ASPECTS OF f-ELEMENTS
A personal itinerary
Pekka PYYKKÖ (Department of Chemistry, University of
Helsinki, Finland)
15 December 2014
IOVI OPTIMO MAXIMO ET GENIO LOCI (IOMGL)
Mentioned 69 times in the ClaussSlaby inscription database.
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JOHAN GADOLIN’S 1794 ANALYSIS
 Swedish version [1], German translation [2].
 Finds a new oxide (’earth’); an unspecified mixture of (Y, La-Lu).
 First confirmation by Ekeberg in 1797 [3]. Names ’yttria’.
 The name ’gadolinium (Gd)’ by de Marignac [4].
 Magnus → Maunula → Magnulin → Gadolin (gadol) .
1. J. Gadolin, Kungl. Vetenskapsakad. Handlingar (1794) 137-155.
2. J. Gadolin, Crells Ann. (1796) 313-329.
3. A. G. Ekeberg, Kungl. Vetenskapsakad. Handlingar (1797) 156-164.
4. J.-C. G. de Marignac, as quoted by Lecoq de Boisbaudran, C.R.
Acad. Sci . 102 (1886) 902.
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Johan Gadolin: Hedersbetygelser
 Mineralet FeBe2Y2Si2O10 gadolinit (Klaproth ≤1801).
 Grundämnet ’Gadolinium (Gd)’ , Lecoq de
Boisbaudran, CR Ac. Sci. 102 (1886) 902:
’M. de
Marignac a bien voulu me charger d’annoncer … qu’il
a choisi le nom de gadolinium (symbole Gd).’
 Finska Vetenskaps-Societetens Festschrift 1910.
 Frimärke 1960.
 Minnesskyltarna vid Kaskisgatan 6.
 ÅA: ’Gadolinia’.
 ’Gadolingatan / Gadolininkatu’ i Gumtäkt.
THE PERIODIC SYSTEM, Z = 1 - 172
P. Pyykkö, PCCP 13 (2011) 161.
1. CRYSTAL-FIELD THEORY 1973
 Pseudocontact NMR shifts due to lanthanide ions.
 Arbitrary set of crystal-field parameters. 2x3 = 6.
 Cp. Bleaney’s 1972 theory with lowest-order terms.

Fortran-code written. Use Racah algebra.
 The issue: Dependence of the shift on the particular
lanthanide. The shift looks like a contact shift but occurs
on a remote C-13 or H-1 nucleus having no overlap with
the lanthanide.
1. R.M. Golding, P. Pyykkö, Mol. Phys. 26 (1973) 1389.
(No27).
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A Ln/An COMPARISON 1978
1. P. Pyykkö, ’Relativistic quantum
chemistry’, Adv. Quantum Chem.
11 (1978) 353-409. (No. 44)
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2. DF-OCE AND THE LANTHANIDE/ACTINIDE
CONTRACTIONS 1978
 Use hydride models, such as CeH4 vs. HfH4. Also ThH4
vs. (104)H4. Contractions 19.0 pm and 30 pm,
respectively.
 Non-relativistic lanthanide contraction 16.4 pm or 86% of
the relativistic one.
 Also mono-, di- and hexahydride models.
1. P. Pyykkö, J-P. Desclaux, Chem. Phys. 34 (1978) 261.
(No46).
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3. REX 1981
 Semiempirical MO:s and their energies for basic actinide






systems, such as uranyl or UF6 [1].
La théorie à trous for the electric field gradient, q, at An [2]
Right or wrong? Later ab initio work, see [3]. 6p+, 5f-.
Once more conforms to the picture of the main valence orbitals
being 6d = 5f > 6p > 7s > 7p.
The covalent molecular orbitals of small d0 f0 U(VI) molecules
contain about 5f 2 6d 1.
Double-zeta STO fits for the radial functions fitted to the DiracFock atomic orbitals.
Much help for these auxiliary developments from Matti Hotokka
Leif Laaksonen, Liisa Laakkonen, Kazuyuki Tatsumi.
P. Pyykkö, L. L. Lohr Jr, Inorg. Chem. 20 (1981) 1950. (No.59).
2. S. Larsson, P. Pyykkö, Chem. Phys. 101 (1986) 355. (No. 94).
3. J. Autschbach &, J. Chem. Theory Comp. 8 (2012) 4239.
1.
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REXNMR 1981
 The first implementation[1] of my relativistic theory of NMR spin-
spin coupling tensors.
 Was used on UF6 in [2].
P. Pyykkö, L. Wiesenfeld, Mol. Phys. 43 (1981) 557. (No.64).
2. N. Rösch, P. Pyykkö, Mol. Phys. 57 (1986) 193. (No. 95).
1.
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THE 1987 REVIEW
 Reviewed the semiempirical and ab initio literature on Ln & An.
Proc. 2nd ICLA, 76 references. Three pages.
1.
P. Pyykkö, Inorg. Chim. Acta 139 (1987) 243. (No.105).
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4. PSEUDOPOTENTIAL AB INITIO-WORK 1991 Only HF-level in the beginning. Correlated calculations and
DFT later.
 Frozen-soft-mode theory of the large variations of the U-O
distances from ’uranyl’ to ’anti-uranyl’ systems. A crude UO6 6model.[1,2].
 Equatorial coordination of uranyl to nitrate etc.[2].
 Predict new isoelectronic species, such as NUO+ .
1. P. Pyykkö, Y-F Zhao Inorg. Chem. 30 (1991) 3787. (No.135).
2. P. Pyykkö, J. Li, N. Runeberg, J. Phys. Chem. 98 (1994) 4809.
(No.146).
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THE ’FROZEN SOFT MODE’ 1991, 1994
1. P. Pyykkö, Y-F Zhao, Inorg. Chem. 30 (1991) 3787. (No. 135)
2. P. Pyykkö, J. Li, N. Runeberg, J. Phys. Chem. 98 (1994) 4809.(No. 146)
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URANYL AND ANTIURANYL SYSTEMS 1991 Frozen-soft-mode theory of the large
variations of the U-O distances from
’uranyl’ to ’anti-uranyl’ systems. A
crude UO6 6- model.[1,2].
1. P. Pyykkö, Y-F Zhao, Inorg. Chem.
30 (1991) 3787. (No.135).
2. P. Pyykkö, J. Li, N. Runeberg, J.
Phys. Chem. 98 (1994) 4809.
(No.146)
3. V.A. Glebov, Electronic Structure
and Properties of Uranyl
Compounds (in Russian),
Energoatomizdat, 1983.
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THE TRIPLE BOND IN URANYL
 First deduced by Pauling[1] from bond lengths.
 Seen in detail from the molecular-orbital structure [2]:
(6p)6 σg2 πg4 πu4 σu2, (5f)0 , 12-e. OΞUΞO2+ !
 Also deduced from vibrational spectroscopy by Denning [3].
 Likewise occurs in isoelectronic species, such as NUO+ .
1. L. Pauling, Proc. Nat. Acad. Sci. 72 (1975) 4200-4202.
2. P. Pyykkö, J. Li, N. Runeberg, J. Phys. Chem. 98 (1994)
4809-4813 (No.146).
3. R.G. Denning, Struct. Bonding 79 (1992) 215-276.
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5. A REALLY WILD PROPOSAL: UO6 (Oh).
IS IT U(XII)?
 A local minimum was found [1].
 Later work [2] reveals that the side-on, peroxide structures lie
much lower.
1. P. Pyykkö, N. Runeberg, M. Straka, K. G. Dyall, Chem. Phys.
Lett. 328 (2000) 415. (No.203).
2. H. Xiao, H-S. Hu, W.H.E. Schwarz, J. Li, J. Phys. Chem. A 114
(2010) 8837.
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6. ACTINIDE OXYFLUORIDES
 The f0 actinyls are actually about f2 d1, as mentioned earlier.
 An interesting symmetry change is from UF8
2-
(D4d) to PuF8 (Oh).
 Energetics of PuO4 etc.
M. Straka, K.G. Dyall, P. Pyykkö Theor. Chem. Acc. 106 (2001) 393.
(No.210).
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7. ”WHY ARE URANIUM CYANIDES RARE WHILE
U-F AND U-O BONDS ARE COMMON AND SHORT? ”
 -CN and U are both σ donors and π
acceptors. Halogens are σ acceptors and
π donors.
 Because of π donation from F(2pπ) to
U(VI), the UF6 has actually some multiplebond character. Theoretically up to 1.5.
 Also ionic bonding.
1. M. Straka, M. Patzschke, P. Pyykkö,
Theor. Chem. Acc 109 (2003) 332.
(No.224).
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8. MODEL (OR REAL) COMPOUNDS FOR
DERIVING COVALENT RADII
 For a summary of the four original papers on new covalent radii, see
Pyykkö [1]. Originals: [4] and Pyykkö & Atsumi.
 Other original calculations on ThO [2], PtTh and AuTh+ [3], LnN [4],
HThThH [5], LnCH2+ [6].
1. P. Pyykkö, J. Phys. Chem. A 000 (2015) 000; DOI: 10.1021/jp5065819.
2.
3.
4.
5.
6.
(No.313).
M. Straka, M. Patzschke, P. Pyykkö, Theor. Chem. Acc 109 (2003) 332
(No.224).
M. Barysz, P. Pyykkö, Chem. Phys. Lett. 368 (2003) 538 (No.227).
P. Pyykkö, S. Riedel, M. Patzschke, Chem. Eur. J. 11 (2005) 3511.
(No.249). Original r3 paper.
M. Straka, P. Pyykkö, J. Am. Chem. Soc. 127 (2005) 13090.(No.253).
B.O. Roos, P.Pyykkö, Chem.Eur.J. 16 (2010) 270. (No289).
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9. NUIr AND ISOELECTRONICS
 Granted that platinum can behave as oxygen, or iridium as nitrogen,
would this analog work with uranyl, OUO 2+ ?
 A: one end can be substituted and the ground state is still singlet [1].
 A very strong and short TM-U triple bond.
 Subsequently, OUIr+ was made [2].
1. L. Gagliardi, P. Pyykkö, Angew. Chem. Int. Ed. 43 (2004) 1573.
(No.239).
2. M. Santos, J. Marçalo, A. Pires de Matos, J. K. Gibson, R. G. Haire,
Eur. J. Inorg. Chem. (2006) 3346.
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10. U2 2+
 The experimentally observed U2 was calculated to have a very short
bond of 243 pm. The dication has an even shorter U-U bond of 230
pm [1].
1. L. Gagliardi, P. Pyykkö, B. O. Roos, PCCP 7 (2005) 2415. (No. 252).
.
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11. LANTHANIDE CONTRACTION IN LnX3
 The structures agree with other work.
 The lanthanide contraction from La to Lu agrees with other work.
NR/R about 0.88.
 The observed ’hybridisation’ of 4f(Lu) and 2p(F) in LuF3 did not
agree with later CASPT2 calculations [2]. It was then attributed to
self-interaction errors. After SIC, no such hybridisation remained [3].
1. J-P. Dognon, C. Clavaguéra, P. Pyykkö, Chem. Phys. Lett. 429
(2006) 8. (No. 258).
2. B. O. Roos, R. Lindh, P-Å. Malmqvist, V. Veryazov, P-O. Widmark,
A. C. Borin, J. Phys. Chem. A 112 (2008) 11431.
3. R. Ramakrishnan, A.V. Matveev, N. Rösch, Chem. Phys. Lett. 468
(2009) 158.
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12. THE 32-ELECTRON PRINCIPLE
 The first example was a predicted PuPb12 [1].
 The second [2] was a predicted dication U@C28 2+. Note that the
neutral is experimentally known.
 A review on the 32-e principle was written for the Dolg book.
(No.312).
1. J-P. Dognon, C. Clavaguéra, P. Pyykkö, Angew. Chem. Int. Ed.46
(2007) 1427. (No. 261).
2. J-P. Dognon, C. Clavaguéra, P. Pyykkö, J. Am. Chem. Soc. 131
(2009) 238. (No.280).
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MAGIC NUMBERS:
8, 18, 32 !
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13. THE LnCO SERIES, Ln=La-Lu
 Both experiment and theory [1]. Eight Ln of the LnCO are new.
 Both OC→M σ donation and M→CO π* back-donation.
 The main Ln bonding orbitals the 5d and 6s..
 The total spin can have both 4f n , doughnut σ and M-C π contributions.
1. W-H. Xu(3), X. Jin(1), M-H. Chen(2), P. Pyykkö, M-F. Zhou(4), J. Li(3),
Chem. Sci. 3 (2012) 1548. (No304).
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The 18-e principle
 Why are the molecules or complexes with effectively 18
valence electrons around a transition metal atom
particularly stable?
 Examples: Mo(CO)6, Fe(CO)5, Ni(CO)4 [1], Co(CO)3(NO)
[2], Fe3(CO)12, OsCl64-, OsCl5(NO)2-, Fe(CN)64- [3].
 Proposed explanation: Effectively s2p6d10 el. conf.
Sometimes little or no p !
New explanation: Ligand nodal structure suffices [4] !
1. I. Langmuir, Science 54 (1921) 59-67.
2. E. Reiff, Z. Anorg. Allg. Chem. 202 (1931) 375-381.
3. N. V. Sidgwick, R. W. Bailey, Proc. Roy. Soc. (London)
A144 (1934) 521-537.
4. P. Pyykkö, J. Organomet. Chem. 691 (2006) 4336-40.
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The kinetic energy for a particle
on a sphere
E(a.u.) = L ( L+1) / 2R
2.
Magic numbers 2, 8, 18, 32, 50, 72, …
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P. Pyykkö, J. Organomet. Chem. 691 (2006) 4336-4340.
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Pu@Pb12: The first 32-e species?
1. J. P. Dognon, C. Clavaguéra, P. Pyykkö, Angew. Chem. Int. Ed.
46 (2007) 1427.
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Pu@Pb12
 Pb122- is experimentally known
as a stiff shell structure.
 Could an endohedral actinide
atom, like Pu2+ bring in six
more electrons and a t2u
orbital? A: Yes!
 This theoretical proposal is the
first 32-electron species.
1. J. P. Dognon, C. Clavaguera,
P. Pyykkö, Angew. Chem. Int.
Ed. 46 (2007) 1427.
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Visual inspection of the MO:s
1. J. P. Dognon, C. Clavaguéra, P. Pyykkö, Angew. Chem. Int. Ed.
46 (2007) 1427.
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U@C282+ : An old new 32e system
1. J. P. Dognon, C. Clavaguéra, P. Pyykkö, JACS 131 (2009) 238.
2. K. Zhao, R.S. Pitzer, JPC 100 (1996) 4798. (Earlier analysis).
3. T. Guo, M.D. Diener, Y. Chai, M.J. Alford, R.E. Haufler, S.M.
McClure, T. Ohno, J.H. Weaver, G.E. Scuseria, R.E. Smalley,
Science 257 (1992) 1661. (Exp. discovery).
4. Third 32e system: [U@Si20]6-, D-C-P, Chem. Sci. 3 (2012) 2843.
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THIRD 32e SERIES: THE PREDICTED [U@Si20]6-
 For An=U, Cm Ih (left), for An=Np-Am, Th (right) [1].
 Charge compensation by counterions: La2[U@Si20].
 Background: Electron count of Singh et al.[2]: Si20 dodecahedron, 80e.
Of these, 60e are eaten by the 30 Si-Si σ bonds. 20e left to a π system.
In Th@Si20, add 4e from the central metal. (ag)2 (t1u)6 (hg)10 (t2u)6.
 We [1]: Filling the previous gu LUMO by 8e has a chance of giving 32e.
1. J-P Dognon, C Clavaguéra, P Pyykkö, Chem. Sci. 3 (2012) 2843.
2. A. K. Singh, V. Kumar, Y. Kawazoe, J. Phys. Chem. B 109 (2005)
15187
La2[U@Si20]
 The purple box is the 32e system.
A review [5] . A further possible
example.
5. P. Pyykkö, C. Clavaguéra, J.-P. Dognon, ’The
32-electron principle: A new magic number’, in
Computational Methods in Lanthanide and
Actinide Chemistry, Ed. M. Dolg, Wiley (to be
published, No.312). Contains further refs.,
6. notably from T. P. Ghanty’s group.
7. S. K. Ritter, C & E News (Sept. 9, 2013) 28-33;
G. S. Girolami (priv. comm., Sept. 25, 2013):
[Th(BH4)6]2- .
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Other spherical boxes:
Particle in a sphere:
1S < 1P < 1D ≤ 2S < 1F < 2P < 1G ..
Spherical harmonic oscillator: Equidistant levels
1S < 1P < 2S + 1D < 2P + 1F < 3S+2D+1G <
3P+2F+1H < …
Wine-bottle potential …
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END OF TALK .
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