chem 125 lecture 11 9/29/08 this material is for the exclusive use of chem 125 students at yale and...
Post on 21-Dec-2015
216 views
TRANSCRIPT
Chem 125 Lecture 119/29/08
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?
MoleculesPlum-Pudding Molecules (the "United Atom" Limit)
Understanding Bonds (Pairwise LCAO)"Energy-Match & Overlap"
Reality: Structure (and Dynamics) of XH3 Molecules
AtomsOrbitals for Many-Electron Atoms (Wrong!)Recovering from the Orbital Approximation
Payoff forOrganic
Chemistry!
ReactivityHOMOs and LUMOs
Recognizing Functional Groups
How Organic Chemistry Really Developed (Intro)
2-e Wave Function
(r1,1,1,r2,2,2)
a(r1,1,1) b(r2,2,2)
=?
Multiply 1-e Wave Functions
2
2 2
No way can electrons be independent!
They repel one another.
Pretend that the other electron(s) just reduce the nuclear charge for the orbital of interest.
"Clementi-Raimondi" values for Zeff(best fit to better calculations)
Atom Z Zeff 1s
He 2 1.69
2s
2p
Z - effective
Zeff 2s Zeff 2p
C 6 5.67 3.22 3.14
Zeff 3s
Na 11 10.63 6.57 6.80 2.51
!
!
2s slightlyless screened
than 2p
vice versa for Na
Pretty
Crude
r2Znao
1s = K e-/2
(subtle)
1s
Self-Consistent Field (SCF)1. Find approximate orbitals for all electrons
(e.g. using Zeff)
2. Calculate potential from nuclei and. .. fixed clouds for all electrons but one.
3. Use this new potential to calculate an. an..improved orbital for that one electron.
4. Repeat steps 2 and 3 to improvethe orbital for another electron.
. . . Improve all orbitals one by one.
Quit When orbital shapes stop changing
Cycle back to improve 1st orbital further, etc. etc.
Still Wrong!because real electronsare not fixed clouds.
They keep out of each other’s way by correlating their motions.
True Energy < SCF Energy
"Correlation Energy"
Hide the residual error after full SCF calculation to the “Hartree-Fock” limit
by giving it a fancy name:
Where to get correct energy (& total electron density)?
by experiment
or by a whopping calculation:
e.g. “Configuration Interaction” (CI)
or
“Density Functional Theory” (DFT)
"Non-bonded" Contacts (1-20)
+
++ ++ +C+6
-- ---
Energy Magnitudes
Should Chemists care about the error in Orbital Theory?
-2log
(Ene
rgy
Cha
nge
kca
l / m
ole
C Core (2 104)
1/2 4 Single Bonds (2 102)
He•He @ 52Å! (2 10-6)
Changes in "correlation energy"
can be ~10-15% of Bond Energy.
Orbital Theory is fine for Qualitative
Understanding of Bonding.
C "Correlation Energy" (102)
-C••
••C
12C Nucleus (2 109)Loses 0.1 amu (E = mc2)Fortunately nuclear energy
is totally unchangedduring chemistry!
0.001% change in nuclear energy would overwhelm all of Coulomb.
correlation error ≈ bond
8
0
6
2
4
~
C Atom (3 103)
Orbitals can't be “true”for >1 electron, because of e-e repulsion
butwe'll use themto understand
bonding, structure,energy, and reactivity
What gives Atomic Orbitals their Shape?
Potential Energyscales r
(via )
Kinetic Energy
creates nodes
4d
2s
double the nuclear charge
If we use orbitals, how should we reckon total electron density?
Density of electron 1 = 1 2(x1,y1,z1)
Density of electron 2 = 2 2(x2,y2,z2)
Total density (x,y,z) = 1 2(x,y,z) + 2
2(x,y,z)
(Sum, not Product. Not a question of joint probability)
How Lumpy is the N Atom?
Total = K(r2) e-
(2px)2 = K x2 e-
(2py)2 = K y2 e-
(2pz)2 = K z2 e-
Total = K(x2 + y2 + z2) e-
Spherical ![from an Organic Text]
TFDCBC
CC
C
F
N
is roundnot clover-leafnor diamond!
C N Triple Bond
2px2 + 2py
2 depends on (x2+y2) It is thus symmetrical
about the z axis
cross section
?
MoleculesPlum-Pudding MOs (the "United Atom" Limit)Understanding Bonds (Pairwise LCAO-MOs)
“Overlap & Energy-Match"
Atoms3-Dimensional Reality (H-like Atoms)
HybridizationOrbitals for Many-Electron Atoms (Wrong!)Recovering from the Orbital Approximation
Set of atoms
Atoms withsmall bonding
distortion
Single “United Atom”
Ways of Looking at a Molecule(or a Molecular Orbital)
e-densitycontours
of H2
Whichcontourshould
we use?
Moleculefrom setof atoms
Moleculeas one atom
distorted by afragmented nucleusNuclei embedded in
a cloud of electronsdispersed and “noded”
by kinetic energy
J. J. Thomson'sPlum Pudding!
(backwards)
Moleculeas atoms
Methane&
Ammonia
Spartan 6-31G* calculates good SCF MOs(on my laptop!)
We want to understand them visually.
1sCH4 NH3
"Core" OrbitalsLike 1s of C/NTightly Held
Little Distortion
Contour Level 0.001 e/Å3
We'll focus onValenceOrbitals
Boring!
..
.. ......
.... ..
8 valence e-
4 MOs8 valence e-
4 MOs
ene
rgy
Three “degenerate”Molecular Orbitals
CH4 NH32pz
HOMOLewis's "unshared pair"
......
CH4 NH3
.... .... ..
+Unoccupied Orbitals +Unoccupied Orbitals