Polar numbers

For certain purposes (e.g. nomenclature), chemists like to work out the charges that the atoms in a compound would have if all the bonds were completely polarized and the bonding was ionic. This can be done as follows  

Use electronegativities to decide which atoms will be positive and which negative, and see whether either element is one that is known to form ions of the appropriate sign, in melts or in solution, of only a single type. Consider, for example, carbon tetrachloride, CCI4. Chlorine is more electronegative than carbon. The only stable anion formed by chlorine is Cf. The completely polarized form of CCI4 must therefore be C (Cr)4. 

Some elements having only one stable cation or anion are as follows  

The charges on the ions when a compound is written in its hypothetical ionic form are called the polar numbers or oxidation numbers of the elements concerned. Thus the polar number of carbon in CCI4 is +4 and of chlorine -1. Polar number is the original term and somewhat more expressive than oxidation number but the latter is now used almost universally. 

What are the oxidation numbers of the elements in each of the following 

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A variety of mechanisms or forces can attract organic chemicals to a soil surface and retain them there. For a given chemical, or family of chemicals, several of these mechanisms may operate in the bonding of the chemical to the soil. For any given chemical, an increase in polarity, number of functional groups, and ionic nature of the chemical can increase the number of potential sorption mechanisms for the chemical. 

Wiener has also formulated 28> the so-called polarity number, p. This is the number of pairs of vertices, separated by three edges, or otherwise, half of the number of distances of lengths three, d3, in D(G), or half of the sum of all entries in the B3 matrix as ... 

It is seen that the Smolenskii term X2 is identical to the N2 index, while the term X3 is identical (in the case of acyclic graphs only) to the polarity number p. 

Amic et developed a simple relationship between experimental retention time by HPLC and the Wiener index (W), polarity number (p), and number of OH groups ( oh) in flavyliums ... 

The polarity number p (or Wiener polarity number) was also defined by Wiener in 1947 [Wiener, 1947c] as the number of pairs of graph vertices which are separated by three edges. It is usually assumed that the polarity number accounts for the flexibility of acyclic structures, p being equal to the number of bonds around which free rotations can take place. Moreover, it relates to the steric properties of molecules. 

The polarity number is usually calculated on the distance matrix as the number of pairs of vertices at a topological distance equal to three, i.e. 

Table D-1. Values of polarity numbers p, p2, pj, P4 and Wiener index W for some molecules.

Wiener polarity number polarity number -> distance matrix... 

Narumi harmonic topological index Narumi geometric topological index Total structure connectivity index Pogliani index Ramification index Polarity number... 

H-depleted molecular graph, distance matrix, and polarity numbers p and p2 for cyclopentane. 

For example, in cyclopropane, the polarity number pis equal to zero because there are no pairs of vertices that are separated by three edges, while the polarity number is equal to 3 because there are three paths of length 3 pii = 1,2, 3,1, P22 = 2, 3,1, 2, p33 = 3,1,2, 3. The polarity number p4 is 1.8 x 3 = 5.4, which is rounded to 5, because the contribution of the acyclic part is zero and there are three ways the path of length 3 can be laid upon the cyclic part of the graph (in this case this number coincides with P3). 

R is the topological radius, D the topological diameter, T the eccentricity, f the average atom eccentricity, At the eccentric, p2 the polarity number, and MS D the mean square distance index. 

Lukovits, I. and Linert, W. (1998) Polarity-numbers of cycle-containing structures. /. Chem. Inf. Comput. Sci., 38, 715-719. 

Half-sum of the cube of the adjacency matrix Polarity number number of third neighbors Gordon-Scantlebury index number of second neighbors Number of paths of length /i = 0-10 Balaban s J index based on distance Balaban s J index based on multigraph bond orders Balaban s J index based on relative electronegativities Balaban s 7 index based on relative covalent radii Balaban s information-based indexes on distance sums... 

Lewis (Ref. 3) states Abegg s Law as the total difference between the maximum negative and positive values or polar numbers of an element is frequently eight and is in no case more than eight. ... 

Apart from the use of the carbon number index, the first use of gri h invariants for the correlation of the measured properties of molecules with their structural features was made in 1947. In that yeax, Wiener [121,122] introduced two parameters designed for this purpose. The first of these was termed the path number and was defined as the "sum of the distances between any two carbon atoms in the molecule, in terms of carbon-carbon bonds. A simple algorithm was given for the calculation of this number and it was shown that its value for normal alkanes assumes the form - n). The second parameter was called the polarity number and was defined as "the number of pairs of carbcm atthree carbon-carbon bonds it took the general value n-3 f< normal alkanes. Wiener proposed that the variation of any physical property for an isomeric structure as compared to a normal alkane would be ven by the linear expression ... 

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