Study of the picture change error at the 2nd order Douglas Kroll Hess level of theory. Electron and spin density and structure factors of the Bis[bis(methoxycarbimido) aminato] copper (II) complex Lukáš Buc ˇinsky ´ a,⇑ , Stanislav Biskupic ˇ a , Dylan Jayatilaka b a Institute of Physical Chemistry and Chemical Physics FCHPT, Slovak University of Technology, Radlinskeho 9, Bratislava SK-812 37, Slovakia b Department of Chemistry, University of Western Australia, 35 Stirling Hwy, Crawley WA 6009, Australia article info Article history: Available online 4 May 2011 Keywords: Picture change error PCE Correction Electron density Spin density Copper atom Mulliken populations DKH Structure factors abstract The analytic correction and the extent of the picture change error (PCE) at the scalar 2nd order Douglas– Kroll–Hess level of theory is considered. The one-dimensional (1D), two-dimensional (2D) spin/electron densities and/or difference densities, structure factors and Mulliken populations of the Bis [bis-(methoxy- carbimido) aminato] copper (II) model compound are presented. For further comparison the radial distri- butions of the electron and spin density of the copper atom (as well as of the copper di-cation) are presented. In addition, the infinite order two component (IOTC) radial distributions of electron and spin density of the copper atom and copper dication are presented as well. The PCE is almost hidden in the 2D densities of the studied model compound. The 1D electron/spin difference densities along the Cu–N bond show the extent of PCE in more detail than the 2D densities, nevertheless the small significance of PCE in the region further from the nucleus of the copper atom is confirmed. The DKH2 and IOTC electron/spin densities of Cu/Cu 2+ do overlap with each other, unless in the vicinity of nucleus where the difference is visible, but still not as significant as PCE or the relativistic effects. The structure factors are found an order of magnitude less affected by PCE than by the relativistic effects. Furthermore, PCE in the Mulliken populations and in the expectation value of the h b S 2 i operator is briefly discussed. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction Although the 2nd order Douglas–Kroll–Hess (DKH2) [1–7] Hamilonian is more approximate than the exact 2-component (X2C) [8–12,10,13,14] and/or the infinite order two component (IOTC) [15–19] approaches, it is implemented in many quantum chemistry softwares still as the basic all-electron quasirelativistic Hamiltonian. For sure, the X2C/IOTC approaches (as well as the higher order DKH approaches) will become day by day – more and more the part of everyday (relativistic) quantum chemistry, nevertheless the DKH2 Hamiltonian will most probably not disap- pear completely from the scene due to either historical reasons or simplicity of the DKH2 approach or systematic reasons, i.e. completeness. Moreover, the picture change error (PCE), which affects the cal- culation of properties at the DKH2 level, has been explored in more detail only in the last decade [3,20–25], although the DKH2- approach is already in use for more than 20 years. (Furthermore, the significance of PCE in the quasirelativistic Mulliken populations and the spin contamination of the scalar quasirelativistic UHF wavefunctions has not been considered yet.) For example, the studies of electron paramagnetic resonance (EPR) parametres [26–28] or the calculation of quadrupole moments [29] are to be mentioned. Furthermore, these calculations are often available only to the groups which have developed either their own working codes or have made ‘‘home’’ and/or ‘‘trunk’’ extensions of different quantum chemistry packages [30–33]. It has to be admited that the PCE is related to the IOTC approach [16,24,25,34] and more indi- rectly to the X2C approach [13] as well. In addition, the PCE corrected DKH electron densities have been reported even more recently [23,24,35,25,36–38]. It is noteworthy that the electron density at the nucleus is interesting by means of the contact density in the Mösbauer spectroscopy [35–37], where besides the huge contribution of relativistic effects, the model of the nucleus [36,38] as well as the electron correlation play a key role [35,36]. A further important instance is the spin density at the nucleus (contact spin density) [39–41] which is explicitly pres- ent in the contribution of the Fermi contact term to the hyperfine coupling (causing the splitting of the EPR signal). Although it is to be mentioned that in the case of relativistic calculations the term spin density is uniquely defined (i.e. by an operator which commutes with the Hamiltonian and thus could be regarded as a constant of motion) at the scalar level only [39]. At the 2- or 0301-0104/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2011.04.026 ⇑ Corresponding author. E-mail address: lukas.bucinsky@stuba.sk (L. Buc ˇinsky ´ ). Chemical Physics 395 (2012) 44–53 Contents lists available at ScienceDirect Chemical Physics journal homepage: www.elsevier.com/locate/chemphys