CHE 450G HW#1
Due Date:
Mon. Oct. 10, 2005
Reading Assignments: Miessler and Tarr Inorganic Chemistry, 3rd Ed.: Chapters 4, 5, 9
Vincent Text-Group Theory and Point Group Determination
Textbook problems: Miessler & Tarr:
CH 4: 10, 14, 15, 18, 19, 24
CH 9: 7, 12 (draw 3D representation; assign
point group also), 15
(1) (a) Determine the number of rotational, translational, and vibrational stretching
modes present in gaseous SO3. (b) Determine which of the vibrational stretching modes
are Raman and infrared active. (c) Indicate by using vectors, how the S and O atoms are
moving to give the IR active stretching mode. (d) Label each IR active mode with the
appropriate Mullikan symbol.
Note: for Problem 4-19 Γ(SF6) = {21 0 –1 3 -3 -3 -1 0 5 3}
Homework problems (3rd ed.) are below
2
3
4
5
6
7
From last class: Ammonia example.
Q. Why is the reducible representation (entire molecule method, Cartesian coordinate
axis transformation), Γcart. = 12 0 2 ?
A. Since your textbook neglected to give you a simple, but useful rule, here it is.
For rotations about an axis by an angle α, the contribution to the character for that
object, bond axis, or coordinate axis becomes cos(α).
(i) via tables or calculator: for C3 operation, cos(α) = cos(120) = -0.5; for C32 cos(240) =
-0.5; C2, cos(180) = -1; C4, cos(90) = 0; etc….so x and y-axes contribute -1/2 to the total
character for the N atom while the z-axis contributes 1 (cos 0, unchanged)
Alternatively, you could do this via (ii) matrices or (iii) by simply knowing the cosine
function, a 1,√3, and 2 (hypotenuse) triangle and the mnemonic: sohcahtoa, where sin α
= opposite/hypotenuse (sin α = o/h), cos α = adjacent/hypotenuse (cos α = a/h), and tan α
= opposite/adjacent (tan α = o/a).
e.g.
C3v
N(x,y,z)
H1(x,y,z)
H2(x,y,z)
H3(x,y,z)
_______________________________________________________________
χE
=
(1+1+1) + (1+1+1) + (1+1+1) + (1+1+1) = 12
χC3
=
(-0.5+-0.5+1)+(0+0+0) + (0+0+0) + (0+0+0) = 0
χσv
=
(1+-1+1) + (0+0+0) + (0+0+0) + (1-1+1) = 2
Hope this helps.
Steve Holmes