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On the Lanthanide and Scandinide l ContractionsD R. LloydTrinity College, Dublin, Ireland

The lan thanide contraction must receive at least a men-tion in all introductory university chemistry courses, as wellas further discussion with th e chemistry of th e f-block ele-ments. Most textbooks of inorganic and general chemistryindicate tha t contractions occur in all rows of the periodictable, but, even so, in the emphasis on this contraction,students can be left with an impression that the effect isparticularly large for the lanthanides. Inspection of ionicradius tables2 should dispel this idea. The decrease across 1 5elements La3+-Lu3+ (117.2-100.1 Dm) is less than th atacross 11 elements in the third row if the 2t ons, of similarsize to the lanthanides. are chosen: Ca2--%n2- ( 1 l PRR om).Even if the much smaller 3 ions are used, sc 3 + - ~ a ~ +(88.5-76 Dm). the average absolute chance per element isalmost identical to that the lanthanide ions, and th e per-cent change is therefore greater in th e scandinide contrac-tion than-in the la nth aii de contraction. Similar remarksapolv to the metallic radii.'I'eats on inorganic chemistry give varying accounts of thecause of the lanthanide contraction. S ome do not discuss thematter. others refer in a eeneral manner to shieldine effects.-and this is clearly correct if not very explicit. However, sometexts give an interpretation which can he generalized in aform such as Shielding of one 4f electron by another fromthe nuclear charee is Door because of the shapes of the 4forbitals , so, as the nuclear charge increases, there is a reduc-tion in size of these orbitals, and this is the origin of thecontraction . Some also draw a direct comparison with thecontraction acrois the Rd series. The various forms of thestatement have the following more or less direct, interrelat-ed implications:

1 The size of the lanthanide atoms or ions is determined to asubstantial extent by the 4f' subshell, i.e., these are outer-most electrons.2 The contraction of the atoms or ions is a consequence of theangularpart of the 4f wavefunctions.The fi rst of these is a litt le surprising when th e small sizeof th e experimentally observedcontr&tion is considered,but , much more seriously, there is an inconsistency with th einterpretation usually given to the magnetic and spectro-scopic properties of the ions LIP, tha t the f electrons arewell shielded from the chemical environment of the ion bvth e 5s2 5p6 configuration. If this is so, and th e experiment&evidence ~ o i n t sn this direction. then im ~li cat ion1) mustbe incorrect, and the implied connectionkith d-orbital ef-

fects in the transition series is suspect.Implication (2) has a similar incongruity, at least in thediscussion of effects on the third transi tion series, where the4f shell is complete. Since the closed shell 4p4configurationhas spherical symmetry, there can be no angular effect here;any effects must he due t o the radial par t of the appropriatewavefunctions.A very elementary approach to point (i) can he made byusing Slater's rules to calculate th e radius R of the maxi-m& in a spherical charge density function 3). as R =~L* ~Z' -' 52.9 pm (Z* is the effective nuclear charge, n* th eeffective quantum number). Taking Gd3+ as an example,this gives values ofR as (5p6) 69 pm an d (457) 24 pm. Thissupports the idea th at the 4f configuration is deep insidethe ion.

More precise analysis is available from the detailed atomiccalculations of Waber and Cromer 4 ) , who have reportedvalues of R . (here R is the orinci~a ladial maximum) andHerman an; skillman (5)wi o give tabulations of th e wave-functions. The Waber and Cromer R values demonstratetha t t he simple Slater approximation Gves remarkably goodestimates; for Gd3+ values are (5p6) 71.0 pm, (4f) 29.1 ~ mFor 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 extractedfrom the Herman-Skillman tables (5).Th e conclusion tha tR for th e (4f ) configuration is little more than one-third ofthat for (5p6) is true for all the lanthanides, though thepercent change in rad ius of the f shell from Ce3+ t o Lu3+(35.624.4 om. 32%) is substantiallv ereater than that forisp (80.(i63.2 pm;21%). Clearly, aithough the 4p subshellcontracts ra~idlv ith . it does so well inside the outermostcore electrons.

The contributions to the size of the atom are difficult toassess precisely, though it is clear from the above that anycontribution bv the 4f shell must be small. An attempt canbe made by calculating electron densities a t various-radii.The tota l 4f and (5p6 5s2) electron densities can readily heobtainedfrom the Herman-Skillman tables. For Gd the ratioof th e densities 457 (5p6 5s2) is 0.21 a t R (5p6) and falls to0.07 a t the ionic radius. Thu s, in the ou ter regions of the ion,4f contributes of th e order of 10% of the electron density.While this is not a neeligible contribution to the size. to afirst approximation it is reasonable t o describe the (5si 5p6)configuration as radius-det errninir~ g.~t may he noted tha tthe small contribution from 4f increases across the series,since the f-shell occupancy increases faster than the f orbitaldensity a t the ionic radius decreases from the contraction, soth e small effects of th e f electrons actually oppose the con-traction.Since the a n d a r part of th e 4f wavefunctions cannot besignificant, thereason for the contraction has to be sought inthe radial part of the functions. The 4f has only one radialmaximum. and so inside R.. I4n there will be onlv a smallshielding bf other elect rons 'bi4f electrons. T he tables 5)show tha t for all the lanthanides, th e third radial maximumof the 5p6 orbital, and t he fourth maximum of the 59, are ustinside the maximum for 4f. Thus the 5s and 5p orbitalspenetrate the 4f shell quit e effectively, and th is is th e sim-olest interoretation of the sensi tivitv of size to nuclearcharge. he lanthanide contraction could well be taught a san unusuallv simple illustration of penetration effects onsize, together with the more usual discussion of penetrationeffectn on orbital energies for polyelectronir atoms. Alterna-tively, in terms of shielding, it is true t ha t th e 4f electronsprovide poor shielding from the nuclear charge, hut the

The name scandinide contraction has been suggested, thoughnot entirely seriously, by E. A. V . Ebsworlh, to emphasize that thecontraction of the lanthanides s not unique.2F~liowingHuheey 0.he Shannon-Prewiti radii 2) re used:values quoted are those for 6-coordination.The calculations of ref 5are relativistic; values quoted for fshellshave been averaged appropriately, though the difference between thef,,, and fi12 radii s not significant n the argument presented here.* A statement of this point is made explicitly in the text by Day andSelbin 6).502 Journal of Chemical Education

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significant shielding is th at for the 5s2 p 6 ) configurationand not tha t for the other 4f electrons.In contrast to the situation in th e lanthanides, in the firsttransition series 3d electrons make a ven, substantial con-tribution LO he ionic radius. R,values fo rihe Bdnconfigura-tion ares lieh tlv ereater than those for the 30 et at the sta rt.of the series, and both sets contract, but the 3d set contractsfaster so that the ~ osi tio ns reversed for t he later members4). In the second transition series the more expanded 4dorbitals extend slightly beyond the 4p configurationthroughout 4).Thus in the series of transition elements it isreasonable to ascribe part of the observed contractions topoor shielding of one electron by another in the same suh-shell, but here also it should be realized th at contraction ofth e outer core electrons is significantConclusions

I t can be shown from th e literature th at t he radius of thelanthanide ions is mainly determined by the outer ( 5 9 5 p 6 )configuration and tha t t he 4f electrons make very little di-rect contribution to size . The observed contraction acrossthe lanth anide series is a contraction of the (5.9 5p6)configu-ration brought ahout by penetration of these outer electrons

inside the 4f radial maximum, and is not an effect of thecontraction nf the 4f shell itself. However, the contractionsohserved in the transition series, such as the scandinidecontraction in the first series, are du e to contractions of bothth e outer core electrons and t he partially filled d shell; thecommonly discussed effect of poor shielding of one electronby another in the same subshell is significant here, hut notfor the lanthanides.cknowledgmentThe impetus for this note comes from students who havedriven me to clarify my own thoughts, the presentation herehas been improved by discussion with several colleagues,particularly D J. Cardin and M E. Bridge.

1) Huheey, J E l n o w n i e C h e m i W , 3 rd sd .j Hsvpsr Rosv: New York. 1983;p722) Shannon .D.;Pre ett . C. T. Acta Cryat.B25 1969 926. b-on, R.D do C v t .,176 rO 711--.. ..--(3) Purcell. K. F.: KO . . C. b organio Chem iatry ;Saundna:New York, 1917;p 42.4) Waber,J. T.; romer,D.T.J Chem.Phys. I%&,42,4116.5) Herman. F :Skillman, S. AtomicStructure Cdeulationa : Prentiee-Hall: En ph oo dCliffs. NJ. 1963.

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