Generation of nano-torus structures

Licensing / Citing

This software is published under a very permissive license to make it as useful as possible for a variety of usecases. If it is useful to you, especially in a scientific context, you are encouraged to cite:

Magnetically Induced Current Densities in Toroidal Carbon Nanotubes, Kevin Reiter, Florian Weigend, Lukas Nico Wirz, Maria Dimitrova, and Dage Sundholm, The Journal of Physical Chemistry C, DOI: 10.1021/acs.jpcc.9b03769

Some parts of geometry{2,3}.{hh,cc} and auxiliary.hh have been borrowed from http://ctcp.massey.ac.nz/index.php?group=&page=fullerenes .

Compiling

There are two ways to build these little programs. Should work on any Linux and related systems as well as macOS.

using the ordinary Makefile

make

using CMake (probably more robust)

mkdir mybuild
cd mybuild
[CXX=clang++] cmake ..
make

Usage

Each of the programs prints the list of required parameters when it's called with no or the wrong number of parameters.

torus-simple

Generate the subset of possible tori which has undistorted hexagons, ie, where the angle between (m,n) and (p,q) is 90 degrees and where we can therefore omit p and q and provide only the length of the vector.

usage: ./torus-simple <m> <n> <l>
  <m>: first component of the chiral vector
  <n>: second component of the chiral vector
  <l>: length (not all lengths are possible!)

The resulting tori will have hexagons with ideal angles, and the atom count will always be 4*n. If you chose an invalid l, you will be suggested valid choices for l.

torus-full

Generate any circular torus with arbitrary angles between (m,n) and (p,q), and choose the ellipticity of the cross section.

usage: ./torus-full <m> <n> <p> <q> <phase> <bl> <ell>
  <m>: first component of the chiral vector
  <n>: second component of the chiral vector
  <p>: first component of the second side
  <q>: second component of the second side
  <phase>: where is the first atom [in rad], eg '0'?
  <target bond length>: 1.43, maybe?
  <elliptic parameter>: choose '1' for none

If the printed shear matrix if far from {{1,0},{0,1}} the obtained structure is probably not sensible and other m,n,p,q should be chosen. Tuning the phase is mostly useful to get the maximal point group symmetry. Note that the bond length is only a target and there will always be a spectrum of shorter and longer bonds (especially for large r and small R). The elliptic parameter can be left at 1.0 for very large R, but should be increased to 1.1 ... 1.5 for smaller R or large r.

torus-extra

Generate closed nano-tube rings which need not be tori. Hardcoded shapes are a torus (0), a lemniscate (2), and a trefoil (1). Other shapes can easily be defined.

like torus-full, without ellipticity, but producing silly knots
usage: ./torus-extra <m> <n> <p> <q> <bl> <structure>
  <m>: first component of the chiral vector
  <n>: second component of the chiral vector
  <p>: first component of the second side
  <q>: second component of the second side
  <target bond length>: 1.43, maybe?
  <structure>: select by index

torus-grid

Generate grids (as xyz file) below, on, and above the surface of a torus.

This program generates grids to be used with the tori generated by torus-full.
usage: ./torus-grid <m> <n> <p> <q> <bl> <ell>
  <m>: first component of the chiral vector
  <n>: second component of the chiral vector
  <p>: first component of the second side
  <q>: second component of the second side
  <target bond length>: 1.43, maybe?
  <elliptic parameter>: choose '1' for none

(And before someone asks: the bond length is required for scaling, even though there are no bonds.)

botch_optimise-torus-full

If one is not sure about the best target bond length or the best elliptical parameter but needs structures that are optimised at some expensive qc-level of theory, it can be efficient to preoptimise the structure in this two-parameter space.

The current version strictly aims at turbomole, but it should be possible to adapt it. Basically, we calculate single points until simplex downhill is converged.

very non-robust two-parameter optimisation of nano tori.  Use at your own risk.
usage: ./botch_optimise-torus-full <m> <n> <p> <q> <ph> <bl> <ell> <tol> <st1> <st2>
  <m>: first component of the chiral vector
  <n>: second component of the chiral vector
  <p>: first component of the second side
  <q>: second component of the second side
  <phase>: in multiples of pi
  <target bond length>: 1.43, maybe?
  <ellipticity>: choose '1' for none
  <tolerance>: the convergence criterion.  Try 0.01
  <step 1>: initial step of the scaling factor.  Try 0.05
  <step 2>: initial step of the ellipticity.  Try 0.05