chem 125 lecture 12 10/4/2005 projected material this material is for the exclusive use of chem 125...
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Chem 125 Lecture 1210/4/2005
Projected material
This material is for the exclusive use of Chem 125 students at Yale and may not
be copied or distributed further.
It is not readily understood without reference to notes from the lecture.
What's Coming for Next Exam?Atoms
3-Dimensional Reality (H-like Atoms)Hybridization
Orbitals for Many-Electron Atoms
Payoff forOrganic
Chemistry!
MoleculesPlum-Pudding Molecules ("United Atom" Limit)
Understanding Bonds (Pairwise LCAO)"Energy-Match & Overlap"
(Wrong!)
Recovering from the Orbital Approximation
ReactivityHOMOs and LUMOs
Recognizing Functional Groups
Structure (and Dynamics) of XH3 Molecules
2
2 2
Table for H-like Atoms
r
x
y
z
e
n
1s = K e-/2
2s = K'(2-) e-/2
Shape of H-like
= K'''( cos()) e-/22pz zGuess what 2px and 2py look like.
Simpler (!) than Erwin 1-D Coulombic
The angular part of a p orbital
Polar Plot of cos() vs.
0.5- 0.5- 1 0 1• •
•
••
•
•
•
= 0°
0.86
0.86
0.71
0.710.5
0.5
= ±30° = ±60° = ±45° = ±90°
+
cos2() vs.
2p
Atom-in-a-Box
http://www.dauger.com/hobbies/
Shape of H-like
Thanks to
Dean Dauger(physicist)
Information from Atom-in-a-Box
r2 R(r)2
ProbabilityDensity
SurfaceWeighting
Where is the density highest?What is the most likely distance?
n,l,m (nickname)
Schrödinger Equation
Energy (ev)
Formula
Information from Atom-in-a-Box
Single Slice
3D 2D
at different levels
near
far
Information from Atom-in-a-Box
Nodes (Shape & Energy)
?3d4d
Scaling H-like forChanging Nuclear Charge (Z)
Size
e-Density
Energy
Scaling Size with Z
r2Z
nao
Increasing Z shrinks wave function(makes r smaller for same)
H+ : C+6 : K+19 = 1 : 1/6 : 1/19
Scaling Size with Z : 1s
H+ : C+6 : K+19 = 1 : 1/6 : 1/19
Scalinge-Density
with ZNormalization:
d= 1(why most constants are there)
Table for H-like Atoms
Note: Z3
H+ : C+6 : K+19 = 1 : 216 : 6859
(Helps X-ray find heavieratoms more easily;H very difficult)
Scaling Kinetic Energy with Z
F(Zr)
Z F'(Zr)
'
Z2 F"(Zr)
"
" Z2
Scaling Potential Energy with Z
Distance Shrinkage 1/Z (thus 1/r Z )
V at fixed distance Z
Coulomb's Law V Zer
V Z2
Scaling Total Energy with Z (and n)
E = -RZ2
n2
Independent of l , m (e.g. 3s = 3p = 3d)for 1-electron atoms
R ≈ 300 kcal/mole
As we saw for 1-D Coulomb
1
2
35
E=0
4
n =
Scaling H-like forChanging Nuclear Charge (Z)
Size
e-Density
Energy
1/Z
Z3
Z2
(n/Z)
/n2
Multiplying and AddingWave Functions
Multiply “pieces” to create 1-electron wave function for atom:
(,,) = R(r) () ()
“ORBITAL”
Add orbitals of an atom to create a “hybrid” atomic orbital:
2py + 2pz = hybrid orbitalFunction of what?
Position of one electron!
Physicist’s 2p (m=1)with “orbital
angular momentum”
Information from Atom-in-a-Box
Superposition (a kind of hybridization)
Chemist’s 2py
End