How to probe the coordination chemistry and electronic spectroscopy of actinide compounds?
DFT versus WFT methods
Valérie Vallet
Laboratoire PhLAM - University of Lille - CNRS
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Physical and chemical properties of actinide complexes
Fundamental knowledge:
Chemical composition (stoichiometry) of species in multi-component systems
Structures of the species present
Thermodynamical properties
Reactivity of complexes
Chemical bonding
Magnetism, photophysics, photochemistry
…
Applications
Reprocessing, separation chemistry, sorption, medical, catalysis
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Challenge of theoretical modeling in actinide science
Objective: interpret and predict macroscopic phenomena
Experimental work has limitations (radioactivity,…)
Simulations at the atomistic, nanoscale: the scale of many relevant processes
Two main goals:
Improve our understanding of existing compounds and help the interpretation of current experimental data
Predict properties for unknown species or species difficult to manipulate experimentally (Plutonium, ….)
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Challenge of theoretical modeling in actinide science
Need for robust and predictive theoretical modeling
Use physically based theory
Be “Ab initio” as much as possible: no experimental input or phenomenological models
Toward a numerical “virtual lab”Able to compute properties difficult
or impossible to measure experimentally
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Multi-scale modeling for actinides
10
100
1 000
10 000
100 000
1 000 000
> 10 000000
Quantum chemistryAb intio methods (first principles)
No adjustable parameters( no approximation)
Or DFT
Simplified HamiltonianClassical/quantum mechanics
Need for inter-atomic potentials
Continuum media (non atomistic)
Nb of atoms
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Which electronic structure methods?
We wish to:
Optimize structures of materials Compute properties: bond length, energies, frequencies,
electronic spectra, …
Specificities of actinides
Relativistic effects (scalar and spin-orbit) Electron correlation Open-shell electronic configurations High-density of states
Single-reference methods can only be applied to single-reference cases: closed-shell systems and high-spin states
For other cases use multiconfigurational methods
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Which electronic structure methods?
Wave-function theoryWave-function theory
Relativistic framework
Hartree-Fock theory (single-reference)
Multi-configurational approaches (MCSCF)
Near-degeneracy effects Multiconfigurational character of
WF
Post-HF / Post-MCSCF approaches:
Dynamic electron correlation MRCI, CASPT2, EOM-CCSD,…
Limitations:
size of the molecular system Number of correlated electrons
Density functional theoryDensity functional theory
Single-determinant approach
Dynamical correlation treated by the exchange and correlation potential VXC
Excited state with linear-response theory: TD-DFT
Limitations:
Single-reference method
VXC optimized and tested for G2 or extended G2 sets (no heavy element) !
Accuracy for f elements?
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Examples taken from early actinide complexes Use a 1-component scalar relativistic framework with a posteriori spin-
orbit treatment Discuss the accuracy of DFT vs WFT:
Structural parameters Energetics, thermodynamics Excited states
Topic of the discussion
A “good computational model for good reasons
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Desired accuracy
Resolve molecular geometries, Raman or infrared spectra
Desirable accuracy:
0.01-0.02 Å for bond length
50 cm-1 for vibrational frequencies (Experimental data include anharmonicity)
Experimental data available:
X-Ray crystallographic structures
EXAFS (X-Ray) for solvated species
Few Raman or infrared spectra for solvated species
Structural parameters
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UF6
E. R. Batista et al., J. Chem. Phys. 121, 2144 (2004).
Structural parameters
= 52 cm-1 = 25 cm-1
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PuN2: multiconfigurational 3Hg5f2+5f3+ + 5f2-5f3-
Clavaguéra et al. J. Chem. Phys. 121, 5312 (2004).
Structural parameters
Multiconfigurational character not
treated by DFT
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Uranyl(VI) aqua ion [UO2(H2O)5]2+
Method R(An-Oyl) [Å] R(U-OH2) [Å] Ref
HF 1.694 2.545 [1]
LDA 1.778 2.423
BLYP 1.803 2.516
B3LYP 1.756 2.516
MP2 1.779 2.48 [2]
B3LYP-CPCM 1.746 2.43 [3]
B3LYP + 2nd sphere
1.767 2.43 [4]
Exp: EXAFS 1.76(1) 2.41(1) [5]
[1] P. J. Hay et al. J. Phys. Chem. A 104 6259 (2000); [2] V. Vallet, et al. Theor. Chem. Acc. 115, 145 (2006)[3] V. Vallet, I. Grenthe, C. R. Chimie 10, 905 (2007); [4] K. E. Gutowski et al., J. Phys. Chem. A 110, 8840 (2006); [5] U. Wahlgren, et al., J. Phys. Chem. A 103, 8257 (1999).
Structural parameters
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Desirable accuracy
Chemical accuracy : 1-2 kcal/mol for reaction thermodynamics and activation parameters
Errors on the absolute energies might be large
Choice of the theoretical approach that provides theoretically funded error compensation
Few thermodynamics data available:
Gas-phase reactions
Activation parameters for ligand exchange reactions in solvent
Solvation energies for some actinides but with large uncertainties
Energetics and thermodynamics
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Reaction energies for gas-phase reactions with U(VI) {5f0}
T. Privalov, et al., J. Phys. Chem. A 106, 11277 (2002).
Breaking strong bonds
Difficult case for all methods: MP2, CCSD(T), B3LYP
Need to benchmark other WFT methods
Energetics and thermodynamics
HF geometries
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Solvation of uranyl(VI) {5f0}
P. Wahlin, et al. J. Chem. Theory Comput. (2007), submitted.
[UO2(H2O)6]2+ [UO2(H2O)5]2+,(H2O) [UO2(H2O)4]2+,(H2O)2
Energetics and thermodynamics
Gas-phase energiesB3LYP geometries
Re
lativ
e e
ne
rgie
s in
kJ/
mol
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precursor
D-transition state D-intermediate
A-transition state A-intermediate
H (UVI): Exp. 26 kJ/mol
H(UVI) = 62 kJ/mol
H(UVI) = 19 kJ/mol
Ligand-exchange dynamics on uranyl(VI) {5f0}
Energetics and thermodynamics
MP2 geometriesMP2-CPCM energies
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Reduction of U(VI) {5f0} to U(IV) {5f2}
Reaction CASPT2 MR-ACPF B3LYP VWN BP
UO22+ (5f0) + 1/2 H2O HOUO2+ (5f1) +
1/4 O2 51.3 44.5 -39.4 -66.9 -
39.7
HOUO2+ (5f1) + 1/2 H2O U(OH)22+ (5f2) +
1/4 O2
18.1 23.3 -0.8 48.9 30.5
Failure of DFT independent on the functional
DFT can not describe the multi-configurational character of U(IV)
Energetics and thermodynamics
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Intermediate remarks
DFT yields accurate geometries, vibrational frequencies
Be VERY cautious for energetics:
Metal-ligand binding energies (DFT favors low coordination numbers)
Wrong energetics for redox reactions
Difficulties to describe breaking of strong bonds (gas-phase reactions)
Single or multiconfigurational ab initio quantum chemical methods yield chemical accuracy
Energetics and thermodynamics
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Available data for electronic spectra
Energy levels of 4f and 5f elements are well analyzed for f impurities in solidscf. Zoila Barandiarán
Spectra of solvated ions are more complex and more difficult to analyze
Few gas-phase electronic spectra: M. Heaven et al.cf. Björn Roos, Luuk Visscher
Electronic spectroscopy
Eliet et al. J. Chem. Soc., Faraday Trans. 91, 2275 (1995))
2 species:
• [UO2(H2O)5]2+(aq)
• (2,2) uranyl-OH complex:
[(UO2)2(OH)2(H2O)6]2+
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g
u
g
u
g
u
gg
uuu
5f
6d
**
*
*
Magnetic Dipole u u (weak)
U
U
U
U
12 Bonding Electrons –M-O Bond Order ~3
Oxygen 2p orbitals
Metal Orbitals
R.G. Denning, ACTINET-ThUL School
Bonding scheme in actinyl(VI)
Electronic spectroscopy
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Computational details
MethodsGeometries and energies computed with LR-CCSD, CASPT2, TD-DFT with various functionals
Basis set and ECP
U: ANO basis set (B. O. Roos) O:ANO basis set (QZVP)
U: The Stuttgart small core ECP with corresponding basis set
O: AE description, triply split in the valence, one d (TZVP)
Packages: Molcas, Molpro, Dalton, TurboMole, Gaussian, EPCISO
Electronic spectroscopy
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Spin-free states of uranyl(VI)
[1] K. Pierloot, J. Chem. Phys. 123, 204309 (2005)
[2] K. Pierloot, J. Chem. Phys. 126, 194311 (2007)
Electronic spectroscopy
Influence of the H0 Hamiltonian
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Geometries of uranyl(VI)
5f state have asymmetric structures
Electronic spectroscopy
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Potential curves along the symmetric U-Oyl stretch
LR-CCSDTDDFT-B3LYP
Similar shape of the potential curves Relaxation energy of the 3g state: 10 kJ/mol TDDFT; 14 kJ/mol LR-CCSD
F. Réal et al. J. Chem. Phys. In press.
Electronic spectroscopy
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Potential curves along one single U-Oyl stretch
LR-CCSDTDDFT-B3LYP
Similar shape of the potential curves Relaxation energy of the 3g state: 89 kJ/mol TDDFT; 80 kJ/mol LR-CCSD
F. Réal et al. J. Chem. Phys. In press.
Electronic spectroscopy
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Remarks on the electronic spectroscopy
Geometries are OK
TD-DFT with present functional is not accurate for excitation energies:
differences up to 7000 cm-1 / 1 eV
Over- or underestimation of transition energies
TD-DFT is OK for potential curves (?)
Electronic spectroscopy
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Conclusions
DFT has problems for energetics and excitation energies problem for Car-Parinello simulations
When absolute numbers are not correct, trends along the f-elements series might be correct useful to extrapolate known experimental data
Need for new functionals specially tested on heavy elements
Need for accurate gas-phase data: thermodynamics, spectra, …. to benchmark quantum chemical methods
Accurate quantum chemical methods interaction potentials
multi-scale modeling
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Take home messageCheck the accuracy of your method to get a good answer for a
good reason
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Acknowledgments & Financial Support
University of Lille
Reda Belmecheri, Cécile Danilo, Dr. Jean-Pierre Flament, Dr. Florent Réal
University of Stockholm
Pernilla Wåhlin, Prof. Ulf Wahlgren, Dr. Peter Macak, Dr. Timofei Privalov
Royal Institute of Technology (Stockholm)
Prof. Ingmar Grenthe
INE, Forschungszentrum Karlsruhe
Dr. Bernd Schimmelpfennig
Financial support:
ACTINET research network of excellence
CNRS & Ministère de la Recherche et de la Technologie
Région Nord Pas de Calais