Taylor Series Reaction Rates
========================

Taylor Series-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) + \sum_{i=0}^{m} C_i T^i

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})`.
- :math:`C_i` are the Taylor series coefficients, and :math:`m` is the order of the Taylor series.

The first two terms are described in Finlayson-Pitts and Pitts (2000) :cite:`Finlayson-Pitts2000`.
The final term before the Taylor series is included to accommodate CMAQ EBI solver type 7 rate constants.
The final term is the Taylor series expansion, which allows for more complex temperature dependencies
beyond the Arrhenius form.

Input data for Taylor Series equations has the following format:

.. tab-set::

    .. tab-item:: YAML

        .. code-block:: yaml
           :force:

            type: TAYLOR_SERIES
            A: 123.45
            Ea: 123.45
            B: 1.3
            D: 300.0
            E: 6.0e-06
            taylor coefficients:
              - 1.0
              - 2.0
              - 3.0
            reactants:
              - species name: spec1
              - species name: spec2
                coefficient: 2
              ...
            products:
              - species name: spec3
              - species name: spec4
                coefficient: 0.65
              ...



    .. tab-item:: JSON

        .. code-block:: json
           :force:

            {
                "type" : "TAYLOR_SERIES",
                "A" : 123.45,
                "Ea" : 123.45,
                "B"  : 1.3,
                "D"  : 300.0,
                "E"  : 0.6E-5,
                "taylor coefficients" : [
                    1.0,
                    2.0,
                    3.0
                ],
                "reactants" : [
                  { "species name" : "spec1" },
                  { "species name" : "spec2", "coefficient" : 2 },
                  ...
                ],
                "products" : [
                  { "species name" : "spec3" },
                  { "species name" : "spec4", "coefficient" : 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. When ``taylor coefficients`` are not included,
the order of the Taylor series is assumed to be 0.