Surface Science 600 (2006) 1637–1640 www.elsevier.com/locate/susc A comparison of hybrid density functional theory with photoemission of surface oxides of d-plutonium M.T. Butterfield a,1, T. Durakiewicz a,*, I.D. Prodan b, G.E. Scuseria b, E. Guziewicz c, J.A. Sordo d, K.N. Kudin e, R.L. Martin f, J.J. Joyce a, A.J. Arko a,z, K.S. Graham a, D.P. Moore g, L.A. Morales g a Condensed Matter and Thermal Physics MST-10, Los Alamos National Laboratory, Los Alamos, NM 8754, USA b Department of Chemistry, Rice University, Houston, TX 77251-1892, USA c Institute of Physics, Polish Academy of Sciences, Warszawa 02-668, Poland d Departamento de Quı́mica Fı́sica y Analı́tica, Universidad de Oviedo, Oviedo 33007, Spain e Department of Chemistry, Princeton University, Princeton, NJ 08544, USA f Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA g Nuclear Materials Science, NMT-16, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Available online 3 February 2006 Abstract We carried out high resolution photoelectron spectroscopy (PES) studies on a gallium stabilized d-phase plutonium sample cleaned by laser ablation and gas dosed with O2. The measurements were made at a sample temperature of 77 K with an overall instrument resolution of 60 meV. At this temperature the PES strongly favor an idealized model of Pu2O3 growth on the metal surface followed by PuO2 growth on the Pu2O3. These experimental results provide an excellent benchmark for a new generation of hybrid density functional calculations that have been used to model a defective plutonium dioxide lattice. The hybrid functional predicts an insulating ground state. This is of paramount importance for the study of actinide oxides because the conventional density functional theory approaches predict them to be metals, when in fact they are insulators with significant band gaps. The calculated density of states for PuO2 and Pu2O3 agree reasonably well with the experimental data.  2006 Elsevier B.V. All rights reserved. Keywords: Plutonium surface; Plutonium oxides; Photoemission; Hybrid density functional 1. Introduction Understanding the behavior of 5f electrons remains an unrealized ambition of condensed matter physics [1,2]. Recently, there has been a large amount of interest in the actinides, particularly plutonium, driven by the complex and intriguing behavior of Pu and several of its compounds [3–5]. This has prompted both theoretical and experimental * Corresponding author. Tel.: +1 505 667 4819; fax: +1 505 665 7652. E-mail address: tomasz@lanl.gov (T. Durakiewicz). 1 Present address: Lawrence Livermore National Laboratory, Livermore, CA 94550, USA. z Deceased. 0039-6028/$ - see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2005.11.051 investigations of 5f metals and compounds. Of the different allotropes of Pu, the d-phase is of particular interest because of the high symmetry crystal structure and the stability of the phase to low temperatures when alloyed with small amounts of trivalent elements. Consequently much of the recent experimental and theoretical work has focused on this allotrope. From an experimental point of view, the reactivity and radioactivity of Pu, and the complexity of the phase diagram, makes it exceedingly complicated to collect high-quality data, Investigations of these complex behaviors all point back to being caused by the complex and intriguing interplay of the various electron states and in particular the behavior of the 5f states. 1638 M.T. Butterfield et al. / Surface Science 600 (2006) 1637–1640 Elemental plutonium rapidly oxidizes to PuO2 when exposed to air and moisture, with Pu2O3 playing an important role in oxidation kinetics [6]. The electronic properties of the dioxide have been the subject of intense discussion since the report of Haschke et al. [7] stating that nonstoichiometric PuO2+x (x 6 0.27) participates in moisture-enhanced corrosion of the metal and that H2 pressurization of sealed storage containers might occur because of the reaction of PuO2 with adsorbed water. Long-term storage of high-level radioactive waste, mainly plutonium and uranium resulting from nuclear power plants and stockpiles, represents a very important environmental issue. Given our incomplete understanding of the Pu oxidation chemistry and the myriad problems associated with experimental studies on these materials, the predictions of theory are of special interest. We have previously reported on high quality photoemission data for the Ga stabilized d-phase of plutonium [8] in which we obtained a very clean d-Pu sample surface using laser ablation. Gas dosing studies were made using the same high quality sample, and the experimental procedure which was used has also previously been presented [9]. Here we present that data as a benchmark for comparison to a hybrid-density-functional-theory calculation. 2. Theory Hybrid density functionals were initially designed and mathematically constructed to faithfully predict the heats of formation of a set of small molecules, e.g., hydrogen (H2), carbon dioxide (CO2), ammonia (NH3), water (H2O), etc., but researchers quickly discovered that they performed quite well outside this set. In particular, they provide excellent bond energies and properties for molecules containing transition metal and actinide centers [10,11]. In addition to significantly improving predictive capability for bond energies, hybrid functionals have greatly improved our ability to predict reaction barriers and understand mechanisms, and to predict excitation energies and oscillator strengths in molecules via linear response theory. They have had a dramatic impact in molecular quantum chemistry. The actinide oxides such as UO2 and PuO2 present a challenge to electronic structure theory because the conventional density functional theory approaches predict them to be metals, when in fact they are insulators with significant band gaps. The hybrid functionals largely seem to remedy this situation. For example, we recently reported the first implementation of hybrid density functional theory capable of describing periodic solids containing f-elements and applied it to the electronic structure of uranium dioxide (UO2) [12]. This approach correctly predicted the anti-ferromagnetic, insulating ground state observed experimentally. In contrast, the LDA and GGA approaches both find a ferromagnetic, metallic ground state. The band gap, lattice constant, bulk modulus, photoemission spectrum, and optical spectrum were all in good agreement with experiment. We have extended this study to PuO2 and Pu2O3. In the ionic limit, formal charges for plutonium in PuO2 and Pu2O3 are +4 and +3, respectively, corresponding to formal populations of f4 and f5. These configurations lead to local S = 2 and S = 5/2 plutonium moments, which can couple with other sites in either a ferromagnetic or anti-ferromagnetic manner. We find the anti-ferromagnetic solution to be the ground state in either case. However, the magnetic coupling is relatively weak and, aside from the energy, most properties are identical between the two states. In the discussion that follows, we therefore focus on the ferromagnetic solution. Full details of the methodology of the calculation can be found elsewhere [13] and in references therein. We point out that the spin–orbit interaction is not yet fully implemented in our codes, and is not included in the calculations. We estimate this omission could influence gaps by a few tenths of an eV [12], however a recent paper by Tobin et al. [14] suggests that this spin orbit splitting in Th, U and Pu could be of the order of 2 eV. 3. Comparison to experimental results From our calculation the lattice constant of PuO2 is predicted to be 5.39 angstroms (Å), in good agreement with the experimental result of 5.40 Å. The unpaired spin density on the plutonium center is similar to the estimate from the ionic limit, yielding 4.1 and 5.1 electrons for PuO2 and Pu2O3, respectively. Both actinide oxides are predicted to be insulators, with gaps of 2.4 and 2.5 eV, respectively. Fig. 1 shows the PES spectra after dosing the surface at 77 K with 1, 5, 10 and 20 L of O2. The O2 dosage is mea- Pu2O3 one week in vacuum at PuO2 6x10-11 Torr and allowed to return to Room Temp. L 20 10 5 1 0 -8 -6 -4 -2 0 2 Binding energy (eV) Fig. 1. PES results of gas dosing of the d-Pu surface with O2 at T = 77 K. 1639 M.T. Butterfield et al. / Surface Science 600 (2006) 1637–1640 sured in Langmuirs (L), where one Langmuir is equivalent to an exposure of 10 6 Torr for one second (for more accurate dosing the equivalence can be maintained by using a lower pressure and increasing the exposure time accordingly). The final spectrum is the result of leaving the 20 L dosed surface undisturbed in vacuum of 6 · 10 11 Torr for a week after allowing it to return to room temperature overnight. The doses were achieved sequentially, so the 5 L coverage is the addition of a further 4 L to the 1 L dose, and so on. We found no observable differences between sequential dosing and individual large doses. After dosing with 1 L of O2 at 77 K an oxide is formed that we associate with Pu2O3. The spectrum however still exhibits a Fermi edge at this temperature, so to compare the calculation with a spectrum that is truly only representative of the oxide, we will use a spectrum taken for a 10 L dose of O2 taken at room temperature [9]. At this temperature there is no change to PuO2 even for large exposures [9], and as can be seen by comparison with Fig. 1 the only observable difference between the 1 L exposure at 77 K and the 10 L exposure at room temperature is the presence of a Fermi edge in the low temperature spectrum. Therefore the two spectra that we will use for comparison are those after dosing with 10 L of O2 at room temperature where an oxide is formed that we associate with Pu2O3 at the metal surface, due to disassociation of O2 [15,6], and after dosing 20 L at 77 K where the oxide is associated with PuO2. The two oxides are each evidenced by two peaks, at approximately 1.6 and 5.5 eV in the case of Pu2O3 and at 2.5 and 4.6 eV for PuO2. Plutonium related features, primarily 5f in character with some 6d contribution, appear in the 0–3 eV energy interval, while oxygen features, primarily O2p, appear in the 4–8 eV energy range. The further addition of O2 causes the gradual disappearance of the Pu2O3 PuO2 Theory Intensity (Arb. Units) (a) -8 PuO2 Experiment -6 -4 -2 0 Binding Energy (eV) Pu2O3 Theory Intensity (Arb. Units) (b) -8 Pu2O3 Experiment -6 -4 -2 0 Binding Energy (eV) PuO2 5:1 Pu2O3 (c) Intensity (Arb. Units) PuO2 Experiment -8 -6 -4 -2 0 Binding Energy (eV) Fig. 2. (a) Calculated total density of states for PuO2 compared with experimental spectrum for 20 L O2 exposure at 77 K. (b) Calculated total density of states for Pu2O3 compared with experimental spectrum for 1 L O2 exposure at room temperature. (c) Sum of calculated density of states for PuO2 and Pu2O3 in a 5:1 ratio compared to experimental spectrum for 20 L O2 exposure. 1640 M.T. Butterfield et al. / Surface Science 600 (2006) 1637–1640 peaks and the gradual growth of the PuO2 peaks. This suggests that the PuO2 is in fact growing on top of the initial Pu2O3 layer, and even at a coverage of 20 L there is still some evidence of the Pu2O3 layer. This may be relevant for our comparison with the calculation, as the calculation considers both oxides independently. The theoretical PuO2 total density of states of Fig. 2(a) shows a very weak feature at around 1.5 eV followed by a strong peak at about 2.3 eV and a weaker one near 4.5 eV. The calculations for both PuO2 and Pu2O3 have been convoluted with a Gaussian to emulate the 60 meV resolution of the experiment. It is encouraging that these peak positions are in good agreement with the experiment. There is, however, an additional feature near 6 eV observed in the experiment, but absent in the calculation. In the experimental data it appears that there is some superposition of both PuO2 and Pu2O3 features in the 20 L spectrum. Addition of the theoretical curves for PuO2 and Pu2O3 in any ratio does not reproduce this feature. This will be further investigated in Fig. 2(c). Another possibility is that there is some degree of hydrogen at the surface which exhibits peaks at approximately 2 and 6 eV, respectively, [9]. Note also that the relative intensity of the 2.5- and 4.5 eV peaks is not well reproduced by the calculation. This relative intensity would also be affected by any superposition of oxides. It should also be noted that we have implicitly assumed identical photoemission cross sections for the oxygen 2p and plutonium 5f orbitals in making this comparison. At 40.8 eV incident photon energy, an intensity ratio of the oxygen 2p photoemission peak to the plutonium 5f photoemission peak approximately 1.5 is probably more appropriate. This adjustment would tend to increase the intensity of the 4.5 eV peak, but not sufficiently to make it stronger than the low-energy one. For Pu2O3, the feature between around 0.5 and 1.8 eV is principally plutonium 5f in character and the higher binding energy feature is mostly oxygen 2p. The main intensity in the first feature is at around 1.5 eV which is also in reasonable agreement with experiment. The second broader feature has local maxima at around 3.5 and 5.5 eV. The 5.5 eV feature is also in good agreement with experiment but the 3.5 eV feature is not observed. This spectrum is similar to that of UO2 [14], which also exhibits two distinct peaks of mostly uranium 5f and oxygen 2p parentage. In contrast, the region near the Fermi edge in PuO2 is nearly a 50:50 mixture of plutonium 5f and oxygen 2p, signifying much greater metal–ligand mixing. This is a surprising result, given the smaller overlap anticipated in plutonium because of the smaller radius of the plutonium 5f orbital. In addition to the reduction in 5f radius in going from uranium to plutonium, one expects a stabilization of the plutonium 5f site orbital energy. In perturbation theory, the mixing between two levels is effectively given by the overlap integral divided by the difference in site energies. It may be that the origin of the stronger mixing is related to the stabilization of the plutonium 5f orbital and an unanticipated degeneracy with the oxygen 2p level. In this hypothesis, the small mixing in the Pu2O3 spectrum would be associated with the higher (less bound) plutonium 5f site energy expected in the less highly charged, formally Pu3+, ion. In Fig. 2(c) the theoretical curves for both PuO2 and Pu2O3 have been summed in a 5:1 ratio, which is not unreasonable compared to the experimental situation and compared to the experimental curve for PuO2. As can be seen a simple summing of both sets of calculations still does not produce all of the features in the experimental spectrum. One possibility for the remaining discrepancy is our omission of the spin–orbit interaction. This would be expected to shift intensity by a few tenths of an eV, although probably not enough to account for the missing spectral features. More intriguing is the observation that our calculations were for the beta (hexagonal) phase of Pu2O3. The DOS for the alpha phase would certainly be expected to be somewhat different. It is difficult to know the relative contributions of these two to the spectrum as the film evolves. A calculation on the alpha phase would certainly be of interest. While there is clearly much to be done, we are encouraged by the agreement between theory and experiment and believe the combination will tell us much about the electronic structure of these complex systems. 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