assignment of quantum numbers for the electronic states of diatomic molecules, basing his assignments on the correlation between the diatomic states and those of the united atom limit. Mulliken, who had earlier considered the problem of this assignment using old quantum theory, followed Hund in 1927, in the new quantum theory, correlating the states of a diatomic molecule from the united to the separated atoms. In 1932, he introduced the term orbital for the one-electron states of an atom or molecule. He was the first to seriously explore the orbitals of polyatomic molecules 1932. Burrau in 1927 made the first successful attempt to solve the Schrodinger's equation for H 2+, and Condon 1927 assigned two electrons to Burrau's orbital to obtain an estimate of the binding energy of H2. Lennard-Jones LJ 1929 introduced the linear combination of atomic orbital model, and following the aufbau principle showed that this explained the paramagnetism of O2. Slater 1929 wrote many-electron wave functions as determinants of spin-orbitals, and LJ 1949 showed that with this formulation molecular orbitals MOs could be transformed into bond-localized functions; this provided the link to the valence bond approach and the traditional view of the chemical bond. Huckel 1930 was the first to develop a semiempirical MO model for π-electron hydrocarbons, and this was later extended by others for all-electron wave functions. Boys 1950 saw the implication of Gaussian functions for calculating the electron repulsion integrals needed for ab initio calculations, and a later approach by Kohn and coworkers 1964 and 1965 produced a density functional MO theory in which electron repulsion is calculated from the whole electron density. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

The origins and later developments of molecular orbital theory - Murrell - 2012 - International Journal of Quantum Chemistry - Wiley Online Library