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)
e- + Molecule+
hn + Molecule
Ehn - Ee-
=
EM+ - EM
= Ionization Energy
IE = Difference in energy between states of M, M+
How do we label states?
Each electronic state has its own term symbol
Use Russell Saunders Coupling to describe electron-electron repulsion
orbital angular momentum
spin multiplicity
2S+1
LJ
L=0
L=1
L=2
L=3
S term
P term
D term
F term
When considering
symmetry use the
Mulliken symbol
spin orbit coupling
J = |L+S| ...|L-S|
L = 0, 1, 2…total orbital angular momentum (term)
ML = -L…+L component of L (ML = S ml)
S = total spin quantum number (S = S s)
Ms = -S….+S component of S (MS = S ms)
Within each term, there can be several degenerate microstates with different ML and MS
Photoelectron Spectra of Atoms (Noble Gases)
Ar
We are observing transitions between the neutral
ground state and cation states formed by removing
an electron from the highest occupied orbital.
What’s the term symbol for the ground state of Ar?
Ground State: 1s22s22p63s23p6
Kr
No unpaired electrons: 1S
Remove one 3p electron:
First Ion State: 1s22s22p63s23p5
Xe
S = |1/2|
(2S+1) = 2
L = 1 (P)
J = L+S ...L-S
17
16
15 14
J = 1/2 and 3/2
13 12 11
Ionization Energy (eV)
2P
1/2
and 2P3/2
Ar
2P
1/2
Energy
Kr
2P
3/2
Xe
1S
17
16
15 14
13 12 11
Ionization Energy (eV)
What about molecules?
σ*
H 1s
↿
⇂
H 1s
↿⇂ σ
18
17
16
Ionization Energy (eV)
15
Transitions between molecular
potential energy surfaces
During an electronic transition
the complex absorbs energy
electrons change orbital
Excited State
molecular rotations
lower energy
microwave radiation
the complex changes energy state
electron transitions
higher energy
visible and UV radiation
Timescale : ≈10-15 sec
Timescale of geometry changes
(vibrations): ≈10-12 sec
Ground State
molecular vibrations
medium energy
IR radiation
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
Potential Energy Surface Description of the
Ionization of Dihydrogen
Ionization Energy (eV)
18
H2+
17
16
15
H2
0
0
1
r (Å)
2
Much more on this next time!!
Molecular Term Symbols
Use Russell Saunders Coupling to describe electron-electron repulsion
molecular orbital angular momentum
spin multiplicity
2S+1
LJ
When considering
symmetry use the
Mulliken symbol
spin orbit coupling (we will ignore this for now)
L = total orbital angular momentum expressed by orbital symmetry (term)
S = total spin quantum number (S = S s)
Ms = -S….+S component of S (MS = S ms)
Consider Dinitrogen
First ion state (X) = 2Sg+
2u
Second ion state (A) = 2u
1g
2p
Third ion state (B) = 2Su+
2p
2g+
1u
2s
1u+
2s
1g+
:N≡N:
Ground state (X) = 1Sg+
20
19
18
17
16
Ionization Energy (eV)
15
Potential Well Description
2u
Eu+
2
1g
2p
2p
2g+
A u+
2
Eg+
2
1u
2s
1u+
1g+
:N≡N:
Ground state (X) = 1Sg+
2s
N2 1Eg
Models to describe molecular
electronic structure
MO Theory compared to
Valence Bond Theory
Consider methane.
VSEPR gives 4 sp3 hybrid orbitals.
Photoelectron Spectroscopy
CH 4
2p
sp3
2s
24
22
20
18
16
14
Ionization Energy (eV)
So why are there two valence ionizations separated by almost 10 eV?
12
Use of reducible representations
in M.O. theory
Consider transformation properties of
vectors aligned with the 4 C-H bonds.
Td
E
8C3
3C2
6S4 6σd
σ
4
1
0
0
2
Apply Reduction Formula:
1
a A1  [4  8  0  0  12]  1
24
1
a A2  [4  8  0  0  12]  0
24
1
aE  [8  8  0  0  0]  0
24
1
aT1  [12  0  0  0  12]  0
24
1
aT1  [12  0  0  0  12]  1
24
C-H = A1 + T2
http://www.mpip-mainz.mpg.de/~gelessus/group.html
LCAO Description of Methane
2p (t2)
CH4
t2 (1, 2, 3)
a1 (1)
2s (a1)
24
C
CH4
H4
22
20
18
16
14
Ionization Energy (eV)
12
M(CO)6 M = Cr, Mo, W, d6 metals
t1u*
L
a1g*
L
L
L
L
L
t2g*
t1u
a1g 4s
eg*
t1g + t2g + t1u + t2u
Ligand * orbitals
Doct
eg
t2g
3d
t2g
eg
t1u
a1g
6 x LGO
a1g eg t1u
Ligand  orbitals
t1g + t2g + t1u + t2u
Photoelectron spectra of d6 metal hexacarbonyls
M(CO)6
vertical
2T
• 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
2g
Cr
Mo
• 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
W
18
16
12
10
8
14
Ionization Energy (eV)
– t1u → 2T1u
– t2u → 2T2u
Open shell ground states
To this point we have only considered molecules with closed shell
ground states: What if there are unpaired electrons in the ground state?
V(CO) 6
V(CO)6 a 17 e- complex.
Ground State: t2g5 : 2T2g
20
18
16
14
12
10
Ionization Energy (eV)
First ion state: t2g4 : T2g x T2g
= 3T1g, 1T2g, 1E1g, 1A1g
8
6
Second ion state: t1u5t2g5 : T1u x T2g
= 3,1T2u, 3,1T1u, 3,1Eu, 3,1A2u
And so on and so on…
But, open-shell molecules aren’t
always this complicated…
H2(oep)
2
2
Au
B1u
Mg(oep)
2
2
A1u
A2u
VO(oep)
10
9
8
7
Ionization Energy (eV)
6
• 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