Monte Carlo-free energy perturbation

C02(aq) Parameterization Through Free Energy Perturbation/Monte Carlo Simulations for Use in C02 Sequestration... 

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]. 

Free Energy Perturbation Monte Carlo Simulations... 

What has been developed within the last 20 years is the computation of thermodynamic properties including free energy and entropy [12, 13, 14]. But the ground work for free energy perturbation was done by Valleau and Torrie in 1977 [15], for particle insertion by Widom in 1963 and 1982 [16, 17] and for umbrella sampling by Torrie and Valleau in 1974 and 1977 [18, 19]. These methods were primarily developed for use with Monte Carlo simulations continuous thermodynamic integration in MD was first described in 1986 [20]. 

Calculations of relative partition coefficients have been reported using the free energy perturbation method with the molecular dynamics and Monte Carlo simulation methods. For example, Essex, Reynolds and Richards calculated the difference in partition coefficients of methanol and ethanol partitioned between water and carbon tetrachloride with molecular dynamics sampling [Essex et al. 1989]. The results agreed remarkably well with experiment... 

The differences in the rate constant for the water reaction and the catalyzed reactions reside in the mole fraction of substrate present as near attack conformers (NACs).171 These results and knowledge of the importance of transition-state stabilization in other cases support a proposal that enzymes utilize both NAC and transition-state stabilization in the mix required for the most efficient catalysis. Using a combined QM/MM Monte Carlo/free-energy perturbation (MC/FEP) method, 82%, 57%, and 1% of chorismate conformers were found to be NAC structures (NACs) in water, methanol, and the gas phase, respectively.172 The fact that the reaction occurred faster in water than in methanol was attributed to greater stabilization of the TS in water by specific interactions with first-shell solvent molecules. The Claisen rearrangements of chorismate in water and at the active site of E. coli chorismate mutase have been compared.173 It follows that the efficiency of formation of NAC (7.8 kcal/mol) at the active site provides approximately 90% of the kinetic advantage of the enzymatic reaction as compared with the water reaction. 

One weakness of this treatment, however, is that it neglects entropic contributions. Entropic contributions were considered in the free energy profiles (FEP) calculated earlier using umbrella sampling [58] and Monte Carlo Free energy Perturbation [59], both using a QM/MM scheme and the AMI Hamiltonian for the QM part. Our group used the same SIESTA DFT-based QM/MM method described above... 

To evaluate solvent effeets, statistieal meehanical Monte Carlo simulations have been carried out. An important quantity to be computed is the potential of mean force, or free energy profile, as a funetion of the reaction coordinate, X, for a chemical reaction in solution using free energy perturbation method. (44) A straightforward approaeh is to determine free energy differences for incremental changes of certain geometrieal variables that characteristically reflect the... 

A review cataloging intramolecular Diels-Alder reactions as key steps in the total synthesis of natural products has been published.78 A key step in the total synthesis (g) of (+)-dihydrocompactin (66) is the intramolecular ionic Diels-Alder reaction of the trienone (63) to yield the (+)-compactin core compound (65) via the intermediate cyclic vinyloxocarbenium ion (64) (Scheme 17).79 The intramolecular Diels-Alder reaction of the Asp-Thr tethered compound (67) produced the cycloadduct (68) with high regio- and stereo-selectivity (Scheme 18).80 Mixed quantum and molec- (g) ular mechanics (QM/MM) combined with Monte Carlo simulations and free-energy perturbation (FEP) calculations have been used to show that macrophomate synthase... 

Free energy perturbation calculations use Monte Carlo or molecular-dynamics approaches to calculate relative free energies (e.g., of solvation or host-guest binding) on the basis of thermodynamic cycles involving the binding processes of two related systems and the artificial mutation of one system into the other. 

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