Molecular Orbital Theory Reading: DeKock and Gray,...

1

Chem 104A, UC, Berkeley

Molecular Orbital Theory

Reading: DeKock and Gray, Chap 4 (but not 4-8) Chap 5 (through 5-8)

Miessler and Tarr, Chap 5


2


Linear Combination of Atomic Orbitals (LCAO)

1. n atomic orbitals n molecular orbitals.

2. Like atomic orbitals, MOs are ortho-normal

)...(0

)...(1

jidv

jidv

ji

ji

nnk ccc ....2211


3


)11()(

)11()( **

BAbb

g

BAu

ssN

ssN

1])1()1)(1(2)1([)(

1])11([)]([

222

22

dvsdvssdvsN

dvssNdv

BBAAb

BAbb

g

1 SAB 1

Overlap integralDegree of spatial overlap between any two AOs From different atoms in a molecule.

AB

AB

b

SN

SN

22

1

22

1

*


Gerade and Ungerade MO symmetry

)1(2

11

)1(2

11

ab

ab

ab

ba

S

ss

S

ss

a, b, exchange position, MO does change, no inversionodd parity, ungerade: German word for “odd”.

)1(2

11

)1(2

11

ab

ab

ab

ba

S

ss

S

ss

a, b, exchange position, MO does not change, inversion Even parity, Gerade: German word for “even”.

4


The energy of these two orbitals are obtained by applying Schrodinger Equation

Orbital Interaction Diagram1. Always draw axis

2. Fill in electron using Aufbau principle


*u

bg

*b

N*=1.4

Nb=0.53

-13.6 eV

* b>

5


•Bond order = ½ (#bonding e-s -#antibonding e-s)

•Bond order = 0 indicates the species will not exist.


Photoelectron Spectroscopy

hv electron

Photoelectric effect (Einstein)

2

2

1eM mvIEh

eMhM

6


PES instruments consist of an X-ray or UV source, an energy analyzer for the photoelectrons, and an electron detector.


5 4 . 7

X-raySource

Optics

Hemispherical Energy Analyzer

Position Sensitive Detector (PSD)

Magnetic ShieldOuter Sphere

Inner Sphere

Sample

Computer System

Analyzer Control

Multi-Channel Plate Electron Multiplier

Resistive Anode Encoder

Lenses for Energy Adjustment (Retardation)

Lenses for Analysis Area Definition

Position Address Converter

7


IE(eV)

Electronemitted

12 16 20 24

13.6 eV

24.59 eV

15.45 eV

H

H2

He

12200 cm


Koopman’s Theorem

IE (n) = - En

The ionization energy of electron n is equal to the negative of itsOrbital energy.

We can obtain orbital energies via PES!

8


*u

bg

*

b

N*=1.4

Nb=0.53

-13.6 eV


Quantum Harmonic Oscillator

k

2

1

9


Energy

Internuclear Distance

H2

2H

Ground state molecule is typically in its lowest vibrational state.Upon ionization, H2

+ could be in a vibrational excited state.

ehv

eHhvHbg

bg

12

22

)()(

hvnEv )2

1(

Probability distributionOf the vibrational wavefunction


Energy


H2

2H

Vibrational Probability Distribution:

For n=0: largest at equil. Distance

For higher levels:

Largest at the extreme of compression& expansion (KE=0)

10


Wave functions, allowed energies, and corresponding probability densities for the harmonic oscillator


Energy


H2

2H

Adiabaticionization

00 , nn

0n

0, n

11


Energy


H2

2H

Adiabaticionization

Vertical ionization

Relative Intensity

overlap of vibrationalWave function


Energy


H2

2H

Adiabaticionization

Vertical ionization

Removing electron from bonding MO

12200 cm

k

2

1

12


IE(eV)

Electronemitted

12 16 20 24

13.6 eV

24.59 eV

15.45 eV

H

H2

He

12200 cm


Energy


Adiabaticionization

Vertical ionization

Removing electron from antibonding MO

13


Energy


Adiabaticionization

Removing electron from nonbonding MO


)11()(

)11()( **

BAbb

g

BAu

ssN

ssN

Overlap integralDegree of spatial overlap between any two AOs From different atoms in a molecule.

Degree of AO interaction is closely related to their overlap

Functions of distance, symmetry.

AB

AB

b

SN

SN

22

1

22

1

*

14


SAB >0, bonding interaction, E stabilized


SAB <0, antibonding interaction, E destabilized

SAB =0, nonbonding, no orbital interaction.

*

*

*

15



Molecular Orbital Theory Reading: DeKock and Gray,...

Documents

Transcript of Molecular Orbital Theory Reading: DeKock and Gray,...