Molecular connectivity indices evaluation

Bojarski, J. and Ekiert, L. (1983). Evaluation of Modified Valence Molecular Connectivity Index for Correlation of Chromatographic Parameters. J. Liquid Chromat., 6,73. 

The relation between this definition and the mathematical expression of and IIP values (Equation 5.13 and Equation 5.14) can be easily seen. The simple represents the vertex valence (a number of skeletal neighbors for each vertex). It can be presented as both = = k - h, and = - h, after the substitution of the number of valence electrons k with the number of electrons assigned to sigma orbitals . It is evident from Equation 5.15 that the greater the number of skeletal neighbors, the larger the value and the lower the connectivity index. Recently, new arguments were evaluated in support of the thesis that the molecular connectivity indices represent molecular accessibility areas and volumes (Estrada, 2002). 

A final useful index of sigma nonbonded interactions between lone pairs is the partial bond order p (Xm, Yn) which is evaluated over the MO s which result from the interaction of the lone pair group MO s with the sigma HOMO and vacant MO s of the coupling unit. This index is intimately connected with the type of analysis employed in this work. In our survey of a variety of problems of molecular structure we shall provide computational results pertinent to the analysis outlined, i e. all or some of the following indices will be provided ... 

Very often, the control problem is posed in terms of performance indices that are not the molecular properties defined previously, but that are directly connected to them. For instance, this is the case of the melt flow index [61], of the Mooney viscosity [62] and of the intrinsic viscosity [63, 64], which maybe regarded as indirect evaluations of... 

Contents Introduction. - Concept of Creation and Annihilation Operators. -Particle Number Operators. - Second Quantized Representation of Quantum Mechanical Operators. - Evaluation of Matrix Elements. - Advantages of Second Quantization. - Illustrative Examples. - Density Matrices. -Connection to Bra and Ket Formalism. - Using Spatial Orbitals. - Some Model Hamiltonians in Second Quantized Form. - The Brillouin Theorem. -Many-Body Perturbation Theory. -Second Quantization for Nonorthogonal Orbitals. - Second Quantization and Hellmann-Feynman Theorem. - Inter-molecular Interactions. - Quasiparticle Transformations. Miscellaneous Topics Related to Second Quantization -Problem Solutions. - References -Index. 

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