1. It is important to remember that the same grouping of orbitals will have diff
ID: 558693 • Letter: 1
Question
1. It is important to remember that the same grouping of orbitals will have different symmetry labels when you solve for their irreducible representations in different point groups. For each point group listed, (i) solve for the reducible representation (red) of two 1s orbitals that are symmetric about the z axis. (ii) List the Mulliken symbols of the two irreducible representations (rep) that you can determine from yourred (iii) If there was a metal atom at (0,0,0), which of its orbitals (s, p, and/or d) could interact with each of yourrep? 1s (a) Example: Point Group (C2) (i) - red (ii) A and B (iii) A (S, pz, dz2, dxy, dx2-y2); B (py, Px, dyz, dxz) (b) C2v (c) D2h (d) C2hExplanation / Answer
(b) (i) Reducible representation red in C2v symmetry:
C2v
E
C2 (z)
v(xz)
v(yz)
red
3
1
3
1
(ii) Their Mullikan symbols are A1, A2, B1 and B2.
(iii) A1 (s, dx2, dy2,dz2)
A2 (pz, dxy)
B1 (py, dxy)
B2 (px, dyz)
(c) (i) Reducible representation red in D2h symmetry:
D2h
E
C2 (z)
C2 (y)
C2 (x)
i
(xy)
(xz)
(yz)
red
12
0
0
0
0
4
0
0
(ii) Their Mullikan symbols are Ag, B1g, B2g, B3g, Au, B1u, B2u, B3u.
(iii) Ag (dx2, dy2,dz2)
B1g (pz, dxy)
B2g (py, dxz)
B3g (px, dyz)
Au
B1u (s)
B2u
B3u
(d) (i) Reducible representation red in D2h symmetry:
C2h
E
C2 (z)
i
h
red
12
0
0
4
(ii) Ag, Bg, Au and Bu.
(iii) Ag (pz,dx2, dy2,dz2, dxy)
Bg (px,py, dxz, dyz)
Au (s)
Bu.
C2v
E
C2 (z)
v(xz)
v(yz)
red
3
1
3
1
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