The Hydrocarbon windows

In CaGe "hydrocarbon" stands for "planar polycyclic hydrocarbon with pentagonal and hexagonal faces" - or mathematically speaking: for 2-connected plane graphs with a distinguished outer face where all bounded faces are pentagons or hexagons, all vertices not in the boundary of the outer face have degree 3 and all vertices in the boundary of the outer face have degree 2 or 3. For the mathematical description the hydrocarbons are considered with the H-atoms removed. The default is also to output and display the structures without the H-atoms. There are 3 different windows for hydrocarbons. These 3 differ in the parameters describing the class.

Hydrocarbons by formula

In this window all hydrocarbons with a given constitutional formula CxHy and a given number of pentagons can be generated. You give the number of C-atoms (x in the example), H-atoms (y) and the number of pentagons and then all hydrocarbons (in the sense described above) are generated.

Further options allow to generate

  • only structures without neighbouring pentagons (IPR)
  • only strictly peri-condensed structures (the removal of the vertices contained in one face or edge will not disconnect the structure)
  • only structures with a bounded number of consecutive 3-valent C-atoms in the cyclic order around the boundary. This parameter influences the local curvature of the boundary and has a connection to local overlaps of the structures.

One can also choose to output the structures with the H-atoms attached.

A hydrocarbon with formula C25H13

By boundary structure

The boundary structure of a planar polycyclic hydrocarbon is described as the cyclic sequence of its boundary degrees. The boundary structure of azulene would e.g. be the cyclic sequence "222322223". This generator generates all planar polycyclic hydrocarbons for a given cyclic sequence of twos and threes that correspond to 0 ≤ p ≤ 5 pentagons. If d stands for the number of vertices of degree two in the boundary and t for the number of vertices of degree 3 then we have p=6-(d-t), so the number of pentagons is uniquely determined by the boundary. The restriction p < 6 is essential because for p ≥ 6 the number of structures can be infinite (see e.g. nanotubes).

An option for the generator is to allow only structures with isolated pentagons and again one can choose to output structures with or without hydrogens attached.


By number of hexagons

Fusenes are planar polycyclic hydrocarbons with all bounded faces hexagons. In this window one can generate all fusenes with a given number of hexagons.

As options one can restrict the generation to

  • benzenoids (that is: fusenes that are subgraphs of the hexagonal lattice)
  • catacondensed fusenes (all the vertices are in the boundary)
  • Kekulean fusenes (fusenes with a perfect matching - that is a subset M of edges so that every vertex is contained in exactly one of the edges of M)

A fusene with 7 hexagons
choosing a generator window <    > output options
the 4-regular plane graphs windows <    > the tubes and cones windows