Photoelectron Spectroscopy

Photoelectron Spectroscopy

• Lecture 2: Ionization Transitions– Transition moment integral– Ionization selection rules and probability– Atomic and molecular term symbols– A bit of molecular orbital theory

Ionization is still a transition between states

• Initial State: Neutral (or anion)• Final State: Atom/Molecule/Anion after an electron

is removed, plus the ejected electron• M → M+ + e-

init = M final = M+ + e-• Transition Probability = ∫ init m final d• For direct photoionization, transition probability is

always > 0• Photoionization probability is typically described in

terms of a cross-section (much more on this later)

hn + Molecule

= Ionization Energy

e- + Molecule+

Ehn - Ee- = EM+ - EM

IE = Difference in energy between states of M, M+

Each electronic state has its own term symbol

spin multiplicityL = 0 S termL = 1 P termL = 2 D termL = 3 F term

Within each term, there can be several degenerate microstates with different ML and MS

Use Russell Saunders Coupling to describe electron-electron repulsion

L = 0, 1, 2…total orbital angular momentum (term)

ML = -L…+L component of L (ML = ml)

S = total spin quantum number (S = s)

Ms = -S….+S component of S (MS = ms)

2S+1

L J

J = |L+S| ...|L-S|

orbital angular momentum

spin orbit coupling

When consideringsymmetry use theMulliken symbol

How do we label states?

Photoelectron Spectra of Atoms (Noble Gases)

Ionization Energy (eV)17 16 15 14 13 12 11

Ar

Kr

Xe


Ar

Kr

Xe

What’s the term symbol for the ground state of Ar?

Ground State: 1s22s22p63s23p6

No unpaired electrons: 1S

Remove one 3p electron:

First Ion State: 1s22s22p63s23p5

S = |1/2| (2S+1) = 2

L = 1 (P)

J = L+S ...L-S J = 1/2 and 3/2

2P1/2 and 2P3/2

We are observing transitions between the neutralground state and cation states formed by removing an electron from the highest occupied orbital.


Ar

Kr

Xe


Ar

Kr

Xe

1S

2P3/2

2P1/2

Ene

rgy

Ionization Energy (eV)

161718 15

↿⇂↿ ⇂H 1sH 1s

σ

σ*

What about molecules?

molecular rotationslower energy microwave radiation

electron transitionshigher energy visible and UV radiation

molecular vibrationsmedium energy IR radiation

Ground State

Excited StateDuring an electronic transition

the complex absorbs energy

electrons change orbital

the complex changes energy state

Timescale : ≈10-15 sec

Timescale of geometry changes (vibrations): ≈10-12 sec

As a result, observe vertical (Franck-Condon) transitions

In other words, we assume that we only have to consider the electronic portion of the ground- and excited-state wavefunctions to understand these transitions: Born-Oppenheimer approximation

Transitions between molecular potential energy surfaces

18

17

16

15

0

Ioni

zatio

n E

nerg

y (e

V)

H2+

r (Å)0 1 2

H2

Potential Energy Surface Description of the Ionization of Dihydrogen

Much more on this next time!!

Molecular Term Symbols

spin multiplicity

Use Russell Saunders Coupling to describe electron-electron repulsion

L = total orbital angular momentum expressed by orbital symmetry (term)

S = total spin quantum number (S = s)

Ms = -S….+S component of S (MS = ms)

2S+1

L J

molecular orbital angular momentum

spin orbit coupling (we will ignore this for now)

When consideringsymmetry use theMulliken symbol

Ground state (X) = 1g+

Ionization Energy (eV)151617181920

:N≡N:

2p

2s

2p

2s

1g+

2g+

1u+

2u

1u

1g

First ion state (X) = 2g+

Second ion state (A) = 2u

Third ion state (B) = 2u+

Consider Dinitrogen

N21g

2g+

2u+

2u+

Ground state (X) = 1g+

:N≡N:

2p

2s

2p

2s

1g+

2g+

1u+

2u

1u

1g

Potential Well Description

Models to describe molecular electronic structure

MO Theory compared to

Valence Bond Theory

Consider methane.

VSEPR gives 4 sp3 hybrid orbitals.

24 22 20 18 16 14 12


CH 4

24 22 20 18 16 14 12


CH 4

Photoelectron Spectroscopy

2s

2p

sp3

So why are there two valence ionizations separated by almost 10 eV?

Use of reducible representations in M.O. theory

Consider transformation properties ofvectors aligned with the 4 C-H bonds.

Td E 8C3 3C2 6S4 6σd

σ 4 1 0 0 2

1]120084[24

11

Aa

0]120084[24

12

Aa

0]00088[24

1Ea

0]1200012[24

11

Ta

1]1200012[24

11

Ta

C-H = A1 + T2

http://www.mpip-mainz.mpg.de/~gelessus/group.html

Apply Reduction Formula:

http://www.mpip-mainz.mpg.de/~gelessus/group.html

24 22 20 18 16 14 12


CH4

24 22 20 18 16 14 12


CH4

CH4

t2 (1, 2, 3)

a1 (1)

2p (t2)

2s (a1)

C H4

LCAO Description of Methane

t2g3d

4s

6 x LGO

L

LL

L

L

L

oct

t1u

t1u*

a1g*

a1g

eg*

eg

t1u

a1g

t2g

eg

a1g t1ueg

M(CO)6 M = Cr, Mo, W, d6 metals

Ligand * orbitals

t1g + t2g + t1u + t2u

t2g*

t1g + t2g + t1u + t2u

Ligand orbitals

18


M(CO)6

Cr

Mo

W

16 14 12 10 8

vertical

2T2g

Photoelectron spectra of d6 metal hexacarbonyls

• Neutral molecules are closed shell; term symbol for ground state in Oh symmetry is 1A1g

• First ionization is from metal t2g orbital; term symbol for resultant state is 2T2g

• Followed by series of overlapping ionizations due to ionization from CO orbitals; M-C σ orbitals, etc.

• States due to ionization from CO orbitals:

– t1g → 2T1g

– t2g → 2T2g

– t1u → 2T1u

– t2u → 2T2u

V(CO)6 a 17 e- complex.

To this point we have only considered molecules with closed shellground states: What if there are unpaired electrons in the ground state?

V(CO)6

68101214161820Ionization Energy (eV)

V(CO)6

68101214161820Ionization Energy (eV)

Ground State: t2g5 : 2T2g

First ion state: t2g4 : T2g x T2g

= 3T1g, 1T2g, 1E1g, 1A1g

Second ion state: t1u5t2g

5 : T1u x T2g

= 3,1T2u, 3,1T1u, 3,1Eu, 3,1A2u

Open shell ground states

And so on and so on…


10 7 689

2Au2B1u

2A1u2A2u

H2(oep)

Mg(oep)

VO(oep)

But, open-shell molecules aren’t always this complicated…

• Energy splitting of ionizations is dependent upon the amount of electronic communication between the unpaired electrons as defined by the exchange integral.

• This is referred to as the exchange splitting.

• If exchange splitting is relatively small, spectra of molecules with open shell ground states can be treated as though they are closed shell systems.

For low symmetries, term symbols often aren’t that useful

Summary

• Photoionization is a transition between states• States are described using term symbols• Simple valence bond theory does not explain all

features observed in spectroscopy, requiring use of molecular orbital theory.

• “Koopmans’ Theorem” begins to break down for systems with unpaired electrons in the initial state

Photoelectron Spectroscopy

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