Theoretical Chemistry Accounts

, Volume 104, Issue 1, pp 82–88

Relativistic electron densities in the four-component Dirac representation and in the two-component picture

Hydrogen-like systems
  • J. Autschbach
  • W. H. E. Schwarz

DOI: 10.1007/s002149900108

Cite this article as:
Autschbach, J. & Schwarz, W. Theor Chem Acc (2000) 104: 82. doi:10.1007/s002149900108


 Analytic formulae of the relativistic radial functions of hydrogen-like atoms in the four-component standard Dirac picture and in two approximations, (Pauli and ZORA), to the two-component (so-called Schrödinger or Newton–Wigner) picture and graphs of the respective relativistic changes of densities are presented and discussed. The two different pictures of the Dirac density of charge position and of the Newton–Wigner density of mass position are remarkably different in strongly inhomogeneous fields and result in respective differences in position-dependent expectation values, <rν>. The fractional magnitudes of Δrel<rν>, of Δcharge/mass<rν>, and of the gauge dependence of ZORA (which for small n states is comparable to the difference of the two kinds of position observables) are all of order Z2α2.

Key words: Relativistic quantum chemistry – Electron density – Hydrogen-like systems – Expectation values – Picture change

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • J. Autschbach
    • 1
  • W. H. E. Schwarz
    • 1
  1. 1.Theoretical Chemistry, University of Siegen, 57068 Siegen, GermanyDE