5.80 | Fall 2008 | Graduate

Small-Molecule Spectroscopy and Dynamics


5.80 includes supplemental lectures as indicated by the (S) symbol.

0 General information
1 Matrices are useful in spectroscopic theory
1 (S) Spectroscopic notation, good quantum numbers, perturbation theory and secular equations, non-orthonormal basis sets, transformation of matrix elements of any operator into perturbed basis set
2 Coupled harmonic oscillators: truncation of an infinite matrix
2 (S) Matrix solution of harmonic oscillator problem, derivation of heisenberg equation of motion, matrix elements of any function of X and P
3 Building an effective hamiltonian
3 (S) Anharmonic oscillator, vibration-rotation interaction, energy levels of a vibrating rotor
4 Atoms: 1e- and alkali
5 Alkali and many e- atomic spectra
6 Many e- atoms
7 How to assign an atomic spectrum
8 The Born-Oppenheimer approximation
8 (S) Excerpts from the spectra and dynamics of diatomic molecules
9 The Born-Oppenheimer approach to transitions
10 The Born-Oppenheimer approach to transitions II
11 Pictures of spectra and notation
12 Rotational assignment of diatomic electronic spectra I
13 Laser schemes for rotational assignment first lines for Ω’, Ω" assignments

Definition of angular momenta and | A α MA >

Evaluation of ĤROT

14 (S) Rotation and angular momenta
15 2∏ and 2∑ matrices
16 Parity and e/f basis for 2∏, 2±
17 Hund’s cases: 2∏, 2± examples
17 (S) Energy level structure of 2∏ and 2∑ states, matrix elements for 2∏ and 2∑ including ∏ ~ ∑ perturbation, parity
18 Perturbations
18 (S) A model for the perturbations and fine structure of the ∏ states of CO, factorization of perturbation parameters, the electronic perturbation parameters
19 Second-order effects
19 (S) Second-order effects: centrifugal distortion and Λ-doubling
20 Transformations between basis sets: 3-j, 6-j, and Wigner-Eckart theorem
21 Construction of potential curves by the Rydberg-Klein-Rees method (RKR)
22 Rotation of polyatomic molecules I
22 (S) Energy levels of a rigid rotor, energy levels of an asymmetric rotor
23 Asymmetric top
23 (S) Energy levels of a rigid rotor, energy levels of an asymmetric rotor
24 Pure rotation spectra of polyatomic molecules
24 (S) Energy levels of a rigid rotor
25 Polyatomic vibrations: normal mode calculations
26 Polyatomic vibrations II: s-vectors, G-matrix, and Eckart condition
27 Polyatomic vibrations III: s-vectors and H2O
28 Polyatomic vibrations IV: symmetry
29 A sprint through group theory
30 What is in a character table and how do we use it?
31 Electronic spectra of polyatomic molecules




33 Vibronic coupling
33 (S) Time-independent Schrodinger equation for a molecular system
34 Wavepacket dynamics
35 Wavepacket dynamics II
36 Wavepacket dynamics III

Course Info

As Taught In
Fall 2008
Learning Resource Types
Problem Sets with Solutions
Lecture Notes
Lecture Videos