typeset mixing rules with embedded math

coefficients for a specific I != J pairing, in which case no mixing is

performed.

mix *geometric*

- mix *geometric*

.. parsed-literal::

  .. math::

   epsilon_ij = sqrt(epsilon_i \* epsilon_j)

   sigma_ij = sqrt(sigma_i \* sigma_j)

     \epsilon_{ij} = & \sqrt{\epsilon_i  \epsilon_j} \\

     \sigma_{ij}   = & \sqrt{\sigma_i  \sigma_j}

mix *arithmetic*

- mix *arithmetic*

.. parsed-literal::

  .. math::

   epsilon_ij = sqrt(epsilon_i \* epsilon_j)

   sigma_ij = (sigma_i + sigma_j) / 2

    \epsilon_{ij} = & \sqrt{\epsilon_i  \epsilon_j} \\

    \sigma_{ij}   = & \frac{1}{2} (\sigma_i + \sigma_j)

mix *sixthpower*

- mix *sixthpower*

.. parsed-literal::

  .. math::

   epsilon_ij = (2 \* sqrt(epsilon_i\*epsilon_j) \* sigma_i\^3 \* sigma_j\^3) /

                (sigma_i\^6 + sigma_j\^6)

   sigma_ij = ((sigma_i\*\*6 + sigma_j\*\*6) / 2) \^ (1/6)

    \epsilon_{ij} = & \frac{2 \sqrt{\epsilon_i \epsilon_j} \sigma_i^3 \sigma_j^3}{\sigma_i^6 + \sigma_j^6} \\

    \sigma_{ij} =   & \left(\frac{1}{2} (\sigma_i^6 + \sigma_j^6) \right)^{\frac{1}{6}}

The *shift* keyword determines whether a Lennard-Jones potential is

shifted at its cutoff to 0.0.  If so, this adds an energy term to each