THE PERIODIC SYSTEM Pekka PYYKKÖ (University of Helsinki, Finland) Winter School in Theoretical Chemistry, December 2009

WHAT IS IT?

SOME RECENT REVIEWS AND HISTORIES E. R. Scerri, The Periodic Table, Oxford U. P. (2007), 346 p. History aspects well told. Perhaps overemphasises the ”window aspect”, the ”correct form of the PT” and the Madelung n+l rule. S-G. Wang and W. H. E. Schwarz, Angew. Chem. Int. Ed. 48 (2009)

WHO DISCOVERED IT? Bits and pieces early on. Based on atomic weights. No ’Z’! Döbereiner’s triads (Ca, Sr, Ba) 1817, (Li, Na, K), (S, Se, Te), (Cl, Br, I) Gmelin 1843, 55 elements, oxygen to right group, chemical properties. Pettenkofer 1850, Dumas 1851, Kremers 1852, Lenssen Karlsruhe conference a 150-Year celebration. de Chancourtois 1862 ’vis tellurique’, Newlands 1863, 1865 ’octaves’, Meyer elements, square table with gaps, Odling 1864, Hinrichs 1867, Naquet D. I. Mendeleev 1869-: Predicts (Sc) 45, (Ga) 68, (Ge) 70. Ga discovered 1875, Sc 1879, Ge Royal Society Davy medal to Mendeleev and Meyer Ramsay: (He, Ne, Ar) form a new group (now ’Group 18’). Seaborg 1945: Introduces the actinide row. So far, the 6d elements boringly similar to their 5d analogues.

WHAT DRIVES IT? N = ’Period’ H-like AufbauReal Aufbau nShells∆ZNShells∆Z 11s s, 2p s, 3p, 3d1833s, 3p8 44s, 4p, 4d, 4f324[4s, 3d], 4p18 55s, 5p, 5d, 5f, 5g505[5s, 4d], 5p18 66s-6h726[6s, 5d, 4f], 6p32 77s-7i987[7s, 6d, 5f], 7p32

SAME IN TERMS OF ENERGY LEVELS

Albert Einstein’s special relativity coupled to Dmitrii Mendeleyev’s Periodic System ! :

Some personal long-term activities

5th-Row versus 6th-Row Compounds

FURTHER EXPERIMENTAL FACTS Mercury is a liquid and has, as crystal, a rhombohedral ’α-Hg’ structure. Cadmium melts at K and has a distorted hexagonal structure.. Cars start.

5th-Row versus 6th-Row Compounds

RELATIVISTIC EFFECTS ”Relativistic effects”: Anything depending on the speed of light. Alternatively: The difference between using a Dirac or a Schrödinger one-electron equation. Alternatively: Letting c increase from au to a very big value. Explain many chemical differences between 5th-Row and 6-th Row elements. Ag/Au. Current textbook explanation, together with the lanthanide contraction. New: Deeper physics (QED effects) will only change the previous conclusions by -1% for heavy elements. The QED was the last train from physics to chemistry.

WHY RELATIVITY? The innermost electrons move fast in heavy elements. The average radial 1s velocity in atomic units (c = au), 1s = Z = 80 for Hg. (1) This leads to a mass increase, m = m 0 /[1 – (v/c) 2 ] 1/2. (2) The increased mass gives a smaller Bohr radius, a 0 = ћ 2 / m e 2. (3) → a relativistic contraction and stabilization of all s and p orbitals. Exact solution of the Dirac equation: The higher s and p states are also strongly ’relativistic’. Due to stronger screening of the nuclear attraction by s and p shells, the d and f shells will have a relativistic expansion and destabilization. For valence shells, effects increase as Z 2.

HYDROGEN-LIKE ATOM Hg 79+ V. M. Burke, I. P. Grant, Proc. Phys. Soc. (London) 90 (1967) 297.

THE ”GOLD MAXIMUM” OF RELATIVISTIC EFFECTS P. Pyykkö, J. P. Desclaux, Acc. Chem. Res. 12 (1979) 276.

Data from J. P. Desclaux, P. Pyykkö, Chem. Phys. Lett. 39 (1976) 300.

Relativity and the Periodic System P. Pyykkö, Chem. Rev. 88 (1988)

CHEMISTRY TEXTBOOKS G. Wulfsberg (1989, 1991). F. A. Cotton, G. Wilkinson (1988, 1999). K. M. Mackay, R. A. Mackay (1989, 1996). R. H. Petrucci (1989) + W. S. Harwood (1993). A. G. Massey (1990). W. L. Jolly (1991). A. G. Sharpe (1992). J. E. Huheey, E. A. Keiter, R. L. Keiter (1993). J. B. Umland (1993) (+ J. M. Bellama !996)). T. M. Klapötke, I.C. Tornieporth-Oetting (1994). N. C. Norman (1994, 1997). School text. ’Hollemann-Wiberg’, 101. Auflage (1995), 102. (2007) S. S. Zumdahl, (1995, 1998).

CHEMISTRY TEXTBOOKS (continued) N. N. Greenwood, A. Earnshaw, 2nd Ed. (1997). D.M.P. Mingos (1998). N. Kaltsoyannis, P. Scott (1999). G. Rayner-Canham, 2nd Ed. (1999). C. E. Housecroft, A.G. Sharpe (2001). J. Barrett (2002). Three fronts: Chemistry, Physics, Mathematics.

SEVEN RULES THAT EXPLAIN THE PERIODIC SYSTEM 1. Main vertical rule. First shell with every l (1s, 2p, 3d, 4f) is anomalously small. increases with n for others. 2. Main horisontal trend: decreases with Z. 3. Main periodicity: Filled shells stable. NR half-filled ones also. 4. Partial screening effects. Lanthanide contraction due to filling the 4f shell on 6s and 6p shells. Analogous 3d, 2p and 1s effects. 5. Relativistic contraction and stabilization. (s, p). 6. Relativistic expansion and destabilization. (d, f). 7. Spin-orbit splitting. (p, d, f shells).

RELATIVISTIC BOND-LENGTH CONTRACTION P. Pyykkö, J. P. Desclaux, Chem. Phys. Lett. 42 (1976) 545. Contraction increases as Z 2. First found for PbH 4 (1974).

BOND-LENGTH CONTRACTION NOT DUE TO ORBITAL CONTRACTION Consider as example the isoelectronic CsH or BaH + molecules. One valence σ MO: |σ> = c 1 |6s> + c 2 |5d> + c 3 |1s H > + c 4 |core>. (1) ΔE (1) = (2) = ΔE (1) (core-core) + ΔE (1) (core-val) + ΔE (1) (val-val). The core-core term (<0) becomes larger with decreasing bond length, R. It provides a driving force for the contraction, already with the NR, uncontracted orbitals. P. Pyykkö, J. G. Snijders, E. J. Baerends, CPL 83 (1981) 432.

Au(I) versus Au(III) AuX 4 - → AuX 2 – +2X P. Schwerdtfeger, J. Am. Chem. Soc. 111 (1989) X ΔU/kJ mol -1 NRR F Cl Br I

MOLYBDENUM AND TUNGSTEN P. Pyykkö, J. P. Desclaux, Chem. Phys. 34 (1978) 261.

ZIRCONIUM AND HAFNIUM P. Pyykkö, J. P. Desclaux, Chem. Phys. Lett. 50 (1977) 503.

TIN, LEAD AND RELATIVITY P. Pyykkö, Chem. Rev. 88 (1988) 563.

THE RELATIVISTIC COLOURS BiPh 5, violet: LUMO shift down. PbCl 6 2-, yellow: LUMO shift down. Metallic gold: 5d band shifts up, 6s Fermi level shifts down. Pb(NO 2 ) 2, yellow. Singlet-triplet mixing of the nitrite, due to spin-orbit coupling of the heavy metal.

TRENDS AMONG ALKALI METALS 1. B. Fricke, J. T. Waber, J. Chem. Phys. 56 (1972) 3246.

TRENDS AMONG ALKALI METALS 1. P. Pyykkö, Int. J. Quantum Chem. 85 (2001) 18.

’RIPPLES ON PERIODICITY’: FINE STRUCTURE Secondary periodicity (Biron 1915). Lanthanide contraction (Goldschmidt 1925). Spin-orbit subshells and Bi(I). Alkali metals, the beginning. ’Honorary d-metals’: Cs, Ca-Ba. Au as ’halogen’, Pt as ’oxygen’, Ir as ’nitrogen’.

SECONDARY PERIODICITY

UNDERSTANDING SECONDARY PERIODICITY P. Pyykkö, J. Chem.Res. (S) (1979) 380.

THE LANTHANIDE CONTRACTION Skrifter Norske Vid. Ak., I. Mat. Naturvid. Klasse, No. 7 (1925).

THE LANTHANIDE CONTRACTION Skrifter Norske Vid. Ak., I. Mat. Naturvid. Klasse, No. 7 (1925).

THE LANTHANIDE CONTRACTION Skrifter Norske Vid. Ak., I. Mat. Naturvid. Klasse, No. 7 (1925).

SPIN-ORBIT SUBSHELLS AND Bi(I) Bi(I) exists in Bi + (Bi 9 5+ )(HfCl 6 2- ) 3. R.M. Friedman, J.D. Corbett, Chem. Comm. (1971) 422; Inorg. Chem. 12 (1973) 1134.

Cs, Ca-Ba AS ’HONORARY d ELEMENTS’ L. Gagliardi, P. Pyykkö, Theor. Chem. Acc. 110 (2003) 210; earlier work since L. Gagliardi, J. Am. Chem. Soc. 124 (2002) 8757: Predicts CsN≡Ba. A. Janczyk &, J. Am. Chem. Soc. 128 (2006) 1109: Make HN≡Ba.

PLATINUM AS OXYGEN: HOW DOES IT WORK? 1. M. Patzschke, P. Pyykkö, Chem. Comm. (2004) 1982.

METALLOACTINYLS: PLATINUM AS ’OXYGEN’ 1. L. Gagliardi, P. Pyykkö, Angew. Chem. Int. Ed. 43 (2004) M. Santos, J. Marçalo, A. Pires de Matos, J.K. Gibson, R.G. Haire, Eur. J. Inorg. Chem. (2006) Make OUIr +. OUIr + prepared [2] !

END OF ’PERIODIC SYSTEM’ TALK