Electronic structures and nonlinear optical properties of trinuclear transition metal clusters M-(mu-S)-M' (M = Mo,W; M' = Cu,Ag, Au)

A series of trinuclear metal clusters MS4(M'PPh3)2(M'PPh3) (M = Mo, W; M' = Cu, Ag, Au) have been studied using the density functional theory (DFT) method. The static polarizabilities and hyperpolarizabilities of the model clusters have been calculated using the finite-field (F-F) method. The model clusters, divided into two groups, are alike in the structure of two fragments of rhombic units M-(mu-S)2-M' (M = Mo, W; M' = Cu, Ag, Au), perpendicular to each other, which are joined by sharing the bridge metal M. It is the charge transfer from one of these moieties to the other in these characteristic sulfido-transitional metal cores that is responsible for the polarizabilities and hyperpolarizabilities. This kind of electronic delocalization, different from that of the planar pi-system, is interesting and warrants further investigation. The structural effects on properties are important. In these models, considerable third-order nonlinearities are exhibited. The element substitution effect of Mo and W is weak, while that of Cu and Ag is relatively substantial. An overall order is gamma xxxx(Mo-Ag) > gamma xxxx(W-Ag) > gamma xxxx(Mo-Au) > gamma xxxx(W-Au) > gamma xxxx (Mo-Cu) > gamma xxxx(W-Cu) and gamma av(Mo-Ag) approximately gamma av(W-Ag) > gamma av(Mo-Au) approximately gamma av(W-Au) approximately gamma av (Mo-Cu) approximately gamma av(W-Cu).     

The effects of the column pressure drop on retention and efficiency in packed and open tubular supercritical fluid chromatography

The effects of the pressure drop across the column on retention and efficiency in SFC have been studied. Numerical methods are described which enable the prediction of hold-up time and pressure drop in both packed and open tubular columns. Predictions of both hold-up time and pressure drop are in good agreement with experimental data. The density gradient along the column can be calculated using the numerical methods and a procedure is described which enables the calculation of the overall capacity factors of the solutes from the density profile in the column. Significant variations of the capacity factor are observed along the column. The effect of the density gradient along the column on local diffusivity and dispersion is studied. The column efficiency in systems with significant pressure drops is affected by changes in: the linear velocity of the mobile phase; the diffusion coefficients; and the capacity factors of the solutes along the column. The overall efficiency of the chromatographic system can be calculated if, as is the case for open tubular columns, adequate plate height equations are available.     

Molecular solutes in nematic liquid crystals: Orientational order and electric field gradients

The difference between liquid-crystal and gas-phase values for the nuclear quadrupole coupling constant in D₂ and HD is used to obtain the mean electric field gradient in various liquid crystals. Order parameters for small molecules dissolved in liquid crystals are calculated assuming that the orientational order arises from the interaction of the molecular quadrupole moment with the average field gradient. The results obtained are in good agreement with experimental values for hydrogen and several other solutes.     

Relativistic bond lengthening of UO 2 2+ and UO2

Summary Relativistic calculations on UO₂ [1] have shown that relativity leads to substantial bondlengthening in this compound, in contrast to the bond contraction found almost exclusively for other compounds. The bond lengthening isnot caused by the relativistic expansion of the 5f valence AO of U, which is the primary bond forming orbital on U in UO₂. The origin of the bond lengthening can be traced back to the semi-core resp. subvalence character of the U 6p AO. The valence character of 6p shows up in an increasing depopulation of the 6p upon bond shortening, and hence loss of mass-velocity stabilization. The core character of 6p shows up in large off-diagonal mass-velocity matrix elements 5p|h _MV|6p which are shown to have an overall bond lengthening effect. The larger expansion in UO₂ than in UO ₂ ²⁺ is due to destabilization of U levels in UO₂, caused by repulsion of the two additional 5f electrons.The present analysis corroborates the picture of relativistic bond length effects of Ref. [2].     

Natural energy orbitals and the one-particle Green's function

It is shown how the properties of the one-particle Green's function lead naturally to the definition of the so-called natural energy orbitals. These orbitals allow the fully correlated total energy of a system to be written in Hartree–Fock-like fashion and might therefore provide a bridge between sophisticated correlated wave functions and approximate theories of chemical structure and reactivity based on a Hartree–Fock-like energy expression. Moreover these orbitals form the basis for a self-consistent scheme to calculate the one-particle Green's function. The relation between these natural energy orbitals and the extended Koopmans' theorem is considered. Finally it is shown that the exactness of the lowest extended Koopmans' ionization potential implies the linear independence of the corresponding Dyson orbital from all other Dyson orbitals.     

Pressure drop effects on selectivity and resolution in packed column supercritical fluid chromatography

The influence of pressure drop on retention, selectivity, plate height and resolution was investigated systematically in packed supercritical fluid chromatography (SFC) using pure carbon dioxide as the mobile phase. Numerical methods developed previously which enabled the prediction of pressure gradients, diffusivities, capacity factors, plate heights and resolutions along the length of the column were used for the model calculations. The effects of inlet pressure and supercritical fluid flow rate on selectivity and resolution are studied. In packed column SFC with pure carbon dioxide as the mobile phase, the pressure drop can have a significant effect on resolution. The flow rate is shown to have a larger effect than generally realized. The calculated data are shown to be in good agreement with the experimental results. Finally, the variation of the chromatographic parameters along a 5.5 meter long model SFC column is illustrated. The possibilities and limitations of using long packed columns in SFC are discussed. It is demonstrated that long columns with large plate numbers do not necessarily yield better separations.     

Effects of relativity in the He(I) photoelectron spectroscopy of the transient species TeCI2 and TeBr2

Valence ionization energies of the transient species TeCl₂ and TeBr₂, obtained with He(I) photoelectron (PE) spectroscopy, are presented. The interpretation is based on the results of Hartree-Fock-Slater calculations, using STF basis sets of double zeta quality. Implementation of relativistic corrections to the ionization energies of TeBr₂ show that off-diagonal matrix-elements of the spin-orbit operator give rise to a splitting in the non-relativistically almost degenerate bromine “lone pair” orbitals. This splitting is observed experimentally. The assignments find additional support in a comparison with PE results of related oxygen-, sulphur- and seleniumdihalogenides, a simple LCBO model, sum rule considerations and a modified Walsh empirical diagram for AB₂ molecules with 20 valence electrons.     

Ionization energies of the diatomic halogens and interhalogens studied with relativistic hartree-fock-slater calculations

Vertical ionization energies from the outermost two π and two σ molecular orbitals in the diatomic halogen and interhalogen molecules have been calculated using a relativistic Hartree-Fock-Slater (HFS) method. The results obtained are in good agreement with the corresponding experimental ionization energies obtained from photoelectron spectroscopy. The spin-orbit splittings of the ²Π cationic states are rationalized in terms of the degree of localization of the partially filled π orbital in the cation on the header atom.