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.