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Molecular Spectra and Molecular Structure

Spring 1996

Image from Lecture 8. Two Linked Multiplets. (Image by Prof. Robert Field.)

Course Description

The goal of this course is to illustrate how molecular structure is extracted from a spectrum. In order to achieve this goal it will be necessary to: master the language of spectroscopists; develop facility with quantum mechanical models; predict the relative intensities and selection rules; and learn how to assign spectra.



The goal of this course is to illustrate how molecular structure is extracted from a spectrum. In order to achieve this goal it will be necessary to:

  1. Master the language of spectroscopists - a bewildering array of apparently capricious notation;
  2. Develop facility with quantum mechanical models by which observed energy levels may be exactly matched by the eigenvalues of some effective Hamiltonian matrix which in turn is expressed in terms of a minimal number of adjustable parameters (molecular constants);
  3. Predict the relative intensities and selection rules governing transitions between eigenstates, since spectra display only transition frequencies and not energy eigenvalues;
  4. Learn how to assign spectra. It is not sufficient to know that there is a molecular eigenstate at a particular energy; it is necessary to know its quantum name as well. Spectral assignment is a topic which is neglected in all textbooks except those by Herzberg, yet it is the most important, difficult, and frequently performed task of a spectroscopist.

This will, in large part, be a course in applied, stationary state quantum mechanics. Aside from the last few lectures, the focus will be on energy levels, structure, and spectra rather than experimental techniques and apparatus.

Formal requirements include:

  1. Six problem sets, (33% of final grade);
  2. Two take home examinations, (67% of final grade);
  3. Reading assignments (listed as below):

Bernath, P. F. Spectra of Atoms and Molecules. New York, NY: Oxford University Press, 1995. ISBN: 9780195075984.

Hougen, J. T. "NBS Monograph 115." A version of "NBS Monograph 115" is available online through the National Institute of Standards and Technology.

Wilson, E. B., J. C. Decius, and P. C. Cross. Molecular Vibrations. New York, NY: McGraw-Hill, 1955.

In class handouts.

The approach and specific material covered in "Spectra of Atoms and Molecules" will be quite different from the lectures.


5.76 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 Coupled harmonic oscillators (part II) and atoms
3 (S) Anharmonic oscillator, vibration-rotation interaction, energy levels of a vibrating rotor
4 How do we get information about V(Q) from molecular constants?
4 (S) Construction of potential curves by the rydberg-klein-rees method
5 Atoms: 1e- and alkali
6 Alkali and many e- atomic spectra
7 Many e- atoms
8 How to assign an atomic spectrum
9 The Born-Oppenheimer approximation
9 (S) Excerpts from the spectra and dynamics of diatomic molecules
10 The Born-Oppenheimer approach to transitions
11 Transitions II
11 (S) Magnetic and electric effects, related papers
12 Pictures of spectra and notation
13 Rotational assignment of diatomic electronic spectra I
13 (S) Drexium monoxide
14 Laser schemes for rotational assignment first lines for ?', ?" assignments

Definition of angular momenta and | A α MA >Evaluation of

15 (S) Rotation and angular momenta
16 2∏ and 2∑ Matrices
17 Parity and e/f basis for 2∏, 2±
18 Hund's cases: 2∏, 2± Examples
18 (S) Energy level structure of 2∏ and 2∑ states, matrix elements for 2∏ and 2∑ including ∏ ~ ∑ perturbation, parity
19 Perturbations
19 (S) A model for the perturbations and fine structure of the ∏ states of CO, factorization of perturbation parameters, the electronic perturbation parameters
20 Second-order effects
20 (S) Second-order effects: Centrifugal distortion and Λ-doubling
21 Rotation of polyatomic molecules I
21 (S) Coefficients for energy levels of a slightly asymmetric top, energy levels of a rigid rotor, transition strengths for rotational transitions
22 Asymmetric top
23 Pure rotation spectra of polyatomic molecules
23 (S) Energy levels of a rigid rotor, energy levels of an asymmetric rotor
24 Polyatomic vibrations: Normal mode calculations
25 Polyatomic vibrations II: s-Vectors, G-matrix, and Eckart condition
26 Polyatomic vibrations III: s-vectors and H2O
27 Polyatomic vibrations IV: Symmetry
28 Normal↔local modes, High-overtone spectra
28 (S) Summaries of articles by K. Lehmann, B. C. Smith, J. S. Winn, K. Lehmann, W. Klemperer, and M. S. Child and R. T. Lawton
29 A Sprint through group theory
30 What is in a character table and how do we use it?
30 (S) Symmetry operations
31 Electronic spectra of polyatomic molecules
31 (S) Excerpts of articles by K. Keith Innes, G. W. King, C. K. Ingold, M. Bogey, H. Bolvin, C. Demuynck, and J. L. Destombes
32 The transition
33 Vibronic coupling
34 Wavepacket dynamics
34 (S) Abstract of article by M. Bixon and J. Jortner
35 Finish wavepacket dynamics
36 CNPI group theory
36 (S) C2H2 has many isomeric forms
37 Laser double resonance studies of electronic spectroscopy and vibrational state mixing in highly vibrationally excited C2H2
38 Laser double resonance studies of Ã1Au C2H2   Tell A Friend