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”