1. Last hour: MO Theory
Uses linear combinations of atomic orbitals (LCAO) as linear variation functions. For a diatomic:
For H2+:
Coulomb integral
Resonance integral
Overlap integral
For multielectron molecules, we need to pay attention to spin, use Slater determinants
Electronic angular momentum: ℓj, L, J not conserved, but their z-projections are!  label MO’s by |mℓ| =  = 0,1,2,3,… (, , , , etc.)  g,u subscripts for even (“gerade”) and odd (“ungerade”) inversion symmetry  * or no *: antibonding or bonding Note that there are other notations as well!

2. McQuarrie & Simon “Physical Chemistry”

3. Angular momentum in multielectron molecules (I):
Classification of molecular states:
From
 = |ML|, the z-projection of is a good quantum number, states with  = 0, 1, 2, 3, ... are denoted , , , , etc.
S, the spin quantum number, is a good quantum number.
 = MS = -S,...,S: the z-projection of is a good quantum number.
 = |+|, the z-projection of is a good quantum number.
Symmetry properties:
“Symmetry” (reflection symmetry on a plane containing the nucleus): /- superscript
Parity (for molecules with inversion symmetry only) g/u subscript
Term symbols for molecules: 2S+1±g/u

4. Angular momentum in multielectron molecules (II):
In a non-rotating molecule, all terms with  > 0 are doubly degenerate. This is split in rotating molecules ( doubling)
Fine structure splitting: Vℓ,s = A··, resulting in 2S+1 terms, each doubly degenerate (for >0 in non-rotating molecules)
The ground state is denoted X.
Excited states with the same multiplicity as the ground state are denoted with capital letters A,B,C,D,... in order of their energy
Excited states that have a different multiplicity are denoted with lower-case letters (a,b,c,d,...) in order of their energy. Unfortunately, the literature is full of inconsistent orderings, since the identification of excited states for many molecules is “historically grown”
Polyatomic molecules often have a tilde above the term symbol to avoid confusion with group theory labels.
Term symbols can be determined using a microstate analysis, but recall that  = |ML| is used, not L
Note that  is used in a confusing manner: as the quantum number for the spin projection and as a designation for a =0 state