### 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).

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## 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:

- Master the language of spectroscopists — a bewildering array of apparently capricious notation;
- 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);
- Predict the relative intensities and selection rules governing transitions between eigenstates, since spectra display only transition frequencies and not energy eigenvalues;
- 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.
- 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:

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

## Textbooks

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.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 M

_{A}>Evaluation of

14 (S) Rotation and angular momenta 15 ^{2}∏ and^{2}∑ matrices16 Parity and e/f basis for ^{2}∏,^{2}∑^{±}17 Hund's cases: ^{2}∏,^{2}∑^{±}examples17 (S) Energy level structure of ^{2}∏ and^{2}∑ states, matrix elements for^{2}∏ and^{2}∑ including ∏ ~ ∑ perturbation, parity18 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 H _{2}O28 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 Field View Small-Molecule Spectroscopy and Dynamics - Lecture 2 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 3 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 4 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 5 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 6 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 7 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 8 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 9 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 10 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 11 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 12 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 13 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 14 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 15 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 16 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 17 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 18 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 19 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 20 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 21 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 22 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 23 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 24 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 25 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 26 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 27 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 28 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 29 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 30 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 31 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 33 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 34 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 35 - Prof. Robert Field View Small-Molecule Spectroscopy and Dynamics - Lecture 36 - Prof. Robert Field View Description Type Link Problem set 2 1996 Download Click Problem set 1 1994 Download Click Problem set 1 solution 1994 Download Click Problem set 2 1994 Download Click Problem set 2 solution 1994 Download Click Problem set 3 1994 Download Click Problem set 4 1994 Download Click Problem set 4 1994 Download Click Problem set 4 1991 Download Click Problem set 1 1987 Download Click Problem set 2 1987 Download Click Problem set 3 1987 Download Click Problem set 4 1987 Download Click Problem set 2 1985 Download Click Problem set 2 solution 1985 Download Click Problem set 3 1985 Download Click Problem set 4 1985 Download Click Problem set 1 1982 Download Click Problem set 3 1982 Download Click Problem set 4 1982 Download Click Problem set 4 1982 Download Click Problem set 2 1980 Download Click Description Type Link Exam 1 1978 Download Click Final exam 1978 Download Click Exam 2 1977 Download Click Exam 1 1976 Download Click Exam 1 solution 1976 Download Click final exam 1976 Download Click Description Type Link Lecture Note 0 - General Information Download Click Lecture Note 1 - Matrices are useful in spectroscopic theory Download Click 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 set Download Click Lecture Note 2 - Coupled harmonic oscillators: truncation of an infinite matrix Download Click Lecture Note 2 - Matrix solution of harmonic oscillator problem, derivation of heisenberg equation of motion, matrix elements of any function of X and P Download Click Lecture Note 3 - Building an effective hamiltonian Download Click Lecture Note 3 - Anharmonic oscillator, vibration-rotation interaction, energy levels of a vibrating rotor Download Click Lecture Note 4 - Atoms: 1e- and alkali Download Click Lecture Note 5 - Alkali and many e- atomic spectra Download Click Lecture Note 6 - Many e- atoms Download Click Lecture Note 7 - How to assign an atomic spectrum Download Click Lecture Note 8 - The Born-Oppenheimer approximation Download Click Lecture Note 8 - Excerpts from the spectra and dynamics of diatomic molecules Download Click Lecture Note 9 - The Born-Oppenheimer approach to transitions Download Click Lecture Note 10 - The Born-Oppenheimer approach to transitions II Download Click Lecture Note 11 - Pictures of spectra and notation Download Click Lecture Note 12 - Rotational assignment of diatomic electronic spectra I Download Click Lecture Note 13 - Laser schemes for rotational assignment first lines for Ω', Ω" assignments Download Click Lecture Note 14 - Definition of angular momenta and | A α MA > Download Click Lecture Note 14 - Rotation and angular momenta Download Click Lecture Notes 15 - 2∏ and 2∑ matrices Download Click Lecture Note 16 - Parity and e/f basis for 2∏, 2∑± Download Click Lecture Note 17 - Energy level structure of 2∏ and 2∑ states, matrix elements for 2∏ and 2∑ including ∏ ~ ∑ perturbation, parity Download Click Lecture Note 18 - Perturbations Download Click Lecture Note 18 - A model for the perturbations and fine structure of the ∏ states of CO, factorization of perturbation parameters, the electronic perturbation parameters Download Click Lecture Note 19 - Second-order effects Download Click Lecture Note 19 - Second-order effects: centrifugal distortion and Λ-doubling Download Click Lecture Note 20 - Transformations between basis sets: 3-j, 6-j, and Wigner-Eckart theorem Download Click Lecture Note 21 - Construction of potential curves by the Rydberg-Klein-Rees method (RKR) Download Click Lecture Note 22 - Rotation of polyatomic molecules I Download Click Lecture Note 23 - Asymmetric top Download Click Lecture Note 24 - Pure rotation spectra of polyatomic molecules Download Click Lecture Note 25 - Polyatomic vibrations: normal mode calculations Download Click Lecture Note 26 - Polyatomic vibrations II: s-vectors, G-matrix, and Eckart condition Download Click Lecture Note 26 - Polyatomic vibrations III: s-vectors and H2O Download Click Lecture Note 28 - Polyatomic vibrations IV: symmetry Download Click Lecture Note 29 - A sprint through group theory Download Click Lecture Not 30 - What is in a character table and how do we use it? Download Click Lecture Note 31 - Electronic spectra of polyatomic molecules Download Click Lecture Note 32 - The H2CO (A1A2 from X1A1) transition Download Click Lecture note 33 - Time-independent Schrodinger equation for a molecular system Download Click Lecture Note 34 - Wavepacket dynamics Download Click Lecture Note 36 - Wavepacket dynamics III Download Click