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