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Recently, a combined experimental–theoretical approach to assess the effect of daughter product formation on the stability of crystalline compounds comprised of radioisotopes has been developed. This methodology was motivated by the potential impact on crystalline nuclear waste form stability of a significant fraction of the constituent atoms undergoing transmutation. What is particularly novel about this approach is the experimental use of very short-lived isotopes to accelerate the chemical evolution that occurs during decay. In this paper, we present results of density functional theory (DFT) calculations that have been performed in support of corresponding experiments on the 109 Cd x 109 Ag 1 - x S material system. 109Cd has been selected in order to simulate the decay of important “short-lived” fission products 137Cs or 90Sr (which decay via β - to 137Ba and 90Zr respectively with ≈ 30-year half-lives). By comparison, 109Cd decays by electron capture with a half-life of 109 days to 109Ag. DFT results predict the formation of heretofore unobserved Cd x Ag 1 - x S structures, which support corresponding experiments and ultimately may have implications for waste form stability.

International audience; Electrical conductivity of UO$_{2+x}$ shows a strong dependence upon oxygen partial pressure and temperature which may be interpreted in terms of prevailing point defects. A simulation of this property along with deviation from stoichiometry is carried out based on a model that takes into account the presence of impurities, oxygen interstitials, oxygen vacancies, holes, electrons and clusters of oxygen atoms. The equilibrium constants for each defect reaction are determined to reproduce the experimental data. An estimate of defect concentrations and their dependence upon oxygen partial pressure can then be determined. The simulations carried out for 8 different temperatures (973–1673 K) over a wide range of oxygen partial pressures are discussed and resulting defect equilibrium constants are plotted in an Arrhenius diagram. This provides an estimate of defect formation energies which may further be compared to other experimental data or ab-initio and empirical potential calculations.

We use first-principles calculations to provide direct evidence of the effect of aluminum, gallium, iron and uranium on the dynamical stability of δ-plutonium. We first show that the δ phase is dynamically unstable at low temperature, as seen in experiments, and that this stability directly depends on the plutonium 5f orbital occupancies. Then, we demonstrate that both aluminum and gallium stabilize the δ phase, contrary to iron. As for uranium, which is created during self-irradiation and whose effect on plutonium has yet to be understood, we show that it leaves a few unstable vibrational modes and that higher concentrations lead to an almost complete stabilization. Finally, we provide an attempt at a consistent analysis of the experimental Pu-Ga phonon density of states. We show that the presence of gallium can reproduce only partially the experimental measurements, and we investigate how point defects, such as interstitials and vacancies, affect the calculated phonon density of states.

Ab initio molecular dynamics calculations are used to investigate the vibrational properties of the high-temperature $\ensuremath{\delta}$ and $\ensuremath{\epsilon}$ phases of plutonium. We combine the local-density approximation (LDA)$+U$ for strong electron correlations and the temperature-dependent effective potential method in order to calculate the phonon spectra of the two phases, as well as their dependence on temperature. Our results show that the $\ensuremath{\epsilon}$ phase can only be stabilized when temperature and correlations are simultaneously accounted for. We are also able to quantify the degree of anharmonicity of the two phases. While the $\ensuremath{\delta}$ phase is fairly harmonic up to 1000 K, we find that the $\ensuremath{\epsilon}$ phase is strongly anharmonic, which explains why this structure dominates the phase diagram at high temperature.

Based on density functional theory (DFT) and empirical potential calculations, the diffusivity of fission gas atoms (Xe) in UO2 nuclear fuel has been calculated for a range of non-stoichiometry (i.e. UO 2 ± x ), under both out-of-pile (no irradiation) and in-pile (irradiation) conditions. This was achieved by first deriving expressions for the activation energy that account for the type of trap site that the fission gas atoms occupy, which includes the corresponding type of mobile cluster, the charge state of these defects and the chemistry acting as boundary condition. In the next step DFT calculations were used to estimate migration barriers and internal energy contributions to the thermodynamic properties and calculations based on empirical potentials were used to estimate defect formation and migration entropies (i.e. pre-exponentials). The diffusivities calculated for out-of-pile conditions as function of the UO 2 ± x non-stoichiometry were used to validate the accuracy of the diffusion models and the DFT calculations against available experimental data. The Xe diffusivity is predicted to depend strongly on the UO 2 ± x non-stoichiometry due to a combination of changes in the preferred Xe trap site and in the concentration of uranium vacancies enabling Xe diffusion, which is consistent with experiments. After establishing the validity of the modeling approach, it was used for studying Xe diffusion under in-pile conditions, for which experimental data is very scarce. The radiation-enhanced Xe diffusivity is compared to existing empirical models. Finally, the predicted fission gas diffusion rates were implemented in the BISON fuel performance code and fission gas release from a Riso fuel rod irradiation experiment was simulated.

authoren We have employed a range of atomistic simulation methods to explore aspects of defect chemistry in ABO3 (where A2+= Ba2+ or Sr2+, and B4+= Zr4+ or Hf4+) perovskites, placing emphasis on processes relevant for application of these materials as high performance scintillators. Specifically, we examined intrinsic defect reactions, A and B excess nonstoichiometry and the solution of Me3+ rare earth cations. As has been predicted in previous studies, we find that Schottky disorder is the lowest energy intrinsic process. For nonstoichiometry, we predict that AO-excess is compensated by oxygen vacancies and BO2-excess is charge compensated by A vacancies (see abstract figure). Finally, for Me3+ solution, we considered several reactions for Me3+ cations ranging in size from Lu3+ to La3+, and the preferred reaction depends on the specific Me3+ cation and whether or not phase separation occurs. Nonstoichiometry mechanisms in ABO3 perovskites. Red spheres correspond to O2−, blue to A2+, and green to B4+.

Uranium and plutonium oxides are subjected to high levels of radiation damage due to the slowing of fission fragments. In addition the composition of the material evolves over time as a result of fission events. Rare gases which constitute an abundant class of fission products are particularly insoluble and therefore tend either to be released from the fuel or form small nanometre size clusters. Bubbles are liable to grow and become trapping sites for migrating defects or other insoluble atoms. Interactions between migrating atoms, defects and existing clusters will determine the rate and extent to which clusters grow. Because the transfer of gas from within the grain to the grain boundaries is thought of as being the rate limiting process for fission gas release, a review of phenomena occurring on the sub-grain scale is carried out. The microstructural modifications induced by neutron irradiations of UO2 fuels are discussed with an emphasis on their relation to fission gas release. Based mainly on TEM studies, the phenomena which are usually taken into account in fission gas behaviour models are looked at and the limitations of these models outlined. More recent experimental and modelling approaches involving ion-irradiation experiments and atomic scale modelling are presented. It is shown that combining these approaches may lead, despite the complexity inherent to the system, to a better understanding of basic radiation induced microstructural changes, clustering events, and rare gas behaviour.

The accommodation of trivalent oxides (M2O3) in uranium dioxide has been investigated using atomic scale simulation. Calculations suggest that all trivalent oxides studied preferentially enter UO2 by associating the substitutional ion with an oxygen vacancy, larger cations forming the cluster { 2 M U ′ : V O } × . Solution into hyper-stoichiometric UO2+x was accompanied by the formation of the { M U ′ : U U } × cluster and smaller solution energies than into stoichiometric UO2. Solubility is a particularly strong function of hyper-stoichiometry for smaller cations such as Cr3+, which has implications for the use of Cr2O3 as a grain enlarger but not so for larger cations such s Gd3+.

Ab initio calculations based on the Density Functional Theory are carried out in order to investigate the incorporation of iodine in uranium dioxide. The GGA+U approximation is used to describe the strong correlations of uranium 5f electrons. We studied several defects that are likely to accommodate the incorporation of iodine in the material, such as uranium and oxygen vacancies, divacancy and Schottky defects. We find the iodine atoms to be stable in a neutral Schottky defects, with an incorporation energy of -1.3 eV. This result may account for the solubility of iodine in uranium dioxide observed experimentally. We also notice that the incorporation of iodine involves steric and electronic contributions. The larger the defect iodine is incorporated in, the lower is its incorporation energy. Besides, we find iodine to be charged -1, thus getting the stable electronic configuration of rare gases. We also highlight the fact that the use of GGA+U increases the number of metastable states (non global energy minima), compared to the LDA/GGA approximations. Consequently, special care has to be taken on the 5f electronic occupancies in order to ensure that the absolute energy minimum has been reached.

International audience; The nuclear oxide fuels are submitted ‘in-pile’ to strong structural and chemical modifications due to thefissions and temperature. The diffusion of species is notably the result of a thermal activation and of radiationinduced diffusion. This study proposes to estimate to what extent the radiation induced diffusioncontributes to the diffusion of lattice atoms in UO2. Irradiations are simulated using molecular dynamicssimulation by displacement cascades induced by uranium primary knock-on atoms between 1 and80 keV. As atoms are easier to displace when their vibration amplitude increases, the temperature rangewhich have been investigated is 300–1400 K. Cascade overlaps were also simulated. The material isshown to melt at the end of cascades, yielding a reduced threshold energy displacement. The nuclear contributionto the radiation induced diffusion is compared to thermally activated diffusion under in-reactorand long-term storage conditions.

ABINIT is a package whose main program allows one to find the total energy, charge density, electronic structure and many other properties of systems made of electrons and nuclei, (molecules and periodic solids) within Density Functional Theory (DFT), Many-Body Perturbation Theory (GW approximation and Bethe-Salpeter equation) and Dynamical Mean Field Theory (DMFT). ABINIT also allows to optimize the geometry according to the DFT forces and stresses, to perform molecular dynamics simulations using these forces, and to generate dynamical matrices, Born effective charges and dielectric tensors. The present paper aims to describe the new capabilities of ABINIT that have been developed since 2009. It covers both physical and technical developments inside the ABINIT code, as well as developments provided within the ABINIT package. The developments are described with relevant references, input variables, tests and tutorials. Program summary: . Program title: ABINIT. . Catalogue identifier: AEEU_v2_0. . Program summary URL: . http://cpc.cs.qub.ac.uk/summaries/AEEU_v2_0.html . . Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland. . Licensing provisions: GNU General Public License, version 3. . No. of lines in distributed program, including test data, etc.: 4845789. . No. of bytes in distributed program, including test data, etc.: 71340403. . Distribution format: tar.gz. . Programming language: Fortran2003, PERL scripts, Python scripts. . Classification: 7.3, 7.8. . External routines: (all optional) BigDFT [2], ETSF_IO [3], libxc [4], NetCDF [5], MPI [6], Wannier90 [7], FFTW [8]. . Catalogue identifier of previous version: AEEU_v1_0. . Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 2582. . Does the new version supersede the previous version?: Yes. The abinit-7.10.5 version is now the up to date stable version of ABINIT. . Nature of problem: . This package has the purpose of computing accurately material and nanostructure properties: electronic structure, bond lengths, bond angles, primitive cell size, cohesive energy, dielectric properties, vibrational properties, elastic properties, optical properties, magnetic properties, non-linear couplings, electronic and vibrational life-times, and others. . Solution method: . Software application based on Density Functional Theory, Many-Body Perturbation Theory and Dynamical Mean Field Theory, pseudopotentials, with plane waves or wavelets as basis functions. . Reasons for new version: . Since 2009, the abinit-5.7.4 version of the code has considerably evolved and is not yet up to date. The abinit- 7.10.5 version contains new physical and technical features that allow electronic structure calculations impossible to carry out in the previous versions. . Summary of revisions: . •new physical features: quantum effects for the nuclei treated by the Path-integral Molecular Dynamics; finding transition states using image dynamics (NEB or string methods); two component DFT for electron-positron annihilation; linear response in a Projector Augmented-Wave approach -PAW-, electron-phonon interactions and temperature dependence of the gap; Bethe Salpeter Equation -BSE-; Dynamical Mean Field Theory (DMFT).•new technical features: development of a PAW approach for a wavelet basis; parallelisation of the code on more than 10,000 processors; new build system.•new features in the ABINIT package: tests; test farm; new tutorials; new pseudopotentials and PAW atomic data tables; GUI and postprocessing tools like the AbiPy and APPA libraries. . Running time: . It is difficult to answer to the question as the use of ABINIT is very large. On one hand, ABINIT can run on 10,000 processors for hours to perform quantum molecular dynamics on large systems. On the other hand, tutorials for students can be performed on a laptop within a few minutes. . References: . 1 http://www.gnu.org/copyleft/gpl.txt 2 http://bigdft.org 3 http://www.etsf.eu/fileformats 4 http://www.tddft.org/programs/octopus/wiki/index.php/Libxc 5 http://www.unidata.ucar.edu/software/netcdf 6 https://en.wikipedia.org/wiki/Message_Passing_Interface 7 http://www.wannier.org 8M. Frigo and S.G. Johnson, Proceedings of the IEEE, 93, 216-231 (2005). . . (Less)

International audience; This article presents a synthesis of the investigations at the atomic scale of the transport properties of defects and fission gases in uranium dioxide, as well as of the transfer of results from the atomic scale to models at the mesoscopic scale, performed during the F-BRIDGE European project (2008-2012). We first present the mesoscale models used to investigate uranium oxide fuel under irradiation, and in particular the cluster dynamics and kinetic Monte Carlo methods employed to model the behaviour of defects and fission gases in UO$_2$ , as well as the parameters of these models. Second, we describe briefly the atomic scale methods employed, i.e. electronic structure calculations and empirical potential methods. Then, we show the results of the calculation of the data necessary for the mesoscale models using these atomic scale methods. Finally, we summarise the links built between the atomic and mesoscopic scale by listing the data calculated at the atomic scale which are to be used as input in mesoscale modelling. Despite specific difficulties in the description of fuel materials, the results obtained in F-BRIDGE show that atomic scale modelling methods are now mature enough to obtain precise data to feed higher scale models and help interpret experiments on nuclear fuels. These methods bring valuable insight, in particular the formation, binding and migration energies of point and extended defects, fission product local-ization, incorporation energies and migration pathways, elementary mechanisms of irradiation induced processes. These studies open the way for the investigation of other significant phenomena involved in fuel behaviour, in particular the thermochemical and thermomechanical properties and their evolution in-pile, complex microstructures, as well as of more complex fuels.

The ab initio calculation of charged defect properties in solids is not straightforward because of the delicate interplay between the long-range Coulomb interaction and the periodic boundary conditions. We derive the projector augmented-wave (PAW) energy and Hamiltonian with special care taken on the potentials from the Coulomb interaction. By explicitly treating the background compensation charge, we find additional terms in the total energy of the charged cells and in the potential. We show that these background terms are needed to accurately reproduce all-electron calculations of the formation energy of a charged defect. In particular, the previous PAW expressions were spuriously sensitive to the pseudization conditions and this artifact is removed by the background term. This PAW derivation also provides insights into the norm-conserving pseudopotential framework.We propose then an alternative definition for the total energy of charged cells and for the Kohn-Sham potential within this framework that better approximates the all-electron results.

International audience; Over the last decade, a significant amount of work has been devoted to point defect behaviour in UO 2 using approximations beyond density functional theory (DFT), in particular DFT + U and hybrid functionals for correlated electrons. We review the results of these studies from calculations of bulk UO 2 properties to the more recent determination of activation energies for self-diffusion in UO 2 , as well as a comparison with their experimental counterparts. We also discuss the efficiency of the three known methods developed to circumvent the presence of metastable states, namely occupation matrix control, U-ramping and quasi-annealing.

We report first-principles DFT$\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}U$ calculations of the paramagnetic phases of uranium dioxide (UO${}_{2}$) and (U,Pu) mixed oxides (MOX). We use a combination of two techniques, the first of which enables us to treat the presence of metastable states and the other the random distribution of spins (for paramagnetism) and of plutonium atoms (for MOX). The resulting method is first used to determine the ground-state properties of paramagnetic UO${}_{2}$ and is then applied to MOX with $12.5%$ and $25%$ Pu, for which both experimental and theoretical studies are lacking. We find the paramagnetic phase of fluorite UO${}_{2}$ to be more stable than the antiferromagnetic phase as expected from experimentation, with ground-state properties in excellent agreement with experimental data. Results on MOX show that most of the ground-state properties of UO${}_{2}$ are affected by addition of $12.5%$ Pu and do not seem to be much different when the plutonium content changes, at least for Pu contents below $30%$. For both UO${}_{2}$ and MOX, it is found that the true paramagnetic order has a significant effect on the calculated elastic constants, compared to the antiferromagnetic and ferromagnetic orders. By contrast, we find that regarding energetics, the antiferromagnetic order may be used as a very good approximation of the paramagnetic state.

The present work reports first-principles DFT $+\phantom{\rule{0.16em}{0ex}}U$ calculations of uranium self-diffusion in uranium dioxide (UO${}_{2}$), with a focus on comparing calculated activation energies to those determined from experiments. To calculate activation energies, we initially formulate a point defect model for UO${}_{2\ifmmode\pm\else\textpm\fi{}x}$ that is valid for small deviations from stoichiometry. We investigate five migration mechanisms and calculate the corresponding migration barriers using both the LDA $+\phantom{\rule{0.16em}{0ex}}U$ and GGA $+\phantom{\rule{0.16em}{0ex}}U$ approximations. These energy barriers are calculated using the occupation matrix control scheme that allows one to avoid the metastable states that exist in the DFT $+\phantom{\rule{0.16em}{0ex}}U$ approximation. The lowest migration barrier is obtained for a vacancy mechanism along the $\ensuremath{\langle}110\ensuremath{\rangle}$ direction. This mechanism involves significant contribution from the oxygen sublattice, with several oxygen atoms being displaced from their original position. The $\ensuremath{\langle}110\ensuremath{\rangle}$ vacancy diffusion mechanism is predicted to have lower activation energy than any of the interstitial mechanisms and comparison to experimental data for stoichiometric UO${}_{2}$ also confirms this mechanism.

Geng et al. [H. Y. Geng, Y. Chen, Y. Kaneta, M. Kinoshita, and Q. Wu, Phys. Rev. B 82, 094106 (2010)] recently reported $\mathrm{DFT}+U$ calculations of xenon behavior in uranium dioxide UO${}_{2}$. One of the main conclusions of their work is that the quasiannealing (QA) procedure allowed them to avoid metastable states created by the $\text{DFT}+U$ approximation. However, based on a comparison of total energies, they stated that an incomplete implementation of occupation matrix control (OMC) had been done in our previous work [B. Dorado, G. Jomard, M. Freyss, and M. Bertolus, Phys. Rev. B 82, 035114 (2010)] and that we failed to reach the ground state of the perfect UO${}_{2}$ fluorite structure. In this Comment, we show that the discrepancy they observed does not stem from an incomplete implementation of OMC, but from the calculation of the compensation charge used in the projector augmented-wave formalism.

International audience; This work provides an illustration that density functional theory (DFT) + U calculations may quantitatively describe transport phenomena in uranium dioxide. Oxygen diffusion mechanisms are investigated using both ab initio calculations and experimental approaches mainly involving self-diffusion coefficient measurements. The dependences of the experimental data upon oxygen potential and sample impurity content demonstrate, by comparison with basic point defect and diffusion theory, that oxygen migration occurs via an interstitial mechanism. The temperature study provides an estimate of interstitial formation and migration energies which compare very favorably to energies calculated using the DFT+U approximation relating to the interstitialcy mechanism. Also, vacancy migration and Frenkel pair formation energies are shown to agree well with existing data.

Density-functional theory (DFT) without spin-orbit coupling (SOC), as implemented in CASTEP, yields structural, energetic, and elastic properties of siderite $({\text{FeCO}}_{3})$ in good agreement with available data from the literature. The electronic ground state is however found ferromagnetic (FM) with a nonzero density of states at the Fermi level, whereas real siderite is antiferromagnetic (AFM) and insulating. We show in both cases how the paradox can be removed. Concerning the metallic/insulating character, a symmetry analysis of the electronic structure performed with the help of ISOTROPY shows that the absence of gap is due to an essential degeneracy of monoelectronic wave functions in the experimental $R\overline{3}c$ symmetry. The small dispersion of individual bands establishes a clear difference with the case of a real metal. Complemented by $\text{DFT}+\text{SOC}$ computations performed using ABINIT this shows the consistency of the DFT description with crystal-field theory data taken from the literature. Thus for DFT the electronic structure of siderite is characterized by correlation, but of exchange origin, as opposed to electrostatic origin. The AFM nature of the ground state is also restored by SOC. Without SOC the total energies of the FM and AFM states are very close. After introducing some modifications in a classical model of superexchange we obtain a satisfactory interpretation of our DFT results in terms of spin polarization in the iron-carbonate bonds, spin-coupling mechanisms between neighboring iron ions and finally of the observed FM over AFM stability. Hence, siderite emerges as an original model system among transition-metal compounds for the application of DFT to open-shell electronic structures.

Point-defect formation energies in uranium dioxide ${\text{UO}}_{2}$ are still a matter of debate due to the significant discrepancies between the various studies published in the literature. These discrepancies stem from the density functional theory $(\text{DFT})+U$ approximation that creates multiple energy minima and complexifies the search for the ground state. We report here $\text{DFT}+U$ values of the formation energies for the single oxygen interstitial and vacancy in ${\text{UO}}_{2}$, both in the fluorite and the Jahn-Teller distorted structures, using a scheme developed on bulk ${\text{UO}}_{2}$ [B. Dorado, B. Amadon, M. Freyss, and M. Bertolus, Phys. Rev. B 79, 235125 (2009)] and based on occupation matrix control. We first investigate the Jahn-Teller distortion in ${\text{UO}}_{2}$ in the noncollinear antiferromagnetic order and we show that the distortion stabilizes the system by $50\text{ }\text{meV}/{\text{UO}}_{2}$ compared to the fluorite structure. Moreover, it is found that the oxygen atoms are displaced in the $⟨111⟩$ directions, in agreement with experiments. For the bulk fluorite structure, we show that the use of the Dudarev approach of the $\text{DFT}+U$ without occupation matrix control systematically yields the first metastable state, located $45\text{ }\text{meV}/{\text{UO}}_{2}$ above the ground state. As a result, all previously published point-defect formation energies are largely underestimated. We then use the occupation matrix control scheme to calculate the formation energies of the single oxygen interstitial and vacancy in ${\text{UO}}_{2}$. We confirm that this scheme always allows one to reach the lowest energy states and therefore yields reliable formation energies. Finally, we compare our values with those obtained in previous studies and show that the discrepancies observed stem from the calculations of defective supercells which have reached different metastable states.

The formation and mobility of point defects in UO 2 have been studied within the framework of the Density Functional Theory. The ab initio Projector Augmented Wave method is used to determine the formation and migration energies of defects. The results relative to intrinsic point defect formation energies using the Generalized Gradient Approximation (GGA) and GGA+U approximations for the exchange-correlation interactions are reported and compared to experimental data. The GGA and GGA+U approximations yield different formation energies for both Frenkel pairs and Schottky trios, showing that the 5 f electron correlations have a strong influence on the defect formation energies. Using GGA, various migration mechanisms were investigated for oxygen and uranium defects. For oxygen defects, the calculations show that both a vacancy and an indirect interstitial mechanism have the lowest associated migration energies, 1.2 and 1.1 eV respectively. As regards uranium defects, a vacancy mechanism appears energetically more favourable with a migration energy of 4.4 eV, confirming that oxygen atoms are much more mobile in UO 2 than uranium atoms. Those results are discussed in the light of experimentally determined activation energies for diffusion.

Using classical molecular dynamics simulations, we have studied the first stages of defect cluster formation resulting from 10 keV displacement cascades in uranium dioxide. Nanometre size cavities and dislocation loops are shown to appear as a result of the irradiation process. A specifically designed TEM experiment involving He implanted thin foils have also been carried out to support this modelling work. These results, in conjunction with several other observations taken from the literature of ion implanted or neutron irradiated uranium dioxide, suggest a radiation damage controlled heterogeneous mechanism for insoluble fission product segregation in UO(2). (C) 2010 Elsevier B.V. All rights reserved.

We report a study of the ground state and metastable states of uranium dioxide using ab initio $\text{DFT}+\text{U}$ calculations. We highlight that in order to avoid metastable states and systematically reach the ground state of uranium dioxide with $\text{DFT}+\text{U}$, the monitoring of occupation matrices is crucial, as well as allowing the $5f$ electrons to break the cubic symmetry. For this purpose, we use a method based on the monitoring of the occupation matrix of the correlated orbitals on which the Hubbard term is applied. We observe the presence of numerous metastable states in calculations both with and without taking into account the symmetries of the wave functions. We investigate the influence of metastable states on the total energy, as well as on the electronic and structural properties of uranium dioxide. We show that the presence of metastable states induces large differences in the total energy and explain the origin of the discrepancies observed in the results obtained by various authors on crystalline and defect-containing ${\text{UO}}_{2}$. Finally, in order to check the consistency of the procedure, we determine the structural and electronic properties of the ground state of uranium dioxide and compare them with results obtained in previous studies using the $\text{DFT}+\text{U}$ approximation and hybrid functionals, as well as experimental data.