Original scientific paper

The McClelland Number of Conjugated Hydrocarbons

Ivan Gutman
Lemi Türker
Boris Furtula
Veselin Vučković

Abstract

The McClelland number of a conjugated hydrocarbon is the integer k, satisfying the condition 2superscript(–(1/2))superscript(k) sqrt (2nm) ≤ E < 22superscript(–(1/2))2superscript(k+1) sqrt(2nm), where E is the HMO total Π-electron energy, n the number of carbon atoms, and m the number of carbon-carbon bonds. If k = 3, then the respective conjugated system is said to be energy-regular. If k ≤ 2 and k ≥ 4, then one speaks of energy-poor and energy-rich Π-electron systems, respectively. We found that all polycyclic Kekuléan hydrocarbons, possessing condensed rings, are energy-regular, with only three exceptions: naphthalene, phenanthrene, and triphenylene (which are energy-rich). Energy-poor Π-electron systems are some (but not all) non-Kekuléans, whereas many of the polycyclic Kekuléan hydrocarbons with non-condensed rings (polyphenyls, phenyl-substituted polyenes and similar) are energy-rich.

Keywords

total Π-electron energy; bounds for total Π-electron energy; McClelland number

Hrčak ID:

2534

URI

https://hrcak.srce.hr/2534

Publication date:

20.12.2005.

Article data in other languages: croatian

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