FEP/MC simulations

To finalize the development of the aqueous CO2 force field parameters, the C02 model was used in free energy perturbation Monte Carlo (FEP/MC) simulations to determine the solubility of C02 in water. The solubility of C02 in water is calculated as a function of temperature in the development process to maintain transferability of the C02 model to different simulation techniques and to quantify the robustness of the technique used in the solubility calculations. It is also noted that the calculated solubility is based upon the change in the Gibbs energy of the system and that parameter development must account for the entropy/enthalpy balance that contributes to the overall structure of the solute and solvent over the temperature range being modeled [17]. 

The zwitterion/neutral relative free energy was theoretically estimated for tyramine (25) in aqueous solution, modeling pH = 7. The experimentally found ratio is 3.7 at T = 25 "C. Using the PCM/MP2/6-31G and the FEP/MC solvation free energy differences, the zwitterionic form was strongly under- and overestimated, respectively [84]. FEP/MC simulations in the same paper pointed out... 

Enol imine-enaminone and phenol—quinone tautomerism in (arylazo) naphthols and in analogous Schiff bases were studied by Fabian et al. [92, 93]. In all these molecules there is a favorable N- -H- -O intramolecular hydrogen bond. Depending on the X-H sigma bond (X = N, O), there are two possible tautomers in solution. The solvent effect was calculated on the equilibrium [92], and a combined effect of the solvent and the benzene substituent was studied in [93]. While the FEP/MC simulations provided consistent organic solvent effects in accord with the experimental results [92], the wide spectrum of the solvent-effect calculation methods could predict rather diverse results for several groups of systems in [93]. 

As a second example, we have determined the influence of solvation on the steric retardation of SN2 reactions of chloride with ethyl and neopentyl chlorides in water, which has recently been studied by Vayner and coworkers [91]. In their study solvent effects were examined by means of QM-MM Monte Carlo simulations as well as with the CPCM model. Solvation causes a large increase in the activation energies of these reactions, but has a very small differential effect on the ethyl and neopentyl substrates. Nevertheless, a quantitative difference was found between the stability of the transition states determined using discrete and continuum treatments of solvation, since the activation free energies for ethyl chloride and neopentyl chloride amount to 23.9 and 30.4kcalmoF1 according to MC-FEP simulations, but to 38.4 and 47.6 kcal moF1 from CPCM computations. 

MC-FEP simulations were performed in 21 windows where charges were gradually annealed using the double-wide sampling technique. For each window the system was equilibrated over at least 10 million configurations, and the average was done for 10 million configurations. In all cases the hysteresis and the standard deviations were small, which lends confidence to the protocol of the simulation. 

Hori K et al (2011) A free-energy perturbation method based on Monte Carlo simulations using quantum mechanical calculations (QM/MC/FEP method) application to highly solvent-dependent reactions. J Comput Chem 32 778-786... 

Choose the master equation method (FEP, TI, or slow growth), the number of windows to be calculated, the amount of equilibration to be performed at each window, and the amount of data collection to be performed at each window. Typically, if high precision results are desired for a simulation, the total data collection time over the simulation will be several hundred picoseconds or more. Parameters associated with standard MD or MC will also need to be set (step size, effective temperature, etc.). 

Tautomerizations are also subject to the dictates of equation (16), with the more polar form increasingly favored in more polar media. This has been another successful target for FEP calculations, with applications ranging from 2-hydroxypyridine and histamine to nucleotide bases. In addition, the influence of solvation on simple carbenium ion rearrangements has been investigated by MC-FEP simulations. For the conversion of the classical to the non-classical 2-norbomyl cation in water and that of a tertiary cyclopentylcarbinyl cation to a secondary cyclohexyl cation in methylene chloride and THF, solvation differences of only ca, 1 kcal mol were obtained. Such ions are all relatively charge-delocalized and are consequently immune to significant differential solvation. 

Figure 1 Free energy profiles for the benzene dimer in water and chloroform at 25 °C and I atm from MC-FEP simulations...

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