Arrhenius Reaction Rates
========================

Arrhenius-like reaction rate constant equations are calculated as follows:

.. math::

   A e^{-\frac{E_a}{k_bT}} \left(\frac{T}{D}\right)^B (1.0 + E \cdot P)

where:

- :math:`A` is the pre-exponential factor (:math:`(\mbox{molecule}\,\mathrm{cm}^{-3})^{-(n-1)}\,\mathrm{s}^{-1}`),
- :math:`n` is the number of reactants,
- :math:`E_a` is the activation energy :math:`(\mathrm{J})`,
- :math:`k_b` is the Boltzmann constant :math:`(\mathrm{J}/\mathrm{K})`,
- :math:`D` :math:`(\mathrm{K})`, :math:`B` (unitless), and :math:`E` (:math:`\mathrm{Pa}^{-1}`) are reaction parameters,
- :math:`T` is the temperature :math:`(\mathrm{K})`, and :math:`P` is the pressure :math:`(\mathrm{Pa})`.

The first two terms are described in Finlayson-Pitts and Pitts (2000) :cite:`Finlayson-Pitts2000`.
The final term is included to accommodate CMAQ EBI solver type 7 rate constants.

Input data for Arrhenius equations has the following format:

.. tab-set::

    .. tab-item:: YAML

        .. code-block:: yaml
           :force:

            type: ARRHENIUS
            A: 123.45
            Ea: 123.45
            B: 1.3
            D: 300.0
            E: 6.0e-06
            time unit: MIN
            reactants:
              spec1:
              spec2:
                qty: 2
              ...
            products:
              spec3:
              spec4:
                yield: 0.65
              ...



    .. tab-item:: JSON

        .. code-block:: json
           :force:

            {
                "type" : "ARRHENIUS",
                "A" : 123.45,
                "Ea" : 123.45,
                "B"  : 1.3,
                "D"  : 300.0,
                "E"  : 0.6E-5,
                "time unit" : "MIN",
                "reactants" : {
                  "spec1" : {},
                  "spec2" : { "qty" : 2 },
                  ...
                },
                "products" : {
                  "spec3" : {},
                  "spec4" : { "yield" : 0.65 },
                  ...
                }
            }

The key-value pairs ``reactants`` and ``products`` are required. Reactants without a ``qty`` value
are assumed to appear once in the reaction equation. Products without a specified ``yield`` are
assumed to have a yield of 1.0.

Optionally, a parameter ``C`` may be included, and is taken to equal :math:`\frac{-E_a}{k_b}`.
Note that either ``Ea`` or ``C`` may be included, but not both. When neither ``Ea`` nor ``C`` are
included, they are assumed to be 0.0. When ``A`` is not included, it is assumed to be 1.0. When
``D`` is not included, it is assumed to be 300.0 K. When ``B`` is not included, it is assumed to be
0.0. When ``E`` is not included, it is assumed to be 0.0. The unit for time is assumed to be s, but
inclusion of the optional key-value pair ``time unit = MIN`` can be used to indicate a rate with
minutes as the time unit.