From 8ef3d77724bd3f5c29c2ae5238d3d4c859fb33ba Mon Sep 17 00:00:00 2001
From: Axel Kohlmeyer <akohlmey@gmail.com>
Date: Sun, 2 Feb 2020 18:22:40 -0500
Subject: [PATCH] Convert documentation of improper styles from images to
 mathjax

---
 doc/src/Eqs/improper_class2.jpg             | Bin 15728 -> 0 bytes
 doc/src/Eqs/improper_class2.tex             |  13 ----
 doc/src/Eqs/improper_cossq.jpg              | Bin 2995 -> 0 bytes
 doc/src/Eqs/improper_cossq.tex              |   9 ---
 doc/src/Eqs/improper_cvff.jpg               | Bin 2826 -> 0 bytes
 doc/src/Eqs/improper_cvff.tex               |   9 ---
 doc/src/Eqs/improper_dist-1.jpg             | Bin 2169 -> 0 bytes
 doc/src/Eqs/improper_dist-1.tex             |   9 ---
 doc/src/Eqs/improper_distharm.jpg           | Bin 2139 -> 0 bytes
 doc/src/Eqs/improper_distharm.tex           |   9 ---
 doc/src/Eqs/improper_fourier.jpg            | Bin 4746 -> 0 bytes
 doc/src/Eqs/improper_fourier.tex            |   9 ---
 doc/src/Eqs/improper_harmonic.jpg           | Bin 2005 -> 0 bytes
 doc/src/Eqs/improper_harmonic.tex           |   9 ---
 doc/src/Eqs/improper_inversion_harmonic.jpg | Bin 4649 -> 0 bytes
 doc/src/Eqs/improper_inversion_harmonic.tex |  15 -----
 doc/src/Eqs/improper_ring.jpg               | Bin 11101 -> 0 bytes
 doc/src/Eqs/improper_ring.tex               |  12 ----
 doc/src/Eqs/improper_sqdistharm.jpg         | Bin 2204 -> 0 bytes
 doc/src/Eqs/improper_sqdistharm.tex         |   9 ---
 doc/src/Eqs/improper_umbrella.jpg           | Bin 9598 -> 0 bytes
 doc/src/Eqs/improper_umbrella.tex           |  13 ----
 doc/src/dihedral_class2.rst                 |  18 +++---
 doc/src/dihedral_opls.rst                   |   4 +-
 doc/src/dihedral_spherical.rst              |   8 +--
 doc/src/dihedral_table_cut.rst              |   4 +-
 doc/src/improper_class2.rst                 |  66 +++++++++++---------
 doc/src/improper_cossq.rst                  |  22 ++++---
 doc/src/improper_cvff.rst                   |  12 ++--
 doc/src/improper_distance.rst               |  10 +--
 doc/src/improper_distharm.rst               |  14 +++--
 doc/src/improper_fourier.rst                |  14 +++--
 doc/src/improper_harmonic.rst               |  24 ++++---
 doc/src/improper_hybrid.rst                 |   9 +--
 doc/src/improper_inversion_harmonic.rst     |  24 +++----
 doc/src/improper_ring.rst                   |  18 ++++--
 doc/src/improper_sqdistharm.rst             |  14 +++--
 doc/src/improper_umbrella.rst               |  19 +++---
 38 files changed, 159 insertions(+), 237 deletions(-)
 delete mode 100644 doc/src/Eqs/improper_class2.jpg
 delete mode 100644 doc/src/Eqs/improper_class2.tex
 delete mode 100644 doc/src/Eqs/improper_cossq.jpg
 delete mode 100644 doc/src/Eqs/improper_cossq.tex
 delete mode 100644 doc/src/Eqs/improper_cvff.jpg
 delete mode 100644 doc/src/Eqs/improper_cvff.tex
 delete mode 100644 doc/src/Eqs/improper_dist-1.jpg
 delete mode 100644 doc/src/Eqs/improper_dist-1.tex
 delete mode 100644 doc/src/Eqs/improper_distharm.jpg
 delete mode 100644 doc/src/Eqs/improper_distharm.tex
 delete mode 100644 doc/src/Eqs/improper_fourier.jpg
 delete mode 100644 doc/src/Eqs/improper_fourier.tex
 delete mode 100644 doc/src/Eqs/improper_harmonic.jpg
 delete mode 100644 doc/src/Eqs/improper_harmonic.tex
 delete mode 100644 doc/src/Eqs/improper_inversion_harmonic.jpg
 delete mode 100644 doc/src/Eqs/improper_inversion_harmonic.tex
 delete mode 100644 doc/src/Eqs/improper_ring.jpg
 delete mode 100644 doc/src/Eqs/improper_ring.tex
 delete mode 100644 doc/src/Eqs/improper_sqdistharm.jpg
 delete mode 100644 doc/src/Eqs/improper_sqdistharm.tex
 delete mode 100644 doc/src/Eqs/improper_umbrella.jpg
 delete mode 100644 doc/src/Eqs/improper_umbrella.tex

diff --git a/doc/src/Eqs/improper_class2.jpg b/doc/src/Eqs/improper_class2.jpg
deleted file mode 100644
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diff --git a/doc/src/Eqs/improper_class2.tex b/doc/src/Eqs/improper_class2.tex
deleted file mode 100644
index 2c41df1a29..0000000000
--- a/doc/src/Eqs/improper_class2.tex
+++ /dev/null
@@ -1,13 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-\begin{eqnarray*}
-  E & = & E_i + E_{aa} \\
-  E_i & = & K [ \frac{\chi_{ijkl} + \chi_{kjli} + \chi_{ljik}}{3} - \chi_0 ]^2 \\
-  E_{aa} & = & M_1 (\theta_{ijk} - \theta_1) (\theta_{kjl} - \theta_3) + \\
-  & & M_2 (\theta_{ijk} - \theta_1) (\theta_{ijl} - \theta_2) + \\
-  & & M_3 (\theta_{ijl} - \theta_2) (\theta_{kjl} - \theta_3)
-\end{eqnarray*}
-
-\end{document}
\ No newline at end of file
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diff --git a/doc/src/Eqs/improper_cossq.tex b/doc/src/Eqs/improper_cossq.tex
deleted file mode 100644
index 27e79c7b16..0000000000
--- a/doc/src/Eqs/improper_cossq.tex
+++ /dev/null
@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-  E = \frac{1}{2} K \cos^2{\left(\chi - \chi_0\right)}
-$$
-
-\end{document}
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diff --git a/doc/src/Eqs/improper_cvff.tex b/doc/src/Eqs/improper_cvff.tex
deleted file mode 100644
index 3a038b6b8c..0000000000
--- a/doc/src/Eqs/improper_cvff.tex
+++ /dev/null
@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-   E = K [1 + d  \cos (n \phi) ] 
-$$
-
-\end{document}
\ No newline at end of file
diff --git a/doc/src/Eqs/improper_dist-1.jpg b/doc/src/Eqs/improper_dist-1.jpg
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diff --git a/doc/src/Eqs/improper_dist-1.tex b/doc/src/Eqs/improper_dist-1.tex
deleted file mode 100644
index 8ef5b5f4c3..0000000000
--- a/doc/src/Eqs/improper_dist-1.tex
+++ /dev/null
@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-   E = K_2 d^2 + K_4 d^4
-$$
-
-\end{document}
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index 218de6a0dd..0000000000
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+++ /dev/null
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-
-\end{document}
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diff --git a/doc/src/Eqs/improper_fourier.tex b/doc/src/Eqs/improper_fourier.tex
deleted file mode 100644
index 47ac58ef01..0000000000
--- a/doc/src/Eqs/improper_fourier.tex
+++ /dev/null
@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-   E = K [C_0 + C_1 \cos ( \omega) + C_2 \cos( 2 \omega) ] 
-$$
-
-\end{document}
diff --git a/doc/src/Eqs/improper_harmonic.jpg b/doc/src/Eqs/improper_harmonic.jpg
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diff --git a/doc/src/Eqs/improper_harmonic.tex b/doc/src/Eqs/improper_harmonic.tex
deleted file mode 100644
index c47020cf9c..0000000000
--- a/doc/src/Eqs/improper_harmonic.tex
+++ /dev/null
@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-  E = K (\chi - \chi_0)^2
-$$
-
-\end{document}
\ No newline at end of file
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diff --git a/doc/src/Eqs/improper_inversion_harmonic.tex b/doc/src/Eqs/improper_inversion_harmonic.tex
deleted file mode 100644
index a1607a1149..0000000000
--- a/doc/src/Eqs/improper_inversion_harmonic.tex
+++ /dev/null
@@ -1,15 +0,0 @@
-\documentclass[12pt]{article}
-
-\pagestyle{empty}
-\begin{document}
-
-$$
-  E = K \left(\theta - \theta_0\right)^2
-$$
-
-\end{document}
-
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: t
-%%% End:
diff --git a/doc/src/Eqs/improper_ring.jpg b/doc/src/Eqs/improper_ring.jpg
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diff --git a/doc/src/Eqs/improper_ring.tex b/doc/src/Eqs/improper_ring.tex
deleted file mode 100644
index b7bd553c37..0000000000
--- a/doc/src/Eqs/improper_ring.tex
+++ /dev/null
@@ -1,12 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-\begin{eqnarray*}
-   E & = &\frac{1}{6} K \left(\Delta_{ijl} + \Delta_{ijk} + \Delta_{kjl} \right)^6 \\
-   \Delta_{ijl} & = & \cos{\theta_{ijl} - \cos{\theta_0}} \\
-   \Delta_{ijk} & = & \cos{\theta_{ijk} - \cos{\theta_0}} \\
-   \Delta_{kjl} & = & \cos{\theta_{kjl} - \cos{\theta_0}}
-\end{eqnarray*}
-
-\end{document}
diff --git a/doc/src/Eqs/improper_sqdistharm.jpg b/doc/src/Eqs/improper_sqdistharm.jpg
deleted file mode 100644
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diff --git a/doc/src/Eqs/improper_sqdistharm.tex b/doc/src/Eqs/improper_sqdistharm.tex
deleted file mode 100644
index 1b50a309a0..0000000000
--- a/doc/src/Eqs/improper_sqdistharm.tex
+++ /dev/null
@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-\thispagestyle{empty}
-$$
-  E = K (d^2 - d_0^2)^2
-$$
-
-\end{document}
diff --git a/doc/src/Eqs/improper_umbrella.jpg b/doc/src/Eqs/improper_umbrella.jpg
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diff --git a/doc/src/Eqs/improper_umbrella.tex b/doc/src/Eqs/improper_umbrella.tex
deleted file mode 100644
index 53dfbf31d5..0000000000
--- a/doc/src/Eqs/improper_umbrella.tex
+++ /dev/null
@@ -1,13 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-E=\frac{1}{2}K\left( \frac{1}{\sin\omega_0}\right) ^2 \left( \cos\omega - \cos\omega_0\right) ^2 \qquad \omega_0 \neq 0^o
-$$
-
-$$
-E=K\left( 1-cos\omega\right)  \qquad \omega_0 = 0^o
-$$
-
-\end{document}
diff --git a/doc/src/dihedral_class2.rst b/doc/src/dihedral_class2.rst
index 427dc299a3..b6afa130f0 100644
--- a/doc/src/dihedral_class2.rst
+++ b/doc/src/dihedral_class2.rst
@@ -38,15 +38,15 @@ The *class2* dihedral style uses the potential
 
 .. math::
 
-  E & = & E_d + E_{mbt} + E_{ebt} + E_{at} + E_{aat} + E_{bb13} \\
-  E_d & = & \sum_{n=1}^{3} K_n [ 1 - \cos (n \phi - \phi_n) ] \\
-  E_{mbt} & = & (r_{jk} - r_2) [ A_1 \cos (\phi) + A_2 \cos (2\phi) + A_3 \cos (3\phi) ] \\
-  E_{ebt} & = & (r_{ij} - r_1) [ B_1 \cos (\phi) + B_2 \cos (2\phi) + B_3 \cos (3\phi) ] + \\
-  & & (r_{kl} - r_3) [ C_1 \cos (\phi) + C_2 \cos (2\phi) + C_3 \cos (3\phi) ] \\
-  E_{at} & = & (\theta_{ijk} - \theta_1) [ D_1 \cos (\phi) + D_2 \cos (2\phi) + D_3 \cos (3\phi) ] + \\
-  & & (\theta_{jkl} - \theta_2) [ E_1 \cos (\phi) + E_2 \cos (2\phi) + E_3 \cos (3\phi) ] \\
-  E_{aat} & = & M (\theta_{ijk} - \theta_1) (\theta_{jkl} - \theta_2) \cos (\phi) \\
-  E_{bb13} & = & N (r_{ij} - r_1) (r_{kl} - r_3)
+  E = & E_d + E_{mbt} + E_{ebt} + E_{at} + E_{aat} + E_{bb13} \\
+  E_d  = & \sum_{n=1}^{3} K_n [ 1 - \cos (n \phi - \phi_n) ] \\
+  E_{mbt}  = & (r_{jk} - r_2) [ A_1 \cos (\phi) + A_2 \cos (2\phi) + A_3 \cos (3\phi) ] \\
+  E_{ebt}  = & (r_{ij} - r_1) [ B_1 \cos (\phi) + B_2 \cos (2\phi) + B_3 \cos (3\phi) ] + \\
+  &  (r_{kl} - r_3) [ C_1 \cos (\phi) + C_2 \cos (2\phi) + C_3 \cos (3\phi) ] \\
+  E_{at}  = & (\theta_{ijk} - \theta_1) [ D_1 \cos (\phi) + D_2 \cos (2\phi) + D_3 \cos (3\phi) ] + \\
+  & (\theta_{jkl} - \theta_2) [ E_1 \cos (\phi) + E_2 \cos (2\phi) + E_3 \cos (3\phi) ] \\
+  E_{aat}  = & M (\theta_{ijk} - \theta_1) (\theta_{jkl} - \theta_2) \cos (\phi) \\
+  E_{bb13}  = & N (r_{ij} - r_1) (r_{kl} - r_3)
 
 
 where :math:`E_d` is the dihedral term, :math:`E_{mbt}` is a middle-bond-torsion term,
diff --git a/doc/src/dihedral_opls.rst b/doc/src/dihedral_opls.rst
index 50ad0dcc5a..ef431b92d2 100644
--- a/doc/src/dihedral_opls.rst
+++ b/doc/src/dihedral_opls.rst
@@ -38,8 +38,8 @@ The *opls* dihedral style uses the potential
 
 .. math::
 
-  E = \frac{1}{2} K_1 [1 + \cos(\phi)] + \frac{1}{2} K_2 [1 - \cos(2 \phi)] +
-      \frac{1}{2} K_3 [1 + \cos(3 \phi)] + \frac{1}{2} K_4 [1 - \cos(4 \phi)]
+  E = & \frac{1}{2} K_1 [1 + \cos(\phi)] + \frac{1}{2} K_2 [1 - \cos(2 \phi)] + \\
+      & \frac{1}{2} K_3 [1 + \cos(3 \phi)] + \frac{1}{2} K_4 [1 - \cos(4 \phi)]
 
 
 Note that the usual 1/2 factor is not included in the K values.
diff --git a/doc/src/dihedral_spherical.rst b/doc/src/dihedral_spherical.rst
index 03dfcecb38..795bd5ad4d 100644
--- a/doc/src/dihedral_spherical.rst
+++ b/doc/src/dihedral_spherical.rst
@@ -32,10 +32,10 @@ The *spherical* dihedral style uses the potential:
 
 .. math::
 
-  E(\phi,\theta_1,\theta_2) & = & \sum_{i=1}^N\nolimits\ C_i\ \Phi_i(\phi)\ \Theta_{1i}(\theta_1)\ \Theta_{2i}(\theta_2) \\
-  \Phi_{i}(\phi)        & = &  u_i - \mathrm{cos}((\phi   - a_i)K_i) \\
-  \Theta_{1i}(\theta_1) & = &  v_i - \mathrm{cos}((\theta_1-b_i)L_i) \\
-  \Theta_{2i}(\theta_2) & = &  w_i - \mathrm{cos}((\theta_2-c_i)M_i)
+  E(\phi,\theta_1,\theta_2) & = \sum_{i=1}^N\nolimits\ C_i\ \Phi_i(\phi)\ \Theta_{1i}(\theta_1)\ \Theta_{2i}(\theta_2) \\
+  \Phi_{i}(\phi)        & = u_i - \mathrm{cos}((\phi   - a_i)K_i) \\
+  \Theta_{1i}(\theta_1) & = v_i - \mathrm{cos}((\theta_1-b_i)L_i) \\
+  \Theta_{2i}(\theta_2) & = w_i - \mathrm{cos}((\theta_2-c_i)M_i)
 
 
 For this dihedral style, the energy can be any function that combines the
diff --git a/doc/src/dihedral_table_cut.rst b/doc/src/dihedral_table_cut.rst
index a369d29302..529a911e0b 100644
--- a/doc/src/dihedral_table_cut.rst
+++ b/doc/src/dihedral_table_cut.rst
@@ -68,8 +68,8 @@ cutoff function:
 
 .. math::
 
-        f(\theta) & = & K \qquad\qquad\qquad\qquad\qquad\qquad \theta < \theta_1 \\
-        f(\theta) & = & K \left(1-\frac{(\theta - \theta_1)^2}{(\theta_2 - \theta_1)^2}\right) \qquad \theta_1 < \theta < \theta_2
+        f(\theta) & = K \qquad\qquad\qquad\qquad\qquad\qquad \theta < \theta_1 \\
+        f(\theta) & = K \left(1-\frac{(\theta - \theta_1)^2}{(\theta_2 - \theta_1)^2}\right) \qquad \theta_1 < \theta < \theta_2
 
 
 The cutoff specifies an prefactor to the cutoff function.  While this value
diff --git a/doc/src/improper_class2.rst b/doc/src/improper_class2.rst
index 9bb5c88618..260348a668 100644
--- a/doc/src/improper_class2.rst
+++ b/doc/src/improper_class2.rst
@@ -32,24 +32,33 @@ Description
 
 The *class2* improper style uses the potential
 
-.. image:: Eqs/improper_class2.jpg
-   :align: center
+.. math::
 
-where Ei is the improper term and Eaa is an angle-angle term.  The 3 X
-terms in Ei are an average over 3 out-of-plane angles.
+  E      = & E_i + E_{aa} \\
+  E_i    = & K [ \frac{\chi_{ijkl} + \chi_{kjli} + \chi_{ljik}}{3} - \chi_0 ]^2 \\
+  E_{aa} = & M_1 (\theta_{ijk} - \theta_1) (\theta_{kjl} - \theta_3) + \\
+           & M_2 (\theta_{ijk} - \theta_1) (\theta_{ijl} - \theta_2) + \\
+           & M_3 (\theta_{ijl} - \theta_2) (\theta_{kjl} - \theta_3)
+
+
+where :math:`E_i` is the improper term and :math:`E_{aa}` is an
+angle-angle term.  The 3 :math:`\chi` terms in :math:`E_i` are an
+average over 3 out-of-plane angles.
 
 The 4 atoms in an improper quadruplet (listed in the data file read by
-the :doc:`read_data <read_data>` command) are ordered I,J,K,L.  X\_IJKL
-refers to the angle between the plane of I,J,K and the plane of J,K,L,
-and the bond JK lies in both planes.  Similarly for X\_KJLI and X\_LJIK.
+the :doc:`read_data <read_data>` command) are ordered I,J,K,L.
+:math:`\chi_{ijkl}` refers to the angle between the plane of I,J,K and
+the plane of J,K,L, and the bond JK lies in both planes.  Similarly for
+:math:`\chi_{kjli}` and :math:`\chi_{ljik}`.
 Note that atom J appears in the common bonds (JI, JK, JL) of all 3 X
 terms.  Thus J (the 2nd atom in the quadruplet) is the atom of
-symmetry in the 3 X angles.
+symmetry in the 3 :math:`\chi` angles.
 
-The subscripts on the various theta's refer to different combinations
-of 3 atoms (I,J,K,L) used to form a particular angle.  E.g. Theta\_IJL
-is the angle formed by atoms I,J,L with J in the middle.  Theta1,
-theta2, theta3 are the equilibrium positions of those angles.  Again,
+The subscripts on the various :math:`\theta`\ s refer to different
+combinations of 3 atoms (I,J,K,L) used to form a particular angle.
+E.g. :math:`\theta_{ijl}` is the angle formed by atoms I,J,L with J
+in the middle.  :math:`\theta_1`, :math:`\theta_2`, :math:`\theta_3`
+are the equilibrium positions of those angles.  Again,
 atom J (the 2nd atom in the quadruplet) is the atom of symmetry in the
 theta angles, since it is always the center atom.
 
@@ -59,34 +68,35 @@ this is not required.
 
 See :ref:`(Sun) <improper-Sun>` for a description of the COMPASS class2 force field.
 
-Coefficients for the Ei and Eaa formulas must be defined for each
+Coefficients for the :math:`E_i` and :math:`E_{aa}` formulas must be
+defined for each
 improper type via the :doc:`improper_coeff <improper_coeff>` command as
 in the example above, or in the data file or restart files read by the
 :doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
 commands.
 
-These are the 2 coefficients for the Ei formula:
+These are the 2 coefficients for the :math:`E_i` formula:
 
-* K (energy/radian\^2)
-* X0 (degrees)
+* :math:`K` (energy/radian\^2)
+* :math:`\chi_0` (degrees)
 
-X0 is specified in degrees, but LAMMPS converts it to radians
+:math:`\chi_0` is specified in degrees, but LAMMPS converts it to radians
 internally; hence the units of K are in energy/radian\^2.
 
-For the Eaa formula, each line in a
+For the :math:`E_{aa}` formula, each line in a
 :doc:`improper_coeff <improper_coeff>` command in the input script lists
-7 coefficients, the first of which is "aa" to indicate they are
+7 coefficients, the first of which is *aa* to indicate they are
 AngleAngle coefficients.  In a data file, these coefficients should be
-listed under a "AngleAngle Coeffs" heading and you must leave out the
-"aa", i.e. only list 6 coefficients after the improper type.
+listed under a *AngleAngle Coeffs* heading and you must leave out the
+*aa*, i.e. only list 6 coefficients after the improper type.
 
-* aa
-* M1 (energy/distance)
-* M2 (energy/distance)
-* M3 (energy/distance)
-* theta1 (degrees)
-* theta2 (degrees)
-* theta3 (degrees)
+* *aa*
+* :math:`M_1` (energy/distance)
+* :math:`M_2` (energy/distance)
+* :math:`M_3` (energy/distance)
+* :math:`\theta_1` (degrees)
+* :math:`\theta_2` (degrees)
+* :math:`\theta_3` (degrees)
 
 The theta values are specified in degrees, but LAMMPS converts them to
 radians internally; hence the units of M are in energy/radian\^2.
diff --git a/doc/src/improper_cossq.rst b/doc/src/improper_cossq.rst
index 7428a7f02e..e8f2032d80 100644
--- a/doc/src/improper_cossq.rst
+++ b/doc/src/improper_cossq.rst
@@ -28,18 +28,20 @@ Description
 
 The *cossq* improper style uses the potential
 
-.. image:: Eqs/improper_cossq.jpg
-   :align: center
+.. math::
 
-where x is the improper angle, x0 is its equilibrium value, and K is a
-prefactor.
+  E = \frac{1}{2} K \cos^2{\left(\chi - \chi_0\right)}
+
+
+where :math:`\chi` is the improper angle, :math:`\chi_0` is its
+equilibrium value, and :math:`K` is a prefactor.
 
 If the 4 atoms in an improper quadruplet (listed in the data file read
-by the :doc:`read_data <read_data>` command) are ordered I,J,K,L then X
-is the angle between the plane of I,J,K and the plane of J,K,L.
+by the :doc:`read_data <read_data>` command) are ordered I,J,K,L then
+:math:`\chi` is the angle between the plane of I,J,K and the plane of J,K,L.
 Alternatively, you can think of atoms J,K,L as being in a plane, and
-atom I above the plane, and X as a measure of how far out-of-plane I
-is with respect to the other 3 atoms.
+atom I above the plane, and :math:`\chi` as a measure of how far
+out-of-plane I is with respect to the other 3 atoms.
 
 Note that defining 4 atoms to interact in this way, does not mean that
 bonds necessarily exist between I-J, J-K, or K-L, as they would in a
@@ -52,8 +54,8 @@ above, or in the data file or restart files read by the
 :doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
 commands:
 
-* K (energy)
-* X0 (degrees)
+* :math:`K` (energy)
+* :math:`\chi_0` (degrees)
 
 
 ----------
diff --git a/doc/src/improper_cvff.rst b/doc/src/improper_cvff.rst
index a6938c7a12..c1086797e2 100644
--- a/doc/src/improper_cvff.rst
+++ b/doc/src/improper_cvff.rst
@@ -31,8 +31,10 @@ Description
 
 The *cvff* improper style uses the potential
 
-.. image:: Eqs/improper_cvff.jpg
-   :align: center
+.. math::
+
+   E = K [1 + d  \cos (n \phi) ] 
+
 
 where phi is the improper dihedral angle.
 
@@ -54,9 +56,9 @@ above, or in the data file or restart files read by the
 :doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
 commands:
 
-* K (energy)
-* d (+1 or -1)
-* n (0,1,2,3,4,6)
+* :math:`K` (energy)
+* :math:`d` (+1 or -1)
+* :math:`n` (0,1,2,3,4,6)
 
 
 ----------
diff --git a/doc/src/improper_distance.rst b/doc/src/improper_distance.rst
index c170be50f2..c29386e010 100644
--- a/doc/src/improper_distance.rst
+++ b/doc/src/improper_distance.rst
@@ -22,8 +22,10 @@ Description
 
 The *distance* improper style uses the potential
 
-.. image:: Eqs/improper_dist-1.jpg
-   :align: center
+.. math::
+
+   E = K_2 d^2 + K_4 d^4
+
 
 where d is the distance between the central atom and the plane formed
 by the other three atoms.  If the 4 atoms in an improper quadruplet
@@ -43,8 +45,8 @@ The following coefficients must be defined for each improper type via
 the improper\_coeff command as in the example above, or in the data
 file or restart files read by the read\_data or read\_restart commands:
 
-* K\_2 (energy/distance\^2)
-* K\_4 (energy/distance\^4)
+* :math:`K_2` (energy/distance\^2)
+* :math:`K_4` (energy/distance\^4)
 
 
 ----------
diff --git a/doc/src/improper_distharm.rst b/doc/src/improper_distharm.rst
index 09f835f575..585285b88e 100644
--- a/doc/src/improper_distharm.rst
+++ b/doc/src/improper_distharm.rst
@@ -22,23 +22,25 @@ Description
 
 The *distharm* improper style uses the potential
 
-.. image:: Eqs/improper_distharm.jpg
-   :align: center
+.. math::
+
+  E = K (d - d_0)^2
+
 
 where d is the oriented distance between the central atom and the plane formed
 by the other three atoms.  If the 4 atoms in an improper quadruplet
 (listed in the data file read by the :doc:`read_data <read_data>`
 command) are ordered I,J,K,L then the L-atom is assumed to be the
 central atom. Note that this is different from the convention used
-in the improper\_style distance. The distance d is oriented and can take
-on negative values. This may lead to unwanted behavior if d0 is not equal to zero.
+in the improper\_style distance. The distance :math:`d` is oriented and can take
+on negative values. This may lead to unwanted behavior if :math:`d_0` is not equal to zero.
 
 The following coefficients must be defined for each improper type via
 the improper\_coeff command as in the example above, or in the data
 file or restart files read by the read\_data or read\_restart commands:
 
-* K (energy/distance\^2)
-* d0 (distance)
+* :math:`K` (energy/distance\^2)
+* :math:`d_0` (distance)
 
 
 ----------
diff --git a/doc/src/improper_fourier.rst b/doc/src/improper_fourier.rst
index 1cc72c7319..734aa75eb9 100644
--- a/doc/src/improper_fourier.rst
+++ b/doc/src/improper_fourier.rst
@@ -28,8 +28,10 @@ Description
 
 The *fourier* improper style uses the following potential:
 
-.. image:: Eqs/improper_fourier.jpg
-   :align: center
+.. math::
+
+   E = K [C_0 + C_1 \cos ( \omega) + C_2 \cos( 2 \omega) ] 
+
 
 where K is the force constant, C0, C1, C2 are dimensionless coefficients,
 and omega is the angle between the IL axis and the IJK plane:
@@ -45,10 +47,10 @@ above, or in the data file or restart files read by the
 :doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
 commands:
 
-* K (energy)
-* C0 (unitless)
-* C1 (unitless)
-* C2 (unitless)
+* :math:`K` (energy)
+* :math:`C_0` (unitless)
+* :math:`C_1` (unitless)
+* :math:`C_2` (unitless)
 * all  (0 or 1, optional)
 
 
diff --git a/doc/src/improper_harmonic.rst b/doc/src/improper_harmonic.rst
index 6c9496dc42..666bd425e8 100644
--- a/doc/src/improper_harmonic.rst
+++ b/doc/src/improper_harmonic.rst
@@ -34,18 +34,22 @@ Description
 
 The *harmonic* improper style uses the potential
 
-.. image:: Eqs/improper_harmonic.jpg
-   :align: center
+.. math::
 
-where X is the improper angle, X0 is its equilibrium value, and K is a
-prefactor.  Note that the usual 1/2 factor is included in K.
+  E = K (\chi - \chi_0)^2
+
+
+where :math:`\chi` is the improper angle, :math:`\chi_0` is its equilibrium
+value, and :math:`K` is a prefactor.  Note that the usual 1/2 factor is
+included in :math:`K`.
 
 If the 4 atoms in an improper quadruplet (listed in the data file read
-by the :doc:`read_data <read_data>` command) are ordered I,J,K,L then X
+by the :doc:`read_data <read_data>` command) are ordered I,J,K,L then
+:math:`\chi`
 is the angle between the plane of I,J,K and the plane of J,K,L.
 Alternatively, you can think of atoms J,K,L as being in a plane, and
-atom I above the plane, and X as a measure of how far out-of-plane I
-is with respect to the other 3 atoms.
+atom I above the plane, and :math:`\chi` as a measure of how far out-of-plane
+I is with respect to the other 3 atoms.
 
 Note that defining 4 atoms to interact in this way, does not mean that
 bonds necessarily exist between I-J, J-K, or K-L, as they would in a
@@ -58,10 +62,10 @@ above, or in the data file or restart files read by the
 :doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
 commands:
 
-* K (energy/radian\^2)
-* X0 (degrees)
+* :math:`K` (energy/radian\^2)
+* :math:`\chi_0` (degrees)
 
-X0 is specified in degrees, but LAMMPS converts it to radians
+:math:`\chi_0` is specified in degrees, but LAMMPS converts it to radians
 internally; hence the units of K are in energy/radian\^2.
 
 
diff --git a/doc/src/improper_hybrid.rst b/doc/src/improper_hybrid.rst
index 75bc592c68..aac53bbb66 100644
--- a/doc/src/improper_hybrid.rst
+++ b/doc/src/improper_hybrid.rst
@@ -38,9 +38,9 @@ In the improper\_coeff command, the first coefficient sets the improper
 style and the remaining coefficients are those appropriate to that
 style.  In the example above, the 2 improper\_coeff commands would set
 impropers of improper type 1 to be computed with a *harmonic*
-potential with coefficients 120.0, 30 for K, X0.  Improper type 2
-would be computed with a *cvff* potential with coefficients 20.0, -1,
-2 for K, d, n.
+potential with coefficients 120.0, 30 for :math:`K`, :math:`\chi_0`.
+Improper type 2 would be computed with a *cvff* potential with coefficients
+20.0, -1, 2 for K, d, and n, respectively.
 
 If the improper *class2* potential is one of the hybrid styles, it
 requires additional AngleAngle coefficients be specified in the data
@@ -67,7 +67,8 @@ MOLECULE package.  See the :doc:`Build package <Build_package>` doc page
 for more info.
 
 Unlike other improper styles, the hybrid improper style does not store
-improper coefficient info for individual sub-styles in a :doc:`binary restart files <restart>`.  Thus when restarting a simulation from a
+improper coefficient info for individual sub-styles in a :doc:`binary restart files <restart>`.
+Thus when restarting a simulation from a
 restart file, you need to re-specify improper\_coeff commands.
 
 Related commands
diff --git a/doc/src/improper_inversion_harmonic.rst b/doc/src/improper_inversion_harmonic.rst
index 735b46a1f6..86cdbc7c8f 100644
--- a/doc/src/improper_inversion_harmonic.rst
+++ b/doc/src/improper_inversion_harmonic.rst
@@ -26,19 +26,21 @@ Description
 The *inversion/harmonic* improper style follows the Wilson-Decius
 out-of-plane angle definition and uses an harmonic potential:
 
-.. image:: Eqs/improper_inversion_harmonic.jpg
-   :align: center
+.. math::
 
-where K is the force constant and omega is the angle evaluated for
-all three axis-plane combinations centered around the atom I.  For
-the IL axis and the IJK plane omega looks as follows:
+  E = K \left(\omega - \omega_0\right)^2
+
+
+where :math:`K` is the force constant and :math:`\omega` is the angle
+evaluated for all three axis-plane combinations centered around the atom I.
+For the IL axis and the IJK plane :math:`\omega` looks as follows:
 
 .. image:: JPG/umbrella.jpg
    :align: center
 
 Note that the *inversion/harmonic* angle term evaluation differs to
 the :doc:`improper_umbrella <improper_umbrella>` due to the cyclic
-evaluation of all possible angles omega.
+evaluation of all possible angles :math:`\omega`.
 
 The following coefficients must be defined for each improper type via
 the :doc:`improper_coeff <improper_coeff>` command as in the example
@@ -46,12 +48,12 @@ above, or in the data file or restart files read by the
 :doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
 commands:
 
-* K (energy)
-* omega0 (degrees)
+* :math:`K` (energy)
+* :math:`\omega_0` (degrees)
 
-If omega0 = 0 the potential term has a minimum for the planar
-structure.  Otherwise it has two minima at +/- omega0, with a barrier
-in between.
+If :math:`\omega_0 = 0` the potential term has a single minimum for
+the planar structure.  Otherwise it has two minima at +/- :math:`\omega_0`,
+with a barrier in between.
 
 
 ----------
diff --git a/doc/src/improper_ring.rst b/doc/src/improper_ring.rst
index 3f6bec718b..1554439380 100644
--- a/doc/src/improper_ring.rst
+++ b/doc/src/improper_ring.rst
@@ -28,11 +28,17 @@ Description
 
 The *ring* improper style uses the potential
 
-.. image:: Eqs/improper_ring.jpg
-   :align: center
+.. math::
 
-where K is a prefactor, theta is the angle formed by the atoms
-specified by (i,j,k,l) indices and theta0 its equilibrium value.
+   E = &\frac{1}{6} K \left(\Delta_{ijl} + \Delta_{ijk} + \Delta_{kjl} \right)^6 \\
+   \Delta_{ijl} = & \cos{\theta_{ijl} - \cos{\theta_0}} \\
+   \Delta_{ijk} = & \cos{\theta_{ijk} - \cos{\theta_0}} \\
+   \Delta_{kjl} = & \cos{\theta_{kjl} - \cos{\theta_0}}
+
+
+where :math:`K` is a prefactor, :math:`\theta` is the angle formed by
+the atoms specified by (i,j,k,l) indices and :math:`\theta_0` its
+equilibrium value.
 
 If the 4 atoms in an improper quadruplet (listed in the data file read
 by the :doc:`read_data <read_data>` command) are ordered i,j,k,l then
@@ -56,8 +62,8 @@ above, or in the data file or restart files read by the
 :doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
 commands:
 
-* K (energy)
-* theta0 (degrees)
+* :math:`K` (energy)
+* :math:`\theta_0` (degrees)
 
 
 ----------
diff --git a/doc/src/improper_sqdistharm.rst b/doc/src/improper_sqdistharm.rst
index ec1e68959a..b9bf53ba34 100644
--- a/doc/src/improper_sqdistharm.rst
+++ b/doc/src/improper_sqdistharm.rst
@@ -22,10 +22,12 @@ Description
 
 The *sqdistharm* improper style uses the potential
 
-.. image:: Eqs/improper_sqdistharm.jpg
-   :align: center
+.. math::
 
-where d is the distance between the central atom and the plane formed
+  E = K (d^2 - {d_0}^2)^2
+
+
+where :math:`d` is the distance between the central atom and the plane formed
 by the other three atoms.  If the 4 atoms in an improper quadruplet
 (listed in the data file read by the :doc:`read_data <read_data>`
 command) are ordered I,J,K,L then the L-atom is assumed to be the
@@ -36,10 +38,10 @@ The following coefficients must be defined for each improper type via
 the improper\_coeff command as in the example above, or in the data
 file or restart files read by the read\_data or read\_restart commands:
 
-* K (energy/distance\^4)
-* d0\^2 (distance\^2)
+* :math:`K` (energy/distance\^4)
+* :math:`{d_0}^2` (distance\^2)
 
-Note that d0\^2 (in units distance\^2) has be provided and not d0.
+Note that :math:`{d_0}^2` (in units distance\^2) has be provided and not :math:`d_0`.
 
 
 ----------
diff --git a/doc/src/improper_umbrella.rst b/doc/src/improper_umbrella.rst
index 8515a94598..33f549ffc8 100644
--- a/doc/src/improper_umbrella.rst
+++ b/doc/src/improper_umbrella.rst
@@ -30,18 +30,21 @@ The *umbrella* improper style uses the following potential, which is
 commonly referred to as a classic inversion and used in the
 :doc:`DREIDING <Howto_bioFF>` force field:
 
-.. image:: Eqs/improper_umbrella.jpg
-   :align: center
+.. math::
 
-where K is the force constant and omega is the angle between the IL
+  E = & \frac{1}{2}K\left( \frac{1}{\sin\omega_0}\right) ^2 \left( \cos\omega - \cos\omega_0\right) ^2 \qquad \omega_0 \neq 0^o \\
+  E = & K\left( 1-cos\omega\right)  \qquad \omega_0 = 0^o
+
+
+where :math:`K` is the force constant and :math:`\omega` is the angle between the IL
 axis and the IJK plane:
 
 .. image:: JPG/umbrella.jpg
    :align: center
 
-If omega0 = 0 the potential term has a minimum for the planar
-structure.  Otherwise it has two minima at +/- omega0, with a barrier
-in between.
+If :math:`\omega_0 = 0` the potential term has a minimum for the planar
+structure.  Otherwise it has two minima at :math:`\omega +/- \omega_0`,
+with a barrier in between.
 
 See :ref:`(Mayo) <umbrella-Mayo>` for a description of the DREIDING force field.
 
@@ -51,8 +54,8 @@ above, or in the data file or restart files read by the
 :doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
 commands:
 
-* K (energy)
-* omega0 (degrees)
+* :math:`K` (energy)
+* :math:`\omega_0` (degrees)
 
 
 ----------