Local shape index

Refinements, parameterization, and the complete COSMO-RS 113 7.1.4 Local shape index... 

As noted, plasmonic response not only depends on polarization and shape but also on the local refractive index of the surrounding medium [145]. A change in local refractive index can be induced by varying the bulk medium in which the nanorod or nanoshell is dispersed, or by an increase or displacanent of adsorbates at the interface of the nanoparticle and bulk medium. Variations in the local refractive index have a pronounced effect on the position of the plasmon resonance peaks of gold nanorods and nanoshells. This effect can be exploited to construct trace chemical or biosensors, where binding events in proximity to the nanoparticles trigger a shift in local refractive index and thus optical response. 

Graphical Models are introduced and illustrated in Chapter 4. Among other quantities, these include models for presentation and interpretation of electron distributions and electrostatic potentials as well as for the molecular orbitals themselves. Property maps, which typically combine the electron density (representing overall molecular size and shape) with the electrostatic potential, the local ionization potential, the spin density, or with the value of a particular molecular orbital (representing a property or a reactivity index where it can be accessed) are introduced and illustrated. 

For example, if the shape domains are defined in terms of local convexity, and if we select the locally convex domains, then the shape groups of G(a) are the homology groups of the truncated isodensity contour surface G(a,2), obtained from the molecular contour surface G(a) by eliminating all domains of index p = 2. This family of shape groups, obtained by cutting out all locally convex domains of G(a), has been studied in most detail for several molecules [192,262,263,342]. 

CCT, critical cracking thickness Boltzmann constant (1.381x10 local permeability [m ] fracture resistance [N m ] average permeability in/of compact [m ] particle shape factor compact thickness [m] initial particle number concentration [m refractive index of particle material refractive index of dispersion material number density of ion i dimensionless number dimensionless number Stokes number Peclet number capillary pressure [N-m ] dynamic pressure [N m ] local liquid pressure in the compact [N-m local solid pressure in the compact [N-m ] superficial fluid velocity [m-s q gas constant [J K ] centre to centre distance [m]... 

The molecular shape indices (also called k, k, K-index) represent the overall molecular shape in three values based on counts of one-bond, two-bond, and three-bond fragments [58, 59]. Local topology (e.g., tetrahedral or planar coordination) as well as atom types are considered using parameter tables, including information such as valence radii and connectivity of the atoms. 

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