Oxidation State Ambiguity in f Element Organometallics a Spectroscopic and Quantum Chemical Journey
Nik Kaltsoyannis
Department of Chemistry, University College London
Outline of presentation
Story 1: X-ray absorption spectroscopy of Ce compounds
Story 2: Gas-phase photoelectron spectroscopy of CeCp3
Story 3: Multiconfigurational quantum chemical calculations of M(COT)2
(COT = 8-C8H8; M = Th, Pa, U, Pu, Cm and Ce)
Story 4: Multiconfigurational quantum chemical calculations of CeCp3 and CeCp3+ (Cp = 5-C5H5)
Ce
Ln(COT)2 the “lanthanocenes”
An(COT)2 the “actinocenes”
CeCp3
Story 1: X-ray absorption spectroscopy of Ce compounds
b1u
b2g
4 (b1u)
d (e1g)
d (e2g)
e3g
e3u
3 (e3g)
d (a1g)
d
Qualitative molecular
orbital diagram for
M(COT)2
M = f element
f (e2u)
f (e1u)
f
f (a2u)
f (e3u)
e2u
e2g
2 (e2u)
e1g
e1u
1 (e1g)
a2u
M
M(COT)2
a1g
0 (a2u)
(COT)2
COT
The traditional view of Ce(COT)2 and Th(COT)2
f (e2u)
f (e1u)
f
f (a2u)
f (e3u)
e2u
e2g
2 (e2u)
Ground state is 1A1g with an electronic configuration e2u(2)4f0
 M(IV) and 2 x COT2-
Correct description of Th(COT)2 BUT NOT Ce(COT)2
M. Dolg, P. Fulde, H. Stoll, H. Preuss, A. Chang and R. M. Pitzer
J. Chem. Phys. 195 (1995) 71
Dolg et al.’s view of Ce(COT)2
f (e2u)
f (e1u)
f
20%
f (a2u)
f (e3u)
e2u
e2g
2 (e2u)
Ground state is 1A1g with two
contributing electronic configurations
e2u(2)4f0 (20%) + e2u(2)3f1 (80%)
 Ce(III) and 2 x COT1.5-
f (e2u)
f (e1u)
f
80%
f (a2u)
f (e3u)
e2u
e2g
2 (e2u)
Can we test this experimentally (how do we measure oxidation state)?
X-ray Absorption Near Edge
Spectroscopy (XANES)
CeO2
(Ce(IV))
Ce K edge (1s electrons)
Need a variable energy light source
capable of delivering c. 40 keV
photons (Stanford Synchrotron)
Representative K-edge spectra of Ce compounds
N. M. Edelstein, P. G. Allen, J. J. Bucher, D. K. Shuh, C. D.
Sofield, A. Sella, M. Russo, N. Kaltsoyannis and G. Maunder
J. Am. Chem. Soc. 118 (1996) 13115
Shift from CeB6 Standard (eV)
Ce K-edge XANES results
Q Ce3+compounds
W Ce4+compounds
L Substituted cerocenes
10
▼ Ce(IV) compounds
■ Ce(III) compounds
5
Substitued cerocenes
Ce(III) !!
0
Compound
1 CeO2 (solid)
8 Ce2(SO4)3 (solid)
15 Ce(NO3)3 (1.2 M HCl solution)
2 Ce(NH4)4(SO4)4.2H2O (solid)
9 CeSi2 (solid)
3 Ce(NH4)4(SO4)4.2H2O (1.6 M HNO3 soln.)
10 CeI3.(THF)x (THF soln.)
16 Ce[1,4(TMS)2C8H6]2 (toluene soln.)
4 Ce(CH3C(O)CHC(O)CH3)4 (toluene soln.)
11 Ce[(Me3C)2C5H3]3 (toluene soln.)
17 Ce[1,3,6(TMS)3C8H5]2 (toluene soln.)
5 CeCl3.6H2O (solid)
12 Ce2(SO4)3 (1.6 M HNO3 soln.)
18 Li{Ce[1,4(TMS)2C8H6]2} (toluene soln.)
6 CeF3 (solid)
13 Ce2(SO4)3 (1.2 M HCl soln.)
19 K{Ce(C8H8)2} (toluene soln.)
7 Ce2O2S (solid)
14 Ce(NO3)3 (1.6 M HNO3 soln.)
H
He
Li
Be
B
C
N
O
F
Ne
Na
Mg
Al
Si
P
S
Cl
Ar
K
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
Ga
Ge
As
Se
Br
Kr
Rb
Sr
Y
Zr
Nb
Mo
Tc
Ru
Rh
Pd
Ag
Cd
In
Sn
Sb
Te
I
Xe
Cs
Ba
La
Hf
Ta
W
Re
Os
Ir
Pt
Au
Hg
Tl
Pb
Bi
Po
At
Rn
Fr
Ra
Ac
Rf
Db
Sg
Bh
Hs
Mt
Ce
Pr
Nd
Pm
Sm
Eu
Gd
Tb
Dy
Ho
Er
Tm
Yb
Lu
Th
Pa
U
Np
Pu
Am
Cm
Bk
Cf
Es
Fm
Md
No
Lr
Increasing tendency toward lanthanide-like chemistry (An(III) dominant)
 Are the ground states of the later actinocenes multiconfigurational?
Need: high-level ab initio calculations (see story 3….)
Story 2: Gas-phase photoelectron spectroscopy of CeCp3
The experiment
e-
UV or X-ray light
Gaseous
molecules
ee-
Measure kinetic energy of electrons and
determine ionization energy as the
difference between the energy of the
incident light photons and the electrons’
kinetic energy
Direct probe of electronic energy levels
Compared with d-block complexes, very few lanthanide complexes have been
studied in the gas phase, because it is very hard to see f-based bands in spectra
Two main reasons
1.
With Ln(III) compounds ionizations from 4f orbitals come at
similar ionization energies to those from ligand orbitals
2.
With photon energies given by discharge lamps 4f cross
sections (ionization probabilities) are low
Ionization cross sections (ionization probabilities)
10
Calculated photoionization cross sections
for C 2p and Ce 4f electrons
(Lindau and Leh)
Cross section
8
At photon energies
accessible with a
discharge lamp, 4f
electrons have very low
ionization cross sections
C 2p
Ce 4f
6
4
Delayed maximum
2
0
0
50
100
Photon energy / eV
150
200
The “Elettra” synchrotron, Trieste, Italy
10
Calculated photoionization cross sections
for C 2p and Ce 4f electrons
(Lindau and Leh)
Photoelectron spectrum of CeCp3
1500
Cross section
8
hv = 25 eV
C 2p
Ce 4f
6
4
counts
2
1000
Cp š
0
0
50
150
Photon energy / eV
Cp 
500
100
Cp 
0
6
8
10
14
12
16
18
20
IE / eV
At low incident photon energies only ionizations from the Cp rings are visible
200
Photoelectron spectrum of CeCp3 (again)
E
250x10
F
6
hv = 40 eV
Counts
200
Cp 
150
C2
C3
100
C1
B
50
A
D
0
6
8
10
12
IE / eV
14
16
18
Low ionization energy band (A) clearly visible BUT also
a band just above 10 eV (D) showing f characteristics
Are there really two f bands?
If the incident photon energy is sufficient to excite a Ce 4d core electron to a 4f
orbital, a resonance will occur. Ionization of a 4f electron can borrow intensity from
this transition and the ionization cross section can show a dramatic increase
 tune hn to the 4d ionization energy…..
Normalized counts
8x10
6
A (f)
hv = 122 eV
6
D (f)
4
Cp 
2
B C
0
6
8
10
12
IE / eV
14
16
18
Resonance structure is observed for bands A and D
i.e. ionization of the single 4f electron gives rise to two cation states with f character
What the…..?
Assume neutral CeCp3 has a ground state with the configuration Lf1,
where L represents the ligand electrons and f1 is the single 4f electron
The matrix element governing the band intensity for f ionization is given by
Lf 1 | Oˆ | Lε
where  is the free electron (g) wave
Note that
(a) L represents a configuration with ligand electrons and no f electrons, i.e. Lf0 and
(b) the ion states corresponding to bands A and D in the photoelectron spectrum must
have L (Lf0) as a contributing configuration
What the…..? (continued)
Assume that ionization of the f electron leads to ligand to metal charge transfer,
generating a cation configuration with a hole in the ligand orbitals and a single Ce
4f electron, i.e. L-1f1 (sound familiar….?)
If Lf0 and L-1f1 have the same symmetry, mixing of the two
configurations can generate two states of CeCp3+
gc1Lf0 + c2L-1f1)
band A – ground state of CeCp3+
ec3Lf0 – c4L-1f1)
band D – excited state of CeCp3+
 Our suggestion was that the ground state of CeCp3+ (formally Ce(IV)) is
multiconfigurational, in a manner comparable with that of neutral Ce(COT)2
M. Coreno, M. DeSimone, J. C. Green, N. Kaltsoyannis, N. Narband and A. Sella,
Chemical Physics Letters 432 (2006) 17
Story 3: Ab initio quantum chemical calculations of M(COT)2
(M = Th, Pa, U, Pu, Cm and Ce)
Computational details
• CASSCF/CASPT2 method
• MOLCAS code
• D2h point group
• Basis sets: correlation consistent, all-electron, ANO
(27s24p18d14f)/[10s9p7d5f] for An, (25s22p15d11f)/[9s8p5d4f] for
Ce, VDZP for C and H
• Scalar relativistic effects incorporated via 2nd order Douglas-Kroll
• Spin-orbit free and spin-orbit coupled calculations
d (e1g)
Active spaces
d (e2g)
Partial ground state geometry optimisations
performed with ((12+n),16) active spaces (n =
0 (Ce, Th), 1 (Pa) and 2 (U)….)
d (a1g)
6d
f (e2u)
f (e1u)
5f
f (a2u)
f (e3u)
e2u
e2g
Ground and excited states calculated with
((8+n),14) active spaces (n = 0 (Ce, Th), 1
(Pa), 2 (U)….)
For the partial geometry
optimisations of the ground
state of Pa(COT)2 (13,16),
11,451,440 configurations
2 (e2u)
were included
e1g
1 (e1g)
M
M(COT)2
(COT)2
COT
Results – Th(COT)2
Ground state is the expected 1Ag (d0f0)
Metal-ring distance; 2.015 Å (calc), 2.004 Å (expt)
Two lowest energy singlet and triplet states of each D2h irrep calculated (32 states)
Lowest energy dipole-allowed transition is to 1B1u (dσ1f0); 2.47 eV (calc), 2.76 eV (expt –
UV/Vis)
Spin-orbit coupling makes essentially no difference to energy spectrum (<0.05 eV).
Th(COT)2 energy level diagram
Ground
state
First
excited
states
(Th(Cp'')3)
Results – Pa(COT)2
Ground state is a degenerate pair of spin-orbit free states 2B2u/2B3u (d0f1)
Metal-ring distance; 1.969 Å (calc), 1.964 Å (“expt”, average of Th(COT)2 and U(COT)2)
Two lowest energy doublet and quartet states of each D2h irrep calculated
Spin-orbit coupling makes a significant difference
Pa(COT)2 energy level diagram
(no spin-orbit coupling)
The effect of spin-orbit coupling on the ground and lowest excited states of Pa(COT)2
A comparison of the spin-orbit coupled Pa(COT)2
energy levels (eV) with those from previous calculations
State
Symmetry
This work
Chang et al. a
Li & Bursten b
1
E5/2u
0
0
0
2
E1/2u
0.003
0.166
0.049
3
E3/2u
0.459
0.477
0.369
4
E7/2u
0.584
0.362
0.379
5
E1/2u
0.642
0.569
0.541
6
E1/2g
0.880
0.925
0.685
7
E3/2u
1.467
1.222
1.122
a SOCI
calculations using the experimental uranocene geometry (1.924 Å)
DFT calculation using the PW91 exchange-correlation functional, using an
optimised geometry with ring-metal separation of 1.975 Å
b
Results – U(COT)2
Metal-ring distance; 1.944 Å (calc), 1.924 Å (expt)
Spin-orbit coupled ground state is E3g
Dominant
configuration of
spin-orbit free state
Total spin of
spin-orbit free
state
This work
Chang et al.
f1f1
1
70.7
68.0
f1f1
1
22.1
22.7
f1f1
0
7.0
5.3
Results – U(COT)2
Comparison of experimental (UV/Vis) excitation energies (eV) with calculation
Expt
This work
1.880
1.934
1.65
2.018
1.79
Both calculated transitions are principally f  dσ in character
Results – Ce(COT)2
Ground state is the expected 1Ag
Metal-ring distance; 1.964 Å (calc), 1.969 Å (expt)
Lowest energy dipole-allowed transitions are to 1B1u (d0fσ1) and 1B2u/1B3u (d0f1);
2.47 eV (calc), 2.18 eV (expt – UV/Vis). Second dipole-allowed transition to 1B1u
(d0f1); 2.93 eV (calc), 2.63 eV (expt)
As with Th(COT)2, spin-orbit coupling makes essentially no difference to energy
spectrum (<0.05 eV).
Ce(COT)2 energy level diagram
A look at the ground and first excited 1Ag states of Ce(COT)2
84.6% f1, 6.2% f2
58.1% f0, 23.4% f1, 8.7% f2
Change in ground state energy
How can we square this result with previous
theory and experiment for Ce(COT)2?
(number of states
in state-average)
Single state total energy = -257724.60 eV
Ce(COT)2 f electron occupancy nf
Experiment (XANES): 0.89 ± 0.03
C.H. Booth, M.D. Walter, M. Daniel, W.W. Lukens and R.A. Andersen
Phys. Rev. Lett. 95 (2005) 267202
Calculation: 0.90 ± 0.04
Configurational admixture of Ce(COT)2 ground state as a function of ns
Occupation (NOO) of the Ce(COT)2 ground
state natural orbitals as a function of ns
A. Kerridge, R. Coates and N. Kaltsoyannis J. Phys. Chem. A 113 (2009) 2896
What about the actinides?
Occupation of the ground state e2u “f” natural orbitals in An(COT)2
0.35
0.3
0.25
0.2
Ce(COT)2 = 0.216
0.15
0.1
0.05
0
Th
Pa
U
Pu
Cm
A. Kerridge and N. Kaltsoyannis J. Phys. Chem. A 113 (2009) 8737
Story 4: Ab initio quantum chemical calculations of CeCp3 and CeCp3+
Recall the PE spectrum of CeCp3…..
Normalized counts
8x10
6
A (f)
hv = 122 eV
6
D (f)
4
Cp 
2
B C
0
6
8
10
12
IE / eV
14
16
18
Active spaces for CeCp3 and CeCp3+
2a2
4a1 (dz2)
5d
2a1 + 3a1 + 3e + 4e
4f
a2
1a2
e
e
1a1
2e
1e
Ce
CeCp3
2,3 (e1'')
a1
Cp3
Cp
Inclusion of all 14 MOs too costly  (5,8) for CeCp3 and (4,8) for CeCp3+ (4  a, 4  a)
Configurational admixture of CeCp3+ 1A ground state as a function of ns
Contribution of configuration (%)
80
70
60
50
2000 2000
2000 u0d0
2000 0020
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10
Number of states in average
 Use natural orbitals and their occupations
NOOs of CeCp3 2A ground state
Active space orbital
Occupation
48a'
49a'
50a'
51a'
33a''
34a''
35a''
36a''
1.967
0.001
0.027
0.005
1.966
0.029
0.005
1.000
Single configurational state
One 4f-localised NO
NOOs of CeCp3+ 1A ground state
Active space orbital
Occupation
48a'
49a'
50a'
51a'
33a''
34a''
35a''
36a''
1.961
0.000
0.000
0.038
1.445
0.000
0.555
0.000
Strongly multi-configurational state
No 4f-localised NO (as expected following 4f ionisation)
Energy relative to CeCp3: 7.07 eV (band A in PE spectrum 6.77 eV)
NOOs of CeCp3+ fifth excited 1A and 1A states
Active space orbital
48a'
49a'
50a'
51a'
33a''
34a''
35a''
36a''
Occupation 1A
1.509
1.000
0.001
0.490
0.963
0.000
0.000
0.037
Occupation 1A
0.985
1.013
0.000
0.002
1.473
0.000
0.526
0.001
Strongly multi-configurational states
No 4f-localised NO (as expected following 4f ionisation)
Energy relative to CeCp3: 10.00 and 10.17 eV (band D in PE spectrum 9.97 eV)
R. Coates, M. Coreno, M. DiSimone, J.C. Green, N. Kaltsoyannis,
A. Kerridge, N. Narband and A. Sella Dalton Trans. (2009) 5943
Conclusions - 1
Calculations (Dolg et al.) suggest that Ce(COT)2 has a multiconfigurational ground
state, with a dominant f1 (Ce(III)) configuration. XANES results (us and Booth et al.)
appear to support this.
Variable energy photoelectron spectroscopy of CeCp3 reveals not one but two f
bands during resonance; is the ground state of CeCp3+ multiconfigurational?
CAS calculations on An(COT)2 (An = Th, Pa, U) yield results consistent with
experiment and previous computational studies.
CAS calculations on Ce(COT)2 produce excellent agreement with experiment for
metal-ring separation, electronic excitation energies and f electron occupancy (nf).
Total energy of Ce(COT)2 ground state, nf, the natural orbitals and their
occupations are essentially invariant to the number of states included in the stateaverage.
Description of ground state in terms of configurational admixture varies wildly as a
function of state average  configurational admixture not a reliable tool to describe
the electronic structure of Ce(COT)2.
Conclusions - 2
Ce(COT)2 is best described as Ce(IV) system in which transfer of electron density from
ligand to metal through occupation of bonding orbitals allows measures of the effective
oxidation state to be lower than the formal +4 value, and indeed closer to +3 in certain
cases.
Occupation of the ground state e2u “f” natural orbitals increases markedly across the
actinide series, indicating that the ground states of the later actinocenes are strongly
multiconfigurational.
The ion states which give rise to bands A and D in the photoelectron spectrum of
CeCp3+ are strongly multiconfigurational, and do not possess a Ce 4f-localised natural
orbital (i.e. they have the characteristics of f ionization).
And finally……
“The effective oxidation state of Ce in cerocene is intermediate between the formal
Ce(IV) and Ce(III) situations. When interpreted as a Ce(IV) system the effective
oxidation number is lowered toward III by strong orbital mixing, whereas when
interpreted as a Ce(III) system a strong configurational mixing increases the
effective oxidation number toward IV. The latter choice however is more compact
since only two configurations…..are needed for building a sufficiently accurate
zeroth-order wavefunction: the cerocene 1A1g ground state can be described as
a…..mixture of about 70% 4f13 and 30% 4f04.”
The without whom department
Berkeley
Norm Edelstein
Pat Allen
Jerry Bucher
Dave Shuh
Chad Sofield
Oxford
Jenny Green
Trieste (Elettra)
Monica DiSimone
Marcello Coreno
UCL
Andy Kerridge
Rosie Coates
Andrea Sella
Maria-Rosa Russo
Graham Maunder
Naima Narband
National Service for Computational Chemistry Software