A new modified-rate approach for gas-grain chemical simulations
  Understanding grain-surface processes is crucial to interpreting the chemistry of the ISM. However, accurate surface chemistry models are computationally expensive and are difficult to integrate with gas-phase simulations. A new modified-rate method for solving grain-surface chemical systems is presented. Its purpose is accurately to model highly complex systems that can otherwise only be treated using the sometimes inadequate rate-equation approach. In contrast to previous rate-modification techniques, the functional form of the surface production rates was modified, and not simply the rate coefficient. This form is appropriate to the extreme "small-grain" limit, and can be verified using an analytical master-equation approach. Various further modifications were made to this basic form, to account for competition between processes, to improve estimates of surface occupation probabilities, and to allow a switch-over to the normal rate equations where these are applicable. The new method was tested against systems solved previously using exact techniques. Even the simplest method is quite accurate, and a great improvement over rate equations. Further modifications allow the master-equation results to be reproduced exactly for the methanol-producing system, within computational accuracy. Small discrepancies arise when non-zero activation energies are assumed for the methanol system, which result from complex reaction-competition processes that cannot be resolved easily without using exact methods. Inaccuracies in computed abundances are never greater than a few tens of percent, and typically of the order of one percent, in the most complex systems tested. Implementation of the method in simple networks, including hydrogen-only systems, is trivial, whilst the results are highly accurate. 
R. T. Garrod