On this page
Draw the Lewis structure of O2 and every electron is paired. Yet oxygen is paramagnetic, which means it has unpaired electrons. The theory that fixes this contradiction is in Unit 4 of NCERT Class 11 Chemistry, and the person most associated with it is Robert Mulliken. This post covers who he was, where molecular orbitals came from, and how to use them in the bond order questions JEE and NEET ask every year.
Who was Robert Mulliken?
The Nobel Prize biography says Robert Sanderson Mulliken was born on 7 June 1896 in Newburyport, Massachusetts, the son of a professor of organic chemistry. He took a BSc at the Massachusetts Institute of Technology in 1917 and a PhD at the University of Chicago in 1921, and spent most of his career at Chicago, where he was Professor of Physics from 1931 and later of chemistry as well. He won the 1966 Nobel Prize in Chemistry "for his fundamental work concerning chemical bonds and the electronic structure of molecules by the molecular orbital method", according to the Nobel facts page. He died in 1986.
Where did molecular orbitals come from?
From spectra. In his Nobel lecture, Mulliken said "it was a study of molecular spectroscopy which pointed the way toward molecular orbitals". Early in his career he worked on the band spectra of diatomic molecules and then on a systematic theory of their electronic states. With quantum mechanics arriving around 1926, he and the German physicist Friedrich Hund, whom he first met in Göttingen in 1925, worked out how electrons could occupy orbitals spread over a whole molecule. Mulliken stressed that the method "has long been known as the Hund-Mulliken theory" in recognition of Hund's part.
He also explained the word itself. An orbital, he said, means "something as much like an orbit as is possible in quantum mechanics", and he borrowed John Van Vleck's phrase for a set of orbitals: "a housing arrangement for electrons". In the same lecture he noted that the name orbital was given "only later, in 1932". That year he published Electronic Structures of Polyatomic Molecules and Valence. II. in Physical Review, part of the series that built the method.
How do you get the bond order of O2?
The NCERT Class 11 chapter on chemical bonding gives this configuration for the 16 electrons of O2:
σ1s2 σ*1s2 σ2s2 σ*2s2 σ2pz2 π2px2 π2py2 π*2px1 π*2py1
Now count.
Bonding electrons (Nb): σ1s2, σ2s2, σ2pz2, π2px2, π2py2 = 10.
Antibonding electrons (Na): σ*1s2, σ*2s2, π*2px1, π*2py1 = 6.
Bond order = (Nb – Na) / 2 = (10 – 6) / 2 = 2.
Magnetism: the last two electrons go one each into the two π* orbitals, following Hund's rule, so O2 has two unpaired electrons and is paramagnetic. NCERT notes that this prediction "corresponds to experimental observation".
The same method handles the oxygen ions. Remove one π* electron to get O2+: bond order (10 – 5) / 2 = 2.5. Add one to get O2–: (10 – 7) / 2 = 1.5. Add two for O2 2–: (10 – 8) / 2 = 1, which matches NCERT's statement that F2 and O2 2– have bond order 1. Higher bond order means a shorter, stronger bond, so bond length increases in the order O2+ < O2 < O2– < O2 2–.
What mistakes do students make with MO diagrams?
**Pairing up the π* electrons.** Hund's rule puts them in separate orbitals first. Pair them and you will wrongly call O2 diamagnetic.
Using the oxygen ordering for N2. For B2, C2 and N2, the π2p orbitals lie below σ2pz. Learn both orderings and when each applies.
Miscounting electrons in ions. Add electrons for negative charge and remove them for positive charge before filling.
Our post on molecular orbital theory has more worked diagrams.
What else did Mulliken contribute?
His Nobel biography lists work on electronegativities, dipole moments and "the quantum-mechanical statement of the concept of hyperconjugation", the same hyperconjugation you meet in Class 11 organic chemistry. In 1934 he published A New Electroaffinity Scale, an electronegativity scale built from ionisation energies and electron affinities.
He also saw where chemistry was heading. In his lecture he described a calculation on the nitrogen molecule by C. W. Scherr, a PhD student at Chicago, that took two years on desk computers; by 1966 the largest computers could repeat it "in about two minutes". He closed by saying that "the era of computing chemists, when hundreds if not thousands of chemists will go to the computing machine instead of the laboratory" for many kinds of chemical information was "already at hand".
What can a student take from Mulliken's way of working?
Start from data. His theory grew out of years of reading spectra. When a rule confuses you, look at the experimental fact it explains.
Give credit. He insisted on the name Hund-Mulliken. Knowing who contributed what helps you remember ideas as a story.
Use more than one model. Lewis structures, VSEPR and MO theory each answer different questions. Pick the one that fits.
If bonding theories still feel like separate islands, the Fermi Concept Library covers every concept in chemistry, physics, biology, mathematics and computing, so you can see how valence bond and molecular orbital ideas connect.
Tonight, fill the MO diagram for N2, N2+ and O2 from memory, calculate each bond order, and say which are paramagnetic.
