Lanthanide and actinide contraction

The filling of inner / shells in lanthanide and actinide atoms is accompanied by a steady decrease of the size of the atom (measured by suitable means such as the first radial moment). As a consequence, the size of atoms from the same group in the second and third transition metal series of the periodic table turns out to be similar. That is, the increased number of electrons with increasing nuclear charge number Z does not lead to an increased size of the atom under consideration. This reduced-size effect is called the lanthanide contraction. It is important to understand that the effect is also witnessed in purely nonrelativistic calculations — the effect is simply amplified in a relativistic description. 

The main difficulty here is to clearly separate effects that can hardly be separated, namely relativistic and electron-correlation effects. Nevertheless, pioneering studies of this effect date back to the mid 1970s [1140]. Four-component methods have been employed to determine the contribution which is solely due to relativity [1141]. The four-component approach, for which Dirac-Hartree-Fock and — to also account for correlation effects — relativistic MP2 calculations have been utilized, confirms results first obtained with relativistic effective core potential methods [1142,1143]. It has been found [1141] that between 10% and 30% of the lanthanide contraction and 40% to 50% of the actinide contraction are caused by relativity in monohydrides, trihydrides, and monofluorides of La, Lu and Ac, Lr, respectively. 

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Thus the rather easily obtained atomic sizes are the best indicator of what the f-electrons are doing. It has been noted that for all metallic compounds in the literature where an f-band is believed not to occur, that the lanthanide and actinide lattice parameters appear to be identical within experimental error (12). This actually raises the question as to why the lanthanide and actinide contractions (no f-bands) for the pure elements are different. Analogies to the compounds and to the identical sizes of the 4d- and 5d- electron metals would suggest otherwise. The useful point here is that since the 4f- and 5f-compounds have the same lattice parameters when f-bands are not present, it simplifies following the systematics and clearly demonstrates that actinides are worthy of that name. 

Values for the lanthanide and actinide contraction from various atomic calculations"... 

Values for the lanthanide and actinide contraction derived from bond lengths from various relativistic (nonrelativistic) molecular calculations and experimental data... 

Pyykko (1979b) used the Dirac-Hartree-Fock one-centre expansion method for the monohydrides to calculate relativistic values for the lanthanide and actinide contraction, i.e. 0.209 A for LaH to LuH and 0.330A for AcH to LrH. The corresponding nonrelativistic value derived from Hartree-Fock one-center expansions for LaH and LuH is 0.191 A, i.e., for this case 9.4% of the lanthanide contraction is due to relativistic effects. The experimental value of 0.179 A would suggest a correlation contribution of-14.4% to the lanthanide contraction if one assumes that the relativistic theoretical values are close to the Dirac-Hartree-Fock limit, which is certainly not true for the absolute values of the bond lengths themselves. Moreover, it is well known that for heavy elements relativistic and correlation contributions are not exactly additive. Corresponding nonrelativistic calculations for AcH and LrH have not been performed and experimental data are not available to determine relativistic and electron correlation effects for the actinide contraction. Table 8 summarizes values for the lanthanide and actinide contraction derived from theoretical or experimental molecular bond lengths. It is evident from Ihese results... 

The results of HF- and DHF-OCE calculations for the tetrahedral molecules CeH4 and TI1H4 were compared by Pyykko and Desclaux (1978). For both molecules small relativistic bond-length expansions were found. By comparison to HfH4 and 104EH4 the values of the lanthanide and actinide contraction were established to be 0.19 A and 0.30 A, respectively (cf. also sect. 1.3). The lanthanide contraction was found to result for 86% from a nonrelativistic shell-structure effect and only for 14% from relativity. Results of similar calculations are available for YbHj (Pyykko 1979a). 

Table 46 shows the computed relativistic and non-relativistic bond lengths of AcH, TmH, LuH and LrH computed by Pyykko. Pyykko (1979) defined lanthanide and actinide contraction as... 

The values computed this way are 0.210 and 0.329 A, respectively. Non-relativisti-cally the lanthanide contraction is only 0.191 A. One could also compare the experimental A 3 as 0.189 A in good agreement with the value of Pyykko. Figure 29, obtained by Pyykko, nicely demonstrates the lanthanide and actinide contraction. 

T. Saue. A fully relativistic Dirac-Hartree-Fock and second-order Moller-Plesset study of the lanthanide and actinide contraction. /. Chem. Phys., 109(24) (1998) 10806-10817. 

V. Kiichle, M. Dolg, H. Stoll. Ab Initio Study of the Lanthanide and Actinide Contraction. /. Phys. Chem. A, 101 (1997) 7128-7133. 

M. Seth, M. Dolg, P. Fulde, P. Schwerdt-feger. Lanthanide and actinide contractions relativistic and shell structure effects. /. Am. Chem. Soc., 117 (1995) 6597-6598. 

Table 1 Bond Lengths (A) of the Diatomics MX (M = La, Lu, Ac, Lr X = H, 0, F) and Resulting Values of the Lanthanide and Actinide Contraction A/ e (A) from Relativistic (rel) and Nonrelativistic (nrel) All-electron Self-consistent Field Calculations ...

There is a decrease in the atomic and ionic sizes (lanthanide and actinide contraction) in both the series with increase in the atomic number. 

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