- Principles of Chemistry I: Honors
Fall 2016, Unique 50015
Lecture Summary, 13 October 2016
Atoms: The Schrodinger equation cannot be solved
exactly for any atom with more than one electron. It can,
however, be approximated using several different techniques, and
it has been shown to produce accurate predictions of experimental
observations. We will therefore use the atomic orbitals that
we built up for our hydrogen atom for multi-electron systems. We
combined the Pauli exclusion principle and Hund's rule into the
Aufbau ("building up") rules.
Pauli Exclusion Principle: No two electrons in the same system (in this case a single atom) can share the same set of quantum numbers. Violations are NOT allowed.
Hund's Rule: When putting electrons into degenerate orbitals, put an electron into an empty degenerate orbital with the same spin as other degenerate orbitals until the degenerate set is half filled. Then beginning pairing electrons of opposite spin in the same orbital. Violations are allowed, but result in a higher energy (i.e. not the lowest energy or "ground") state.
Making Molecules: We are now going to use our atomic orbitals to form molecular orbitals, which will provide the mechanism of keeping stable electron density between two nuclei, which will in turn lower the potential energy of the system and form a molecular bond. The technique that we are going to use to do this is called "linear combination of atomic orbitals to molecular orbitals," LCAO-MO. Our coordinate system will be defined with the internuclear axis lying along the z-axis. From that simple definition, we spent a lot of time drawing the structure of s and p orbitals of same and opposite phase and figuring out what the resulting structure would look like. These are also drawn in your book, and you should spend some time getting comfortable with these images.
We also reviewed the naming convention for these orbitals. For each orbital, we need to ask 3 questions about the orbitals shape and phase:
1) Does the MO have cylindrical symmetry around the internuclear (z) axis?
2) Is the MO symmetric with respect to inversion?
yes: g (for "gerade" (even))
no: u (for "ungerade" (uneven))
3) Is there a nodal plane perpendicular to the internuclear (z) axis in the center of the molecule?