L'Étude de la Structure Électronique des Métaux des Terres Rares

In rare earth metals, one can neglect interactions between 4f shells centred on neighbouring sites. The conduction band is occupied by three sd electrons (eventually two in europium and ytterbium). These sd electrons are coupled to the f electrons through an interaction of the form where s _e is the spin of a conduction electron and Sf _i the spin of the ith f electron of a given ion. It is therefore possible to consider two groups of properties:

1. The ones, related to the nature of the conduction electrons, change very little through the series: this is the case of the crystalline structure, of the atomic volume.

2. The others, such as the magnetic properties, are related to the internal shells and vary with the filling of the 4f shell. Experiment shows a correlation between those two groups of properties. De Gennes formalism, essentially valid in the hypothesis of tightly bound 4f electrons, gives a satisfactory picture of the properties of the metals in the second half of the series, but it does not give as good a picture for the first rare earth metals, especially for cerium. In the cerium free atom, the 4f, 5d, 6s states have comparable energies and one might think that, in the trivalent metal, the 4f states are broadened in energy by resonances with the extended sd states, but still do not overlap from one atom to the other. They would then occupy virtual bound states analogous to the virtual bound states described by Blandin and Friedel for the transition impurities in noble metals.

An identical situation seems to occur in ytterbium under pressure: one observes a huge increase of the electrical resistivity which goes back to low values at very high pressures. This might also be the case of the actinide metals, especially of Plutonium, in which the 5f states begin to stabilize. So we have to consider two cases:

1. The 4f electrons occupy bound states.

2. The 4f electrons occupy virtual bound states.

In the first part (§ 2), we use de Gennes formalism for 4f bound states. The energy related to magnetic interactions is computed making the assumption of a spherical Fermi surface. A correlation between the crystalline structure and the magnetic properties shows up. In the second half of the series, one can neglect the crystalline field effects and the total energy is the sum of the magnetic term and of the elastic term due to the contribution of the conduction electrons. For every state of magnetic order, the crystalline structure is well defined, corresponding to the minimum of the total energy, and conversely. It is possible to explain in this manner:

1. The b.c.c. structure of europium, which is unusual for a divalent transition metal.

2. The variation of the c/a ratio of the h.c.p. structure both through the series and with temperature.

3. The anomalies in the thermal expansion coefficient observed below the magnetic order-disorder transitions.

4. The helix pitch of the magnetic configurations of this type.

The anomalies of the thermoelectric power observed at the transition points are related to the different dependences of the spin correlations above and below the transition temperatures. The agreement between theory and experiment is satisfactory. Some discrepancy can be attributed to the rather crude approximation of a spherical Fermi surface.

In the second part (§ 3), we deal with a situation where the 4f electrons occupy virtual bound states. These levels are very narrow, about 10^?2 ev wide, and separated in energy by the correlations between electrons. Using Blandin's formalism we calculate the electrical and magnetic properties associated with such a situation. Calculations lead to very strong magnetic coupling; the indirect interaction between magnetic ions is antiferromagnetic for first nearest neighbours, whereas in the case of 4f bound states it is ferromagnetic. Finally, it is possible to explain the properties of cerium and ytterbium.

1. In Cerium, the two first levels overlap at the Fermi level, in such a way that the f electron be almost entirely distributed in the first level.

2. In ytterbium, under pressure, the fourteenth level comes across and above the Fermi level. The maximum resistivity is obtained for a half filling of this level.

In the third part (§ 4), we attempt to apply this model of virtual bound states to plutonium, although in this metal, the 5f shells have a larger spatial extension than the 4f orbitals in rare earths. Anomalies in several physical properties of plutonium seem to indicate a magnetic transition at about 65° K, but no anomaly shows up in the magnetic susceptibility. Using a virtual bound state model associated with a very small polarization of the 5f states, it is possible to explain all the physical properties of plutonium. This model leads to a very small magnetic moment, that cannot be detected by experiment.     

Non-collinear spin DFT for lanthanide ions in doped hexagonal NaYF4

Trivalent lanthanide ions (Ln³⁺) doped in hexagonal (β)-NaYF₄ nanocrystals (Na₂₄Y₂₃Ln₁F₉₆, Ln = La, Ce, Pr, Nd, Pm, Sm, Eu, Gd) were systematically studied by density functional theory (DFT) with a perturbative account for spin–orbit coupling. The simulated results, including the optimised molecular structures, electronic and magnetic properties, are compared to previous spin-polarised DFT studies in the same system. The spin–orbit coupling effects become significant with the increase in the number of unpaired 4f electrons in the doped lanthanide ions, particularly for the Sm³⁺-, Eu³⁺- and Gd³⁺-doped nanocrystals. Abnormal behaviour of Eu³⁺-doped nanocrystals was observed due to the Wybourne–Downer mechanism. A ‘sandwich-like’ 2p–4f–4d,5d electronic structure for Na₂₄Y₂₃Ln₁F₉₆ and the energies of the highest occupied 4f electrons from Ce³⁺ to Gd³⁺ are consistent with Dorenbos's relationship. The energy difference between the first and second Russell–Saunders terms (^2S+1L) of the lanthanide dopant is consistent with Carnall's experimental results and with earlier spin-polarised DFT calculations.     

High-pressure behaviour and elastic properties of heavy rare-earth Gd monopnictides

Pressure-induced structural phase transition of gadolinium monopnictides GdX (X=As and Sb) has been studied theoretically using an inter-ionic potential theory. This method has been found quite satisfactory in case of the pnictides of rare-earth and describes the crystal properties in the framework of rigid-ion model. We have modified the ionic charge so that it may include the Coulomb-screening effect by the delocalization of f electron of the rare-earth ion. The anomalous structural properties of these compounds with many f electrons have been interpreted in terms of the hybridization of f electrons with the conduction band and strong mixing of f states of Gd ion with the p orbital of neighbouring pnictogen ion. Both the compounds are found to undergo from their initial NaCl (B₁) structure to body centered tetragonal (BCT) structure at high pressure and agree well with the experimental results. The BCT structure is viewed as distorted CsCl structure and is highly anisotropic with c/a=0.82–0.85. The nature of bonds between the ions is predicted by simulating the ion–ion (Gd–Gd and Gd–X) distance at high pressure. Elastic properties of these compounds have also been studied with their second-order elastic constants.     

Electronic structure and magnetic susceptibility of monoclinic α-plutonium

The electronic structure of the α-phase of plutonium has been calculated by the band methods with allowance for the spin-orbit interaction and Coulomb correlations in the complete matrix form (the LDA + U + SO method). The strong spin-orbit interaction of the 5 f electrons is manifested in the splitting of the calculated density of the 5f states, which makes a small contribution at the Fermi level on the order of the contribution from the 6d states. Using the results of the ab initio calculations, the spin and orbit contributions to the magnetic susceptibility of α-plutonium have been determined. Along with the impurity contribution, they describe well the experimental data on the susceptibility of this plutonium phase to a temperature of 300 K.     

Pressure induced phase transition in rare earth mono-antimonides

Pressure induced structural phase transition of mono-antimonides of lanthanum, cerium, praseodymium and neodymium (LnSb, Ln=La, Ce, Pr and Nd) has been studied theoretically using an inter-ionic potential with modified ionic charge which parametrically includes the effect of Coulomb screening by the delocalized f electrons of rare earth (RE) ion. The anomalous structural properties of these compounds have been interpreted in terms of the hybridization of f electrons with the conduction band and strong mixing of f states of Ln ion with the p orbital of neighbouring antimonide ion. All the four compounds are found to undergo from their initial NaCl (B₁) phase to body centered tetragonal (BCT) phase at high pressure and agree well with the experimental results. The body centered tetragonal phase is viewed as distorted CsCl structure and is highly anisotropic with c/a=0.82. The transition pressure of LnSb compounds is observed to increase with decreasing lattice constant in NaCl phase. The nature of bonds between the ions is predicted by simulating the ion-ion (Ln-Ln and Ln-Sb) distances at high pressure. The calculated values of elastic constants are also reported.     

Density of states and the problem of Sm valence

Density of states for Sm metal has been calculated in DFT/GGA approximation using the same treatment for f and s-d bands. It is concluded that the 4f electrons of Sm must be considered as valence electrons, not shallow core states. Therefore the 4f-5d transition cannot change the valence of Sm, which may be characterized (if necessary) by the sum of all electrons in the s-d-f valence bands. The possibility of alternative interpretation of UPS spectra of Sm adsorbed films is illustrated by calculations of DOS (density of states) for oxygen-contaminated Sm crystal.     

Tunneling of 6<Emphasis Type="Italic">s</Emphasis><Superscript><Emphasis Type="Italic">2</Emphasis></Superscript> electrons in PbO and Bi<Subscript>2</Subscript>O<Subscript>3</Subscript>: XANES spectroscopy and DFT calculations

The results of XANES spectroscopy and DFT calculations are evidence for the occurrence of anomalous 2p_2/3→6s_1/2 electronic transitions in lead(II) and bismuth(III) oxides. The observed transitions may be due to the tunneling of outer 6s² electrons.     

High pressure structural investigations on hexagonal YInO3

Hexagonal (space group P6₃cm) form of YInO₃ has been investigated under high pressure using synchrotron-based angle-dispersive X-ray diffraction and Raman scattering methods. Our experimental investigations suggest that it undergoes the phase transition to a new phase in the pressure range 12–15?GPa, while the ambient hexagonal phase is found to coexist with the new phase up to 29?GPa. DFT based calculations within the LDA approach on the hexagonal phase of YInO₃ showed that the unit cell volume matches well with the experimentally obtained volume at ambient pressure. As the pressure increases, theoretically obtained values of unit cell volume of the hexagonal phase were found to be significantly lower than that of experimentally obtained values. This discrepancy has been corrected using LDA?+?U_In(4d) (Hubbard interaction parameter between Indium 4d electrons) method. We have proposed the high pressure phase of YInO₃ to be orthorhombic with space group Pnma.     

Pressure induces major changes in the nature of Americium's 5f electrons

Americium occupies a pivotal position in the actinide series with regard to the behavior of 5f electrons. High-pressure techniques together with synchrotron radiation have been used to determine the structural behavior up to 100 GPa. We have resolved earlier controversial findings regarding americium and find that our experimental results are in discord with recent theoretical predictions. We have two new findings: (1) that there exists a critical, new structural link between americium under pressure and its near neighbor, plutonium; and (2) that the 5f electron delocalization in americium occurs in two rather than one step.     

A density functional study of molecular oxygen adsorption and reaction barrier on Pu (100) surface

Oxygen molecule adsorptions on a Pu(100) surface have been studied in detail, using the generalized gradient approximation to density functional theory. Dissociative adsorption with a layer by layer alternate spin arrangement of the plutonium layer is found to be energetically more favorable compared to molecular adsorption. Hor2 approach on a bridge site without spin polarization was found to the highest chemisorbed site with an energy of 8.787 eV among all the cases studied. The second highest chemisorption energy of 8.236 eV, is the spin-polarized Hor2 or Ver approach at center site. Inclusion of spin polarization affects the chemisorption processes significantly, non-spin-polarized chemisorption energies being typically higher than the spin-polarized energies. We also find that the 5f electrons to be more localized in spin-polarized cases compared to the non-spin-polarized counterparts. The ionic part of O-Pu bonding plays a significant role, while the Pu 5f-O 2p hybridization was found to be rather week. Also, adsorptions of oxygen push the top of 5f band deeper away from the Fermi level, indicating further bonding by the 5f orbitals might be less probable. Except for the interstitial sites, the work functions increase due to adsorptions of oxygen.     

Few-electron semiconductor quantum dots with Gaussian confinement

We have performed Hartree-Fock calculations of the electronic structure of N ≤ 10 electrons in a quantum dot modeled with a confining Gaussian potential well. We discuss the conditions for the stability of N bound electrons in the system. We show that the most relevant parameter determining the number of bound electrons is V ₀ R ². Such a feature arises from widely valid scaling properties of the confining potential. Gaussian Quantum dots having N = 2, 5, and 8 electrons are particularly stable in agreement with the Hund rule. The shell structure becomes less and less noticeable as the well radius increases.      

Structural and electronic relationships between the lanthanide and actinide elements

The similarity and difference between the solid state properties of the 4f and 5f transition metals are pointed out. The heavier 5f elements show properties which have direct correspondence to the early 4f transition metals, suggesting a localized behaviour of the 5f electrons for those metals. On the other hand, the fact that Pu metal has a 30% lower volume than its neighbour heavier element, Am, suggests a tremendous difference in the properties of the 5f electrons for this element relative to the heavier actinides. This change in behaviour between Pu and Am can be viewed as a Mott transition within the 5f shell as a function of the atomic number Z. On the metallic 5f side of the Mott transition (i.e., early actinides), the elements show most unusual crystal structures, the common feature being their low symmetry. An analogous behaviour for the lanthanides is found in cerium metal under compression, where structures typical for the light actinides have been observed experimentally. A generalized phase diagram for the actinides is shown to contain features comparable to the individual phase diagram of Ce metal. The crystal structure behaviour of the lanthanides and heavier actinides is determined by the number of 5d (or 6d) electrons in the metallic state, since for these elements the f electrons are localized and nonbonding. For the earlier actinide metals electronic structure calculations - where the 5f orbitals are treated as part of the valence bands - account very well for the observed ground state crystal structures. The distorted structures can be understood as Peierls distortions away from the symmetric bcc structure and originate from strongly bonding 5f electrons occupying relatively narrow 5f states. High pressure is an extremely useful experimental tool to demonstrate the interrelationship between the lanthanides and the actinides. This revised version was published online in July 2006 with corrections to the Cover Date.     

Structural, electronic and optical properties of AgI under pressure

We report results of first-principles total-energy calculations for structural properties of the group I-VII silver iodide (AgI) semiconductor compound under pressure for B1 (rocksalt), B2 (cesium chloride), B3 (zinc-blende) and B4 (wurtzite) structures. Calculations have been performed using all-electron full-potential linearized augmented plane wave plus local orbitals FP-LAPW + lo method based on density-functional theory (DFT) and using generalised gradient approximation (GGA) for the purpose of exchange correlation energy functional. In agreement with experimental and earlier ab initio calculations, we find that the B3 phase is slightly lower in energy than the B4 phase, and it transforms to B1 structure at 4.19 GPa. Moreover, we found AgI has direct gap in B3 structure with a band gap of 1.378 eV and indirect band gap in B1 phase with a bandgap around 0.710 eV. We also present results of the effective masses for the electrons in the conduction band (CB) and the holes in the valence band (VB). To complete the fundamental characteristics of this compound we have analyzed their linear optical properties such as the dynamic dielectric function and energy loss function for a wide range of 0-25 eV.     

金红石型TiO2(110)表面性质及STM形貌模拟

采用密度泛函理论从头计算了金红石型TiO₂(110)表面的相关性质,切片模型含有9层原子,采用化学整比表面结构,晶胞真空层厚度为1.5nm,原子价电子采用超软赝势表达.差分电子密度分布图发现原子附近区域电子密度分布以球对称为主,电子定域形成离子键的趋势较强,但在Ti和O原子之间存在较弱的共价键.模拟了金红石型TiO₂(110)表面结构的扫描隧道显微镜(scanning tunneling microscope,简称STM)图像,利用Tersoff-Hamann的成像理论,在+2V的正向偏压下,采用一系列变化的数值作为STM探针离表面桥式氧的距离,分析了相关态密度的变化,发现(110)表面的STM形貌凸起部分来自于5—Ti原子,而不是2—O原子(桥式氧),在TiO₂(110)表面结构成像中,电子效应起主导作用,证实了STM实验观察到的亮行是Ti原子的结果. 关键词： 功能材料 密态泛函理论 表面结构 STM像     

UV filter 2‐ethylhexyl 4‐methoxycinnamate: a structure,energetic and UV–vis spectral analysis based on density functional theory

2‐Ethylhexyl 4‐methoxycinnamate (EHMC) is a very commonly used UVB filter that is known to isomerize from the (E) to the (Z) isomer in the presence of light. In this study, we have performed high level quantum chemical calculations using density functional theory (DFT) with the B3LYP density functional and extended basis sets to study the gas‐phase molecular structure of EHMC and its energetic stability. Calculations were also performed for related smaller molecules cinnamic acid and 4‐methoxycinnamic acid. Charge delocalization has been analyzed using natural charges and Wiberg bond indexes within the natural bond orbital analysis and using nucleus independent chemical shifts. Density functional theory calculations reveal that the (E) isomer of EHMC is more stable than the (Z) by about 20 kJ mol^?1 in both the gas and aqueous phases. The enthalpy of formation in the gas phase of (E)‐EHMC was derived from an isodesmic bond separation reaction. Long‐range corrected DFT calculations in implicit water were made in order to understand the excited state properties of the (E) and (Z) isomers of EHMC. Copyright © 2013 John Wiley & Sons, Ltd.     

Effect of spin fluctuations on the superconducting phase of Hubbard fermions in the t-t′-t″-J* model

The effect of spin-fluctuation scattering processes on the region of the superconducting phase in strongly correlated electrons (Hubbard fermions) is investigated by the diagram technique for Hubbard operators. Modified Gor’kov equations in the form of an infinitely large system of integral equations are derived taking into account contributions of anomalous components $ P_{0\sigma ,\bar \sigma 0} The effect of spin-fluctuation scattering processes on the region of the superconducting phase in strongly correlated electrons (Hubbard fermions) is investigated by the diagram technique for Hubbard operators. Modified Gor’kov equations in the form of an infinitely large system of integral equations are derived taking into account contributions of anomalous components of strength operator . It is shown that spinfluctuation scattering processes in the one-loop approximation for the t-t′-t″-J* model taking into account long-range hoppings and three-center interactions are reflected by normal (P _{0σ, 0σ}) and anomalous () components of the strength operator. Three-center interactions result in different renormalizations of the kernels of the integral equations for the superconducting d phase in the expressions for the self-energy and strength operators. In this approximation for the d-type symmetry of the order parameter for the superconducting phase, the system of integral equations is reduced to a system of nonhomogeneous equations for amplitudes. The resultant dependences of critical temperature on the electron concentrations show that joint effect of long-range hoppings, three-center interactions, and spin-fluctuation processes leads to strong renormalization of the superconducting phase region. Original Russian Text ? V.V. Val’kov, A.A. Golovnya, 2008, published in Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2008, Vol. 134, No. 6, pp. 1167–1180.     

High-pressure characteristics of α-Fe2O3 using DFT+U

We have calculated the structural, magnetic and electronic properties of corundum-type α-Fe₂O₃ from first principles using density-functional theory (DFT) and the DFT?+?U method to account for correlation effects in this material. Although the correct magnetic ground state is obtained by pure DFT, the magnetic moments and the band gap are too small, and the predicted structural phase transition coupled with a transition from the insulating high-spin to a metallic low-spin phase at a pressure of 14?GPa is not observed experimentally. We find that considering the Coulomb interaction directly by including a Hubbard-like term U in the density functional greatly improves the results with respect to band gap and magnetic moments. The phase transition is shifted to higher pressures with increasing values of U and disappears for U?>?3?eV. The best overall agreement of structural, magnetic and electronic properties with experimental data is obtained for U?=?4?eV.     

Electron-density distribution and physical properties of plutonium-gallium alloys: Ab initio cluster calculations

A cluster model based on ab initio density-functional theory was used to model gallium-stabilized δ-plutonium alloys, and to calculate the electron-density distribution, its pressure dependence, bond lengths, elastic properties (second order and third order), and inelastic properties for Pu₁₂Ga (7.7 at% Ga) and Pu₁₈Ga (5.3 at% Ga). The electron distribution was found to contain localized, semi localized, and delocalized contributions, with the second possessing covalent character. Two of plutonium’s 8 valence electrons were found to be itinerant, consistent with a recent prediction based on an electrostatic model, with the electron configuration for plutonium being 7s^0.57p^0.55f¹ (itinerant) and 6d¹5f⁵ (localized), and that for gallium being 4s¹4p². Applied hydrostatic pressure shifts the charge density toward a more localized Pu(d)-based distribution. The onset of the pressure-induced δ-Pu to α-Pu phase change is accompanied by a ∼0.2 electron increase in the localized population that may serve as a driving force for the phase change. Interior bonding within the Pu₁₂Ga subunits is stronger than that of the surrounding plutonium lattice, and the Pu-Ga bonds therein relax in a direction opposite to lattice strain. This study predicts covalency in metallic plutonium, both in the Pu-Ga bonding and in the Pu-Pu bonding.     

de Haas–van Alphen effect in strongly correlated electron systems

We present the Fermi surface properties in strongly correlated electron systems of rare earth and uranium compounds via de Haas–van Alphen experiments. The conduction electrons with large cyclotron effective masses over 100m₀ (m₀: rest mass of an electron) are detected in CeRu₂Si₂, CeCoIn₅ and UPt₃. These electrons move slowly in the crystal. The topology of the Fermi surface and the cyclotron mass are compared to those of energy band calculations.