Professor McBride uses this lecture to show that covalent bonding depends primarily on two factors: orbital overlap and energy-match. First he discusses how overlap depends on hybridization; then how bond strength depends on the number of shared electrons. In this way quantum mechanics shows that Coulomb's law answers Newton's query about what "makes the Particles of Bodies stick together by very strong Attractions." Energy mismatch between the constituent orbitals is shown to weaken the influence of their overlap.

This lecture begins by applying the united-atom "plum-pudding" view of molecular orbitals, introduced in the previous lecture, to more complex molecules. It then introduces the more utilitarian concept of localized pairwise bonding between atoms. Formulating an atom-pair molecular orbital as the sum of atomic orbitals creates an electron difference density through the cross product that enters upon squaring a sum. This "overlap" term is the key to bonding.

The lecture opens with tricks ("Z-effective" and "Self Consistent Field") that allow one to correct approximately for the error in using orbitals that is due to electron repulsion. This error is hidden by naming it "correlation energy." Professor McBride introduces molecules by modifying J.J. Thomson's Plum-Pudding model of the atom to rationalize the form of molecular orbitals. There is a close analogy in form between the molecular orbitals of CH4 and NH3 and the atomic orbitals of neon, which has the same number of protons and neutrons.

Midterm Exam covers the first quarter of the course.

In discussions of the Schrödinger equation thus far, the systems described were either one-dimensional or involved a single electron. After discussing how increased nuclear charge affects the energies of one-electron atoms and then discussing hybridization, this lecture finally addresses the simple fact that multi-electron systems cannot be properly described in terms of one-electron orbitals.

After showing how a double-minimum potential generates one-dimensional bonding, Professor McBride moves on to multi-dimensional wave functions. Solving Schrödinger's three-dimensional differential equation might have been daunting, but it was not, because the necessary formulas had been worked out more than a century earlier in connection with acoustics. Acoustical "Chladni" figures show how nodal patterns relate to frequencies. The analogy is pursued by studying the form of wave functions for "hydrogen-like" one-electron atoms.

Professor McBride expands on the recently introduced concept of the wave function by illustrating the relationship of the magnitude of the curvature of the wave function to the kinetic energy of the system, as well as the relationship of the square of the wave function to the electron probability density. The requirement that the wave function not diverge in areas of negative kinetic energy leads to only certain energies being allowed, a property which is explored for the harmonic oscillator, Morse potential, and the Columbic potential.

After pointing out several discrepancies between electron difference density results and Lewis bonding theory, the course proceeds to quantum mechanics in search of a fundamental understanding of chemical bonding. The wave function ψ, which beginning students find confusing, was equally confusing to the physicists who created quantum mechanics. The Schrödinger equation reckons kinetic energy through the shape of ψ. When ψ curves toward zero, kinetic energy is positive; but when it curves away, kinetic energy is negative!

Professor McBride uses a hexagonal "benzene" pattern and Franklin's X-ray pattern of DNA, to continue his discussion of X-ray crystallography by explaining how a diffraction pattern in "reciprocal space" relates to the distribution of electrons in molecules and to the repetition of molecules in a crystal lattice. He then uses electron difference density mapping to reveal bonds, and unshared electron pairs, and their shape, and to show that they are only one-twentieth as dense as would be expected for Lewis shared pairs.

Professor McBride introduces the theory behind light diffraction by charged particles and its application to the study of the electron distribution in molecules by x-ray diffraction. The roles of molecular pattern and crystal lattice repetition are illustrated by shining laser light through diffraction masks to generate patterns reminiscent of those encountered in X-ray studies of ordered solids.