W2013CHM2311 Part 3b Notes(1)

D2d d4d d6d based on s2n not cn no need to memorize

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Unformatted text preview: the point group for BF3. 2.  Place BF3 on the Cartesian coordinate system with the z- axis corresponding to the principle axis of rota0on. Use diagrams to demonstrate how each of the symmetry opera0ons in the BF3 point group (found in a character table) will affect the pz orbital of the boron atom. 3.  Based on the informa0on from part 2, write the irreducible representa0on for the pz orbital. Check your answer using a character table. Symmetry Labels Symmetry labels for each irreducible representa0on are given in the far lek column 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 Understanding how to interpret symmetry labels can provide a significant amount of informa0on about the symmetry proper0es of an orbital – just by looking at the label. Symmetry Labels Symmetry labels for each irreducible representa0on are given in the far lek column of the table: A C2v E A1 Func0on is symmetric wrt n- fold rota0on about main axis. 1 B C2 A2 1 1 or 2 1 1 B1 1 B2 -1 ´ or ʺȃ 1 -1 g or u E or T σv (xz) σv’ (yz) Func0on is an0- symmetric wrt n- fold rota0on about main axis. 1 1 z x2, y2, z2 Func0on is symmetric (or an0) wrt C2 perpendicular to main axis, or (if missing) a vRz er0cal mirror. -1 -1 xy 1 -1 x, Ry xz Func0on is symmetric (or an0) wrt horizontal mirror plane. -1 1 y, Rx yz Func0on is symmetric (or an0) wrt inversion. Degenerate func0ons (interconvert with symmetry opera0ons). Understanding how to interpret symmetry labels can provide a significant amount of informa0on about the symmetry proper0es of an orbital – just by looking at the label. Assigning Symmetry Labels to Irreducible Representa0ons 1.  Look at the character of the iden?ty opera?on: If it is 1 then the symmetry label is either “A” or “B” The label is “A” if the character of Cn = 1 The label is “B” if the character of Cn = - 1 If it is 2 then the symmetry label is “E” If it is 3 then the symmetry label is “T” Excep0ons: D2 and D2h have no principle axis, so look at the sum of the characters of the C2’s. D2d, D4d, D6d: Based on S2n not Cn (No need to memorize these excep?ons.) Assigning Symmetry Labels to Irreducible Representa0ons 2.  If the symbol is either A or B, then look at the character of th...
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