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Small-Molecule Spectroscopy and Dynamics

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  • Course Description

    The goal of this course is to illustrate the spectroscopy of small molecules in the gas phase: quantum mechanical effective Hamiltonian models for rotational, vibrational, and electronic structure; transition selection rules and relative intensities; diagnostic patterns and experimental methods for the assignment of non-textbook spectra; breakdown of the Born-Oppenheimer approximation (spectroscopic perturbations); the stationary phase approximation; nondegenerate and quasidegenerate perturbation theory (van Vleck transformation); qualitative molecular orbital theory (Walsh diagrams); the notation of atomic and molecular spectroscopy.

    About Prof. Robert Field

    Robert W. Field is the Haslam and Dewey Professor of Chemistry at the Massachusetts Institute of Technology, where he has been a professor since 1974. His AB degree is in chemistry from Amherst College, and his PhD is in chemistry from Harvard University, where he worked with Bill Klemperer. He was a postdoc with Herbert Broida at the University of California, Santa Barbara. He is a physical chemist, specializing in spectroscopy of small molecules in the gas phase. He performed the first microwave-optical and optical-optical double resonance experiments on small molecules, and invented the Stimulated Emission Pumping (SEP, or "PUMP and DUMP") spectroscopic method. He is also particularly known for studies of the molecules acetylene (C2H2) and calcium monofluoride (CaF).

    Note: Contents for this page are Licensed from http://ocw.mit.edu under the Creative Commons Attribution Share-Alike license.

    School
    Massachusetts Institute of Technology

    Course Code
    5.80

    Date Taught
    Fall 2008

    Level
    Graduate (First Year)
  • Course Meeting Times

    Lectures: 3 sessions / week, 1 hour / session

    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:

    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 that is neglected in all textbooks except those by Herzberg, yet it is the most important, difficulty, and frequently performed task of a spectroscopist.
    5. Experimental techniques will not be discussed, except in the most superficial, photons-as-bullets formalism.

    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. Occasional homework problems;
    2. Frequent end-of-lecture 5 minute quizzes;
    3. Some sort of group (2 or 3 students per group) project near the end of term;
    4. A brief oral final exam;
    5. Reading assignments (listed as below):

    Textbooks

    Amazon logo 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.

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

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


    SES # TOPICS
    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
    14

    Definition of angular momenta and | A α MA >

    Evaluation of

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


  • Lectures
    Small-Molecule Spectroscopy and Dynamics - Lecture 1 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 2 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 3 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 4 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 5 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 6 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 7 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 8 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 9 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 10 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 11 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 12 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 13 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 14 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 15 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 16 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 17 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 18 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 19 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 20 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 21 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 22 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 23 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 24 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 25 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 26 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 27 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 28 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 29 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 30 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 31 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 33 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 34 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 35 - Prof. Robert FieldView
    Small-Molecule Spectroscopy and Dynamics - Lecture 36 - Prof. Robert FieldView
  • DescriptionTypeLink
    Problem set 2 1996DownloadClick
    Problem set 1 1994DownloadClick
    Problem set 1 solution 1994DownloadClick
    Problem set 2 1994DownloadClick
    Problem set 2 solution 1994DownloadClick
    Problem set 3 1994DownloadClick
    Problem set 4 1994DownloadClick
    Problem set 4 1994DownloadClick
    Problem set 4 1991DownloadClick
    Problem set 1 1987DownloadClick
    Problem set 2 1987DownloadClick
    Problem set 3 1987DownloadClick
    Problem set 4 1987DownloadClick
    Problem set 2 1985DownloadClick
    Problem set 2 solution 1985DownloadClick
    Problem set 3 1985DownloadClick
    Problem set 4 1985DownloadClick
    Problem set 1 1982DownloadClick
    Problem set 3 1982DownloadClick
    Problem set 4 1982DownloadClick
    Problem set 4 1982DownloadClick
    Problem set 2 1980DownloadClick
  • DescriptionTypeLink
    Exam 1 1978DownloadClick
    Final exam 1978DownloadClick
    Exam 2 1977DownloadClick
    Exam 1 1976DownloadClick
    Exam 1 solution 1976DownloadClick
    final exam 1976DownloadClick
  • DescriptionTypeLink
    Lecture Note 0 - General InformationDownloadClick
    Lecture Note 1 - Matrices are useful in spectroscopic theoryDownloadClick
    Lecture Note 1 - Spectroscopic notation, good quantum numbers, perturbation theory and secular equations, non-orthonormal basis sets, transformation of matrix elements of any operator into perturbed basis setDownloadClick
    Lecture Note 2 - Coupled harmonic oscillators: truncation of an infinite matrixDownloadClick
    Lecture Note 2 - Matrix solution of harmonic oscillator problem, derivation of heisenberg equation of motion, matrix elements of any function of X and PDownloadClick
    Lecture Note 3 - Building an effective hamiltonianDownloadClick
    Lecture Note 3 - Anharmonic oscillator, vibration-rotation interaction, energy levels of a vibrating rotorDownloadClick
    Lecture Note 4 - Atoms: 1e- and alkaliDownloadClick
    Lecture Note 5 - Alkali and many e- atomic spectraDownloadClick
    Lecture Note 6 - Many e- atomsDownloadClick
    Lecture Note 7 - How to assign an atomic spectrumDownloadClick
    Lecture Note 8 - The Born-Oppenheimer approximationDownloadClick
    Lecture Note 8 - Excerpts from the spectra and dynamics of diatomic moleculesDownloadClick
    Lecture Note 9 - The Born-Oppenheimer approach to transitionsDownloadClick
    Lecture Note 10 - The Born-Oppenheimer approach to transitions IIDownloadClick
    Lecture Note 11 - Pictures of spectra and notationDownloadClick
    Lecture Note 12 - Rotational assignment of diatomic electronic spectra IDownloadClick
    Lecture Note 13 - Laser schemes for rotational assignment first lines for Ω', Ω" assignmentsDownloadClick
    Lecture Note 14 - Definition of angular momenta and | A α MA >DownloadClick
    Lecture Note 14 - Rotation and angular momentaDownloadClick
    Lecture Notes 15 - 2∏ and 2∑ matricesDownloadClick
    Lecture Note 16 - Parity and e/f basis for 2∏, 2∑±DownloadClick
    Lecture Note 17 - Energy level structure of 2∏ and 2∑ states, matrix elements for 2∏ and 2∑ including ∏ ~ ∑ perturbation, parityDownloadClick
    Lecture Note 18 - PerturbationsDownloadClick
    Lecture Note 18 - A model for the perturbations and fine structure of the ∏ states of CO, factorization of perturbation parameters, the electronic perturbation parametersDownloadClick
    Lecture Note 19 - Second-order effectsDownloadClick
    Lecture Note 19 - Second-order effects: centrifugal distortion and Λ-doublingDownloadClick
    Lecture Note 20 - Transformations between basis sets: 3-j, 6-j, and Wigner-Eckart theoremDownloadClick
    Lecture Note 21 - Construction of potential curves by the Rydberg-Klein-Rees method (RKR)DownloadClick
    Lecture Note 22 - Rotation of polyatomic molecules IDownloadClick
    Lecture Note 23 - Asymmetric topDownloadClick
    Lecture Note 24 - Pure rotation spectra of polyatomic moleculesDownloadClick
    Lecture Note 25 - Polyatomic vibrations: normal mode calculationsDownloadClick
    Lecture Note 26 - Polyatomic vibrations II: s-vectors, G-matrix, and Eckart conditionDownloadClick
    Lecture Note 26 - Polyatomic vibrations III: s-vectors and H2ODownloadClick
    Lecture Note 28 - Polyatomic vibrations IV: symmetryDownloadClick
    Lecture Note 29 - A sprint through group theoryDownloadClick
    Lecture Not 30 - What is in a character table and how do we use it?DownloadClick
    Lecture Note 31 - Electronic spectra of polyatomic moleculesDownloadClick
    Lecture Note 32 - The H2CO (A1A2 from X1A1) transitionDownloadClick
    Lecture note 33 - Time-independent Schrodinger equation for a molecular systemDownloadClick
    Lecture Note 34 - Wavepacket dynamicsDownloadClick
    Lecture Note 36 - Wavepacket dynamics IIIDownloadClick
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