convert pair style bop to class2

doc/src/Eqs/pair_bop.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-  E = \frac{1}{2} \sum_{i=1}^{N} \sum_{j=i_1}^{i_N} \phi_{ij} \left( r_{ij} \right) - \sum_{i=1}^{N} \sum_{j=i_1}^{i_N} \beta_{\sigma,ij} \left( r_{ij} \right) \cdot \Theta_{\sigma,ij} - \sum_{i=1}^{N} \sum_{j=i_1}^{i_N} \beta_{\pi,ij} \left( r_{ij} \right) \cdot \Theta_{\pi,ij} + U_{prom}
-$$
-
-\end{document}

doc/src/Eqs/pair_born.tex

@@ -1,10 +0,0 @@
-\documentstyle[12pt]{article}
-
-\begin{document}
-
-$$
-E = A \exp \left(\frac{\sigma - r}{\rho} \right) - 
-    \frac{C}{r^6} + \frac{D}{r^8} \qquad r < r_c
-$$
-
-\end{document}

doc/src/Eqs/pair_buck.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-   E = A e^{-r / \rho} - \frac{C}{r^6} \qquad r < r_c
-$$
-
-\end{document}

doc/src/Eqs/pair_buck6d.tex

@@ -1,10 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-\pagestyle{empty}
-
-\begin{eqnarray*}
-  E = A e^{-\kappa r} - \frac{C}{r^6} \cdot \frac{1}{1 + D r^{14}} \qquad r < r_c \\
-\end{eqnarray*}
-
-\end{document}

doc/src/Eqs/pair_charmm.tex

@@ -1,22 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-\begin{eqnarray*}
- E & = & LJ(r) \qquad \qquad \qquad r < r_{\rm in} \\
-   & = & S(r) * LJ(r) \qquad \qquad r_{\rm in} < r < r_{\rm out} \\
-   & = & 0 \qquad \qquad \qquad \qquad r > r_{\rm out} \\
- E & = & C(r) \qquad \qquad \qquad r < r_{\rm in} \\
-   & = & S(r) * C(r) \qquad \qquad r_{\rm in} < r < r_{\rm out} \\
-   & = & 0 \qquad \qquad \qquad \qquad r > r_{\rm out} \\
- LJ(r) & = & 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - 
-         \left(\frac{\sigma}{r}\right)^6 \right] \\
- C(r) & = & \frac{C q_i q_j}{ \epsilon r} \\
- S(r) & = & \frac{ \left[r_{\rm out}^2 - r^2\right]^2  
-   \left[r_{\rm out}^2 + 2r^2 - 3{r_{\rm in}^2}\right]} 
- { \left[r_{\rm out}^2 - {r_{\rm in}}^2\right]^3 }
-\end{eqnarray*}                           
-
-\end{document}
-
-

doc/src/Eqs/pair_class2.tex

@@ -1,11 +0,0 @@
-\documentstyle[12pt]{article}
-
-\begin{document}
-
-$$
-  E = \epsilon \left[ 2 \left(\frac{\sigma}{r}\right)^9 - 
-    3 \left(\frac{\sigma}{r}\right)^6 \right]
-  \qquad r < r_c
-$$
-
-\end{document}

doc/src/pair_bop.rst

@@ -36,7 +36,7 @@ Description
 """""""""""
 
 The *bop* pair style computes Bond-Order Potentials (BOP) based on
-quantum mechanical theory incorporating both sigma and pi bonding.
+quantum mechanical theory incorporating both :math:`\sigma` and :math:`\pi` bonding.
 By analytically deriving the BOP from quantum mechanical theory its
 transferability to different phases can approach that of quantum
 mechanical methods.  This potential is similar to the original BOP
@@ -53,47 +53,50 @@ discussed below.
 
 The BOP potential consists of three terms:
 
-.. image:: Eqs/pair_bop.jpg
-   :align: center
+.. math::
 
-where phi\_ij(r\_ij) is a short-range two-body function representing the
-repulsion between a pair of ion cores, beta\_(sigma,ij)(r\_ij) and
-beta\_(sigma,ij)(r\_ij) are respectively sigma and pi bond integrals,
-THETA\_(sigma,ij) and THETA\_(pi,ij) are sigma and pi bond-orders, and
-U\_prom is the promotion energy for sp-valent systems.
+   E = \frac{1}{2} \sum_{i=1}^{N} \sum_{j=i_1}^{i_N} \phi_{ij} \left( r_{ij} \right) - \sum_{i=1}^{N} \sum_{j=i_1}^{i_N} \beta_{\sigma,ij} \left( r_{ij} \right) \cdot \Theta_{\sigma,ij} - \sum_{i=1}^{N} \sum_{j=i_1}^{i_N} \beta_{\pi,ij} \left( r_{ij} \right) \cdot \Theta_{\pi,ij} + U_{prom}
+
+
+where :math:`\phi_{ij}(r_{ij})` is a short-range two-body function
+representing the repulsion between a pair of ion cores,
+:math:`\beta_{\sigma,ij}(r_{ij})` and :math:`\beta_{\sigma,ij}(r_{ij})`
+are respectively sigma and :math:`\pi` bond integrals, :math:`\Theta_{\sigma,ij}`
+and :math:`\Theta_{\pi,ij}` are :math:`\sigma` and :math:`\pi`
+bond-orders, and U\_prom is the promotion energy for sp-valent systems.
 
 The detailed formulas for this potential are given in Ward
 (:ref:`Ward <Ward>`); here we provide only a brief description.
 
-The repulsive energy phi\_ij(r\_ij) and the bond integrals
-beta\_(sigma,ij)(r\_ij) and beta\_(phi,ij)(r\_ij) are functions of the
-interatomic distance r\_ij between atom i and j.  Each of these
-potentials has a smooth cutoff at a radius of r\_(cut,ij).  These
+The repulsive energy :math:`\phi_{ij}(r_{ij})` and the bond integrals
+:math:`\beta_{\sigma,ij}(r_{ij})` and :math:`\beta_{\phi,ij}(r_{ij})` are functions of the
+interatomic distance :math:`r_{ij}` between atom *i* and *j*\ .  Each of these
+potentials has a smooth cutoff at a radius of :math:`r_{cut,ij}.  These
 smooth cutoffs ensure stable behavior at situations with high sampling
 near the cutoff such as melts and surfaces.
 
 The bond-orders can be viewed as environment-dependent local variables
-that are ij bond specific.  The maximum value of the sigma bond-order
-(THETA\_sigma) is 1, while that of the pi bond-order (THETA\_pi) is 2,
-attributing to a maximum value of the total bond-order
-(THETA\_sigma+THETA\_pi) of 3.  The sigma and pi bond-orders reflect the
-ubiquitous single-, double-, and triple- bond behavior of
-chemistry. Their analytical expressions can be derived from tight-
-binding theory by recursively expanding an inter-site Green's function
-as a continued fraction. To accurately represent the bonding with a
-computationally efficient potential formulation suitable for MD
-simulations, the derived BOP only takes (and retains) the first two
-levels of the recursive representations for both the sigma and the pi
-bond-orders. Bond-order terms can be understood in terms of molecular
-orbital hopping paths based upon the Cyrot-Lackmann theorem
-(:ref:`Pettifor\_1 <Pettifor_1>`).  The sigma bond-order with a half-full
-valence shell is used to interpolate the bond-order expression that
-incorporated explicit valance band filling.  This pi bond-order
-expression also contains also contains a three-member ring term that
-allows implementation of an asymmetric density of states, which helps
-to either stabilize or destabilize close-packed structures.  The pi
-bond-order includes hopping paths of length 4.  This enables the
-incorporation of dihedral angles effects.
+that are ij bond specific.  The maximum value of the :math:`\sigma`
+bond-order (:math:`\Theta_{\sigma}` is 1, while that of the :math:`\pi`
+bond-order (:math:`\Theta_{\pi}`) is 2, attributing to a maximum value
+of the total bond-order (:math:`\Theta_{\sigma}+\Theta_{\pi}`) of 3.
+The :math:`\sigma` and :math:`\pi` bond-orders reflect the ubiquitous
+single-, double-, and triple- bond behavior of chemistry. Their
+analytical expressions can be derived from tight- binding theory by
+recursively expanding an inter-site Green's function as a continued
+fraction. To accurately represent the bonding with a computationally
+efficient potential formulation suitable for MD simulations, the derived
+BOP only takes (and retains) the first two levels of the recursive
+representations for both the :math:`\sigma` and the :math:`\pi` bond-orders. Bond-order
+terms can be understood in terms of molecular orbital hopping paths
+based upon the Cyrot-Lackmann theorem (:ref:`Pettifor\_1 <Pettifor_1>`).
+The :math:`\sigma` bond-order with a half-full valence shell is used to
+interpolate the bond-order expression that incorporated explicit valance
+band filling.  This :math:`\pi` bond-order expression also contains also contains
+a three-member ring term that allows implementation of an asymmetric
+density of states, which helps to either stabilize or destabilize
+close-packed structures.  The :math:`\pi` bond-order includes hopping paths of
+length 4.  This enables the incorporation of dihedral angles effects.
 
 .. note::
 

doc/src/pair_born.rst

@@ -102,11 +102,15 @@ Description
 The *born* style computes the Born-Mayer-Huggins or Tosi/Fumi
 potential described in :ref:`(Fumi and Tosi) <FumiTosi>`, given by
 
-.. image:: Eqs/pair_born.jpg
-   :align: center
+.. math::
 
-where sigma is an interaction-dependent length parameter, rho is an
-ionic-pair dependent length parameter, and Rc is the cutoff.
+   E = A \exp \left(\frac{\sigma - r}{\rho} \right) - 
+   \frac{C}{r^6} + \frac{D}{r^8} \qquad r < r_c
+
+
+where :math:`\sigma` is an interaction-dependent length parameter,
+:math:`\rho` is an ionic-pair dependent length parameter, and
+:math:`r_c` is the cutoff.
 
 The styles with *coul/long* or *coul/msm* add a Coulombic term as
 described for the :doc:`lj/cut <pair_lj>` pair styles.  An additional
@@ -138,8 +142,8 @@ above, or in the data file or restart files read by the
 commands, or by mixing as described below:
 
 * A (energy units)
-* rho (distance units)
-* sigma (distance units)
+* :math:`\rho` (distance units)
+* :math:`\sigma` (distance units)
 * C (energy units \* distance units\^6)
 * D (energy units \* distance units\^8)
 * cutoff (distance units)

doc/src/pair_buck.rst

@@ -109,11 +109,13 @@ Description
 The *buck* style computes a Buckingham potential (exp/6 instead of
 Lennard-Jones 12/6) given by
 
-.. image:: Eqs/pair_buck.jpg
-   :align: center
+.. math::
 
-where rho is an ionic-pair dependent length parameter, and Rc is the
-cutoff on both terms.
+   E = A e^{-r / \rho} - \frac{C}{r^6} \qquad r < r_c
+
+
+where :math:`\rho` is an ionic-pair dependent length parameter, and
+:math:`r_c` is the cutoff on both terms.
 
 The styles with *coul/cut* or *coul/long* or *coul/msm* add a
 Coulombic term as described for the :doc:`lj/cut <pair_lj>` pair styles.
@@ -147,14 +149,14 @@ above, or in the data file or restart files read by the
 commands:
 
 * A (energy units)
-* rho (distance units)
+* :math:`\rho` (distance units)
 * C (energy-distance\^6 units)
 * cutoff (distance units)
 * cutoff2 (distance units)
 
-The second coefficient, rho, must be greater than zero.
-The coefficients A, rho, and C can be written as analytical expressions
-of epsilon and sigma, in analogy to the Lennard-Jones potential
+The second coefficient, :math:`\rho`, must be greater than zero.
+The coefficients A,:math:`\rho`, and C can be written as analytical expressions
+of :math:`\epsilon` and :math:`\sigma`, in analogy to the Lennard-Jones potential
 :ref:`(Khrapak) <Khrapak>`.
 
 The latter 2 coefficients are optional.  If not specified, the global

doc/src/pair_buck6d_coul_gauss.rst

@@ -50,12 +50,14 @@ interactions following the MOF-FF force field after
 :ref:`(Schmid) <Schmid>`. The vdW term of the *buck6d* styles
 computes a dispersion damped Buckingham potential:
 
-.. image:: Eqs/pair_buck6d.jpg
-   :align: center
+.. math::
 
-where A and C are a force constant, kappa is an ionic-pair dependent
+  E = A e^{-\kappa r} - \frac{C}{r^6} \cdot \frac{1}{1 + D r^{14}} \qquad r < r_c \\
+
+
+where A and C are a force constant, :math:`\kappa` is an ionic-pair dependent
 reciprocal length parameter, D is a dispersion correction parameter,
-and the cutoff Rc truncates the interaction distance.
+and the cutoff :math:`r_c` truncates the interaction distance.
 The first term in the potential corresponds to the Buckingham
 repulsion term and the second term to the dispersion attraction with
 a damping correction analog to the Grimme correction used in DFT.
@@ -78,14 +80,16 @@ distributions which effectively dampen electrostatic interactions
 for high charges at close distances.  The electrostatic potential
 is thus evaluated as:
 
-.. image:: Eqs/pair_coul_gauss.jpg
-   :align: center
+.. math::
 
-where C is an energy-conversion constant, Qi and Qj are the
-charges on the 2 atoms, epsilon is the dielectric constant which
-can be set by the :doc:`dielectric <dielectric>` command, alpha is
-ion pair dependent damping parameter and erf() is the error-function.
-The cutoff Rc truncates the interaction distance.
+  E = \frac{C_{q_i q_j}}{\epsilon r_{ij}}\,\, \textrm{erf}\left(\alpha_{ij} r_{ij}\right)\quad\quad\quad r < r_c
+
+
+where C is an energy-conversion constant, :math:`q_i` and :math:`q_j`
+are the charges on the 2 atoms, epsilon is the dielectric constant which
+can be set by the :doc:`dielectric <dielectric>` command, alpha is ion
+pair dependent damping parameter and erf() is the error-function.  The
+cutoff Rc truncates the interaction distance.
 
 The style *buck6d/coul/gauss/dsf* computes the Coulomb interaction
 via the damped shifted force model described in :ref:`(Fennell) <Fennell>`
@@ -107,14 +111,14 @@ above, or in the data file or restart files read by the
 commands:
 
 * A (energy units)
-* rho (distance\^-1 units)
+* :math:`\rho` (distance\^-1 units)
 * C (energy-distance\^6 units)
 * D (distance\^14 units)
-* alpha (distance\^-1 units)
+* :math:`\alpha` (distance\^-1 units)
 * cutoff (distance units)
 
-The second coefficient, rho, must be greater than zero. The latter
-coefficient is optional.  If not specified, the global vdW cutoff
+The second coefficient, :math:`\rho`, must be greater than zero. The
+latter coefficient is optional.  If not specified, the global vdW cutoff
 is used.
 
 

doc/src/pair_charmm.rst

@@ -160,8 +160,21 @@ artifacts.
    the CHARMM force field energies and forces, when using one of these
    two CHARMM pair styles.
 
-.. image:: Eqs/pair_charmm.jpg
-   :align: center
+.. math::
+
+ E = & LJ(r) \qquad \qquad \qquad r < r_{\rm in} \\
+   = & S(r) * LJ(r) \qquad \qquad r_{\rm in} < r < r_{\rm out} \\
+   = & 0 \qquad \qquad \qquad \qquad r > r_{\rm out} \\
+ E = & C(r) \qquad \qquad \qquad r < r_{\rm in} \\
+   = & S(r) * C(r) \qquad \qquad r_{\rm in} < r < r_{\rm out} \\
+   = & 0 \qquad \qquad \qquad \qquad r > r_{\rm out} \\
+ LJ(r) = & 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - 
+         \left(\frac{\sigma}{r}\right)^6 \right] \\
+ C(r) = & \frac{C q_i q_j}{ \epsilon r} \\
+ S(r) = & \frac{ \left[r_{\rm out}^2 - r^2\right]^2  
+   \left[r_{\rm out}^2 + 2r^2 - 3{r_{\rm in}^2}\right]} 
+ { \left[r_{\rm out}^2 - {r_{\rm in}}^2\right]^3 }
+
 
 where S(r) is the energy switching function mentioned above for the
 *charmm* styles.  See the :ref:`(Steinbach) <Steinbach>` paper for the
@@ -209,14 +222,13 @@ above, or in the data file or restart files read by the
 :doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
 commands, or by mixing as described below:
 
-* epsilon (energy units)
-* sigma (distance units)
-* epsilon\_14 (energy units)
-* sigma\_14 (distance units)
+* :math:`\epsilon` (energy units)
+* :math:`\sigma` (distance units)
+* :math:`\epsilon_{14}` (energy units)
+* :math:`\sigma_{14}` (distance units)
 
-Note that sigma is defined in the LJ formula as the zero-crossing
-distance for the potential, not as the energy minimum at 2\^(1/6)
-sigma.
+Note that :math:`\sigma` is defined in the LJ formula as the zero-crossing
+distance for the potential, not as the energy minimum at :math:`2^{1/6} \sigma`.
 
 The latter 2 coefficients are optional.  If they are specified, they
 are used in the LJ formula between 2 atoms of these types which are

doc/src/pair_class2.rst

@@ -82,10 +82,14 @@ Description
 
 The *lj/class2* styles compute a 6/9 Lennard-Jones potential given by
 
-.. image:: Eqs/pair_class2.jpg
-   :align: center
+.. math::
 
-Rc is the cutoff.
+  E = \epsilon \left[ 2 \left(\frac{\sigma}{r}\right)^9 - 
+    3 \left(\frac{\sigma}{r}\right)^6 \right]
+  \qquad r < r_c
+
+
+:math:`r_c` is the cutoff.
 
 The *lj/class2/coul/cut* and *lj/class2/coul/long* styles add a
 Coulombic term as described for the :doc:`lj/cut <pair_lj>` pair styles.
@@ -98,8 +102,8 @@ above, or in the data file or restart files read by the
 :doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
 commands, or by mixing as described below:
 
-* epsilon (energy units)
-* sigma (distance units)
+* :math:`\epsilon` (energy units)
+* :math:`\sigma` (distance units)
 * cutoff1 (distance units)
 * cutoff2 (distance units)
 
@@ -121,11 +125,12 @@ specified in the pair\_style command.
 
 
 If the pair\_coeff command is not used to define coefficients for a
-particular I != J type pair, the mixing rule for epsilon and sigma for
-all class2 potentials is to use the *sixthpower* formulas documented
-by the :doc:`pair_modify <pair_modify>` command.  The :doc:`pair_modify mix <pair_modify>` setting is thus ignored for class2 potentials
-for epsilon and sigma.  However it is still followed for mixing the
-cutoff distance.
+particular I != J type pair, the mixing rule for :math:`\epsilon` and
+:math:`\sigma` for all class2 potentials is to use the *sixthpower*
+formulas documented by the :doc:`pair_modify <pair_modify>` command.
+The :doc:`pair_modify mix <pair_modify>` setting is thus ignored for
+class2 potentials for epsilon and sigma.  However it is still followed
+for mixing the cutoff distance.
 
 
 ----------