Finding reliable and feasible ab initio methods for computing properties of matter at extreme conditions: high-P & T and strongly correlated electronic systems.Extensive validation of the computational methodology on available experimental data and its subsequent applications to simulation of various materials properties.

Joint atomistic modeling and experimental investigation of matter at high pressure and temperature.

Computational details

Motivation and approach: DFT often fails to properly describe properties of f-electron systems [11] and other ab initio methods are usually computationally unfeasible. We have tested the DFT+U method with the Hubbard U=ULR parameters (Table 1) [12,13] calculated ab initio using the linear response approach [4,5].

Results: The DFT+U method with ULR parameter calculated ab initio significantly decreases the mean absolute error (MAE). Mixing functionals [E=E(PBE)-5(E(PBE)-(BPBE))] (PBE-BPBE corr. in Fig. 2) gives smaller MAE than GGA functionals. MAE of 30 kJ/mol can be achieved by setting the value of the ĸ parameter in the PBE exchange functional enhancement function, F(s), to 6 (modified PBE in Fig. 2), but the new functional often fails for the structural properties [12].

Affordable methods for f-elements

Fig. 12. The mean absolute error (MAE) for the 11 reaction enthalpies reported in [6], for which the experimental values are known. Black, striped and red bars represent our results while green bars are the results of [6] obtained with higher order post Hartree-Fock methods.

Molecule Hubbard ULRU(VI)F6 3.1

U(VI)O2F2 3.1

U(VI)OF4 2.8

U(VI)O3 2.6

U(V)F5 2.3

U(IV)F4 1.8

U(IV)O2 2.0

Table 1. The Hubbard U parameter values for uranium atoms in uranium-bearing molecular complexes calculated ab initio using the linear response approach [4].

High P & T solid state chemistry

aInstitute of Nuclear Waste Management and Reactor Safety (IEK-6), Forschungszentrum Jülich, Jülich, Germany *Contact: p.kowalski@fz-juelich.debUniversité de Montréal, Canada cUniversity of Cologne, Germany, dGerman Research Centre for Geosciences, Potsdam, Germany

Piotr Kowalski, E. Alekseev, G. Beridze, P. Keglera, S. Blouin, P. Dufourb, S. Jahnc, and B. Wunderd

02NUK021A

Fig. 11. Optimized structures of UF6, UOF4, UF5, and UO3.

UF6→UF5+FUF5→UF4+F UOF4→UF4+OUO2F2→UO2+2FUF6+2UO3→3UO2F2

2UOF4→UF6+UO2F2

UOF4+UO3→2UO2F2

UO3→UO2+OUF6+H2O→UOF4+2HFUF6+2H2O→UO2F2+4HFUF6+3H2O→UO3+6HF

Mitg

lied

der

He

lmho

ltz-G

emei

nsch

aft

Fig. 8. Different phases of U2O

5.

Phase diagrams

Results:➢ New phase of U

2O

5 has been synthesized at high-P (10 GPa).

➢ Only when accounting for f-electrons correlations with the DFT+U method the δ-U

2O

5 is predicted to be the stable phase at ambient

conditions. The phase transition is predicted at P~4 to 8 GPa.

Motivation and approach: Investigation of new high-P phases (P up to 25 GPa).

References:[1] P. Giannozzi et al., J. Phys.: Condens. Matter, 21, 395502 (2009) ; www.quantum-espresso.org.[2] www.cpmd.org.[3] www.flapw.de.[4] V. I. Anisimov, et al., Phys. Rev. B, 48, 16929 (1993). [5] M. Cococcioni and S. de Gironcoli, Phys. Rev. B, 71, 035105 (2005).[6] K. Karlsson, F. Aryasetiawan et al., Phys. Rev. B, 81, 245113 (2010). [7] P. M. Kowalski & S. Jahn, Geochimica & Cosmochimica Acta 75, 6112 (2011). [8] P. M. Kowalski, S. Blouin & P. Dufour, ASP Conf. Series, 509, 155 (2017);P. M. Kowalski, Astronomy and Astrophysics (Letters), 566, L8 (2014).[9] P. M. Kowalski, Astronomy and Astrophysics (Letters), 519, L8 (2010)[10] B. Xiao et al., Chemistry – European Journal, 22, 946 (2016).[11] G. A. Shamov, G. Schreckenbach et al., Chem. Eur. J., 13, 4932 (2007). [12] G. Beridze and P. M. Kowalski, J. Phys. Chem. A, 118, 11797 (2014).[13] G. Beridze, et al., Prog. Nucl. Ener.gy, 92, 142 (2016).[14] A. Blanca-Romero, et al., J. Comput. Chem., 35, 1339 (2014).

Motivations and aims

Results

Pseudopotentials-based DFT codes: Quantum-ESPRESSO, CPMD and all-electron codes FLEUR, FLEUR SPEX [1-3]. Various exchange-correlation functionals (PBE, PBEsol, BPBE…) and the DFT+U method [4] with the Hubbard U parameter obtained ab initio using the linear response (cLDA) [5] and the constrained random phase approximation (cRPA) [6] methods.

IR opacities (WDs atmospheres)

Acknowledgments:

We acknowledge German Federal Ministry of Education and Research for the financial support (02NUK021A) and JARA-HPC for providing the computational resources.

Phosphate ceramics

Results: Compared to the ambient ThMo2O8 phases, the density of HP phase is increased by nearly 20% for the HT/HP ThMo2O8 at 3.5 GPa [10]. Transition to the HT/HP polymorph can occur even at room temperature for pressures higher than 2.1 GPa [10].

Motivation: Understanding the polymorphism in ThMo2O8 system.

Fig. 10. The derived P–T phase diagram of ThMo2O8 derived from DFT calculations.

Fig. 13. Monoclinic lattice (P21/n) (Z=4).

Fig. 14. Ln-O in monazite obtained with DFT and DFT+ULR methods in comparison with experimental data.

The DFT+ULR method gives the best match to the Ln-O bond-lengths [13] and performs much better than DFT [14].

Fig. 15. The formation enthalpies for monazite (filled symbols) and xenotime (open symbols) computed considering the 1/2Ln2O3 + 1/2P2O5 → LnPO4 reaction and using the DFT and DFT+ULR methods.

Thermochemistry

For monazite and xenotime the formation enthalpies are improved with the DFT+ULR calculations, however the best results are obtained when the f electrons are treated as core electrons.

Structural properties

Isotope fractionation factors

P-distortion of WDs spectra

Experimental setup:➢ Two well established high

pressure / high temperature methods in one machine.

➢ Allows to apply hydrostatic pressures of up to 25 GPa and temperatures up to 2400°C.

➢ Large samples volumes of up to 800 mg.

δ-U2O5 (ambient phase)

Results:➢ Most rocks forming minerals contain 6-fold coordinated Li (micas) and should be enriched in light isotope while aqueous fluids containing 4-5 fold coordinated Li should carry heavy isotope to the melt and the surface [7].

Enrichment in heavy Li,no variation across the volcanic arc.

LHS 290“peculiar” DQ

LHS 179 DQ

Te, wDOS

DFT calculationspredict increase in the electronic transition energy!

Observed C/He of Dufour et al.,

ApJ, (2005)

Log C/He=-4

-5

-6-7

C/He=0FLUID

GAS

New spectrum, plot

LHS 290 “peculiar”DQ

Teff

=5800K

Fig. 1. Li isotopic signature across a subduction zone and volcanic arc.

Fig. 2. The computed Li isotopes fractionation factors between different minerals and aqueous fluid at P=2 GPa [7].

7Li/6Li

Motivation and approach: Understanding the isotopic signature along a subduction zone

Motivation and approach: Understanding of the P-distortion of the C

2 Swan bands in DQp

stars.

Fig. 3. The computed H2-He CIA

absorption coefficients at different densities compared to gas phase calculations of Abel et al. J. Chem. Phys 136, 044319 (2012) (density correction of Hare & Welsh, Can. J. Phys. 36, 94 (1958)).

Results:➢ Enhancement of the roto-translational band and splitting and depletion of the vibrational band with redistribution of the absorption towards the higher frequencies for ρ > 0.2 g/cc [8].

Motivation and approach: Understanding the density(P)-distortion of the IR H

2-He

collision-induced absorption (CIA).

Fig. 4. Swan Band observed in DQ (LHS 179) and DQp stars (LHS 290) [9].

Fig. 5. The photospheric densities in DQ stars and computed density-induced (P-induced) change in the electronic transition energy T

e [9].

Fig. 6. Simulated distortion of the C

2

Swan bands for DQp star LHS 290 [9].

Fig. 7. High pressure press.

Motivation: Reliable ab initio modeling of Ln-phosphates (LnPO

4) as

prospective ceramic nuclear waste forms.

Results: DQp stars explained as DQs with P-distorted C

2 Swan bands.

Knowledge gain➢ Performing experiments under high pressure / high temperature

conditions allows a deep insight in the chemistry of actinides.➢ Investigation of the P-induced change of electron configuration (especially

5f electrons) and cations coordination.

Fig. 9. The enthalpy difference

between the HP-and δ-U2O

5

phases computed with the DFT+U method using different exchange-correlation functionals.

HP-U2O5 (high-P phase)