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

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-(methoxycarbimido)aminato]copper(II) model compound are presented. For further comparison the radial distributions 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/Cu2+ 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 〈S^2〉 operator is briefly discussed.