Quantum Chemistry 5.12 – Polyatomic Molecular Vibrations

Short lecture on vibrations of polyatomic molecules.

A general polyatomic molecule has N atoms and 3N Cartesian coordinates (x, y, and z for each atom). The potential energy is a function of all 3N coordinates. A typical molecular structure is a “stationary point”, or minimum energy geometry with an energy gradient of zero. Computing all (3N)^2 second mixed-partial derivatives gives the Hessian matrix, whose eigenvalues form vibrational frequencies and whose eigenvalues form the normal modes of motion. These modes include 3 translations (zero frequency), 3 rotations (zero frequency), and 3N-6 vibrations (unique, positive, non-zero frequencies). Each vibrational normal mode has its own vibrational quantum number, but due to vibrational frequencies in the 1000’s of cm^-1 most are in the ground state at room temperature (300 K).

Notes Slide: http://i.imgur.com/mbqSbOX.png

— About TMP Chem —

All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker.

Email: tmpchemistry@gmail.com

— Video Links —

Chapter Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicL4kdvchwcgETYWXlt-HyzH

Course Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicL3jKr_0nHHs5TwfhdkMFhh

Course Review: https://www.youtube.com/playlist?list=PLm8ZSArAXicLTRn3cJyyU1TiU7n_Pp4X1

Other Courses: https://www.youtube.com/playlist?list=PLm8ZSArAXicIXArfap9Tcb8izqRPvE0BK

Channel Info: https://www.youtube.com/playlist?list=PLm8ZSArAXicLlGO4Rvpz-D6vX8MFbOn4V

— Social Links —

Facebook: https://www.facebook.com/tmpchem

Twitter: https://www.twitter.com/tmpchem

LinkedIn: https://www.linkedin.com/in/tmpchem

Imgur: https://tmpchem.imgur.com

GitHub: https://www.github.com/tmpchem

— Equipment —

Microphone: Blue Yeti USB Microphone

Drawing Tablet: Wacom Intuos Pen and Touch Small

Drawing Program: Autodesk Sketchbook Express

Screen Capture: Corel Visual Studio Pro X8