How to probe the coordination chemistry and electronic spectroscopy of actinide compounds? DFT...

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

3

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, ….)

4

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

5

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

6

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

7

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?

8

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).


= 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).


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).


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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


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


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}


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)


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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


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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)


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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


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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)


Influence of the H0 Hamiltonian

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Geometries of uranyl(VI)

5f state have asymmetric structures


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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.


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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.


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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 (?)


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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

How to probe the coordination chemistry and electronic spectroscopy of actinide compounds? DFT...

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