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Last updated:

October 6, 2022


Unlimited Duration


This course includes:

Unlimited Duration

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Certificate of completion

Unlimited Duration


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.

Course Curriculum

  • General information Unlimited
  • Matrices are useful in spectroscopic theory Unlimited
  • Spectroscopic notation Unlimited
  • Coupled harmonic oscillators: truncation of an infinite matrix Unlimited
  • Matrix solution of harmonic Unlimited
  • Building an effective hamiltonian Unlimited
  • Anharmonic oscillator, Unlimited
  • Atoms: 1e- and alkali Unlimited
  • Alkali and many e- atomic spectra Unlimited
  • Many e- atoms Unlimited
  • How to assign an atomic spectrum Unlimited
  • The Born-Oppenheimer approximation Unlimited
  • Excerpts from the spectra and dynamics of diatomic molecules Unlimited
  • The Born-Oppenheimer approach to transitions Unlimited
  • The Born-Oppenheimer approach to transitions II Unlimited
  • Pictures of spectra and notation Unlimited
  • Rotational assignment of diatomic electronic spectra I Unlimited
  • Laser schemes for rotational assignment first lines for Ω’, Ω” assignments Unlimited
  • Definition of angular momenta Unlimited
  • Rotation and angular momenta Unlimited
  • 2∏ and 2∑ matrices Unlimited
  • Parity and e/f basis for 2∏, 2∑± Unlimited
  • Hund’s cases: 2∏, 2∑± examples Unlimited
  • Energy level structure of 2∏ and 2∑ states Unlimited
  • Perturbations Unlimited
  • A model for the perturbations Unlimited
  • Second-order effects Unlimited
  • Second-order effects: centrifugal distortion and Λ-doubling Unlimited
  • Transformations between basis sets: 3-j, 6-j, and Wigner-Eckart theorem Unlimited
  • Construction of potential curves by the Rydberg-Klein-Rees method (RKR) Unlimited
  • Rotation of polyatomic molecules I Unlimited
  • Energy levels of a rigid rotor, energy levels of an asymmetric rotor Unlimited
  • Asymmetric top Unlimited
  • Energy levels of a rigid rotor, energy levels of an asymmetric rotor Unlimited
  • Pure rotation spectra of polyatomic molecules Unlimited
  • Energy levels of a rigid rotor Unlimited
  • Polyatomic vibrations: normal mode calculations Unlimited
  • Polyatomic vibrations II: s-vectors, G-matrix, and Eckart condition Unlimited
  • Polyatomic vibrations III: s-vectors and H2O Unlimited
  • Polyatomic vibrations IV: symmetry Unlimited
  • A sprint through group theory Unlimited
  • What is in a character table and how do we use it? Unlimited
  • Electronic spectra of polyatomic molecules Unlimited
  • transition Unlimited
  • Vibronic coupling Unlimited
  • Time-independent Schrodinger equation for a molecular system Unlimited
  • Wavepacket dynamics Unlimited
  • Wavepacket dynamics III Unlimited

About the instructor

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Massachusetts Institute of Technology