Density surface, mapping properties

This chapter introduces and illustrates isosurface displays of molecular orbitals, electron and spin densities, electrostatic potentials and local ionization potentials, as well as maps of the lowest-unoccupied molecular orbital, the electrostatic and local ionization potentials and the spin density (on top of electron density surfaces). Applications of these models to the description of molecular properties and chemical reactivity and selectivity are provided in Chapter 19 of this guide. 

As discussed earlier in this chapter, the spin density of a radical indicates where its unpaired electron resides. This in turn allows qualitative assessment of radical stability. A radical in which the unpaired electron is localized onto a single center is likely to be more labile than a radical in which the unpaired electron is delocalized over several centers. An even more useful indicator of radical stability and radical reactivity is provided by a so-called spin density map. Like the other property maps considered in this chapter, this measures the value of the property (in this case the spin density) on an electron density surface corresponding to overall molecular size. 

It is also possible to map a calculated property onto an electron-density surface. Because all three Cartesian coordinates are used to define the points on the surface, the property must be mapped in color, with the colors of the spectrum red-orange-yellow-green-blue representing a range of values. In effect, this is a four-dimensional plot (x, y, z, -i- property mapped). One of the most common plots of this type is the density-electrostatic potential, or density-elpot, plot. The electrostatic potential is determined by placing a unit positive charge at each point... 

To perform this experiment, you must use computer software that can perform semiempirical molecular orbital calculations at the AMI or MNEKD level. In addition, the later experiments require a program that can display orbital shapes and map various properties onto an electron-density surface. Either your instructor will provide direction for using the software, or you will be given a handout with instructions. 

Besides molecular orbitals, other molecular properties, such as electrostatic potentials or spin density, can be represented by isovalue surfaces. Normally, these scalar properties are mapped onto different surfaces see above). This type of high-dimensional visualization permits fast and easy identification of the relevant molecular regions. 

The density is a maximum in all directions perpendicular to the bond path at the position of a bond CP, and it thus serves as the terminus for an infinite set of trajectories, as illustrated by arrows for the pair of such trajectories that lie in the symmetry plane shown in Fig. 7.2. The set of trajectories that terminate at a bond-critical point define the interatomic surface that separates the basins of the neighboring atoms. Because the surface is defined by trajectories of Vp that terminate at a point, and because trajectories never cross, an interatomic surface is endowed with the property of zero-flux - a surface that is not crossed by any trajectories of Vp, a property made clear in Fig. 7.2. The final set of diagrams in Fig. 7.1 depict contour maps of the electron density overlaid with trajectories that define the interatomic surfaces and the bond paths to obtain a display of the atomic boundaries and the molecular structure. 

The most commonly employed and (to date) most important property map is the electrostatic potential map. This gives the electrostatic potential at locations on a particular surface, most commonly a surface of electron density corresponding to overall molecular size (a size surface). 

Property Map. A representation or map of a property on top of an Isosurface, typically an Isodensity Surface. Electrostatic Potential Maps, and HOMO and LUMO Maps and Spin Density Maps are useful property maps. 

Although solvent samples have been observed for approximately one year without any solids formation, work was completed to define a new solvent composition that was thermodynamically stable with respect to solids formation and to expand the operating temperature with respect to third-phase formation.109 Chemical and physical data as a function of solvent component concentrations were collected. The data included BC6 solubility cesium distribution ratio under extraction, scrub, and strip conditions flowsheet robustness temperature range of third-phase formation dispersion numbers for the solvent against waste simulant, scrub and strip acids, and sodium hydroxide wash solutions solvent density viscosity and surface and interfacial tension. These data were mapped against a set of predefined performance criteria. The composition of 0.007 M BC6, 0.75 M l-(2,2,3,3-tetrafluoropropoxy)-3-(4-.sw-butylphenoxy)-2-propanol, and 0.003 M TOA in the diluent Isopar L provided the best match between the measured properties and the performance criteria. 

In essence, the test battery should include XRPD to characterize crystallinity of excipients, moisture analysis to confirm crystallinity and hydration state of excipients, bulk density to ensure reproducibility in the blending process, and particle size distribution to ensure consistent mixing and compaction of powder blends. Often three-point PSD limits are needed for excipients. Also, morphic forms of excipients should be clearly specified and controlled as changes may impact powder flow and compactibility of blends. XRPD, DSC, SEM, and FTIR spectroscopy techniques may often be applied to characterize and control polymorphic and hydrate composition critical to the function of the excipients. Additionally, moisture sorption studies, Raman mapping, surface area analysis, particle size analysis, and KF analysis may show whether excipients possess the desired polymorphic state and whether significant amounts of amorphous components are present. Together, these studies will ensure lotto-lot consistency in the physical properties that assure flow, compaction, minimal segregation, and compunction ability of excipients used in low-dose formulations. 

The distributions of charge for molecules in this series are illustrated in Fig. 1.1 in terms of an outer envelope of the charge density p and, specifically for the five- and six-carbon members, in Fig. 6.9 in the form of contour maps of p. The latter maps show the bond paths linking the nuclei and indicate the intersection of the interatomic surfaces with the plane of the diagram. The intersection of these same surfaces with the density envelopes are shown in Fig. 1.1 and they define the methyl and methylene groups as envisaged by chemists and as defined by theory. The diagrams show qualitatively what the atomic properties will demonstrate quantitatively, that the methyl and... 

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