Lanthanide binding energies

When the f sub-shell is less than half-filled the stabilization of the divalent state (f"" " ) relative to the trivalent state is more rapid for the lanthanides than for the actinides. But the behaviour is reversed in the second half of the series. In part, this must be due to the low binding energy of the 6 d electrons compared to the 5 d. 

In light lanthanides (La, Ce, Pr, Nd) the pulled down 4f state is nearly localized and hybridizes only weakly with conduction states. The bandwidth W4f will be very narrow, U high and negative, and the occupation probabiUty by conduction electrons rather low. This results in the occurrence of shake-down satellites at a lower binding energy for lanthanides, accompanying a poorly screened main peak (Fig. 7 a). When proceeding to heavier lanthanides, the occupation probability and the intensity of the shake-down satellite are depressed the symmetric, poorly screened core level is left, i.e. the 4f states are completely localized. 

The only UPS/XPS photoemission study of Am shows a lanthanide like valence band feature as displayed in Fig. 16. The 5f emission is nearly completely withdrawn from Ep except possibly for some very weak 5 f contribution seen only in high resolution He-I-spectra (AE 0.12 eV) as a very sharp peak just at Ep. The 5 f intensity is concentrated in a structured peak around 2.8 eV binding energy (for MgR excitation, upper curve, the structures are not resolved) as deduced from the excitation energy dependence of the spectra. If one compares with Sm metal, the peaks at 1.8, 2.6 and 3.2 eV are attributed to the H, F, and P states, respectively, of the 5f final state multiplet originating from the initial 5f ground state of trivalent Am. 

The binding energies of 3ds/2 level are given in Table 9.5. Upon complexation, electron density of the valence levels of the lanthanide increases, and hence contributes to a decrease... 

It is neither intended nor possible to give a comprehensive review of relativistic density functional calculations on small molecules. To be able to compare the methods described in Sec. 2, we will primarily discuss molecules for which computational results from a variety of different methods are aveulable. Molecules containing heavy elements from the left half of the periodic table (including lanthanides and actinides) will not be discussed, as most of this is covered in the eirti-cle by V. Pershina in this volume. Likewise, only calculations of molecular spectroscopic constants such as bond lengths (r ), (harmonic) vibrational frequencies ((0 ) and binding energies (D ) are... 

Besides the two examples discussed above, the DK approach was applied to various other diatomics of heavy-main group elements, like AuH, AuCl, PbO, Pb2, TIH [14,15,18,19]. The close similarity of ZORA and DK results was also confirmed for hydrides, oxides, and fluorides of the f-elements La, Lu, Ac, and Lr at the scalar relativistic level [143]. Differences in bond lengths, vibrational frequencies, and binding energies amounted to at most 0.7 pm, 6 cm" and 6 kJ/mol, respectively. Except for cases where the quality of the basis set may be questioned, calculated results for the lanthanide species agree well with available experimental data. 

The binding energy of an electron to its nucleus is proportional to its mass, so the electrons of the lanthanides are bound more strongly and thus the ionic size is reduced more strongly than would be expected from the increase in nuclear charge and orbital penetration" (Platt 2012). 

One of the most striking properties of lanthanide metals and compounds is the relative insensitivity of electrons in the unfilled 4f shell to the local environment, compared to non-f electron shells with similar atomic binding energies. Whereas the 5d and 6s electrons form itinerant electron bands in the metallic solids, the 4f electrons remain localised with negligible overlap with neighbouring ions. For the maximum in the 4f radial charge distribution lies within those of the closed 5s and 5p shells, so the 4f shell is well shielded from external perturbations on the atomic potential, such as the crystal field. 

This semiempirical method (often referred to as ZINDO/1), although not specifically parameterized to favor any experimental quantity, can be used for calculation of binding energies, geometries, ionization energies, and dipole moments of TM and lanthanide species. In INDO/1, the one-center TERIs are calculated theoretically over Slater-type AOs and scaled (if necessary). 

Fig. 9.6. Melting slope dT/dP and ionization energy I for divalent lanthanide ions against atomic number, from Jayaraman (1965) and Johansson and Rosengren (1975> respectively. To be noted is the remarkable resemblance of the two sets of data. The smooth curve is the interpolated binding energy difference between divalent and trivalent metallic states.

To predict the influence of pressure on the location of the levels of Ln " and Ln " with respect to the bands edges of the host, one should consider how the chemical environment of the lanthanide changes the 4f binding energy. It is known that the host lattice diminishes the binding energy of 4f electrons several times with respect to the free-ion energies (see Ref [192]). Dorenbos [154] proposed a model... 

Dorenbos P, Rogers EG (2014) Vacuum referred binding energies of the lanthanides in transition metal oxide compounds. ECS J Sol State Sci Tech 3 R150... 

Models based on the electric multipole expansion have been used to explain structures, force constants and binding energies of lanthanide compounds (Guido and Gigli 1974, Ackermann et al. 1976, Myers 1976, Jia and Zhang 1988). 

Binding energies D, bond lengths R, vibrational frequencies o) and dipole moments for the lanthanide monohydtides from configuration interaction calculations including the LanghoflF-Davidson size-consistency correction in comparison with experimental data"... 

Fig, 7. Linear behavior of the binding energies of the lanthanide monohydrides for fixed 4f occupation number. Data taken from Dolg and Stoll (1989). 

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