HOMO-LUMO Maps for Chemical Graphs

作者：Fowler Patrick W^*; Pisanski Tomaz

来源：MATCH-Communications in Mathematical and in Computer Chemistry, 2010, 64(2): 373-390.

Electron configurations of pi systems are represented on the HOMO-LUMO map: a scatterplot of the middle eigenvalues of the n-vertex molecular graph (For an n-electron pi system, with eigenvalues are arranged in non-increasing order, for even a the HOMO eigenvalue is equal to that at position n/2 and the LUMO eigenvalue to that at position n/2 + 1, and for odd n the HOMO and LUMO eigenvalues are necessarily equal to each other and to the eigenvalue at position (n+1)/2.) Chemically different types of electron configuration appear in distinct regions, and graphs with equal values of invariants appear along special lines: isohomal, isolumal and isodiastemal lines are the loci of graphs that share HOMO eigenvalues, LUMO eigenvalues and HOMO-LUMO gaps, respectively. A plausible conjecture for chemical graphs (simple, connected and of maximum degree <= 3) is that all but a finite number of exceptions lie within the 'chemical triangle' of the map, with vertices at (HOMO, LUMO) = (-1, 1), (+1, -1) and (+1, +1). It is proved that all chemical trees lie within the triangle, as do all chemical graphs with up to 12 vertices. The smallest exceptional chemical graph is the Heawood graph, at (+root 2, -root 2)

• 出版日期2010