compute_R

sknano.core.structures.compute_R(*Ch, bond=None, length=False, **kwargs)

Compute symmetry vector \(\mathbf{R} = (p, q)\).

The symmetry vector is any lattice vector of the unfolded graphene layer that represents a symmetry operation of the nanotube. The symmetry vector \(\mathbf{R}\) can be written as:

\[\mathbf{R} = p\mathbf{a}_1 + q\mathbf{a}_2\]

where \(p\) and \(q\) are integers. The symmetry vector represents a symmetry operation of the nanotube which arises as a screw translation, which is a combination of a rotation \(\psi\) and translation \(\tau\). The symmetry operation of the nanotube can be written as:

\[R = (\psi|\tau)\]

Parameters:

• *Ch –

  Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector \(\mathbf{C}_h = n\mathbf{a}_1 + m\mathbf{a}_2 = (n, m)\).

• bond (float, optional) – Distance between nearest neighbor atoms (i.e., bond length). Must be in units of Å. Default value is the carbon-carbon bond length in graphite, approximately \(\mathrm{a}_{\mathrm{CC}} = 1.42\) Å
• length (bool, optional) – If True, return \(|\mathbf{R}|\).

Returns:

• (p, q) (tuple) – 2-tuple of ints – components of \(\mathbf{R}\).
• float – Length of \(\mathbf{R}\) (\(|\mathbf{R}|\)) if length is True in units of Å.