Naphthalene, C₁0H8 (shown at right) can be simplified by constructing SALC-AOs to serve as a basis. If we set the molecular plane to be the xy-plane, then the л-system is built from the 2pz orbitals on each carbon. Naphthalene is in the D2h point group and a table is provided at the end of the problem set showing all the symmetry operations on the 2pz orbitals. D2h Ag B1g B2g B3g Au В 14 B₂u B3u E 1 1 1 1 1 1 1 1 C2(z) C2(y) C₂(x) i 1 1 1 1 1 -1 1 -1 −1 1 -1 -1 1 1 1 1 1 1 -1 -1 -1 1 -1 -1 -1 -1 ܝܕ (a) Upon examining the symmetry transformations of the ten 2pz orbitals in naphthalene, one would find that they are the basis for the reducible representation given by Ê Ĉ₂(z) Ĉ₂(y) Ĉ₂ (x) î ô(xy) ô(xz) ô(yz) -2 0 0 -10 0 2 Fred (2pz) = 10 0 Reduce this representation into its irreducible representations using the D2h character table provided here. ܝ -1 ܝ ܝ ܝ ܝܕ -1 -1 o(xy) o(xz) 1 1 1 -1 -1 -1 -1 -1 -1 1 1 -1 1 1 177 2 -1 3 4 10 o(yz) 1 -1 -1 1 -1 1 1 -1 8 5 7 6 X

Naphthalene, C₁0H8 (shown at right) can be simplified by constructing SALC-AOs to serve as a basis. If we set the molecular plane to be the xy-plane, then the л-system is built from the 2pz orbitals on each carbon. Naphthalene is in the D2h point group and a table is provided at the end of the problem set showing all the symmetry operations on the 2pz orbitals. D2h Ag B1g B2g B3g Au В 14 B₂u B3u E 1 1 1 1 1 1 1 1 C2(z) C2(y) C₂(x) i 1 1 1 1 1 -1 1 -1 −1 1 -1 -1 1 1 1 1 1 1 -1 -1 -1 1 -1 -1 -1 -1 ܝܕ (a) Upon examining the symmetry transformations of the ten 2pz orbitals in naphthalene, one would find that they are the basis for the reducible representation given by Ê Ĉ₂(z) Ĉ₂(y) Ĉ₂ (x) î ô(xy) ô(xz) ô(yz) -2 0 0 -10 0 2 Fred (2pz) = 10 0 Reduce this representation into its irreducible representations using the D2h character table provided here. ܝ -1 ܝ ܝ ܝ ܝܕ -1 -1 o(xy) o(xz) 1 1 1 -1 -1 -1 -1 -1 -1 1 1 -1 1 1 177 2 -1 3 4 10 o(yz) 1 -1 -1 1 -1 1 1 -1 8 5 7 6 X

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

Naphthalene, C₁0H8 (shown at right) can be simplified by
constructing SALC-AOs to serve as a basis. If we set the
molecular plane to be the xy-plane, then the л-system is built
from the 2pz orbitals on each carbon.
Naphthalene is in the D2h point group and a table is provided
at the end of the problem set showing all the symmetry
operations on the 2pz orbitals.
D2h
Ag
B1g
B2g
B3g
Au
(a) Upon examining the symmetry transformations of the ten 2pz orbitals in naphthalene,
one would find that they are the basis for the reducible representation given by
Ê Ĉ₂(z) Ĉ₂(y) Ĉ₂(x)
î ô(xy) ô(xz) ô(yz)
-2
0
0 -10
0
2
Fred (2pz) = 10 0
Reduce this representation into its irreducible representations using the D2h character
table provided here.
В 14
B2u
B3u
E
1
1
1
1
1
1
1
C2(z) C2(y) C₂(x) i
1
1
1
1
1
-1
-1
-1
1
-1
-1
-1
1
1
1
-1
-1
1
-1 -1
1
−1
-1
1
1
1
-1
-1
-1
-1
17 77 1
o(xy) o(xz) o(yz)
1
1
1
-1
-1
-1
-1
1
1
-1
11 14 11
-1
-1
-1
1 YA 8
-1
10
4 5
-1
6
X
(b) Using these techniques, one can construct a symmetry adapted orbital (SALC) that has
the mathematical form,
ф = Ф9 — Ф10
By applying each of the symmetry operations, Â, in the D2h point group to this function,
and recording its effect (+1 if Â½ = +½, or −1 if Â½ = −4), determine the irreducible
representation for which serves as a basis.

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