C566lecture6_000

C566lecture6_000 - C566 Master Lecture Notes Lecture 6...

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C566 Master Lecture Notes Lecture 6 Review of Molecular Symmetry (pp 181-201, Hollas) Elements of Symmetry (0) Identity, E E(x,y,z) = (x,y,z) z y x z y x 1 0 0 0 1 0 0 0 1 (1) n -fold axis of symmetry, C n . Rotation of molecule by 2 / n radians (n = 1, 2, …, ) results in a nuclear arrangement that is indistinguishable from the initial state. 1 0 0 0 2 cos 2 sin 0 2 sin 2 cos 2 n n n n n R z In cylindrical coordinates, it can be represented as: C n (r, , z) = (r, +2 / n , z) (2) Plane of symmetry, : Reflection of the nuclei through a plane of symmetry resultes in a molecular structure (nuclear arrangement) that is indistinguishable from the initial structure. Convention: Highest-n C n axis is the principle (or primary) axis, called z v is || to the principle axis h is to the principle axis v , xz , perpendicular to plane: xz (x, y, z) = (x, -y, z) v,yz parallel to plane: yz (x, y, z) = (-x, y, z)
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Some molecules have no uniquely highest-fold axis of symmetry, so the reflection planes are not labeled h or v . CCJ molecule as an example: Planes of symmetry are sometimes labeled d in cases where the plane is parallel to the principle C n axis and an orthogonal C 2 axis bisecting a bond angle (d is for dihedral). PtCl 4 is an example. (3) Center of inversion, i : for molecules with inversion symmetry, transposing nuclei along a line passing through the center of symmetry to the same distance opposite results in a nuclear arrangement identical to the initial state. i (x,y,z) = (-x,-y,-z) Example: high-symmetry Mo(CO) 6 , Lower-symmetry dipropene: (4) Generated symmetry operations/elements (i) n -fold rotation-reflection axis of symmetry, S n Rotating the molecule by 2 /n with subsequent reflection through a plane to the axis results in a nuclear arrangement that is indistinguishable from the initial arrangement.
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This note was uploaded on 01/18/2012 for the course C 566 taught by Professor Carolinechickjarroll during the Spring '11 term at Indiana.

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C566lecture6_000 - C566 Master Lecture Notes Lecture 6...

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