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I want to estimate rates of substitution reaction of esters with nucleophiles in water. How can I estimate them with a computational chemistry software (preferably GAMESS(US))? Or is it practically impossible? I know that this is possible in gas phase, but I don't know how to do it in solution.

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Finding solvent effect in computational chemistry is still a crucial part and subject to deep research effort. Now there are two types of models that are being used in computational chemistry.
One is explicit solvation model: Here you will use explicit solvent molecule with your reactant or products and then using first principles you will find the equilibrium configuration but the problem is, it is very expensive and the configuration space is so much high that it is practically impossible. For that you have to use molecular dynamics or monte carlo techniques. In our group we use 1000 to 5000 explicit water molecule but we can't do it for large reaction.
Another method is implicit solvation model: Here electrostatic potential is applied to account the solvent effect but this procedure is so expensive that now that potential is replaced by the solvent induced reaction field energy.
In our group we are using a hybrid approach that involves communication of several software at different level of theory. In my quantum chemistry class i used spartan and qchem and they have some implicit solvation but i didn't use GAMESS.
From GAMESS manual i found that they have solvation module. They are using QM/MM approach. That's actually a very good approach. Please see page 9 of this file: http://www.sdsc.edu/~kimb/gamesstut.pdf
In this following file at page 3 & 4 you will also find the list of keywords that are needed to start a solvation model run
http://www.msg.ameslab.gov/gamess/GAMESS_Manual/input.pdf

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