1 / 20

Anharmonicity

In real molecules, highly sensitive vibrational spectroscopy can detect overtones , which are transitions originating from the n = 0 state for which Δn = +2, +3, …. Anharmonicity.

bitting
Download Presentation

Anharmonicity

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. In real molecules, highly sensitive vibrational spectroscopy can detect overtones, which are transitions originating from the n = 0 state for which Δn = +2, +3, … Anharmonicity Overtones are due to anharmonicity. A good approximation of realistic anharmonicity is given by the Morse potential.

  2. Put x = r – r0 and Taylor expand: Comparing to the harmonic oscillator we see that So we do to keep the force constant the same but change the anharmonicity

  3. use De = 40, α = 1; then scale by c

  4. Energy levels

  5. Morse model dissociated above this are the generalized Laguerre polynomials

  6. Harmonic oscillator model are the Hermite polynomials

  7. Wavefunctions: harmonic oscillator

  8. Wavefunctions: Morse oscillator

  9. Wavefunctions: harmonic vs. Morse

  10. Wavefunctions

  11. Wavefunctions

  12. Expectation value of position

  13. Expectation value of position

  14. Expectation value of position

  15. Selection rules For anharmonicity, can replace the H.O. wavefunctions with Morse wavefunctions… …or can keep more terms in the Taylor expansion of the dipole moment

  16. Selection rules

  17. Correspondence principle Where xturn is the maximum value of x

  18. Correspondence principle

  19. Correspondence principle

  20. Correspondence principle

More Related