scholarly journals Topology and stability of conjugated hydrocarbons: The dependence of total π-electron energy on molecular topology

2005 ◽  
Vol 70 (3) ◽  
pp. 441-456 ◽  
Author(s):  
Ivan Gutman
Keyword(s):  
Present Article ◽  
Molecular Orbital ◽  
Electron Energy ◽  
Molecular Topology ◽  
Total Electron ◽  
Conjugated Hydrocarbons ◽  
Mathematical Properties ◽  
Total Electron Energy ◽  
Orbital Approximation

In spite of the fact that research on the mathematical properties of the total ?-electron energy E (as computed by means of the H?ckel molecular orbital approximation) started already in the 1940s, many results in this area have been obtained also in the newest times. In 1978 this author published in this journal a review on E. The present article is another review on E, summarizing the progress in the theory of E, achieved since then.

scholarly journals Estimating the total π-electron energy

2013 ◽  
Vol 78 (12) ◽  
pp. 1925-1933 ◽  
Author(s):  
Ivan Gutman ◽  
Kinkar Das
Keyword(s):  
Electron Energy ◽  
Upper Bound ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Total Electron ◽  
Molecular Graphs ◽  
Conjugated Hydrocarbons ◽  
Short Survey ◽  
Total Electron Energy ◽  
Graph Energy

The paper gives a short survey of the most important lower and upper bounds for total ?-electron energy, i.e., graph energy (E). In addition, a new lower and a new upper bound for E are deduced, valid for general molecular graphs. The strengthened versions of these estimates, valid for alternant conjugated hydrocarbons, are also reported.

scholarly journals The McClelland approximation and the distribution of π-electron molecular orbital energy levels

2007 ◽  
Vol 72 (10) ◽  
pp. 967-973 ◽  
Author(s):  
Ivan Gutman
Keyword(s):  
Molecular Orbital ◽  
Electron Energy ◽  
Energy Levels ◽  
Orbital Energy ◽  
Total Electron ◽  
Molecular Orbital Energy ◽  
Total Electron Energy ◽  
Carbon Carbon Bonds ◽  
Uniform Manner

The total ?-electron energy E of a conjugated hydrocarbon with n carbon atoms and m carbon-carbon bonds can be approximately calculated by means of the McClelland formula E ? g 2mn, where g is an empirical fitting constant, g ? 0.9. It was claimed that the good quality of the McClelland approximation is a consequence of the fact that the ?-electron molecular orbital energy levels are distributed in a nearly uniform manner. It will now be shown that the McClelland approximation does not depend on the nature of the distribution of energy levels, i.e., that it is compatible with a large variety of such distributions. .

scholarly journals Dependence of the total -electron energy on large number of non-bonding molecular orbitals

2004 ◽  
Vol 69 (10) ◽  
pp. 777-782 ◽  
Author(s):  
Ivan Gutman ◽  
Dragan Stevanovic ◽  
Slavko Radenkovic ◽  
Svetlana Milosavljevic ◽  
Natasa Cmiljanovic
Keyword(s):  
Electron Energy ◽  
Molecular Orbitals ◽  
Total Electron ◽  
Total Electron Energy

Using a recently developed method for computing the effect of non-bonding molecular orbitals (NBMOs) on the total ?-electron energy (E), it was found that the dependence of E on the number n0 of NBMOs is almost perfectly linear. We now show that this regularity remains valid for very large values of n0, in particular, to hold up to n0 = 20.

A topological index for the total?-electron energy

1975 ◽  
Vol 38 (1) ◽  
pp. 37-47 ◽  
Author(s):  
Haruo Hosoya ◽  
Kikuko Hosoi ◽  
Ivan Gutman
Keyword(s):  
Electron Energy ◽  
Topological Index ◽  
Total Electron ◽  
Total Electron Energy

scholarly journals Tripartite graphs with energy aggregation

2019 ◽  
Vol 38 (7) ◽  
pp. 149-167 ◽  
Author(s):  
Nawras A. Alawn ◽  
Nadia M. G. Al-Saidi ◽  
Rashed T. Rasheed
Keyword(s):  
Electron Energy ◽  
Degree Sequence ◽  
Maximum Energy ◽  
Chemical Components ◽  
Research Attention ◽  
Total Electron ◽  
Tripartite Graph ◽  
Total Electron Energy ◽  
Irregular Graphs ◽  
Tripartite Graphs

The aggregate of the absolute values of the graph eigenvalues is called the energy of a graph. It is used to approximate the total _-electron energy of molecules. Thus, finding a new mechanism to calculate the total energy of some graphs is a challenge; it has received a lot of research attention. We study the eigenvalues of a complete tripartite graph Ti,i,n−2i , for n _ 4, based on the adjacency, Laplacian, and signless Laplacian matrices. In terms of the degree sequence, the extreme eigenvalues of the irregular graphs energy are found to characterize the component with the maximum energy. The chemical HMO approach is particularly successful in the case of the total _-electron energy. We showed that some chemical components are equienergetic with the tripartite graph. This discovering helps easily to derive the HMO for most of these components despite their different structures.

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