Chirality index

Natarajan, R., Basak, S. C., Balaban, A. T., Klun, J. A., Schmidt, W. F. Chirality index, molecular overlay and biological activity of diastereoisomeric mosquito repellents. Pest. Manag. Sci. 2005, 61, 1193-1201. 

Here 1 labels the electronic states of the SWCNT with the chiral index (p,0), which are described by a simple two-band k p model based on an effective mass approximation [4], p being equal to 3M + v with integer M and v = 0( 1) for metallic (semiconducting) SWCNTs. The energy bands in Eq.(3) are given by... 

Since the smallest chiral lattice animals have four cells [54], the minimum possible value for chirality index is n (J)=4. The degree of chirality X(J) of a Jordan curve J is defined as... 

A molecular descriptor proposed with the aim of quantifying the chirality of a molecule by means of the positive or negative quantification of the chirality of the environment of the atoms in the molecule for any scalar atomic property [Moreau, 1997], The basic idea is that asymmetrical environments are not the exclusive privilege of atoms in chiral molecules, however they are the most frequent situations. The Moreau chirality index is defined as ... 

According to this approach, the corresponding chirality index as... 

To calculate the relative chirality index, the least important chemical group (d) is placed at the rear, and the clockwise and anticlockwise arrangement of the other three groups (a, b, c) are used to represent the R- and S-configurations, respectively. 

The chirality correction factor for the calculation of the —> Chi chirality index is 0.00029. 

Let us consider the phonon scattering in nanotubes at the electric quantum limit, i.e. when the angular momentum of all electrons is equal to zero [4,5]. To meet this condition the nanotubes with small diameter d < 3 nm are considered. Such nanotubes correspond to (n, n) armchair nanotubes with the chirality index... 

The Wiener index for isopentane is 18. The Wiener index is used as a mathematical descriptor used in structure - property relationships. There are many other related descriptors for molecular graphs, including shape index, chirality index, Szeged index [12]. A comparison of the boiling points of alkanes against the different indices has been shown in the literature [13]. 

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