Centre for Theoretical Chemistry and Physics
at Massey University (Albany Campus), New Zealand

Program Fullerene webpage


Version 4.5 (October 29, 2015)

A Fortran/C++ Program for Creating Fullerene Structures
and for Performing Topological Analyses

by Peter Schwerdtfeger, Lukas Wirz and James Avery
Centre for Theoretical Chemistry and Physics
The Quantum Chemistry and Physics Group
The New Zealand Institute for Advanced Study
Massey University Auckland
0745 Auckland, New Zealand (Middle Earth)

click picture for larger image

The program generates cartesian/internal coordinates for fullerene isomers and performs a topological/graph theoretical analysis. The results can be used for plotting 2D/3D fullerene graphs (e.g. Schlegel diagrams and 3D structures), and serves as a starting point for further quantum theoretical treatment. Version 4 incorporated C++ routines for the first time linked to the original Fortran program using much improved algorithms. Version 4.5 is more robust than previous versions, and contains a more extended evaluation of topological indicators, a harmonic oscillator force field including dihedral angles, vibrational frequencies (although the force constants have not been adjusted yet), general Goldberg-Coxeter transformations of any fullerene, access to both the Yoshida and House of Graphs databases, an improved Tutte embedder, a correct ring spiral count, a generalized ring spiral algorithm with jumps, tight lower and upper bounds for Hamiltonian cycles, and a neighbourhood spiral ring search algorithm. The fullerene database has been brought into a more compact form and extended up to C150, and up to C200 for IPR isomers, and is now more compact.

This is an open-source code and free for distribution (except for commercial purposes). Please cite the following paper if you use this program for publishing data:

1) P. Schwerdtfeger, L. Wirz, and J. Avery, "Program Fullerene - A Software Package for Constructing and Analyzing Structures of Regular Fullerenes", Version 4.4, J. Comput. Chem. 34, 1508-1526 (2013).
We also recommend to cite the following book (many of the concepts used can be found here):
2) P. W. Fowler and D. E. Manolopoulos, "An Atlas of Fullerenes" (Dover Publ., New York, 2006).
3) P. Schwerdtfeger, L. Wirz, and J. Avery, "The Topology of Fullerenes", Wiley Interdisciplinary Reviews (WIRE): Computational Molecular Science 5, 96-145 (2015).
The Hamiltonian cycle part of the program uses the code by Babic:
4) D. Babic, "Nomenclature and Coding of Fullerenes", J. Chem. Inf. Comput. Sci. 35, 515-526 (1995).
For further literature see the User's Manual. Note that the program is currently not being further developed due to the lack financial support, even though many good ideas have been put forward to extend it to general polyhedra and to add a gui.

The program has been tested for the gnu compiler collection (gfortran and g++). You need to use the Makefile included in fullerene.zip. The executable runs just fine on a PC or Mac running LINUX/UNIX. The program is written in standard Fortran and C++ and has been checked for a large number of fullerenes up to 35,000 vertices. A number of input and output files are included in the fullerenev4.5.zip file and a more detailed description is found in the User's Manual.

Download for Manual: UserManualv4.5.pdf (29/10/2015) (3.0 MB)

Download for fullerene program:
If you are a new user or if your password expired, please supply Title (Prof., Dr., Mr., Mrs.), First and Last name, Institution etc, and Email address. You will receive automatically an email message with the password to download the program. Your entry will be stored and kept confidentially in our internal user-file database. This has the advantage that you will receive an email message if a new major upgrade becomes available.

Maximum 30 characters allowed per box (except for comment and email)
First name:
Last name:

Once you have a password you can download the program here: (Version 4.5, last update 20/10/2015)

Database files: The database is provided for general isomers up to C150 and for IPR isomers up to C200, including the number of Hamiltonian cycles for general isomers up to C110 and for IPR isomers up to C122. The database can be copied into the main program folder and can be used to read the ring spiral pentagon indices. The numbering scheme is identical to that chosen in the "Atlas of Fullerenes" by Fowler and Manolopoulos, that is each isomer in the book's appendix can be constructed easily from the database. The data files are gzipped. before usage of a specific fullerene database you need to unzip the specific file. Once printed by the program the data can easily be read. It is our intention to extend the isomer list beyond C150/C200 in due time (without Hamiltonian cycles). A link to the "House of Graphs" database by Brinkmann and co-workers is already implemented, and the database can be downloaded from House of Graphs Database.

A link to the Yoshida database is also implemented and the database can be downloaded from Yoshida Database.

Download for DatabaseY (Yoshida selected fullerenes):
C20-C720 Yoshida.zip (31/10/2012) (compressed 4.4 MB, uncompressed 15.4 MB)
The following database files are more compact than the ones used in the previous version 4.3. They are now obsolete. Once the new database has been downloaded, the gzipped files require about 2.3 GB of space. In order to save disk space, only gunzip the files which are to be used in the calculation. Start downloading here for the various fullerene database files (in tar format):
Download for DatabaseAllC20-C200 (General fullerenes):
C020-C110 databaseAll.C020-110.tar (20/03/2013) (compressed 60.4 MB)
C112-C120 databaseAll.C112-120.tar (20/03/2013) (compressed 66.3 MB)
C122-C130 databaseAll.C122-130.tar (20/03/2013) (compressed 144.8 MB)
C132-C140 databaseAll.C132-140.tar (20/03/2013) (compressed 298.7 MB)
C142-C146 databaseAll.C142-146.tar (20/03/2013) (compressed 303.0 MB)
C148-C150 databaseAll.C148-150.tar (03/04/2013) (compressed 278.3 MB)
Download for DatabaseIPRC60-C200 (IPR fullerenes):
C060-C160 databaseIPR.C060-160.tar (20/03/2013) (compressed 45.8 MB)
C162-C170 databaseIPR.C162-170.tar (20/03/2013) (compressed 67.1 MB)
C172-C180 databaseIPR.C172-180.tar (20/03/2013) (compressed 145.9 MB)
C182-C186 databaseIPR.C182-186.tar (20/03/2013) (compressed 153.5 MB)
C188-C190 databaseIPR.C188-190.tar (20/03/2013) (compressed 144.3 MB)
C192-C194 databaseIPR.C192-194.tar (20/03/2013) (compressed 188.0 MB)
C196-C198 databaseIPR.C196-198.tar (20/03/2013) (compressed 243.6 MB)
C200 databaseIPR.C200.tar (20/03/2013) (compressed 146.8 MB)

Important steps in the program are:
  • Read in cartesian coordinates for a fullerene.
  • Establish connectivities between vertices to construct the adjacency matrix.
  • Construct cartesian coordinates for the Ih isomer of C60 or C20.
  • Construct cartesian coordinates using the ring-spiral pentagon indices of Fowler and Manolopoulos.
  • Construct cartesian coordinates for non-spiral fullerenes using generalized ring-spiral pentagon indices with jumps.
  • Construct cartesian coordinates from a Goldberg-Coxeter transformation of C20.
  • Use matrix-eigenvector or Tutte embedding algorithms to obtain cartesian coordinates.
  • Goldberg-Coxeter including leapfrog and halma transformations of any fullerene.
  • Endo-Kroto 2-vertex, Yoshida-Fowler 4- and 6-vertex and Brinkmann-Fowler 6-vertex insertions.
  • Use of program SPIRAL of Fowler and Manolopoulos for face-spiral fullerenes.
  • Find fullerenes in the neighbourhood of given ring-spiral pentagon indices.
  • Use of program HAMILTON of Babic for Hamiltonian cycles and IUPAC Nomenclature.
  • Tight upper and lower bounds for Hamiltonian cycles
  • Perform a Hueckel analysis. This gives you a good hint if the fullerene is open or closed shell.
  • Topological Indices: Wiener, Estrada, Balaban, Szeged, and many more.
  • Identify all pentagons and hexagons and perform a topological analysis for ring connectivities.
  • Calculate the enthalpy of formation using Martin's or Cioslowski's scheme of motifs.
  • Use Fletcher-Reeves-Polak-Ribiere geometry optimization with analytical gradients for the harmonic oscillator force field including dihedrals.
  • Get Hessian for the force field and calculate the vibrational frequencies.
  • Calculate the volume of the fullerene through the convex hull or trigonal pyramidal tesselation.
  • Calculate the surface area.
  • Calculate the minimum covering sphere (MCS) of the fullerene using the Yildirim algorithm.
  • Calculate the minimum distance sphere (MDS) and maximum inner sphere (MIS).
  • Measure of distortion from spherical symmetry and convexity.
  • Produce (x,y) coordinates of a fullerene graph (Schlegel diagram) using a variety of different algorithms.
  • Produce Schlegel diagram, with Hamiltonian cycle or the dual graph included, in .tex format.
  • The output file ending with .xyz or .cc1 can be used as input for CYLVIEW, AVOGADRO, VMD or PYMOL.
  • The output file ending with .dat can be used as input for drawing Schlegel diagrams.

  • Obelix

    Note: The program is under construction and new features are being added. You can check the date on the right hand side of the download button to see if you already have the newest version. The next intended version 5 will undergo major restructuring. Please report any bug to p.a.schwerdtfeger@massey.ac.nz.
    The program is used in over 30 countries worldwide.

    PS is indebted to the Alexander von Humboldt Foundation (Bonn) for financial support in terms of a Humboldt Research Award. The first version of the program was written during his stay at the Philipps University Marburg. We acknowledge the help of Darko Babic (Zagreb), Patrick W. Fowler (Sheffield) and David E. Manolopoulos (Oxford) to kindly allow their Fortran routines to be modified and implemented in our program system. We also thank Prof. Ottorino Ori (Rome) for fruitful discussions.
    Maintained by Peter Schwerdtfeger | Last updated: June 2019 | Copyright 2014 | Massey University