W2013CHM2311 Part 3b Notes(1)

C2 f f xe f f c2 c2 c2 c2 2 d symmetry elements

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Unformatted text preview: tors x, y, and z are consistent with their representa?ons. Character Tables & Symmetry Elements Example: Ammonia Point Group: C3v N H H H C3v Character Table: C3v E 2 C3 3σv A1 1 1 1 z A2 1 1 -1 Rz E 2 -1 0 (x,y) (Rx, Ry) (x2-y2, xy) (xz,yz) x2+y2, z2 Ammonia’s Symmetry Elements: E C3 axis of rota0on (2C3 summarizes the two opera0ons C31 and C32) Three ver0cal mirror planes, σv Character Tables & Symmetry Elements Example: XeF4 F Point Group: F Xe F D4h F Character Table (top row only): D4h E 2 C4 C2 2 C2’ 2C2’’ i 2S4 σh 2 σv 2 σd Symmetry Elements D4h E 2C4 C2 2C2’ 2C2’’ E 2 C4 C2 2 C2’ 2C2’’ i 2S4 σh 2 σv iden0ty Represents the C41 and C43 opera0ons (Same as C42, which is why C42 is not included above) axes of rota0on perpendicular to C4 and including terminal atoms axes of rota0on perpendicular to C4 and bisec0ng bond angles C4 , C2 F F Xe F F C2'' C2 ' C2 '' C2' 2 σd Symmetry Elements D4h E 2 C4 C2 2 C2’ 2C2’’ i 2S4 σh 2 σv 2 σd i inversion 2S4 C4 rota0on followed by reflec0on through the plane perpendicular to the C4 axis. (2S4 summarizes the 2 opera0ons S41 and S43. S42 = C2 so is already accounted for; S2 = i, so is already accounted for) σh one horizontal mirror plane (the plane of the atoms) 2σv there are two ver0cal mirror planes (the planes containing the C4 axis and also containing terminal atoms) 2σd there are two dihedral mirror planes (the planes containing the C4 axis and bisec0ng the FXeF bond angles) Character Tables & Irreducible Representa0ons The body of a character table contains rows called “irreducible representa:ons” C2v E C2 σv (xz) σv’ (yz) A1 1 1 1 1 z x2, y2, z2 A2 1 1 -1 -1 Rz xy B1 1 -1 1 -1 x, Ry xz B2 1 -1 -1 1 y, Rx yz The C2v point group contains Orbitals and Func0ons Each irreducible representa0on corresponds to a set of spectroscopic func0ons and/or orbitals, which are listed in the last two columns of the table. C2v E C2 σv (xz) σv’ (yz) A1 1 1 1 1 z x2, y2, z2 A2 1 1 -1 -1 Rz xy B1 1 -1 1 -1 x, Ry xz B2 1 -1 -1 1 y, Rx yz In this course, we are only interested in the func:ons corresponding to atomic orbitals. Orbitals and Character Tables Atomic orbitals are indicated by their symmetry func0on or algebraic descrip:ons appearing in the appropriate row of each table. Algebraic Descrip0on Orbital x px y py z pz xy dxy xz dxz yz dyz x2- y2 dx2- y2 z2 dz2 Orbitals and Character Tables s px pz dxz dxy z py dyz y x dx2- y2 dz2 How are the Characters Interpreted? The n...
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This note was uploaded on 03/28/2014 for the course CHM 2311 taught by Professor Richardson during the Winter '09 term at University of Ottawa.

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