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.