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The local-spin-density (LSD) and semi-local generalized gradient approximations (GGA) to density-functional theory have proven very useful and accurate in describing bonding properties of solids with weakly correlated electrons. [1,2] The LSD approximation however ignores exchange and correlation effects beyond those of the homogeneous electron gas, and cannot account for on-site localization of strongly correlated f-electrons. The lanthanide 4f-orbitals tend to be very localized in space, and the electrons occupying these orbitals interact strongly with each other, as a consequence of which hopping to neighboring sites becomes energetically unfavorable. A purely band picture description fails to fully capture the physics of rare earth materials. For 5f orbitals, the situation is complicated because electrons are less localized than in the lanthanides but still correlated [3]: Depending on the specific actinide, the chemical environment, and/or the external conditions (pressure), the f-electrons behave as either localized, delocalized or, as is the case in Pu, [4] they are situated at the borderline of the localization-delocalization transition with the resulting very complex phase diagram. Furthermore, spin-orbit coupling effects are important in these materials leading to a complex magnetism, with an important orbital contribution. [5]

In spite of the necessity to take into account correctly the correlations, studies have been carried out in the LSD, assuming magnetic ordering, which leads to surprisingly good results for structural data for e.g. delta Pu. [6] Furthermore state of the art calculations within the LSD/GGA approximation are being applied to bulk actinide oxides and surfaces, as well as in simulations of radiation defects or impurity migration in nuclear materials. [7,8] Considerable new insights into impurity/vacancy formation as well as structural changes associated with relaxation has been achieved, providing, among other, valuable starting points for multiscale modeling of nuclear fuels. [9]

Additional approximations and/or assumptions that go beyond the LSD seem however to be required in order to have a more physical description of the underlying electronic structure. To address the issues of electron-electron correlations, in the last few years a number of highly sophisticated modeling approaches have been developed. A first approach is to take into account explicitly the interaction between electrons with a Hubbard like term in the Hamiltonian, which thus depends on the parameter U. [10] When solved in a mean field way, this leads to the LDA+U approximation. It gives a better description of Mott insulators:  the f-manifold is separated into lower and upper Hubbard bands, and the f-degrees of freedom are removed from the Fermi level. The recently developed dynamical mean field theory (DMFT) goes beyond the mean field approximation by taking into account fluctuations between electronic configurations on one site. [11] Depending on the value of the U parameter, the DMFT is capable of reproducing both the Hubbard bands and the quasi particle peak at the Fermi level, and represents currently the most sophisticated approach to the strongly correlated electron problem. It can in particular describe both delocalized and localized correlated electron systems making it an adequate tool for the description of actinides. The self-interaction corrected (SIC) local spin density approximation takes an altogether different approach, as it corrects the LSD approximation for the unphysical interaction of an electron with itself. [12] The groundstate of the system is determined from total energy considerations and it has the advantage of being a parameter free theory. In the hybrid functional approach, the exchange is taken to be a combination of Hartree-Fock exact exchange with LSD exchange and correlations. [13] This can mimic the physical effect of a screened exchange, as a consequence, the self-interaction is partially removed.  

The development of these new methodologies is still very much a work in progress, but has already led to considerable new insight into the electronic structure of actinide materials. Striking examples are the impressive number of theoretical studies on the electronic, magnetic, and spectroscopic properties of actinide metals, [5] especially delta-Pu, [14] the study of phonons and heat conductivities of UO2/PuO2 with DMFT, [15] the investigation of phase transitions under pressure or temperature, the electronic structure of actinide oxides with hybrid functionals [13] and LDA+U, [16] the PuO2 oxidation with SIC-LSD. [17] The capability of reproducing the spectroscopies of strongly correlated materials enables the direct comparison between electronic structure and experimental measurements. [18] Here the potential application of the GW approximation, which incorporates many body effects to first order, is bound to lead to considerable progress when combined with the described beyond-LSD methodologies. Because of the difficulty of these calculations, it is only very recently that GW calculations on f-electrons systems have appeared. [19]

Despite considerable progress, understanding the experimental evidence emerging from studies of correlated electron systems remains a challenge. Despite considerable theoretical and experimental efforts, the absence of magnetism in delta-Pu for example still remains unexplained, as is the case with the so-called hidden order in URu2Si2. [20] Many of the actinide compounds display Kondo behaviour or superconductivity, which so far remains largely inaccessible to first principles methodologies. X-ray absorption and XPS studies show compounds situated at the boundary of localization/delocalization transition, and from EELS studies it emerges that a number of actinide metals are governed by intermediate coupling. [21] Also, recent experimental developments call for an improved theoretical description of higher order multipole ordering. [22]

A fully first-principles description of the actinides thus will require considerable work for years to come. Nevertheless the achieved accuracy of the current methodologies makes it a timely enterprise to investigate the impact of electron-electron correlations on the physics and chemistry of the nuclear materials. In combination with the already existing modeling approaches the above mentioned electronic structure codes will provide guidelines for producing improved fuels and less toxic wasteforms. Among many others, topics that need to be addressed range from the composition dependent properties of mixed oxide fuels [23] and the chemistry of minor actinides in inert matrix fuels, [24] to the influence of the actinide oxidation state on the mobility of radionuclides [25] and the potential performance of novel actinide carbides and nitrides fuels in GEN-IV reactors.

The challenge is in the description of the electronic structure of increasingly complex systems, and which are close to the actual issues (radiation defects, minor actinide impurities, surface chemistry, etc.) related to the nuclear fuel and the treatment of waste. In this respect, the intricate nature of the 5f electrons in the actinides adds an additional layer of complexity to an already highly demanding modelling problem. In particular a correct description of the bonding properties of f-electrons is crucial to the understanding of oxidation processes and impurity migration. The surface behavior in contact with the environment is strongly influenced by the f-electron structure, as are the properties of nuclear fuels such as heat conductivities. The study of surface interaction with molecules [26] is particularly challenging because it requires handling in the same theoretical framework the f-electrons and molecular physics. A number of results have recently being obtained in these fields: the stability of point and external defects in actinides oxides has been the subject of various studies using DFT [7] and DFT+U, [27] and interesting results have been obtained in the description of surfaces and thermal properties.

Understanding the actinides is a prerequisite for understanding the behaviour of nuclear materials, and implies understanding the fundamental physics of correlated electrons. On the other hand, the large amount of experimental data that is derived from experimental investigation of nuclear fuels under operating conditions, or nuclear waste under storage conditions, can give valuable additional feedback with regards to understanding actinide physics, and ultimately provide new insight into the complex nature of correlated electrons.