Bond index valency

KEYWORDS bond index, valency, energy partition, population analysis... 

A further extension of this approach was done by Kier and Hall8> so as to provide different values of the connectivity index for molecules depicted by one and the same graph, but differing by the chemical nature of atoms as well as by the presence of single, double or triple bonds. The valency of the atom i (vertex degree), Vj, is replaced by the atom connectivity ... 

As explained in the preceding section, the bond index and the valency have definite physical meanings only when basis functions are orthonormalized. MOPAC satisfies this assumption(6), but general MO methods, including DV-Xa, don t satisfy it. Fortunately basis functions can be orthonormalized after MO calculation without any loss of accuracy, provided that all overlap integrals are known. 

Armstrong, Perkins and Stewart s bond index and valency, which have been used in MOP AC, were extended to general MO methods including DV-Xa, by the way of basis function orthonormalization. 

HBi is zero for all hydrocarbons and, therefore, was deleted from analyses of BP. Twelve of the TIs were deleted for the analysis of the 140 hydrocarbons as well. These indexes included the third- and fourth-order chain connectivity indexes, which were zero for all chemicals, the fourth- and sixth-order bond and valence corrected cluster connectivity indexes, which were perfectly correlated with the simple cluster connectivity indexes (r = 1.0), and and which were perfectly correlated with 7 for hydrocarbons. 

The Staudinger index is a measure of the macromolecular dimensions. Thus, for flexible macromolecules, chain skeleton parameters (bond lengths, valence angles, degree of polymerization, mass of the monomeric unit),... 

In order to understand the behaviour of the valence transition and its (l/af dependence, we arran the different /bond index plot. For brevity the six equal 1/a values for R(l) are represented by a single lozen. We also give in this plot the /cf values (shaded squares) for the ionic radii of Pr(III) and Pr(IV) in the octahedral coordination (Shannon and Pretwitt 1969). We immediately see that at least four points of the gr h lie on a plateau. We draw a mean horizontal line passing through them. The points falling... 

Sannigrahi, A.B. 1992. Abinitio molecular orbital calculations of bond index and valency. Adv. Quantum Chem. 23 301—351. 

Draw bond order and free valency index diagrams for the butadienyl system. Write a counter into program MOBAS to detemiine how many iterations are executed in solving for the allyl system. The number is not the same for all computers or operating systems. Change the convergence criterion (statement 300) to several different values and determine the number of iterations for each. 

Tervalent organophosphorus compounds containing one single P-N bond with the valency of each atom saturated by protons or carbons (but no other heteroatoms) have been known since their discovery by MichaeUs more than one century ago [ 1 ] and named indistinctly as aminophosphanes, phosphanamines, phosphazanes, or phosphinous amides. This last chemical nomenclature is the one used by the Chemical Abstracts Service (CAS) for indexing these compounds and is also the one that best delimits the scope of this review those species derived from the parent H2P-NH2 (phosphinous amide in CAS nomenclature) by partial or total substitution of protons by hydrocarbon radicals (Table 1). 

The values 1/V(dj dj) are for the atoms i and j, which make up this bond, and the connectivity index, x, is obtained as the sum of the bond connectivities. In molecules containing heteroatoms, the d values were considered to be equal to the difference between the number of valence electrons (E") and the number of hydrogen atoms (hi). Thus, for an alcoholic oxygen atom, d = 1, and d = 5. The valence connectivity-index, y can then be calculated the use of removes redundancies that can occur through the use of y alone. The calculation of connectivity indices and for the case of two isomeric heptanols is as follows. 

Here the indices a and b stand for the valence orbitals on the two atoms as before, n is a number operator, c+ and c are creation and annihilation operators, and cr is the spin index. The third and fourth terms in the parentheses effect electron exchange and are responsible for the bonding between the two atoms, while the last two terms stand for the Coulomb repulsion between electrons of opposite spin on the same orbital. As is common in tight binding theory, we assume that the two orbitals a and b are orthogonal we shall correct for this neglect of overlap later. The coupling Vab can be taken as real we set Vab = P < 0. 

Table 2.2 contains mean values of the Cu—Oz bond lengths ((<7Cu—())), copper valence index [11] (FCu) and partial charge (<2Cu), one-electron energies of the HOMO and LUMO ( HOmo> lumo) levels along with the bonding energy of Cu1 to the hosting cluster. 

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