Monte Carlo simulation force fields

M. Jalaie, K. B. Lipkowitz, Published force field parameters for molecular mechanics, molecular dynamics, and Monte Carlo simulations, in Reviews in Computational Chemistry, Vol. 14, K.B. Lipkowitz, D. B. Boyd (Eds.), Wiley-VCH, New York, 2000, pp. 441-486. 

An important though demanding book. Topics include statistical mechanics, Monte Carlo simulations, equilibrium and n on -equilibrium m olecular dyn am ics, an alysis of calculation al results, and applications of methods to problems in liquid dynamics. The authors also discuss and compare many algorithms used in force field simulations. Includes a microfiche containing dozens of Fortran-77 subroutines relevant to molecular dynamics and liquid simulations. 

Molecular Dynamics and Monte Carlo Simulations. At the heart of the method of molecular dynamics is a simulation model consisting of potential energy functions, or force fields. Molecular dynamics calculations represent a deterministic method, ie, one based on the assumption that atoms move according to laws of Newtonian mechanics. Molecular dynamics simulations can be performed for short time-periods, eg, 50—100 picoseconds, to examine localized very high frequency motions, such as bond length distortions, or, over much longer periods of time, eg, 500—2000 ps, in order to derive equiUbrium properties. It is worthwhile to summarize what properties researchers can expect to evaluate by performing molecular simulations ... 

Jorgensen et al. has developed a series of united atom intermolecular potential functions based on multiple Monte Carlo simulations of small molecules [10-23]. Careful optimisation of these functions has been possible by fitting to the thermodynamic properties of the materials studied. Combining these OPLS functions (Optimised Potentials for Liquid Simulation) with the AMBER intramolecular force field provides a powerful united-atom force field [24] which has been used in bulk simulations of liquid crystals [25-27],... 

OPLS force field Monte Carlo simulation NB = Non-bonded cutoff distance in A... 

The OPLS parameters (charges and Lennard-Jones terms) were obtained primarily via Monte Carlo simulations with particular emphasis on reproducing the experimental densities and heats of vaporization of liquids. Those simulations were performed iteratively as part of the parametrization, so better agreement with experiment is obtained than in previous studies where the simulations were usually carried out after the parametrization. Once the OPLS parametrization was completed, further simulations were also performed in order to test the new set of parameters in the calculation of other thermodynamic and structural properties of the system, besides its density and its heat of vaporization. Parameters have now been generated, among others, for water, alkanes, alkenes, alcohols, amides, alkyl chlorides, amines, carboxylic esters and acids, various sulfur and nitrogen compounds, and nitriles. A protein force field has been established as well. 

The combined QM/MM model can be used along with Statistical Perturbation Theory to carry out a Monte Carlo simulation of a chemical reaction in solution, with the advantage of allowing solute electronic structure relaxation in solution. Particularly, the combined AM1/TIP3P force field has recently been applied to simulate several chemical processes in solution. We will refer here briefly to the Claisen rearrangement and to the Menshutkin reaction. 

Mehran Jalaie and Kenny B. Lipkowitz, Appendix Published Force Field Parameters for Molecular Mechanics, Molecular Dynamics, and Monte Carlo Simulations. 

Semiclassical techniques like the instanton approach [211] can be applied to tunneling splittings. Finally, one can exploit the close correspondence between the classical and the quantum treatment of a harmonic oscillator and treat the nuclear dynamics classically. From the classical trajectories, correlation functions can be extracted and transformed into spectra. The particular charm of this method rests in the option to carry out the dynamics on the fly, using Born Oppenheimer or fictitious Car Parrinello dynamics [212]. Furthermore, multiple minima on the hypersurface can be treated together as they are accessed by thermal excitation. This makes these methods particularly useful for liquid state or other thermally excited system simulations. Nevertheless, molecular dynamics and Monte Carlo simulations can also provide insights into cold gas-phase cluster formation [213], if a reliable force field is available [189]. 

The last term in the formula (1-196) describes electrostatic and Van der Waals interactions between atoms. In the Amber force field the Van der Waals interactions are approximated by the Lennard-Jones potential with appropriate Atj and force field parameters parametrized for monoatomic systems, i.e. i = j. Mixing rules are applied to obtain parameters for pairs of different atom types. Cornell et al.300 determined the parameters of various Lenard-Jones potentials by extensive Monte Carlo simulations for a number of simple liquids containing all necessary atom types in order to reproduce densities and enthalpies of vaporization of these liquids. Finally, the energy of electrostatic interactions between non-bonded atoms is calculated using a simple classical Coulomb potential with the partial atomic charges qt and q, obtained, e.g. by fitting them to reproduce the electrostatic potential around the molecule. 

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],... 

Nuclear and Electronic Sampling Monte Carlo Simulations in the Gibbs Ensemble Application to Polarizable Force Fields for Water. 

The explicit modeling approach surrounds a solute molecule with solvent molecules and then examines each molecule in that solvated environment. Quantum chemical methods, both semiempiricaP and ab initio" have been used to do this however, molecular dynamics and Monte Carlo simulations using force fields are used most often.Calculations on ensembles of molecules are more complex than those on individual molecules. Dykstra et al. discuss calculations on ensembles of molecules in a chapter in this book series. Because of the many conformations accessible to both solute and solvent molecules, in addition to the great number of possible solute molecule-solvent molecule orientations, such direct QM calculations are very computer intensive. However, the information resulting from this type of calculation is comprehensive because it provides molecular structures of the solute and solvent, and takes into account the effect of the solvent on the solute. This is the method of choice for assessing specific bonding information. 

In principle, the diffusion steps (a) and (e) could be studied through molecular dynamics simulations as long as rehable forces fields are available to describe the zeolite structure and its interaction with the substrates. Also, if the adsorption takes place without charge transfer between the reagents/products and the zeolite, steps (b) and (d) could also be investigated either by molecular dynamics or Monte Carlo simulations. Step (c) however can only be followed by quantum mechanical techniques because the available force fields cannot yet describe the breaking and formation of chemical bonds. 

Jorgensen has parameterized by fitting properties of bulk liquids to Monte Carlo simulations to give the AMBER/OPLS force field (26,157, 158). Conceptually, one is attracted ly the use of liquids and their observable properties as constraints during the derivation of a force field that is destined to study the properties of solvated molecules. 

---