Density gradients calculations

Philipsen P H T, te Velde G and Baerends E J 1994 The effect of density-gradient corrections for a molecule-surface potential energy surface. Slab calculations on Cu(100)c(2x2)-C0 Chem. Phys. Lett. 226 583... 

The value for the heat of fusion of PPS, extrapolated to a hypothetical 100% crystalline state, is not agreed upon in the literature. Reported values range from approximately 80 J/g (19 cal/g) (36,96,101) to 146 J/g (35 cal/g) (102), with one intermediate value of 105 J/g (25 cal/g) (20). The lower value, 80 J/g, was originally measured by thermal analysis and then correlated with a measure of crystallinity deterrnined by x-ray diffraction (36). The value of 146 J/g was deterrnined independendy on uniaxiaHy oriented PPS film samples by thermal analysis, density measurement via density-gradient column, and the use of a calculated density for 100% crystalline PPS to arrive at a heat of fusion for 100% crystalline PPS (102). The value of 105 J/g was obtained by measuring the heats of fusion of weU-characterized linear oligomers of PPS and extrapolation to infinite molecular weight. 

To make matters worse, the use of a uniform gas model for electron density does not enable one to carry out good calculations. Instead a density gradient must be introduced into the uniform electron gas distribution. The way in which this has been implemented has typically been in a semi-empirical manner by working backwards from the known results on a particular atom, usually the helium atom (Gill, 1998). It has thus been possible to obtain an approximate set of functions which often serve to give successful approximations in other atoms and molecules. As far as I know, there is no known way of yet calculating, in an ab initio manner, the required density gradient which must be introduced into the calculations. 

The local density approximation is highly successful and has been used in density functional calculations for many years now. There were several difficulties in implementing better approximations, but in 1991 Perdew et al. successfully parametrised a potential known as the generalised gradient approximation (GGA) which expresses the exchange and correlation potential as a function of both the local density and its gradient ... 

The density functional calculations were performed using the Vienna Ab Initio Simulation Package (VASP). ° The spin-polarized generalized gradient approximation, Perdue—Wang exchange correlation function, and ultrasoft pseudopotentials were used. ... 

Figure 5.16 Gradients of the charge density, Ap, calculated for complex 1 in Figure 5.15 in the Ir-H- -H-N plane. (Reproduced with permission from ref. 25.)...

Bioinorganic systems often contain heavy elements that need to be treated with an explicit relativistic method. It is now possible to carry out an explicit relativistic electronic structure calculation on the fly (152). The scalar-relativistic Douglas - Kroll - Hess method was implemented by us recently in the BOMD simulation framework (152). To use the relativistic densities in a non-relativistic gradient calculations turned out to be a valid approximation of relativistic gradients. An excellent agreement between optimized structures and geometries obtained from numerical gradients was observed with an error smaller than 0.02 pm. 

Since it is assumed that the density gradient is not influenced by dissolved chemicals, the stability frequency, N, can be calculated from the temperature profiles alone ... 

For calculation it was assumed that these five phospholipids together accounted for all of the phospholipids of the membrane. In the actual analyses, other phospholipids (primarily lysophosphatidyl choline and lysophosphatidyl ethanolamine) were found to account for less than 5% of the total. The heavy and light microlipid droplet fractions were obtained by sucrose density gradient centrifugation. Heavy fractions were collected between 0.5 and 1.0 M sucrose and light fractions banded at the 0.5 M sucrose-buffer interface. 

This effect can be suppressed by covering the spin-fluid surface with a thin layer of a nonvolatile oil such as dodecane. A density gradient protected in this manner can be used for several hours after injection into the rotor. Since many sample types can be introduced into the spin fluid through such an oil layer, consecutive runs can be made with the same spin fluid. The standard deviation in particle sizes calculated from peak positions can be reduced to <1% by using these techniques along with careful monitoring of the spin-fluid temperature. 

Guan J, Casida ME, Salahub DR (1995) 11-Electron Local and Gradient-Corrected Density-Functional Calculations of Na n Dipole Polarizabilities for n=l-6, Phys Rev B, 52 2185-2200... 

When a cesium chloride solution is spun in an ultracentrifuge, a density gradient is formed. The position of DNA in the gradient is determined by its G + C content, which can be calculated from the relative position of a second DNA of known density. Determinations are generally made in an analytical ultracentrifuge, but a preparative ultracentrifuge will also serve for this purpose. 

Sedimentation-FFF. Retention measurements give the effective particle mass m (buoyant mass). If the particle density is known, the particle mass m, particle volume Vp, and hydrodynamic diameter dH can be calculated [80,81]. Apart from the particle dimensions, the density can be determined as well [82] as the difference in the densities of the solute and the solvent, Ap, is linearly correlated to X. Fractionation can be used in regions where the solvent density is lower than the solute density (pps. The determination of particle density in a single experiment is possible by sedimentation-flotation focusing-FFF [72,73,83] analogous to density gradient ultracentrifugation. 

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