Core Distortions and Geometries of the Difluorides and Dihydrides of Ca, Sr, and Ba

Abstract

Studies of the Laplacian of the calculated electron density (V^) for the fluorides of Mg, Ca, Sr, and Ba, for the hydrides of Ca, Sr, and Ba, and for Ca(CH3)2 were undertaken in order to understand why these molecules with the exception of Mgp2 have a bent rather than a linear geometry. A linear geometry is expected on the basis of the simple ionic model or the VSEPR model and is observed for BeF2 and Mgp2. The Laplacian distribution for the metal atom in each of the remaining molecules shows that the outer shell of its core is perturbed by the polarizing field of the ligands and is distorted in a manner corresponding to the presence of four approximately tetrahedrally localized concentrations of electronic charge. The angular shapes of these molecules can be understood in terms of the interaction between the distorted core and the ligands. In contrast, the distortion of the magnesium core in Mgp2 exhibits only two charge concentrations, one associated with each Mg-F bond, so that no deviation from the linear geometry is expected or found. This paper helps to establish the generality of the formation of localized concentrations of electronic charge in positions that are spatially opposed to the attached ligands, in the outer shell of the core of an element with accessible (nl)d orbitals, where n is the valence shell. The distortions of the cores of the heavier alkaline earth elements that are revealed by the Laplacian of the electron density have the same form as that proposed some years ago in an extension of the VSEPR model to account for the angular shape of these molecules. main group elements, for which the VSEPR model is very successful. It was pointed out some time ago, however, that

Topological studies of the charge density of some group 2 metallocenes M(η5-C5H5)2 (M = Mg or Ca)

“…The charges for MgCp, indicate a large degree of metal-ligand charge separation, with the Mg atom and Cp ligands having approximate charges of +1.75 and -0.88 respectively (see Table 2). These charges are similar to those obtained previously for MgF, (18) and suggest that the ionic model used to describe MgF, is applicable to MgCp,. Similarly, charges obtained for the Ca atom and the Cp ligand are of the order of 1.6 and -0.8 respectively, which are similar to the analogous charges obtained previously for C a b , CaH,, and Ca(CH,), (18).…”

“…A summary of the different atomic graphs obtained for the various calculations of CaCp2 are shown in Fig. 6, along with that obtained previously for CaF, (18). These diagrams show how the various atomic graphs are related through the joining and splitting of charge concentration maxima.…”

“…We have presented charge density analyses for both magnesium and calcium dicyclopentadienes, and have shown that their preferred geometries can be understood using arguments similar to those used to explain the geometries of both MgF, and CaF, (18). Metallocene formation results in sufficient distortion of the metal atom such that it can no longer be considered spherical, as is usually assumed in the VSEPR model.…”

“…Calculations were performed at both the Hartree-Fock (HF) and the B3LYP density functional methods using all-electron basis sets. The extended Wachters basis set was used for Ca (40) as this was found to give an adequate description of Ca in previous calculations (18) and the standard 6-3 1 IG* basis set was used to describe Mg (4 1). For C and H the standard 6-3 lG* was used (4 1) after preliminary results suggested that the addition of the polarization function to carbon was required in order to obtain a bent equilibrium geometry for CaCp,.…”

Meaningful Structural Descriptors from Charge Density

“…[68] The spatial arrangement of the VSCCs can be used to determine the density-related bonding geometry of an atom. [69][70][71][72] Hybridization can thus much better be understood than from the traditional interatomic vectors as VSCCs stand for bonding as well as nonbonding contributions. The use of the density-related bonding angles leads to a higher agreement with those anticipated from the VSEPR theory (Figure 8).…”