Download CHEM 5581: Graduate Level Quantum Chemistry

Last hour:
• Good angular momentum quantum numbers in linear molecules (e.g. diatomic):
|ML| = ;
S;
MS= ;
• Molecular terms constructed similar to atomic terms:
 = | + |
2S+1
additional information for symmetry (+/- superscript) and parity (only in
molecules with inversion symmetry, g/u subscript)
• MO diagrams  MO energies and occupation
– for homonuclear diatomic molecules: mix “like” AO’s to MO’s
– for heteronuclear diatomic molecules: mix AO’s close in energy
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
From W. Demtröder “Molecular Physics”
Learning Goals for Chapter 23 – MO Theory of diatomic molecules
After this chapter, the related homework problems, and reading the relevant parts
of the textbook, you should be able to:
•
explain the fundamental assumptions leading to MO theory;
•
construct MO diagrams and electron configurations for diatomic molecules;
•
construct molecular term symbols for a given electron configuration;
•
explain shortcomings of MO theory.
sp Hybrid Orbitals
sp hybrid orbital in BeH2
from McQuarrie & Simon “Physical Chemistry”
BeH2 MO diagram
from Demtröder “Molecular Physics”
AH2 molecules – linear vs. bent
from McQuarrie & Simon “Physical Chemistry”
AH2 MO diagram
from Demtröder “Molecular Physics”
AH2 molecules – Walsh diagram
from Demtröder “Molecular Physics”
Walsh diagrams
from Demtröder “Molecular Physics”