# School of Chemistry

## Functionality

MESMER solves the chemical master equation using an eigenvector/eigenvalue approach and phenomenological rate coefficients are efficiently obtained using a Bartis Widom analysis. Micro-canonical rate coefficients can be calculated using either RRKM theory or through taking an inverse Laplace transform of canonical, high pressure limited, rate coefficients. In particular the latter offers a pragmatic way of treating barrierless reactions. Energy transfer processes are considered using an exponential down model. In addition MESMER incorporates a large amount of additional functionality including:

Hindered Rotors: MESMER can calculate energy levels for 1 dimensional hindered rotations described by either an analytical potential or by a number of discrete potential energy points. New for version 3.0, Hessian matrices can be read by MESMER and used to project out internal rotation contributions from the vibrational normal modes according to the method used by Sharma Raman and Green. Example file

Spin forbidden RRKM: MESMER can treat non-adiabatic processes using spin-forbidden RRKM theory with crossing coefficients from Landau Zener theory, and optional tunnelling corrections from WKB theory. Example File

Quantum mechanical tunnelling: MESMER can calculate transmission coefficients assuming either an asymmetric Eckhart barrier, or by using a semi-classical WKB method for a barrier potential described by discrete data points. Example file

Marquardt fitting: A Levenburg Marquardt algorithm is built into MESMER in enable fitting of MESMER input parameters to match experimental yields, rates or eigenvalues. Example file.

Prior Distribution: An initial energy distribution can be introduced assuming that a given molecule is formed activated from a previous reaction. Example file.

Chebyshev polynomial representation: Calculated MESMER rate coefficients as a function of P and T can now be represented using Chebyshev polynomials according to the methodology given here. This is designed to provide input for modelling software such as Chemkin or Cantera. Example File. An example excel worksheet for determining rate coefficients from a given set of Chebyshev Coefficients can be downloaded here.

Pseudo-isomerisation reaction: A modelled species can now undergo an association reaction with some species whose concentration is assumed to be in large excess, in such a way that detailed balance is satisfied. Example file

And much more ….

Further details can be found in the user manual or in our recent publication:

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