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Update dipoles.rst
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Trovemaster committed Aug 26, 2024
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Expand Up @@ -425,7 +425,7 @@ XY3_MB
.. figure:: img/XY3_DMF_frame.jpg
:alt: XY3 frame

Rigid XY\ :subs:`3` frame for ``XY3_MB``.
Rigid XY\ :subs:\ `3` frame for ``XY3_MB``.


This DMF is implemented as a subroutine :code:`MLdms2xyz_xy3_mb` and was reported in [06YuCaTh]_. This form was used to produce a line list for PH\ :sub:`3` in [13SoYuTe]_. An input example is in :download:`31P-1H3__SAlTY__TROVE.model` and can be also found at `<https://exomol.com/models/PH3/31P-1H3/SAlTY/>`__.
Expand All @@ -450,8 +450,7 @@ where the three functions :math:`\bar{\mu}_i^{\rm Bond}`, :math:`i` :math:`=` 1
\vec{\bf e}_i = \frac{\vec{\bf r}_i-\vec{\bf r}_4}{|\vec{\bf r}_i-\vec{\bf r}_4|}
with
:math:`\vec{\bf r}_i` (:math:`i` :math:`=` 1, 2, 3) as the position vector of proton :math:`i` and :math:`\vec{\bf r}_4` as the position vector of X. The representation of :math:`\bar{\bf \mu}` in Eq. :eq:`e-dm-bond-r` is "body-fixed" in the sense that it relates the dipole moment vector directly to the instantaneous positions of the nuclei (i.e., to the vectors :math:`\vec{\bf r}_i`).
with :math:`\vec{\bf r}_i` (:math:`i` :math:`=` 1, 2, 3) as the position vector of proton :math:`i` and :math:`\vec{\bf r}_4` as the position vector of X. The representation of :math:`\bar{\bf \mu}` in Eq. :eq:`e-dm-bond-r` is "body-fixed" in the sense that it relates the dipole moment vector directly to the instantaneous positions of the nuclei (i.e., to the vectors :math:`\vec{\bf r}_i`).

Following [06YuCaTh]_, we express the three functions :math:`\bar{\mu}_i^{\rm Bond}`, :math:`i` :math:`=` 1, 2, 3, as

Expand Down Expand Up @@ -616,17 +615,11 @@ Here
and :math:`\sin(\rho_{\rm e})` is the equilibrium value of :math:`\sin(\rho)`. The factor :math:`\cos\rho = \pm \sqrt{1-\sin^2 {\rho}}` ensures that the dipole moment function :math:`\mu_{A''_1}` changes sign when :math:`\rho = 0\ldots \pi` is changed to :math:`\pi - \rho`. As in the rigid MB case, the factor :math:`\exp \left[ -\beta (r_k-r_{\rm e})^2 \right]` is used in order to keep the expansion from diverging at large :math:`r_i`.


Chanin type ABCD-type molecules
-------------------------------

XY3_MB4
^^^^^^^

XY3_NSS_MB
^^^^^^^^^^


ABCD
-----

HOOH_MB

HPPH_MB
Expand Down Expand Up @@ -677,5 +670,10 @@ XY2_G-TENS-RANK3

XY2_G-TENS-NUC


XY3_NSS_MB
^^^^^^^^^^


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