No abstract

The octahedral CrF3−6 cluster is studied in two different crystal environments. The available experimental data reveal that the cluster with the largest Cr–F bond distance is at the same time characterized by the largest value of the spectrochemical strength. This paradoxical fact has been shown to be due to the effect of the two different Madelung potentials. In K2NaCrF6, the central Cr ion is situated at a maximum of the Madelung potential; in CrF3, it is situated at a minimum. For the different crystal environments it has also been shown that the increase in covalency, that goes with the introduction of correlation, parallels the covalency that is present already at the Hartree–Fock level.

Ab initio molecular orbital calculations at the MP2/6-31G* level of the structure, vibrational spectra, and thermochemical properties of triphospha[ 1.1, llpropellane (4), diphosphabicyclo[ 1.1 .O]butane (5), and phosphirane (6) have been carried out and compared with those of their all-carbon analogues. 4 possesses a ring strain even smaller than that of [l.l.l]propellane and is characterized by a bridgehead C-C distance of 1.63 %, and a heat of formation (AHof,o) of 560 f 20 kJ/mol. The observable IR bands of 4 are centered in the regions of 2291, 947, 755, and 459 cm-I, while the first vertical UV absorption of 4 is expected at 5.3 f 0.5 eV. Although the C-C bridgehead distance in triphospha[ 1.1 .l]propellane (4) is rather long, it has been shown by atoms-in-molecule calculations that a bridgehead bond exits and has a pronounced covalent character.

SUMMARYA subdomain approach for dynamic soil-structure interaction is proposed for the linear elastic seismic analysis of an anchored sheet pile, retaining a horizontally layered soil on rigid bedrock. A hybrid solution technique is used, employing a finite element formulation for the generalized sheet pile, a thin layer formulation for the soil and a direct stiffness formulation for the tieback; the displacement vectors of the sheet pile and the soil are decomposed, using the eigenmodes of the sheet pile and the propagating or decaying modes in the soil. The discretization can be limited to the interface(s), where pointwise continuity of the displacements is enforced, whereas a weak variational formulation is used for the stress equilibrium. The solution technique is illustrated by means of a numerical example, where the harmonic response of a flexible anchored sheet pile is considered and compared to the case where no tieback is present.

The electronic absorption spectra of Cr4+ in Rb2CrF6 and Cr2+ in KCrF3 have been studied using ab initio molecular orbital methods. Near-degeneracy effects within the dn (n=2,4) manifold are treated using the complete active space (CAS) self-consistent field method, while dynamical correlation is dealt with using both the averaged coupled-pair functional (ACPF) method or second-order perturbation theory (CASPT2). The ground state electronic structure of the CrFn−6 (n=2,3,4) clusters in the ionic crystals Rb2CrF6, K2NaCrF6, KCrF3 was analyzed first using Bader’s theory of atoms in molecules. The topological analysis of the charge density is consistent with an ionic picture of the chemical bond in all three compounds, although the contribution of covalent effects clearly increases in the series CrF4−6<CrF3−6<CrF2−6. The ligand field strength exerted by the first coordination sphere of fluorine ligands increases within the same series. The present results indicate that the ligand field strength in the d2 system CrF2−6 has always been underestimated in the past. Indeed, our calculations do not confirm the earlier assignment of a band at 21 000 cm−1 as the 10Dq transition. Both the ligand field strength and the Jahn–Teller splitting of CrF4−6 in KCrF3 are reasonably well reproduced by the calculations. The composition of the excited triplet states was used as a guideline for the analysis of the complex quintet–triplet spectrum of this system.