scholarly journals Total π-electron energy and Laplacian energy: How far the analogy goes?

2007 ◽  
Vol 72 (12) ◽  
pp. 1343-1350 ◽  
Author(s):  
Slavko Radenkovic ◽  
Ivan Gutman
Keyword(s):  
Electron Energy ◽  
Linear Correlation ◽  
Molecular Graph ◽  
Total Electron ◽  
Good Linear ◽  
Molecular Graphs ◽  
Acyclic Graphs ◽  
Laplacian Energy ◽  
Total Electron Energy ◽  
Good Linear Correlation

The Laplacian energy LE is a newly introduced molecular-graph-based analog of the total ?-electron energy E. It is shown that LE and E have a similar structure-dependency only when molecules of different sizes are compared, when a good linear correlation between them exists. Within classes of isomers, LE and E are either not correlated at all or (as in the case of acyclic systems) are inversely proportional. The acyclic graphs and molecular graphs having the greatest and smallest LE values (determined in this work) differ significantly from those (previously known) having the greatest and smallest E values.

scholarly journals A graph theoretical approach to cis/trans isomerism

2014 ◽  
Vol 79 (7) ◽  
pp. 805-813 ◽  
Author(s):  
Boris Furtula ◽  
Giorgi Lekishvili ◽  
Ivan Gutman
Keyword(s):  
Graph Theory ◽  
Electron Energy ◽  
Theoretical Approach ◽  
Adjacency Matrix ◽  
Molecular Graph ◽  
Energy Difference ◽  
Simple Graph ◽  
Total Electron ◽  
Total Electron Energy ◽  
Graph Theoretical Approach

A simple graph-theory-based model is put forward, by means of which it is possible to express the energy difference between geometrically non-equivalent forms of a conjugated polyene. This is achieved by modifying the adjacency matrix of the molecular graph, and including into it information on cis/trans constellations. The total ?-electron energy thus calculated is in excellent agreement with the enthalpies of the underlying isomers and conformers.

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 Upgrading the Wiener index

2002 ◽  
Vol 67 (10) ◽  
pp. 647-651 ◽  
Author(s):  
Eduardo Castro ◽  
Ivan Gutman ◽  
Damian Marino ◽  
Pablo Peruzzo
Keyword(s):  
Shortest Path ◽  
Linear Correlation ◽  
Euclidean Distance ◽  
Topological Index ◽  
Molecular Graph ◽  
Wiener Index ◽  
Bond Lengths ◽  
Good Linear ◽  
Structure Descriptor ◽  
Good Linear Correlation

The Wiener index Wis the oldest molecular-graph-based structure-descriptor. It is defined as the sum of the distances of all pairs of vertices of the molecular graph G, where the distance is the number of edges in the shortest path connecting the respective vertices, and where G is the hydrogen-depleted molecular graph. This seemingly very simple topological index could be "upgraded" (a) by using as the distance the sum of the bond lengths along the shortest path, or (b) by using the Euclidean distance between the respective pairs of atoms. Each of these "upgraded" Wiener indices could be computed either (?) for the hydrogen- depleted or (?) for the hydrogen-filled molecular graph. We provide examples showing that none of the modifications (a?), (a?), (b?), (b?) yields better results than the ordinary Wiener index, and that there is a very good linear correlation between W and its "upgraded" variants.

On the Relationship between π-Electron Energy and Topological Resonance Energy

2006 ◽  
Vol 61 (7-8) ◽  
pp. 345-348
Author(s):  
Ivan Gutman ◽  
Slavko Radenković ◽  
Nenad Trinajstić ◽  
Andrej Vodopivec
Keyword(s):  
Electron Energy ◽  
Linear Correlation ◽  
Regression Line ◽  
Resonance Energy ◽  
Benzenoid Hydrocarbons ◽  
Good Linear ◽  
The Relationship ◽  
Topological Resonance Energy ◽  
Good Linear Correlation

Within series of isomeric benzenoid hydrocarbons there is a very good linear correlation between the topological resonance energy (TRE) and the total π-electron energy (Eπ ). Furthermore, the slope of the TRE vs. Eπ regression line is almost independent of the benzenoid isomers considered, and (for all sets of isomers) is nearly equal to 0.5. This implies that comparison of benzenoid isomers with regard to their aromaticity can be made, with equal success, by using both TRE and Eπ . However, Eπ is computed significantly simpler than TRE, and thus advantage should be given to the former. Correlations between TRE and Eπ exist also in the case of non-benzenoid isomers (both alternant and non-alternant), but are of much inferior quality.

scholarly journals Wiener-type indices and internal molecular energy

2003 ◽  
Vol 68 (4-5) ◽  
pp. 401-408 ◽  
Author(s):  
Ivan Gutman ◽  
Dusica Vidovic ◽  
Boris Furtula ◽  
Igor Zenkevich
Keyword(s):  
Linear Correlation ◽  
Molecular Graph ◽  
Wiener Index ◽  
Single Line ◽  
Good Linear ◽  
Wiener Type ◽  
Structure Descriptor ◽  
Good Linear Correlation

In earlier studies it was established that internal molecular energies (Eint) of alkanes can be reproduced, in an approximate yet reliable manner by means of a molecular-graph-based structure-descriptor U. It was also established that U is linearly correlated with the Wiener index W. We now show that the correlation between U and W is more complicated than earlier expected, and that it cannot be represented by a single line. We also show that a very good linear correlation exists between U and a modified version Wm(?) of the Wiener index, which is thus more suitable for modeling Eint than the ordinary Wiener index. .

scholarly journals Quantifying Mold Biomass on Gypsum Board: Comparison of Ergosterol and Beta-N-Acetylhexosaminidase as Mold Biomass Parameters

2003 ◽  
Vol 69 (7) ◽  
pp. 3996-3998 ◽  
Author(s):  
M. Reeslev ◽  
M. Miller ◽  
K. F. Nielsen
Keyword(s):  
Stationary Phase ◽  
Linear Correlation ◽  
Stachybotrys Chartarum ◽  
Gypsum Board ◽  
Biomass Density ◽  
Activity Data ◽  
Good Linear ◽  
Ergosterol Content ◽  
Good Linear Correlation

ABSTRACT Two mold species, Stachybotrys chartarum and Aspergillus versicolor, were inoculated onto agar overlaid with cellophane, allowing determination of a direct measurement of biomass density by weighing. Biomass density, ergosterol content, and beta-N-acetylhexosaminidase (3.2.1.52) activity were monitored from inoculation to stationary phase. Regression analysis showed a good linear correlation to biomass density for both ergosterol content and beta-N-acetylhexosaminidase activity. The same two mold species were inoculated onto wallpapered gypsum board, from which a direct biomass measurement was not possible. Growth was measured as an increase in ergosterol content and beta-N-acetylhexosaminidase activity. A good linear correlation was seen between ergosterol content and beta-N-acetylhexosaminidase activity. From the experiments performed on agar medium, conversion factors (CFs) for estimating biomass density from ergosterol content and beta-N-acetylhexosaminidase activity were determined. The CFs were used to estimate the biomass density of the molds grown on gypsum board. The biomass densities estimated from ergosterol content and beta-N-acetylhexosaminidase activity data gave similar results, showing significantly slower growth and lower stationary-phase biomass density on gypsum board than on agar.

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.

Evaluation of Natural Rubber from Clones of Hevea Brasiliensis

2002 ◽  
Vol 75 (1) ◽  
pp. 171-177 ◽  
Author(s):  
Mariselma Ferreira ◽  
Rogério M. B. Moreno ◽  
Paulo S. Gonçalves ◽  
Luiz H. C. Mattoso
Keyword(s):  
Natural Rubber ◽  
Linear Correlation ◽  
Hevea Brasiliensis ◽  
Cold Season ◽  
The State ◽  
Rubber Content ◽  
Good Linear ◽  
Mooney Viscosity ◽  
In The Beginning ◽  
Good Linear Correlation

Abstract The latex and natural rubber from rubber trees [Hevea brasiliensis (Willd. exAdr. de Juss.) Muell. Arg.] from clones (RRIM 600, IAN 873, GT 1 and PB 252) recommended to the state of São Paulo, Brazil, were studied in three different tapping systems. The parameters studied were dry rubber content (DRC), percentages of ash and of nitrogen, Wallace Plasticity (P0) and Mooney Viscosity (VR). The rubber properties vary considerably as a function of clone type, tapping method and season of the year. DRC tends to decrease in the beginning of the dry, cold season (May and June), whereas both nitrogen % and ash % increase in the same period. A good linear correlation was obtained for P0 and VR. The highest P0 and VR were obtained for RRIM 600.

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