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added clarification about 3b conc for troe
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pjsingal committed Oct 9, 2024
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Expand Up @@ -278,7 +278,7 @@ $$
k_{\text{LMR-R}}(T,P,\boldsymbol{X}) = \sum_{n} k_{n}(T,P_{n,\text{LMR}}^{\text{ eff}})\tilde{X}_{n,\text{LMR}} + k_{M}(T,P_{M,\text{LMR}}^{\text{ eff}}) \left(1-\sum_{n}\tilde{X}_{n,\text{LMR}}\right)
$$

where the sum over $n$ is only for the colliders for which unique $k_n(T,P)$ are available.
where the sum over $n$ is only for the colliders for which unique $k_n(T,P)$ are available. Each $k_n(T,P)$ can be specified in the user's choice of Troe, Plog, or Chebyshev formats. For the Troe format, the effective third-body concentration is calculated by dividing $P_{i}^{\text{ eff}}$ by the temperature and ideal gas constant. For the other formats, $P_{i}^{\text{ eff}}$ is implemented directly as the 'pressure' of interest.

While not required if unique $k_i(T,P)$ data are available, this approximation, like LMR-R, takes advantage of the fact that rate constants for colliders with even very different third-body efficiencies often are much more similar at the same reduced pressure ($R$) than at the same pressure ($P$) and, in fact, are exactly the same if they differ in only their collision frequency (but have the same energy- and angular-momentum-transfer kernel). This equation forms the basis of the computational implementation of LMR-R in Cantera via the Linear Burke Rate reaction class, as it enables the most accurate representation of $k_{\text{LMR-R}}(T,P,\boldsymbol{X})$ possible given limitations in the completeness of the dataset at any given moment. Further description of the LMR-R theory and computational method is available in {cite:t}`singal2024`.

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