On the Lanthanide and "Scandinide"l Contractions D. R. Lloyd Trinity College, Dublin, Ireland The lanthanide contraction must receive a t least a mention in all introductory university chemistry courses, as well as further discussion with the chemistry of the f-block elements. Most textbooks of inorganic and general chemistry indicate that contractions occur in all rows of the periodic table, but, even so, in the emphasis on this contraction, students can be left with an impression that the effect is particularly large for the lanthanides. Inspection of ionic radius tables2 should dispel this idea. The decrease across 15 elements La3+-Lu3+ (117.2-100.1 Dm) is less than that across 1 1 elements in the third row if the 2t ions, of similar size to the lanthanides. are chosen: Ca2--%n2- (1lPRR om). Even if the much smaller 3+ ions are used, s c 3 + - ~ a ~ + (88.5-76 Dm). the average absolute chance per element is almost identical to that the lanthanide ions, and the percent change is therefore greater in the "scandinide" contraction than-in the lanthaiide contraction. Similar remarks apolv .. . to the metallic radii. 'I'eats on inorganic chemistry give varying accounts of the cause of the lanthanide contraction. Somedo not discuss the matter. others refer in a eeneral manner to shieldine effects. and this is clearly correct if not very explicit. However, some texts give an interpretation which can he generalized in a form such as "Shielding of one 4f electron by another from the nuclear charee is Door because of the shapes of the 4f orbitals, so, as the nuclear charge increases, there is a reduction in size of these orbitals, and this is the origin of the contraction". Some also draw a direct comparison with the contraction acrois the Rd series. The various forms of the statement have the following more or less direct, interrelated implications:
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1 The "size" of the lanthanide atoms or ions is determined to a
substantial extent by the 4f' subshell, i.e., these are "outermost" electrons. 2 The contraction of the atoms or ions is a consequence of the angular part of the 4f wavefunctions. The first of these is a little surprising when the small size of the experimentally observedcontr&tion is considered, but, much more seriously, there is an inconsistency with the interpretation usually given to the magnetic and spectroscopic properties of the ions LIP, that the 1f electrons are well shielded from the chemical environment of the ion bv the 5s2 5p6 configuration. If this is so, and the experiment& evidence ~ o i n t in s this direction. then im~lication(1) must be incorrect, and the implied connectionkith d-orbital effects in the transition series is suspect. Implication (2) has a similar incongruity, a t least in the discussion of effects on the third transition series, where the 4f shell is complete. Since the closed shell 4p4 configuration has spherical symmetry, there can be no angular effect here; any effects must he due to the radial part of the appropriate wavefunctions. A very elementary approach to point (i) can he made by using Slater's rules to calculate the radius R, of the maxim& in a spherical charge density function (3). as R, = ~L*~Z'-' X 52.9 pm (Z* is the effective nuclear charge, n* the effective quantum number). Taking Gd3+ as an example, this gives values of R, as (5p6) 69 pm and (457) 24 pm. This supports the idea that the 4f configuration is "deep inside" the ion. 502
Journal of Chemical Education
More precise analysis is available from the detailed atomic calculations of Waber and Cromer ( 4 ) , who have reported values of R,. (here R, is the o r i n c i ~ aradial l maximum) and Herman an; skillman (5) w i o give tabulations of the wavefunctions. The Waber and Cromer R, values demonstrate that the simple Slater approximation Gves remarkably good estimates; for Gd3+ values are (5p6) 71.0 pm, (4f) 29.1 ~ m . ~ For the Gd atom, values are (6s) 182.6 pm, (5d1) 96.0 pm, (5p6)71.0 pm, (4f) 29.1 pm. Similar values can be extracted from the Herman-Skillman tables (5).The conclusion that R, for the (4f") configuration is little more than one-third of that for (5p6) is true for all the lanthanides, though the percent change in radius of the f shell from Ce3+ t o Lu3+ (35.624.4 om. 32%) is substantiallv ereater than that for isp" (80.(i63.2 pm;21%). Clearly, aithough the 4p subshell contracts r a.~ i d. l vwith %. it does so well inside the outermost core electrons. The contributions to the "size"of the atom are difficult t o assess precisely, though it is clear from the above that any contribution bv the 4f shell must be small. An attempt can be made by calculating electron densities a t various-radii. The total 4f" and (5p6 5s2) electron densities can readily he obtainedfrom the Herman-Skillman tables. For Gd the ratio of the densities 457 (5p6 5s2) is 0.21 a t R, (5p6) and falls to 0.07 a t the ionic radius. Thus, in the outer regions of the ion, 4f contributes of the order of 10% of the electron density. While this is not a neeligible contribution to the size. to a first approximation i t is reasonable to describe the (5si 5p6) configuration as radius-deterrninir~g.~ I t may he noted that the small contribution from 4f increases across the series, since the f-shell occupancy increases faster than the f orbital density a t the ionic radius decreases from the contraction, so the small effects of the f electrons actually. oppose the con.. traction. Since the a n d a r part of the 4f wavefunctions cannot be significant, thereason for the contraction has to be sought in the radial part of the functions. The 4f has only one radial maximum. and so inside R.. I4n there will be onlv a small shielding bf other electrons'bi4f electrons. The tables (5) show that for all the lanthanides, the third radial maximum of the 5p6 orbital, and the fourth maximum of the 59, are just inside the maximum for 4f. Thus the 5s and 5p orbitals penetrate the 4f shell quite effectively, and this is the simolest interoretation of the sensitivitv of size to nuclear charge. he lanthanide contraction could well be taught as an unusuallv simple illustration of penetration effects on size, together with the more usual discussion of penetration effectn on orbital energies for polyelectronir atoms. Alternatively, in terms of shielding, i t is true that the 4f electrons provide poor shielding from the nuclear charge, hut the
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The name "scandinide contraction" has been suggested, though not entirely seriously, by E. A. V. Ebsworlh, to emphasize that the contraction of the lanthanides is not unique. 2F~liowingHuheey (0.the Shannon-Prewiti radii (2)are used: values quoted are those for 6-coordination. The calculations of ref 5are relativistic; values quoted for fshells have been averaged appropriately, though the difference between the f,,, and fi12 radii is not significant in the argument presented here. * A statement of this point is made explicitly in the text by Day and Selbin (6).
significant shielding is that for the (5s25 p 6 ) configuration and not that for the other 4f electrons. In contrast to the situation in the lanthanides, in the first transition series 3d" electrons make a ven, substantial contribution LO the ionic radius. R,values forihe Bdn configuration aresliehtlv ereater than those for the 30"et at the start " .of the series, and both sets contract, but the 3d set contracts faster so that the ~ o s i t i o nis reversed for the later members (4). In the second transition series the more expanded 4d orbitals extend slightly beyond the 4p configuration throughout (4).Thus in the series of transition elements it is reasonable to ascribe part of the observed contractions to poor shielding of one electron by another in the same suhshell, but here also i t should be realized that contraction of the outer core electrons is significant Conclusions I t can be shown from the literature that the radius of the lanthanide ions is mainly determined by the outer ( 5 9 5 p 6 ) configuration and that the 4f electrons make very little direct contribution to "size". The observed contraction across thelanthanide series is a contraction of the (5.9 5p6)configuration brought ahout by penetration of these outer electrons
inside the 4f radial maximum, and is not an effect of the contraction nf the 4f shell itself. However, the contractions ohserved in the transition series, such as the "scandinide" contraction in the first series, are due t o contractions of both the outer core electrons and the partially filled d shell; the commonly discussed effect of poor shielding of one electron by another in the same subshell is significant here, hut not for the lanthanides. Acknowledgment The impetus for this note comes from students who have driven me to clarify my own thoughts, the presentation here has been improved by discussion with several colleagues, particularly D. J. Cardin and M. E. Bridge. (1)
(2)
Huheey, J. E. "lnownie C h e m i W , 3rdsd.j Hsvpsr & Rosv: New York. 1983;p 72. Shannon,R.D.; Preett. C. T. Acta Cryat. B25,1969,926.Sb-on, R.D. A d o C v t . ,176 rO9 --..,..--,
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(3) Purcell. K. F.: KO*.J. C. "borganio Chemiatry";Saundna:New York, 1917; p 42. (4) Waber,J. T.;Cromer, D.T. J. Chem.Phys. I%&,42,4116. (5) Herman. F.: Skillman, S. "Atomic Structure Cdeulationa": Prentiee-Hall: Enphood Cliffs. NJ. 1963.
Volume 63
Number 6
June 1986
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