chemcoord.Zmat.minimize_dihedrals

Zmat.minimize_dihedrals()

Give a representation of the dihedral with minimized absolute value.

Mathematically speaking the angles in a zmatrix are representations of an equivalence class. We will denote an equivalence relation with \(\sim\) and use \(\alpha\) for an angle and \(\delta\) for a dihedral angle. Then the following equations hold true.

\[\begin{split}(\alpha, \delta) &\sim (-\alpha, \delta + \pi) \\ \alpha &\sim \alpha \mod 2\pi \\ \delta &\sim \delta \mod 2\pi\end{split}\]

This function asserts:

\[-\pi \leq \delta \leq \pi\]

The main application of this function is the construction of a transforming movement from zmat1 to zmat2. This is under the assumption that zmat1 and zmat2 are the same molecules (regarding their topology) and have the same construction table (get_construction_table()):

with cc.TestOperators(False):
    D = zm2 - zm1
    zmats1 = [zm1 + D * i / n for i in range(n)]
    zmats2 = [zm1 + D.minimize_dihedrals() * i / n for i in range(n)]

The movement described by zmats1 might be too large, because going from \(5^\circ\) to \(355^\circ\) is \(350^\circ\) in this case and not \(-10^\circ\) as in zmats2 which is the desired \(\Delta\) in most cases.

Parameters:None
Returns:Zmatrix with accordingly changed angles and dihedrals.
Return type:Zmat