
Miniworkshop on "Numerical challenges in relativistic quantum mechanics"
Organizers: Werner Kutzelnigg (Bochum), Eric Séré (ParisDauphine)
Pekka Pyykkö (Helsinki, Finland): "Aspects of DiracCoulomb systems"
Friday 19 April 2013, 09:30  10:15
Amphi Hermite
Pekka PYYKKO
Department of Chemistry, University of Helsinki, P.O.B. 55, FIN–00014 Helsinki, Finland.
Tel: +3589191 50171. Email: Pekka.Pyykko@helsinki.ﬁ
Abstract
The DiracCoulomb problem was solved in 1928 by Darwin and by Gordon. The twocentre problems, such as H+ or the model system Th179+ can be solved numerically with a high precision [1]. For manyelectron mean ﬁeld models, such as DiracFock (Breit), the oneelectron equations can be solved numerically by imposing the proper boundary conditions at R → 0 and R → ∞ [2,3]. A number of further physical contributions exist: 1) The ﬁnite nuclear size is for heavy atoms the largest one. It also allows one to continue the Periodic Table to about Z = 172. For a new shape of the PT, see [4]. 2) The Breit twoelectron interaction and the quantum electrodynamical oneelectron eﬀects are of comparable magnitude [5]. The lowestorder QED terms are the vacuum polarisation and the selfenergy ones. Attempts have been made to reproduce the latter by a local potential [6]. The various contributions can be compared against experiment on one or fewelectron
systems, such as Au78+ . For a recent review on molecular QED data, see [7]. An interesting deviation occurs between the proton radii, determined by electron scattering and by hyperﬁne structure in a muonic atom [8]. A part of the deviation could be understood by scaling the secondorder hyperﬁne interaction [9] to the muonic case. A massive litterature of applications exists [10]. As an example, the available highresolution microwave spectra on MCN molecules (M=CuAu) provide an excellent testing ground for quantum chemistry. MP2 or CCSD(T) calculations with basissets up to ccpVQZ, correlating all 19 VE of Au and including BSSE and SO corrections, are able to give MC bond lengths to 0.6 pm, or better [11].
References
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[2] J.P. Desclaux, Comp. Phys. Comm. 9 (1975) 31.
[3] I. P. Grant, Comp. Phys. Comm. 11 (1976) 397.
[4] P. Pyykkö, Phys. Chem. Chem. Phys. 13 (2011) 161.
[5] P. Pyykkö, M. Tokman, L. Labzowsky, Phys. Rev. A 57 (1998) R689.
[6] P. Pyykkö, L.B. Zhao, J. Phys. B 36 (2003) 1469.
[7] P. Pyykkö, Chem. Rev. 112 (2012) 371.
[8] A. Antognini et al., Science 339 (2013) 417.
[9] E. Latvamaa, L. Kurittu, P. Pyykkö, L. Tataru, J. Phys. B 6 (1973) 591.
[10] P. Pyykkö, rtam.csc.ﬁ; Relativistic Theory of Atoms and Molecules. III, Springer, Berlin (2000) (Lecture Notes in Chemistry 76, in all 10369 references).
[11] P. ZaleskiEjgierd, M. Patzschke, P. Pyykkö, J. Chem. Phys. 128 (2008) 224303.