scholarly journals Notes on Quantitative Structure-Properties Relationships (QSPR) Part Four: Quantum Multimolecular Polyhedra, Collective Vectors, Quantum Similarity, and Quantum QSPR Fundamental Equation

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Ramon Carbó-Dorca ◽  
Silvia González
Keyword(s):  
Fundamental Equation ◽  
Quantum Similarity ◽  
Quantitative Structure ◽  
Quantum Qspr ◽  
Quantum Multimolecular Polyhedra ◽  
Structure Properties

Molecular Spaces Quantum Quantitative Structure-Properties Relations (QQSPR)

2016 ◽  
Vol 1 (2) ◽  
pp. 1-22
Author(s):  
Ramon Carbó-Dorca ◽  
Silvia González
Keyword(s):  
Fundamental Equation ◽  
Space Structure ◽  
Molecular Properties ◽  
Quantum Mechanical ◽  
Density Functions ◽  
Quantitative Structure ◽  
Expectation Values ◽  
Quantum Qspr ◽  
Structure Properties

Quantum QSPR can be described as a set of procedures, which can be obtained from molecular space structure, where quantum (multi)molecular polyhedra (QMP) can be defined. The collective vectors, which can be described characteristic of a given QMP and their condensed scalar values, can be used in turn to construct Hermitian QQSPR operators, which can be further employed to obtain expectation values of complex molecular properties. The linear QQSPR fundamental equation constructed from this quantum mechanical idea is able to fundament, not only an algorithm capable to obtain estimates of unknown molecular properties from the knowledge of quantum mechanical density functions, but also from the empirical, classical numerical description of molecular sets.

scholarly journals Multiplicative Zagreb Indices of Molecular Graphs

2019 ◽  
Vol 2019 ◽  
pp. 1-19 ◽  
Author(s):  
Xiujun Zhang ◽  
H. M. Awais ◽  
M. Javaid ◽  
Muhammad Kamran Siddiqui
Keyword(s):  
Mathematical Modeling ◽  
Vital Role ◽  
Molecular Structures ◽  
Quantitative Structure ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Molecular Graphs ◽  
Structure Properties

Mathematical modeling with the help of numerical coding of graphs has been used in the different fields of science, especially in chemistry for the studies of the molecular structures. It also plays a vital role in the study of the quantitative structure activities relationship (QSAR) and quantitative structure properties relationship (QSPR) models. Todeshine et al. (2010) and Eliasi et al. (2012) defined two different versions of the 1st multiplicative Zagreb index as ∏Γ=∏p∈VΓdΓp2 and ∏1Γ=∏pq∈EΓdΓp+dΓq, respectively. In the same paper of Todeshine, they also defined the 2nd multiplicative Zagreb index as ∏2Γ=∏pq∈EΓdΓp×dΓq. Recently, Liu et al. [IEEE Access; 7(2019); 105479–-105488] defined the generalized subdivision-related operations of graphs and obtained the generalized F-sum graphs using these operations. They also computed the first and second Zagreb indices of the newly defined generalized F-sum graphs. In this paper, we extend this study and compute the upper bonds of the first multiplicative Zagreb and second multiplicative Zagreb indices of the generalized F-sum graphs. At the end, some particular results as applications of the obtained results for alkane are also included.

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