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Advanced Topics of Current Special Interest

Units arranged · Graduate

Advanced topics of current special interest.

Fall 2008 · Small-Molecule Spectroscopy and Dynamics

Topics

  • General information
  • Matrices are useful in spectroscopic theory
  • 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
  • Coupled harmonic oscillators: truncation of an infinite matrix
  • Matrix solution of harmonic oscillator problem, derivation of heisenberg equation of motion, matrix elements of any function of X and P
  • Building an effective hamiltonian
  • Anharmonic oscillator, vibration-rotation interaction, energy levels of a vibrating rotor
  • Atoms: 1e- and alkali
  • Alkali and many e- atomic spectra
  • Many e- atoms
  • How to assign an atomic spectrum
  • The Born-Oppenheimer approximation
  • Excerpts from the spectra and dynamics of diatomic molecules
  • The Born-Oppenheimer approach to transitions
  • The Born-Oppenheimer approach to transitions II
  • Pictures of spectra and notation
  • Rotational assignment of diatomic electronic spectra I
  • Laser schemes for rotational assignment first lines for Ω’, Ω" assignments
  • Rotation and angular momenta
  • 2 ∏ and 2 ∑ matrices
  • Parity and e/f basis for 2 ∏, 2 ∑ ±
  • Hund’s cases: 2 ∏, 2 ∑ ± examples
  • Energy level structure of 2 ∏ and 2 ∑ states, matrix elements for 2 ∏ and 2 ∑ including ∏ ~ ∑ perturbation, parity
  • Perturbations
  • A model for the perturbations and fine structure of the ∏ states of CO, factorization of perturbation parameters, the electronic perturbation parameters
  • Second-order effects
  • Second-order effects: centrifugal distortion and Λ-doubling
  • Transformations between basis sets: 3-j, 6-j, and Wigner-Eckart theorem
  • Construction of potential curves by the Rydberg-Klein-Rees method (RKR)
  • Rotation of polyatomic molecules I
  • Energy levels of a rigid rotor, energy levels of an asymmetric rotor
  • Asymmetric top
  • Pure rotation spectra of polyatomic molecules
  • Energy levels of a rigid rotor
  • Polyatomic vibrations: normal mode calculations
  • Polyatomic vibrations II: s-vectors, G-matrix, and Eckart condition
  • Polyatomic vibrations III: s-vectors and H 2 O
  • Polyatomic vibrations IV: symmetry
  • A sprint through group theory
  • What is in a character table and how do we use it?
  • Electronic spectra of polyatomic molecules
  • Vibronic coupling
  • Time-independent Schrodinger equation for a molecular system
  • Wavepacket dynamics
  • Wavepacket dynamics II
  • Wavepacket dynamics III

Readings

  • Bernath, P. F. Spectra of Atoms and Molecules . New York, NY: Oxford University Press, 1995. ISBN: 9780195075984.
    Listed reading
  • Wilson, E. B., J. C. Decius, and P. C. Cross. Molecular Vibrations . New York, NY: McGraw-Hill, 1955.
    Listed reading
  • The approach and specific material covered in Bernath’s “ Spectra of Atoms and Molecules ” will be quite different from the lectures.
    Listed reading

Prerequisites & course information

Prereq: None G (Fall, Spring) Units arranged

Sources