Computing ionization free energies of indicator dyes in micelles with fast growth alchemical transformation
Abstract
The problem of calculating free energy change in a process using molecular dynamic simulation has wide practical application, but is non-trivial. The developed methods are classified into equilibrium and non-equilibrium ones. In general, equilibrium methods have lower systematic error but require longer simulation time. This contributes to the interest in non-equilibrium methods, in particular the fast growth method. Here, this method is applied to the process of ionization of acid-base indicators bound by micelles of ionic surfactants. The alchemical transformation approach was utilized, where the interactions of the indicator's acidic proton with the rest of the system are coupled to coupling parameter λ ranged from 0 in the acidic form to 1 in the basic form. The values of deprotonation free energy of the typical indicator dye 4-n-dodecyl-2,6-dinitrophenol in water and micellar solutions of two common cationic and anionic surfactants were estimated and compared with the results of the equilibrium method. A simulation procedure allowing minimize the effect of non-equivalent sampling between the two methods was employed. It is noted that for the studied systems the method can provide the discrepancy within 2% while requiring significantly shorter total simulation time. Specifically, the duration of simulating non-physical intermediate states drastically reduces. The optimal duration of the fast growth runs is 20 ps in this case, while both shortening and prolonging the runs increase the error. The optimal number of fast growth runs can be found as one per each 100 ps of simulation of acidic or basic form. Reducing the number of runs also increases the discrepancy with the equilibrium method. The obtained results show the promise of the fast growth method for calculating shifts of the dissociation constants of acid-base indicators in micellar solutions with the perspective of further estimating the surface electrostatic potential of micelles.
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References
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