Relativistic effects on the topology of the electron density

Abstract

Microsymposia C86performance in electronegativity equalization methods discussed [9]. Finally, based on Hirshfeld-I derived density matrices [10], an AIM is formulated in momentum space.[1] F.L. Hirshfeld, Theor. Chim. Acta, 1977, 44, 129. [2] P. Bultinck, C. Van Alsenoy, P.W. Ayers, R.J. Carbó-Dorca, J. Chem. Phys., 2007, 126, 144111. [3] P. Bultinck, P. Faraday Discussions, 2007, 135, 244. [4] P. Bultinck, P.W. Ayers, S. Fias, K. Tiels, C. Van Alsenoy, Chem. Phys. Lett., 2007, 444, 205. [5] The topological analysis of electron densities obtained either from X-ray diffraction experiments or from quantum chemical calculations provides detailed insight into the electronic structure of atoms and molecules. Of particular interest is the study of compounds containing (heavy) transition-metal elements, which is still a challenge for experiment as well as from a quantum-chemical point of view.Accurate calculations on such systems need to take relativistic effects into account explicitly. Regarding the valence electron density distribution, these effects are often only included indirectly through relativistic effective core potentials. But as different variants of relativistic Hamiltonians have been developed all-electron calculations of heavy elements in combination with various electronic structure methods are feasible. In a previous study on the topology of the total electron density distribution of model systems M(C 2 H 2 ) (TM = Ni, Pd, Pt) calculated in different relativistic approximations we have compared several relativistic Hamiltonians with respect to their effect on the electron density in terms of a topological analysis [1].In the present work we extended these studies to model systems containing lanthanide elements (for example [La(CH 3 )] 2+ and La(CH 3 ) 3 ). Besides the investigation of relativistic effects on the topology of the electron density, we concentrated on two additional aspects: We analyzed the general polarization pattern of lanthanide atoms in metal organic complexes as revealed by the Laplacian of the electron density, L(r) = -∇ 2 ρ(r), and the Electron Localization Function (ELF). For L(r) it is known for example from studies on isolated La atoms that starting from n = 5 the valence shells can only be resolved as local maxima with L(r) < 0 (see Figure a) [2] .The results of our study indicate that the general pattern of local charge concentrations (LCCs) in the valence region of 6 th row elements can still be observed in L(r) and that in the case of the Lanthanum model complexes investigated this pattern shows a clear effect of the 4f-orbital contributions to the bonding molecular orbitals (see Figure b).The second aspect of the present study concerns the possibility to recover the polarization patterns of such heavy elements by a multipolar refinement of structure factors calculated from electron density distributions obtained by relativistic density functional theory calculations. The results indicate that several independent sets of multipolar functions at one atomic site are r...

Crystallographic structure and crystal field parameters in the [AnIV(DPA)3]2− series, An = Th, U, Np, Pu

“…These latter have been calculated using the Kirzhnits approximation [50]. As has been shown previously [51,52], the termed relativistic picture change error on the electron density is significant only in the vicinity of heavy atoms and consequently, it does not significantly affect the values of descriptors at the BCP. Topological analyses have been performed using a modified version of the TopMoD09 [53] and TopChem [54,55] program packages using the total density of the SO-CASPT2 ground state.…”

QTAIM Analysis in the Context of Quasirelativistic Quantum Calculations

“…It is worth noting that recently, some authors have studied the spin-dependent relativistic effects on the electron density, but only a crude analysis of the impact on the bonding pictures is reported. 41,42 As a support for the originality of the proposed approach, illustrations of the SOC effects on the bond representation are given for selected astatine species. Astatine (At, Z = 85) is the heaviest naturally occurring halogen, traditionally located below iodine in the periodic table of the elements.…”

“…Introduced back in 1970s by Richard F. W. Bader, QTAIM provides the theoretical framework for studying the topology of the total electron density, ρ( r ), thus providing a route for analyzing, evaluate and classify the nature of chemical bonds and interactions. , The sound basis of the QTAIM analysis, from a chemist point of view, is that this approach (at least in its pure form) relies on an observable, which can be probed via X-ray diffraction experiments. It is worth noting that recently, some authors have studied the spin-dependent relativistic effects on the electron density, but only a crude analysis of the impact on the bonding pictures is reported. , …”

Importance of Relativistic Effects and Electron Correlation in Structure Factors and Electron Density of Diphenyl Mercury and Triphenyl Bismuth

“…The Dirac−Coulomb Hamiltonian difference electron density and Laplacian were considered with respect to ZORA, 10th order Douglas−Kroll−Hess Hamiltonian and the nonrelativistic Hamiltonian for the series TM(C 2 H 2 ) (TM = Ni, Pd and Pt). 37,38 Batke and Eickerling 45,46 have studied the extent of relativistic effects in electron density as well as structure factors and residual density for the same series of TM(C 2 H 2 ) compounds including a direct comparison of experimental and theoretical data for Pd(C 2 H 2 ). 46 They have shown, that relativistic effects are discernible theoretically in the structure factors of heavy element complexes, but being at the limit of the experimental error.…”