Post on 20-Dec-2015
transcript
Chem 125 Lecture 1310/6/2006
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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