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Rotational Structure of Vibration-Rotation Transitions

Understand the selection rules for vibration-rotation transitions and the rotational structure of molecules. Analysis of J’, v’, J”, v” levels, and transitions with Harry Kroto's 2004 findings on CN band.

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Rotational Structure of Vibration-Rotation Transitions

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  1. v’ J’= 5 0 The selection rules for vibration rotation transitions are ∆v = ±1 ∆J = ±1 v” J”= 5 0

  2. Rotational Structure J’= 5 v’ = 0 0 R(3) R(2) R(1) R(0) J”= 5 v” = 0 0 R Branch

  3. Rotational Structure J’= 5 v’ = 0 0 P(4) R(3) P(3) P(2) R(2) R(1) P(1) R(0) J”= 5 v” = 0 0 R Branch P Branch

  4. J V’ J V”

  5. J + 1 J V’ J – 1 J V”

  6. J + 1 J B’ J (J+ 1) V’ J – 1 J B”J (J+ 1) V”

  7. B’ (J+ 1)(J+2) J + 1 J B’ J (J+ 1) V’ J – 1 J B”J (J+ 1) V”

  8. B’ (J+ 1)(J+2) J + 1 J B’ J (J+ 1) V’ J – 1 B’ (J – 1) J J B”J (J+ 1) V”

  9. B’ (J+ 1)(J+2) J + 1 J B’ J (J+ 1) V’ J – 1 B’ (J – 1) J J B”J (J+ 1) V”

  10. B’ (J+ 1)(J+2) J + 1 J B’ J (J+ 1) V’ J – 1 B’ (J – 1) J R(J) J B”J (J+ 1) V”

  11. B’ (J+ 1)(J+2) J + 1 J B’ J (J+ 1) V’ J – 1 B’ (J – 1) J R(J) P(J) J B”J (J+ 1) V”

  12. B’ (J+ 1)(J+2) J + 1 J J – 1 B’ (J – 1) J R(J) P(J) J B”J (J+ 1)

  13. B’ (J+ 1)(J+2) J + 1 B’ (J2 + 3J +2) J J – 1 B’ (J – 1) J R(J) P(J) J B”J (J+ 1) V”

  14. B’ (J+ 1)(J+2) J + 1 B’ (J2 + 3J +2) J J – 1 B’ (J – 1) J B’ (J2 – J) R(J) P(J) J B”J (J+ 1) V”

  15. B’ (J+ 1)(J+2) J + 1 B’ (J2 + 3J +2) J J – 1 B’ (J – 1) J B’ (J2 – J) R(J) P(J) J B”J (J+ 1) V” Harry Kroto 2004

  16. B’ (J+ 1)(J+2) J + 1 B’ (J2 + 3J +2) J J – 1 B’ (J – 1) J B’ (J2 – J) B’ (4J + 2) R(J) P(J) J B”J (J+ 1) V”

  17. B’ (J+ 1)(J+2) J + 1 B’ (J2 + 3J +2) J J – 1 B’ (J – 1) J B’ (J2 – J) B’ (4J + 2) = 4B’(J + ½) R(J) P(J) J B”J (J+ 1) V”

  18. Rotational Structure J’= 5 v’ = 0 0 P(4) R(3) P(3) P(2) R(2) R(1) P(1) R(0) J”= 5 v” = 0 0 R Branch P Branch Harry Kroto 2004

  19. Rotational Structure J’= 5 v’ = 0 0 P(4) R(3) P(3) R(2) P(2) R(1) P(1) R(0) J”= 5 v” = 0 Central section of the CN 0-0 Band 0 R Branch P Branch Harry Kroto 2004

  20. Rotational Structure J’= 5 v’ = 0 0 P(4) R(3) P(3) R(2) P(2) R(1) P(1) R(0) J”= 5 v” = 0 Central section of the CN 0-0 Band 0 R Branch P Branch Harry Kroto 2004

  21. Rotational Structure J’= 5 v’ = 0 0 P(4) R(3) P(3) P(2) R(2) R(1) P(1) R(0) J”= 5 v” = 0 Central section of the CN 0-0 Band 0 R Branch P Branch Harry Kroto 2004

  22. Rotational Structure J’= 5 v’ = 0 0 P(4) R(3) P(3) R(2) P(2) R(1) P(1) R(0) J”= 5 v” = 0 0 R Branch P Branch Harry Kroto 2004

  23. Harry Kroto 2004

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