Structure, bonding, and spectroscopy
of actinides in crystals
A quantum chemical perspective
Zoila Barandiarán
Departamento de Química &
Instituto Universitario de Ciencia de Materiales Nicolás Cabrera
Universidad Autónoma de Madrid, Spain.
http://www.uam.es/zoila.barandiaran
Structure, bonding, and spectroscopy of actinides in crystals
A quantum chemical perspective
Actinides
advanced nuclear energy systems
challenge basic and applied research
societal interest: controversial energy source; security & waste problems
in crystals
ions in crystals, solid fuel and fission products (UO2, PuO2)
extreme conditions (temperature, pressure)
spectroscopy
open shells: 5f,
6d, 7s
large manifolds of excited states: 5fN, 5fN-1 6d1, and others
spectroscopy: a basic tool
expected/exotic electronic structures beyond the gs
figerprints of local structure and bonding
models of coordination chemistry
quantum chemical perspective
2
Actinide ions doped in solids – an example
point defect:
+ local distortion
+ new electronic states in the energy gap
how many states ? how to calculate them ?
N electrons formally in 5f, 6d shells in a crystal field
U4+ in Cs2GeF6
3
f and d electrons in an octahedral field
Pa4+ in Cs2ZrCl6
4
f and d electrons in an octahedral field
Pa4+ in Cs2ZrCl6
U4+ in Cs2ZrCl6
5
Structure, bonding, and spectroscopy of actinides in crystals
A quantum chemical perspective
A quantum chemical model
(for ground and excited states)
Results
an overview
type of results
accuracies
a show case
Conclusions and what is next
6
A quantum chemical model
for ground and excited states
Relativisticcore-AIMP
(spin-orbit)
• •relativistic
(ECP)
Electron correlation
• •wave-function
based correlation methods
n
• Large f + and
fn-1 d1 manifolds
(CASSCF
MS-CASPT2)
Defect cluster
fn , fn-1d1
embedding-AIMP
Embedding
host
7
Ab Initio Model Potentials as Effective Core+Embedding Potentials
Active (cluster valence)
(UF6)2- 68 electrons
Material
Cs2GeF6 with
U4+ impurities
Inactive (core)
U [Kr],4f
F 1s
Inactive (environment)
Cs2GeF6
• Non-parametric & produced directly from the frozen orbitals
• Inactive-active explicit interactions
– Coulomb, Exchange, Linear independence
8
Embedded Cluster Hamiltonian
Relativistic Cowan-Griffin-Wood-Boring Hartree-Fock
all-electron atomic calculations
+
long-range local Frozen core approximation
+

AIMP recipe for representation of operators
local
Coulomb
Exchange + scalar relativistic
Linear independence
9
Embedded Cluster Hamiltonian
Relativistic Cowan-Griffin-Wood-Boring Hartree-Fock
all-electron atomic calculations
+
short-range
Frozen core
approximation
+
spectral
AIMP recipe for representation
of operators
representation
Coulomb
Exchange + scalar relativistic
Linear independence
10
Embedded Cluster Hamiltonian
Relativistic Cowan-Griffin-Wood-Boring Hartree-Fock
all-electron atomic calculations
+
Frozen core approximation
+
AIMP recipe for representation of operators
Coulomb
Exchange + scalar relativistic
Linear independence
11
Embedded Cluster Hamiltonian
Self-Consistent Embedded Ion calculations
Perfect crystal lattice
loop over lattice ions until convergence
perform a single embedded-ion calculation (SCF, CASSCF)
produce its embedding-AIMP out of its orbitals
update the lattice embedding potentials
end loop
12
Embedded Cluster Hamiltonian
13
Spin-orbit coupling / electron correlation
Spin-orbit splittings
depend on:
which demand:
spin-orbit couplings
spin-free spectrum
small CI space P
large CI space G
An aproximate decoupling of correlation and spin-orbit
Use G space for the spin-free spectrum
Use P space for the spin-orbit couplings
14
Spin-free state shifted Hamiltonian
small CI space P
large CI space G
Use G space for the spin-free spectrum
Use P space for the spin-orbit couplings
15
Spin-free state shifted Hamiltonian
small CI space P

large CI space G

Use G space for the spin-free spectrum
Use P space for the spin-orbit couplings
16
Spin-free state shifted Hamiltonian
– Codes:
MOLCAS
Björn O. Roos et al., Lund University
COLUMBUS
EPCISO
Russ M. Pitzer et al., Ohio State University
Valérie Vallet et al., Université de Lille
Use G space for the spin-free spectrum
Use P space for the spin-orbit couplings
17
Details of the calculations
 Embedded-cluster
(embedding AIMP for ionic solids)
 Effective core potential
(Cowan-Griffin-Wood-Boring based AIMP)
 spin-free:
CASSCF/CASPT2
 spin-orbit:
sfss-SOCI [MRCI(S)]
– Embedding potentials:
– Cluster: (AnL6)q-
~ 500 AIMPs + 3000 point charges
at experimental sites
so that E(R) is stable
18
Details of the calculations
 Embedded-cluster
(embedding AIMP for ionic solids)
 Effective core potential
(Cowan-Griffin-Wood-Boring based AIMP)
 spin-free:
CASSCF/CASPT2
 spin-orbit:
sfss-SOCI [MRCI(S)]
– Core AIMPs:
An: [Xe,4f] 5d,6s,6p, 5f,6d,7s
Cl: [Ne] 3s,3p
– Valence basis sets:
An: (14s10p12d9f3g)/[6s4p5d4f1g]
Cl: (7s7p1d)/[3s4p1d]
19
Details of the calculations
 Embedded-cluster
(embedding AIMP for ionic solids)
 Effective core potential
(Cowan-Griffin-Wood-Boring based AIMP)
 spin-free:
CASSCF/CASPT2
 spin-orbit:
sfss-SOCI [MRCI(S)]
– SA-CASSCF:
[5f,6d,7s]N
– MS-CASPT2:
An: 5d106s26p6 [5f,6d,7s]N + 6 x Cl:
3s23p6
20
Details of the calculations
 Embedded-cluster
(embedding AIMP for ionic solids)
 Effective core potential
(Cowan-Griffin-Wood-Boring based AIMP)
 spin-free:
CASSCF/CASPT2
 spin-orbit:
sfss-SOCI [MRCI(S)]
– spin-free-state-shifted Spin-Orbit CI:
Wood-Boring spin-orbit operator scaled by 0.9
Basis of double-group adapted functions
MRCI(S)
CAS[5f,6d,7s]N
21
Results: type of results
Local structure (ground/excited states)
bond lengths, vibrational frequencies
22
Results: type of results
Local structure (ground/excited states)
lengths, (and
vibrational
Wavebond
functions
theirfrequencies
analyses)
bonding interactions
23
Results: type of results
Local structure (ground/excited states)
lengths, (and
vibrational
Wavebond
functions
theirfrequencies
analyses)
bonding interactions spectra
Absorption/emission
transition energies, transition moments, emission lifetimes
24
Results: type of results
Green-to-blue
light upconversion in Cs2ZrCl6: U4+
Local structure (ground/excited
states)
lengths, (and
vibrational
Wavebond
functions
theirfrequencies
analyses)
UO22+ impurities
U4+ impurities
bonding
interactions
Absorption/emission spectra
transition energies,
transition
moments, emission lifetimes
Mechanisms
of energy
transfer
5f16d1 levels
upconversion/quantum cutting mechanisms
5f2 levels
25
Results: type of results
Local structure (ground/excited states)
lengths, (and
vibrational
frequencies
3+ under pressure
Wavebond
functions
their
analyses)
Cs
2NaYCl6:Ce
bonding interactions spectra
Absorption/emission
transition energies,
transition
moments, emission lifetimes
Mechanisms
of energy
transfer
upconversion/quantum
Pressure
effects cutting mechanisms
d(eg)1
d(t2g)1
P=25 kbar
P=0
f1
26
Results: type of results
Local structure (ground/excited states)
lengths, (and
vibrational
Wavebond
functions
theirfrequencies
analyses)
bonding interactions spectra
Absorption/emission
transition energies,
transition
moments, emission lifetimes
Mechanisms
of energy
transfer
upconversion/quantum
Pressure
effects cutting mechanisms
27
Results: accuracies (validation + applications)
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
Cs2NaYCl6
Cs2ZrCl6
Cs2GeF6
SrF2
BaF2
YAG
(Y3Al5O12)
CsCaBr3
0.01Å
presumably (no
EXAFS available)
very good
(exceptions?)
Cs2ZrCl6:Pa4+
YAG:Ce3+
Vibrational frequencies
5%
Ce3+,Pr3+,Sm2+,Pa4+
Electronic transitions
10%
Ce3+,Pa4+,U3+,U4+
Pressure induced shifts
of electronic transitions
semiquantitative
Sm2+
Intensidades relativas
semiquantitative
Ce3+,U3+,U4+
Bond distances
Bond length changes
28
Results: a show case
Predicting the luminescence of a new material
+ experimental & theoretical study
U4+ in fluorides
U4+
5f2, 5f16d1 manifolds
fluorides
large transparency window
~90 excited states
Potentiality as
● UV solid state laser
● Phosphor based on quantum cutting or cascade luminescence
29
quantum cutting or
cascade luminescence
UV solid state laser
5f16d1 levels
1S
0
5f2 levels
Strong, broad, fast
6d→5f luminescence
YLiF4:U4+
Weak, slow, two-step 5f→5f
luminescence
YF3:U4+
30
UV solid state laser
quantum cutting or
cascade luminescence
•The electronic structure of the 5f2 manifold
•The 5f1 6d1 manifold
• Promote the synthesis and experimental study
• An unexpected 5f1 7s1 manifold: U-trapped excitons
U4+ in Cs2GeF6
31
Cs2GeF6:U4+, a potential quantum cutter or solid state laser ?
1S
0
5f2 levels
32
Cs2GeF2:U4+, a potential quantum cutter or solid state laser ?
quantum cutting or
cascade luminescence
1S
0
5f16d1 levels
5f16d1 levels
1S
0
5f2 levels
3P
0
5f2 levels
3H
4
33
Cs2GeF2:U4+, a potential quantum cutter or solid state laser ?
UV solid state laser
5f16d1 levels
1S
1S
0
5f16d1 levels
0
5f2 levels
5f2 levels
Strong, broad, fast
6d→5f luminescence
34
Absorption spectrum.
Miroslaw Karbowiak, University of
Wroklaw
• growth of Cs2GeF6:U4+ single crystals
• experimental absorption spectrum (7 K)
• broad, intense bands 37000 – 45000cm-1
• most prominent at 38000 cm-1
• no appreciable fine vibronic structure
35
Absorption spectrum.
• Theoretical spectrum
• Five 5f16d1 origins: 1A1g → iT1u
• 2500cm-1 too high
(0.3 eV)
( i = 1,5)
(7 %)
36
Absorption spectrum.
• Theoretical spectrum
• Five 5f16d1 origins: 1A1g → iT1u
• 2500cm-1 too high
(0.3 eV)
( i = 1,5)
(7 %)
• Intensities:
+ most prominent band 1A1g → 1T1u
+ relative intensities ok,
- except for 1A1g → 2T1u
37
Emission spectrum.
1T2g
1Eu
5f16d1 levels
5f2 levels
2T1g, 2T2g
3T2g
1T1g
38
Emission spectrum.
Large Stokes shift: 6200 cm-1
1Eu
1T2g
2T1g, 2T2g
3T2g
1T1g
1A1g
39
Emission spectrum.
Spontaneous emission lifetime: 
Experiments underway
40
An unexpected 5f17s1 manifold: U-trapped exciton?
2.09
2.154, 2.174, 2.21
Å
U(IV)
• Bond length ~ U(V) cluster
• Very diffuse 7s orbital
• Energy sensitive to basis
set delocalization
U - trapped exciton ?
41
An unexpected 5f17s1 manifold: U-trapped exciton?
Impurity-trapped exciton
D. S. McClure, et al. Phys. Rev. B, 32, 8465 (1985)
SrF2:Yb2+ anomalous emission
“The excited state ... could be called an impurity-trapped exciton,
since it consists of a bound electron-hole pair with the hole localized
on the impurity and the electron on nearby lattice sites...”
“The trapped exciton geometry is probably that expected for a
trivalent impurity ion, Yb3+...”
Yb2+ → Yb3+ +
1e(Sr)
very short bond length
localised
hole
delocalised
42
Analysis of the wavefunctions
7s AO [5f17s1-3F U4+]
7s MO [5f17s1-23A2u (UF6Cs8)6+]
43
Microscopic description of an impurity trapped exciton
• ~ U(V) bond length
• Hole localized
in the U(5f)
• Electronic density
in the frontier of
the UF6 unit
Diffuse orbitals of Ln/An in solids can lead to
impurity trapped excitons
44
Conclusions
Wavefunction based ab initio embedded cluster calculations on
Lnq+ and Anq+ impurities in ionic hosts
– Reliable enough (complement experiments, predict)
– Can be used to progress in the understanding of
Advanced Nuclear Energy Systems
What is next ?
Nuclear fuel and nuclear wastes materials
– UO2 (experimental spectroscopy available) , PuO2
– diluted UO2/PuO2 mixtures UO2:Pu4+, PuO2:U4+
Transuranium systems (the f7 configuration)
– Cm3+ in Cs2NaYCl6 (experimental spectroscopy available)
– and Am2+ and Bk4+
45
Acknowledgments
Noémi Barros
Luis Seijo
Belén Ordejón
Ana Muñoz
José Luis Pascual
me
José Gracia
Fernando Ruipérez
on campus, UAM 2006
Goar Sánchez
in La Sierra, Madrid 2007
http://www.uam.es/quimica/aimp/
46
Acknowledgments
•
•
•
•
•
•
Miroslaw Karbowiak, Faculty of Chemistry, University of Wroclaw, Wroclaw, Poland
Norman Edelstein, Lawrence Berkeley National Laboratory, Berkeley, California,
USA
Björn Roos, Rolandh Lindh, (MOLCAS) Lund University, Lund, Sweden
Russell Pitzer, (COLUMBUS) Ohio State University, Columbus, Ohio, USA
Valérie Vallet, Jean-Pierre Flament (EPCISO) Université de Lille, Lille, France
Spanish Ministry of Education and Science, DGI-BQU2002-01316,DGI-CTQ200508550.
47
Structure, bonding, and spectroscopy
of actinides in crystals.
A quantum chemical perspective
Universidad Autónoma de Madrid
48