Chem 125 Lecture 1310/6/2006

Projected material

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It is not readily understood without reference to notes from the lecture.

Which shell (1 or 2) has higher density?

12

Which shell contains more stuff (probability)?

2 has ~ 3 the radius ~9 the volume of 1.

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!

Change Orientation by Hybridization

a 2py + b 2pz (a weighted sum)

2pz 2py25%50%75%

50:50 mixture of pz and py?Other mixtures of pz and py?

0.000.020.040.060.090.110.180.250.330.501.00

Change Shape by Hybridization

spn = a 2 + b 2px

(spn)2 = a2 22 + b2 2px2 + 2ab 2 2px

b2

a2n

(a weighted sum)

Maximumextension

for sp1

hybrid

(see Web& A-i-B)

E

1.00

Change Shape by Hybridization

spn = a 2 + b 2px

(spn)2 = a2 22 + b2 2px2 + 2ab 2 2px

b2

a2n

(a weighted sum)

E

2 3 4 924 (Pure 2p)

Two (or more) ElectronsJoint Probability

Prob (A and B) = Prob (A) Prob (B)

Tossing two coins for two heads

IF the events are independent

2

2 2

No way the electrons can be independent!

2-e Wave Function

“An Orbital is a One-Electron

Wave Function”

(r1,1,1,r2,2,2)

a(r1,1,1) b(r2,2,2)

=?

Multiply 1-e Wave Functions

function of what?

Tricks to

SalvageOrbitals

Approximate e-Repulsion for He

H Z = 1

Approximate e-Repulsion for He

He Z = 2

Approximate e-Repulsion for He

"He" Z = 1.69

Z effective

"Clementi-Raimondi" values for Zeff

Atom Z Zeff 1s

He 2 1.69

Zeff 2s Zeff 2p

C 6 5.67 3.22 3.14

Zeff 3s

Na 11 10.63 6.57 6.80 2.51

Let other electron(s) "screen" nuclear charge

!

?

Self-Consistent Field (SCF)

"Correlation Energy"

Error after full SCF calculation

Get correct energy by experiment

or by a whopping calculation:

e.g. “Configuration Interaction” (CI)

or

“Density Functional Theory” (DFT)

Might "Correlation Energy"be Negligible?

End