27_580ln_fa08

# 27_580ln_fa08 - MIT OpenCourseWare http/ocw.mit.edu 5.80...

This preview shows pages 1–4. Sign up to view the full content.

MIT OpenCourseWare http://ocw.mit.edu 5.80 Small-Molecule Spectroscopy and Dynamics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
5.80 Lecture #27 Fall, 2008 Page 1 of 8 pages Lecture #27: Polyatomic Vibrations III: s-Vectors and H 2 O Last time: F -matrix: too many F ij ’s even at quadratic-only level Internal coordinates: types 3N–6 independent ones constraints * translation * rotation s -vectors α S t s t α * direction of fastest increase * magnitude resulting from unit displacement in optimum direction ρ ρ s t α α α N ( ) = S t { } α = 1 rigid translation ρ α = ε for all α constraint s t α = 0 no center of mass translation α R α × d rigid rotation by d Ω ρ α ) = ( d Ω Ω s t α × R α constraint s t α × R α e = 0 ECKART α (minimizes vibrational angular momentum) If the normal displacements are built from s t α vectors that satisfy these constraints, then, for infinitesimal displacements from equilibrium, there is no rotation. For large displacements, or for small displacements away from a non-equilibrium configuration, there is a small vibrational angular momentum. This definition of vibrations embeds a specific partitioning between rotation and vibration. TODAY: G from s t α ’s Examples of s t α ’s 1. valence bond stretch r 2. valence angle bend φ G matrix using diagrams and tables from WDC pages 304 and 305 H 2 O FG handout G DD recall | S = B | ξ〉 = D | q = D Μ 1/2 | ξ〉 B = DM 1/2 BM 1/2 = D G = DD = BM 1/2 ( M 1/2 ) B = BM 1 B S t ( d Ω ) = d Ω α
5.80 Lecture #27 Fall, 2008 Page 2 of 8 pages G tt = 1 B ti B * t i i = 1 3N m i definition of | S = B | ξ〉 → ⎛∂ ∂ξ

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 9

27_580ln_fa08 - MIT OpenCourseWare http/ocw.mit.edu 5.80...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online