From 81c79beac8fb33e282105b514b2ac3b5e810248b Mon Sep 17 00:00:00 2001 From: Sergey Yurchenko Date: Sat, 27 May 2023 15:03:46 +0200 Subject: [PATCH] Update symmetry.rst --- docs/source/symmetry.rst | 27 +++++++++++++++++++++++++++ 1 file changed, 27 insertions(+) diff --git a/docs/source/symmetry.rst b/docs/source/symmetry.rst index 00fa10f..e4785db 100644 --- a/docs/source/symmetry.rst +++ b/docs/source/symmetry.rst @@ -48,6 +48,33 @@ C\ :sub:`2v`\ (M) where :math:`E`, (12), :math:`E^*` and (12)\ :sup:`*` are the 4 point group operations. Typical C\ :sub:`2v`\ (M) molecules are XY\ :sub:`2` (e.g. water, H\ :sub:`2`\ S), ZXY\ :sub:`2` (e.g. formaldehyde.) + +Symmetry properties of the vibrational coordinates +-------------------------------------------------- + +TROVE uses the symmetry properties of the vibrational coordinates, i.e. how they transform upon applying the symmetry operations, to build symmetry adapted vibrational basis functions. The symmetrisation method is described in [17YuYaOv]_. In the following, we show how the coordinates, we show these transformation properties for the corresponding coordination frames implemented in TROVE. + + +``R-RHO-Z``, ``R-ALPHA-Z`` +^^^^^^^^^^^^^^^^^^^^^^^^^^ + + ++--------------+---------------+--------------+---------------+---------------+ +| | :math:`E` | (12)\ | :math:`E^*` |(12)\ :sup:`*` | ++==============+===============+==============+===============+===============+ +|:math:`r_1` | :math:`r_1` | :math:`r_2` |:math:`r_1` | :math:`r_2` | ++--------------+---------------+--------------+---------------+---------------+ +|:math:`r_2` | :math:`r_2` | :math:`r_1` |:math:`r_2` | :math:`r_1` | ++--------------+---------------+--------------+---------------+---------------+ +| :math:`\rho` | :math:`\rho` | :math:`\rho` |:math:`\rho` | :math:`\rho` | ++--------------+---------------+--------------+---------------+---------------+ +|:math:`\alpha`| :math:`\alpha`|:math:`\alpha`|:math:`\alpha` | :math:`\alpha`| ++--------------+---------------+--------------+---------------+---------------+ + + + + + C3v(M) ======