Group description

To calculate the profiles and the differential capacitance of the interface numerically we have to choose a differential equation solver. However, the usual packages require that the problem is posed on a finite interval rather than on a semi-infinite interval as in our problem. In principle, we can transform the semi-infinite interval into a finite one, but the price to pay is a loss of translational invariance of the equations and the point mapped from that at infinity is singular, which may pose a problem on the solver. Most of the solvers are designed for initial-value problems while in our case we deal with a boundary-value problem. To circumvent these inconveniences we follow a procedure strongly influenced by the Lie group description. 

Space group Descriptive comments Symmetrical sites on the canal axis... 

The derivation of the topological distance matrix from the molecular graph is followed by the assignment of PPPs to the nodes of the graph. The following list provides chemical definitions of the five PPP types that are implemented in the CATS descriptor. The upper-case letter in parentheses is the abbreviation of each PPP type. Additionally, a functional group description is paired with its corresponding SMARTS in square brackets ... 

Sets of keys For all k, T e N, a key K = (q, desc, g) for the bundling homomorphisms is considered both good and acceptable if (q, desc) is an acceptable group description and g really consists of two generators. Thus... 

De Dominicis, L., Fantoni. R.. Botti, S., Asilyan. L.S., Ciardi. R., Fiori, A., Appolloni, R. Symmetry point group description of second harmonic generation in carbon nanotubes. Las. Phys. Lett 1, 172-17.5 (2004)... 

Functional group Description Structure Text Examples... 

The unit cell group description of the normal modes of vibration within a unit cell, many of which are degenerate, given above is adequate for the interpretation of IR or Raman spectra. The complete interpretation of vibronic spectra or neutron inelastic scattering data requires a more generalized type of analysis that can handle 30N (N=number of unit cells) normal modes of the crystal. The vibrations, resulting from interactions between different unit cells, correspond to running lattice waves, in which the motions of the elementary unit cells may not be in phase, if ky O. Vibrational wavefunctions of the crystal at vector position (r+t ) are described by Bloch wavefunctions of the form [102]... 

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