What is it about?
HMO quantities, viz., electron densities, charge densities, bond orders, free valences, total p-electron energies, HOMO-LUMO or band gaps of {X,Y}-cyclacene graphs under next-nearest-neighbor (nnn) approximations are expressed in analytical forms within a certain range of nnn approximations parameter (m). The cyclic dimer (CD) is constructed in obtaining the eigenvalues corresponding to the singular points of the density of states (DOS) of such {X,Y}-cyclacene. Although the HOMO-LUMO gap of the CD differs from that of the cyclacene with large number of repeating units (i.e., n→infinity) but becomes same for m = 0.
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Why is it important?
Analytical forms of HMO quantities, viz., electron densities, charge densities, bond orders, free valences, total p-electron energies, HOMO-LUMO or band gaps of {X,Y}-cyclacene with next-nearest-neighbor (nnn) interaction-approximations that we have obtained are very useful in obtaining the values of the quantities easily with time saving manner as well as in reaching other important conclusions regarding stability-reactivity of such systems. Such analytical expressions can be used for facile computer programming in obtaining the respective quantities.
Perspectives
{X,Y}-Cyclacene graphs represent a large variety of molecules with varying X (= C, B, N, etc.) and Y (= C, B, N, etc.). Some of them are synthesized/ exit and many of yet to be synthesized/exist. Thus the formulas derived here may have some significance.
Dr Bholanath Mandal
The University of Burdwan
Read the Original
This page is a summary of: Hückel Molecular Orbital Quantities of {X,Y}-Cyclacene Graphs Under Next-Nearest-Neighbour Approximations in Analytical Forms, Zeitschrift für Naturforschung A, February 2019, De Gruyter,
DOI: 10.1515/zna-2018-0488.
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