1 / 51

Structural Determination Approach for Linear Molecules

Detailed methodology for determining atom position from the Center of Mass in linear molecules using moments of inertia and coordinate calculations.

tmasters
Download Presentation

Structural Determination Approach for Linear Molecules

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. General Method of Structure Determination for Linear Molecules

  2. General Method of Structure Determination for Linear Molecules We wish to determine r2 the position of a particular atom (mass m2) from the Center of Mass (C of M)

  3. General Method of Structure Determination for Linear Molecules We wish to determine r2 the position of a particular atom (mass m2) from the Center of Mass (C of M) a m1 m2 r2

  4. General Method of Structure Determination for Linear Molecules We wish to determine r2 the position of a particular atom (mass m2) from the Center of Mass (C of M) a m1 m2 I = Moment of Inertia of the normal species about a the C of M

  5. General Method of Structure Determination for Linear Molecules We wish to determine r2 the position of a particular atom (mass m2) from the Center of Mass (C of M) a b d m1 m2 I = Moment of Inertia of the normal species about a the C of M I* = Moment of Inertia of the substituted species about b its C of M

  6. General Method of Structure Determination for Linear Molecules We wish to determine r2 the position of a particular atom (mass m2) from the Center of Mass (C of M) a b d m1 m2 → m2+∆m I = Moment of Inertia of the normal species about a the C of M I* = Moment of Inertia of the substituted species about b its C of M

  7. General Method of Structure Determination for Linear Molecules We wish to determine r2 the position of a particular atom (mass m2) from the Center of Mass (C of M) a b m1 m2 I = Moment of Inertia of the normal species about a the C of M I* = Moment of Inertia of the substituted species about b its C of M I’ = Moment of Inertia of the substituted species about a

  8. a m1 m2 r1 r2

  9. a is the axis of the normal molecule a m1 m2 r1 r2

  10. a is the axis of the normal molecule b is the axis of the substituted molecule mass m2+ ∆m a b m1 m2 r1 r2

  11. a is the axis of the normal molecule b is the axis of the substituted molecule mass m2+ ∆m a b m1 m2 → m2+∆m r1 r2

  12. a is the axis of the normal molecule b is the axis of the substituted molecule mass m2+ ∆m a b d m1 m2 → m2+∆m r1 r2

  13. a is the axis of the normal molecule b is the axis of the substituted molecule a b d m1 m2 r1 r2 For the substituted molecule the parallel axis theorem yields

  14. a is the axis of the normal molecule b is the axis of the substituted molecule a b d m1 m2 r1 r2 • For the substituted molecule the parallel axis theorem yields • I’ = I* + (M + ∆m)d2

  15. a is the axis of the normal molecule b is the axis of the substituted molecule a b d m1 m2 r1 r2 • For the substituted molecule the parallel axis theorem yields • I’ = I* + (M + ∆m)d2 • I’ = I +∆mr22

  16. a is the axis of the normal molecule b is the axis of the substituted molecule a b d m1 m2 r1 r2 • For the substituted molecule the parallel axis theorem yields • I’ = I* + (M + ∆m)d2 • I’ = I +∆mr22 • I* + (M + ∆m)d2 = I +∆mr22

  17. a is the axis of the normal molecule b is the axis of the substituted molecule a b d m1 m2 r1 r2 • For the substituted molecule the parallel axis theorem yields • I’ = I* + (M + ∆m)d2 • I’ = I +∆mr22 • I* + (M + ∆m)d2 = I +∆mr22 • I* - I = ∆mr22 – (M + ∆m) d2

  18. a is the axis of the normal molecule b is the axis of the substituted molecule a b d m1 m2 r1 r2 • For the substituted molecule the parallel axis theorem yields • I’ = I* + (M + ∆m)d2 • I’ = I +∆mr22 • I* + (M + ∆m)d2 = I +∆mr22 • I* - I = ∆mr22 – (M + ∆m) d2 = ∆I

  19. ∆I = ∆mr22 – (M + ∆m) d2 m2+∆m a b m1 m2 r1 r2 d

  20. ∆I = ∆mr22 – (M + ∆m) d2 • m1(r1 + d) = (m2 + ∆m)(r2 – d) m2+∆m a b m1 m2 r1 r2 d

  21. ∆I = ∆mr22 – (M + ∆m) d2 • m1(r1 + d) = (m2 + ∆m)(r2 – d) • m1r1 + m1d = m2r2 – m2d + ∆mr2 – ∆md m2+∆m a b m1 m2 r1 r2 d

  22. ∆I = ∆mr22 – (M + ∆m) d2 • m1(r1 + d) = (m2 + ∆m)(r2 – d) • m1r1 + m1d = m2r2 – m2d + ∆mr2 – ∆md • m1r1 = m2r2 m2+∆m a b m1 m2 r1 r2 d

  23. ∆I = ∆mr22 – (M + ∆m) d2 • m1(r1 + d) = (m2 + ∆m)(r2 – d) • m1r1 + m1d = m2r2 – m2d + ∆mr2 – ∆md • m1r1 = m2r2 • m1r1+ m1d = m2r2 – m2d + ∆mr2 – ∆md m2+∆m a b m1 m2 r1 r2 d

  24. ∆I = ∆mr22 – (M + ∆m) d2 • m1(r1 + d) = (m2 + ∆m)(r2 – d) • m1r1 + m1d = m2r2 – m2d + ∆mr2 – ∆md • m1r1 = m2r2 • m1r1+ m1d = m2r2 – m2d + ∆mr2 – ∆md • m1d = – m2d + ∆mr2 – ∆md m2+∆m a b m1 m2 r1 r2 d

  25. ∆I = ∆mr22 – (M + ∆m) d2 • m1(r1 + d) = (m2 + ∆m)(r2 – d) • m1r1 + m1d = m2r2 – m2d + ∆mr2 – ∆md • m1r1 = m2r2 • m1r1+ m1d = m2r2 – m2d + ∆mr2 – ∆md • m1d = – m2d + ∆mr2 – ∆md • d(m1 + m2 + ∆m) = ∆mr2 m2+∆m a b m1 m2 r1 r2 d

  26. ∆I = ∆mr22 – (M + ∆m) d2 • m1(r1 + d) = (m2 + ∆m)(r2 – d) • m1r1 + m1d = m2r2 – m2d + ∆mr2 – ∆md • m1r1 = m2r2 • m1r1+ m1d = m2r2 – m2d + ∆mr2 – ∆md • m1d = – m2d + ∆mr2 – ∆md • d(m1 + m2 + ∆m) = ∆mr2 • d = [∆m/(M + ∆m)]r2 m2+∆m a b m1 m2 r1 r2 d

  27. ∆I = ∆mr22 – (M + ∆m) d2 • m1(r1 + d) = (m2 + ∆m)(r2 – d) • m1r1 + m1d = m2r2 – m2d + ∆mr2 – ∆md • m1r1 = m2r2 • m1r1+ m1d = m2r2 – m2d + ∆mr2 – ∆md • m1d = – m2d + ∆mr2 – ∆md • d(m1 + m2 + ∆m) = ∆mr2 • d = [∆m/(M + ∆m)]r2 = ∆mr2/(M + ∆m) m2+∆m a b m1 m2 r1 r2 d

  28. ∆I = ∆mr22 – (M + ∆m) d2 • d = ∆m r2 /(M + ∆m)

  29. ∆I = ∆mr22 – (M + ∆m) d2 • d = ∆m r2 /(M + ∆m) • ∆I = ∆mr22 – (M + ∆m) ∆m2 r22/(M + ∆m)2

  30. ∆I = ∆mr22 – (M + ∆m) d2 • d = ∆m r2 /(M + ∆m) • ∆I = ∆mr22 – (M + ∆m) ∆m2 r22/(M + ∆m)2 • ∆I = ∆mr22 – ∆m2 r22/(M + ∆m)

  31. ∆I = ∆mr22 – (M + ∆m) d2 • d = ∆m r2 /(M + ∆m) • ∆I = ∆mr22 – (M + ∆m) ∆m2 r22/(M + ∆m)2 • ∆I = ∆mr22 – ∆m2 r22/(M + ∆m) • ∆I = r22 [∆m – ∆m2 /(M + ∆m)]

  32. ∆I = ∆mr22 – (M + ∆m) d2 • d = ∆m r2 /(M + ∆m) • ∆I = ∆mr22 – (M + ∆m) ∆m2 r22/(M + ∆m)2 • ∆I = ∆mr22 – ∆m2 r22/(M + ∆m) • ∆I = r22 [∆m – ∆m2 /(M + ∆m)] • ∆I = r22[∆m(M + ∆m) – ∆m2 ]/(M + ∆m)

  33. ∆I = ∆mr22 – (M + ∆m) d2 • d = ∆m r2 /(M + ∆m) • ∆I = ∆mr22 – (M + ∆m) ∆m2 r22/(M + ∆m)2 • ∆I = ∆mr22 – ∆m2 r22/(M + ∆m) • ∆I = r22 [∆m – ∆m2 /(M + ∆m)] • ∆I = r22[∆m(M + ∆m) – ∆m2 ]/(M + ∆m) • ∆I = r22[∆mM + ∆m2 – ∆m2 ]/(M + ∆m)]

  34. ∆I = ∆mr22 – (M + ∆m) d2 • d = ∆m r2 /(M + ∆m) • ∆I = ∆mr22 – (M + ∆m) ∆m2 r22/(M + ∆m)2 • ∆I = ∆mr22 – ∆m2 r22/(M + ∆m) • ∆I = r22 [∆m – ∆m2 /(M + ∆m)] • ∆I = r22[∆m(M + ∆m) – ∆m2 ]/(M + ∆m) • ∆I = r22[∆mM + ∆m2 – ∆m2 ]/(M + ∆m)] • ∆I = r22[∆mM]/(M + ∆m)]

  35. ∆I = r22[∆mM]/(M + ∆m)]

  36. ∆I = r22[∆mM]/(M + ∆m)] ∆I = μr22

  37. ∆I = r22[∆mM]/(M + ∆m)] ∆I = μr22 where μ = M∆m/(M + ∆m)

  38. ∆I = r22[∆mM]/(M + ∆m)] ∆I = μr22 where μ = M∆m/(M + ∆m) The reduced mass on substitution

  39. ∆I = r22[∆mM]/(M + ∆m)] ∆I = μr22 where μ = M∆m/(M + ∆m) The reduced mass on substitution ~ Analogue of m1m2/(m1+m2)

  40. ∆I = r22[∆mM]/(M + ∆m)] ∆I = μr22 where μ = M∆m/(M + ∆m) The reduced mass on substitution ~ Analogue of m1m2/(m1+m2) or Mm/(M+m)

  41. Problem Determine the bond lengths for the molecule H-C≡C-H

  42. Problem Determine the bond lengths for the molecule H-C≡C-H H-C≡C-H B = 1.17692 cm-1

  43. Problem Determine the bond lengths for the molecule H-C≡C-H H-C≡C-H B = 1.17692 cm-1 H-C≡C-D B = 0.99141 cm-1

  44. ∆I = ∆mr22 – (M + ∆m) d2 m1(r1 + d) = (m2 + ∆m)(r2 – d) m1r1 + m1d = m2r2 – m2d + ∆mr2 – ∆md m1r1 = m2r2 m1r1+ m1d = m2r2 – m2d + ∆mr2 – ∆md m1d = – m2d + ∆mr2 – ∆md d(m1 + m2 + ∆m) = ∆mr2 d = [∆m/(M + ∆m)]r2 m2+∆m a b m1 m2 r1 r2 d

  45. I’ = I* + (M + ∆m)d2 • I’ = I +∆mr22 • I* + (M + ∆m)d2 = I +∆mr22 • I’ = I* + (M + ∆m)d2 • I’ = I +∆mr22 • I* - I = ∆mr22 – (M + ∆m) d2 I • m1r1 = m2r2 • M1(r1 + d) = (m2 + ∆m)(r2 – d) • m1r1 + m1d = m2r2 – m2d + ∆mr2 – ∆md • d(m1 + m2 + ∆m) = ∆mr2 • d = {∆m/(M + ∆m)}r2 a b m1 m2 r1 r2 d

  46. a is the axis of the normal molecule b is the axis of the substituted molecule a b d m1 m2 r1 r2 For the substituted molecule the parallel axis theorem yields I’ = I* + (M + ∆m)d2 I’ = I +∆mr22 I* + (M + ∆m)d2 = I +∆mr22 I* - I = ∆mr22 – (M + ∆m) d2

  47. I’ = I* + (M + ∆m)d2 • I’ = I +∆mr22 • I* + (M + ∆m)d2 = I +∆mr22 • I’ = I* + (M + ∆m)d2 • I’ = I +∆mr22 • I* - I = ∆mr22 – (M + ∆m) d2 I • m1r1 = m2r2 • M1(r1 + d) = (m2 + ∆m)(r2 – d) • m1r1 + m1d = m2r2 – m2d + ∆mr2 – ∆md • d(m1 + m2 + ∆m) = ∆mr2 • d = {∆m/(M + ∆m)}r2 a b d m1 m2

  48. General Method of Structure Determination for Linear Molecules We wish to determine r2 the position of a particular atom (mass m2) from the Center of Mass (C of M) a is the axis of the normal molecule b is the axis of the substituted molecule a b d m1 m2 r1 r2 • For the substituted molecule the parallel axis theorem yields • I’ = I* + (M + ∆m)d2 • I’ = I +∆mr22 • I* - I = ∆mr22 – (M + ∆m) d2

More Related