sknano.structures.compute_R

sknano.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 : {tuple or ints}

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.