Chem 125 Lecture 1410/9/2006

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Orbital Paradise

(3Ne variables) = 1 (x1,y1,z1) 2 (x2,y2,z2) …

Total e-density (x,y,z) = 1 2(x,y,z) + 2

2(x,y,z) + …

Total e-Energy = 1 + E2 + …

e.g. Ne (1s)2 (2s)2 (2px)2 (2py)2 (2pz) 2

"Correlation Energy"

Error after full SCF calculation to “Hartree-Fock” limit:

Get correct energy / total electron density

by experiment

or by a whopping calculation:

e.g. “Configuration Interaction” (CI)

or

“Density Functional Theory” (DFT)

If we’re really lucky, "Correlation Energy"might be Negligible.

+

++ ++ +C+6

-- ---

Energy Magnitudes

Should Chemists care about the error in Orbital Theory?

8

0

6

2

4

-2

log

(Ene

rgy)

k

cal /

mol

e

C Atom (2 104)

1/2 4 C-C Bonds (2 102)

"Non-bonded" Contact (1-10)

He•He 52Å! (2 10-6)

Changes in "correlation energy"

are ~10-15% ofBond Energy.

Orbital Theory is fine for Qualitative

Understanding of Bonding.

C "Correlation Energy" (102)

-C••

••C

12C Nucleus (2 109)

Nuclear energy totally unchanged by chemistry!

Loses 0.1 amu (E = mc2)

Orbitals can't be “true”(for >1 electron)

butwe'll use themto understand

bonding, structure,energy, and reactivity

What gives Atomic Orbitals their Shape?

Potential Energyscales r

Kinetic Energy

creates nodes

4d

2s

double 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?

spherical “dumb-bells”

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 !

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 upon any

rotation about the z axis

What's Coming for Next Exam?

MoleculesPlum-Pudding Molecules ("United Atom" Limit)

Understanding Bonds (Pairwise LCAO)"Energy-Match & Overlap"

Structure (and Dynamics) of XH3 Molecules

Atoms3-Dimensional Reality (H-like Atoms)

HybridizationOrbitals for Many-Electron Atoms (Wrong!)Recovering from the Orbital Approximation

Payoff forOrganic

Chemistry!

ReactivityHOMOs and LUMOs

Recognizing Functional Groups

Ways of Looking at an Elephant

Set of atoms

Atoms withweak bonding

Single “United Atom”

distorted by afragmented nucleus

Ways of Looking at a Molecule(or a Molecular Orbital)

e-densitycontours

of H2

Whichcontourshould

we use?

Moleculefrom atomsMolecule

as one atom

Nuclei embedded ina cloud of electrons

dispersed and “noded”by kinetic energy

J. J. Thomson'sPlum Pudding!

Moleculeas atoms

How the PlumsDistort

Electronic Puddings

Methane&

Ammonia

Spartan 6-31G* calculates good SCF MOs(on my laptop!)

We want to understand them visually.

4 Pairs of Valence Electrons

H

C HHH

NH H

H

Compare MOsto AOs of Ne

(4 electron pairs n=2)

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

1s.... ....

...... ..

1s.... ....

...... ..

But we'll neglect the tiny spherical node for this discussion.

Actually 2s

2px

.. ......

..

CH4 NH3

.. ....

CH4 NH32py

.. ..

......

CH4 NH3

.. ....

CH4 NH32py

.. ..

......

CH4 NH3

.. ....

CH4 NH32pz

HOMOLewis's "unshared pair"

......

CH4 NH3

.... .... ..

+Unoccupied Orbitals +Unoccupied Orbitals

End