Monte Carlo simulations free-energy calculations

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... 

Mesoscale simulations model a material as a collection of units, called beads. Each bead might represent a substructure, molecule, monomer, micelle, micro-crystalline domain, solid particle, or an arbitrary region of a fluid. Multiple beads might be connected, typically by a harmonic potential, in order to model a polymer. A simulation is then conducted in which there is an interaction potential between beads and sometimes dynamical equations of motion. This is very hard to do with extremely large molecular dynamics calculations because they would have to be very accurate to correctly reflect the small free energy differences between microstates. There are algorithms for determining an appropriate bead size from molecular dynamics and Monte Carlo simulations. 

For reasons of space and because of their prime importance, we focus here on free energy calculations based on detailed molecular dynamics (MD) or Monte Carlo (MC) simulations. However, several other computational approaches exist to calculate free energies, including continuum dielectric models and integral equation methods [4,14]. 

MD simulations in expHcit solvents are stiU beyond the scope of the current computational power for screening of a large number of molecules. However, mining powerful quantum chemical parameters to predict log P via this approach remains a challenging task. QikProp [42] is based on a study [3] which used Monte Carlo simulations to calculate 11 parameters, including solute-solvent energies, solute dipole moment, number of solute-solvent interactions at different cutoff values, number of H-bond donors and acceptors (HBDN and HBAQ and some of their variations. These parameters made it possible to estimate a number of free energies of solvation of chemicals in hexadecane, octanol, water as well as octanol-water distribution coefficients. The equation calculated for the octanol-water coefficient is ... 

When the two phases separate the distribution of the solvent molecules is inhomogeneous at the interface this gives rise to an additional contribution to the free energy, which Henderson and Schmickler treated in the square gradient approximation [36]. Using simple trial functions, they calculated the density profiles at the interface for a number of system parameters. The results show the same qualitative behavior as those obtained by Monte Carlo simulations for the lattice gas the lower the interfacial tension, the wider is the interfacial region in which the two solvents mix (see Table 3). 

Quirke, N. Jacucci, G., Energy difference functions in Monte Carlo simulations application to the calculation of free energy of liquid nitrogen. II. The calculation of fluctuation in Monte Carlo averages, Mol. Phys. 1982, 45, 823-838... 

Marchi, M. Sprik, M. Klein, M. L., Calculation of the free energy of electron solvation in liquid ammonia using a path integral quantum Monte Carlo simulation, J. Phys. Chem. 1988, 92, 3625-3629... 

In both solvents, the variational transition state (associated with the free energy maximum) corresponds, within the numerical errors, to the dividing surface located at rc = 0. It has to be underlined that this fact is not a previous hypothesis (which would rather correspond to the Conventional Transition State Theory), but it arises, in this particular case, from the Umbrella Sampling calculations. However, there is no information about which is the location of the actual transition state structure in solution. Anyway, the definition of this saddle point has no relevance at all, because the Monte Carlo simulation provides directly the free energy barrier, the determination of the transition state structure requiring additional work and being unnecessary and unuseful. 

In chapter 3, Profs. A. Gonzalez-Lafont, Lluch and Bertran present an overview of Monte Carlo simulations for chemical reactions in solution. First of all, the authors briefly review the main aspects of the Monte Carlo methodology when it is applied to the treatment of liquid state and solution. Special attention is paid to the calculations of the free energy differences and potential energy through pair potentials and many-body corrections. The applications of this methodology to different chemical reactions in solution are... 

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... 

Now a and the pressure (computed as the derivative of the free energy per unit area) will be calculated, using the procedure outlined in this article. For the Hamaker constant and the bending modulus, typical values from literature, namely, 1.0 x 10"20 and 1.0 x 10 l l J, respectively, will be used. For th and tc we employed the values obtained from X-rav data,1 th = 7.6 A and tc = 37.8 A for EPC and th = 7.6 A and tc = 36.4 A for DMPC, respectively. Because the hydrocarbon thicknesses tc of EPC and DMPC produced almost no difference (see eq 27), in the following only the results for the EPC are presented (tc = 37.8 A). For the degree of asymmetry a the value of 1.4, which is in agreement with the Monte Carlo simulations,17 was selected. 

The atomic radii may be further refined to improve the agreement between experimental and theoretical solvation free energies. Work on this direction has been done by Luque and Orozco (see [66] and references cited therein) while Barone et al. [67] defined a set of rules to estimate atomic radii. Further discussion on this point can be found in the review by Tomasi and co-workers [15], It must be noted that the parameterization of atomic radii on the basis of a good experiment-theory agreement of solvation energies is problematic because of the difficulty to separate electrostatic and non-electrostatic terms. The comparison of continuum calculations with statistical simulations provides another way to check the validity of cavity definition. A comparison between continuum and classical Monte Carlo simulations was reported by Costa-Cabral et al. [68] in the early 1980s and more recently, molecular dynamics simulations using combined quantum mechanics and molecular mechanics (QM/MM) force-fields have been carried out to analyze the case of water molecule in liquid water [69],... 

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