Force Fields for Small Molecules

MM2 was, according the web site of the authors, released as MM2 87). The various MM2 flavors are superseded by MM3, with significant improvements in the functional form [10]. It was also extended to handle amides, polypeptides, and proteins [11]. The last release of this series was MM3(%). Further improvements followed by starting the MM4 series, which focuses on hydrocarbons [12], on the description of hyperconjugative effects on carbon-carbon bond lengths [13], and on conjugated hydrocarbons [14] with special emphasis on vibrational frequencies [15]. For applications of MM2 and MM3 in inorganic systems, readers are referred to the literature [16-19]. 

Variations of these releases are implemented in almost every commercial or academic software package, which cannot be fisted in this context. A comprehensive comparison of several force fields focusing the calculation of conformational energies of organic molecules has been published by Pettersson and liljefors [1]. 

The Universal Force Field, UFF, is one of the so-called whole periodic table force fields. It was developed by A. Rappe, W Goddard III, and others. It is a set of simple functional forms and parameters used to model the structure, movement, and interaction of molecules containing any combination of elements in the periodic table. The parameters are defined empirically or by combining atomic parameters based on certain rules. Force constants and geometry parameters depend on hybridization considerations rather than individual values for every combination of atoms in a bond, angle, or dihedral. The equilibrium bond lengths were derived from a combination of atomic radii. The parameters [22, 23], including metal ions [24], were published in several papers. 

The authors emphasize on their web pages that UFF is not designed to be used in conjunction with partial atomic charges, as it is the default option in several software packages. A second point is that UFF is often used to model biological 

The modeling of inorganic compounds in general is gaining more and more interest [25-28]. The authors of MOMEC addressed this in a monograph describing how molecular modeling techniques can be applied to metal complexes and how the results can be interpreted [29]. The current force field parameter set is available on the author s web site. 

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Historical Overview of the CHARMM Drude Polarizable Force Field for Small Molecules and Biological Polymers... 

The SIBFA (sum of interactions between fragments ab initio computed) force field for small molecules and flexible proteins, developed by Gresh, Piquemal et al. is one of the most sophisticated polarizable force fields because it incorporates polarization, electrostatic penetration, " and charge transfer effects. ... 

Our conclusion is that the MM4 force field for alkanes can indeed be improved somewhat, but the improvements would be small, and there appears to be no strong reason for making such improvements at this time. Force fields for organic molecules beyond alkanes are another matter, and will be discussed briefly in the following pages. 

Molecules with Central Force Fields. For these molecules equation (25) is directly applicable it is necessary to assume a functional form for (/ ), then to perform the required integration. From general observations of the properties of matter it is obvious that u is large positive when r is small. It is also obvious that = 0 when r = oo. Many equations to describe (r) between r = oo and r = small have been proposed and plots of some of them are shown in Figure 11. The hard sphere and soft sphere representations of (r) (curves a and b) allow for repulsive forces only. The other representations illustrated in Figure 11 allow additionally for... 

In the past, force fields were determined from experiment. Now they may be determined either by experiment, or by quantum mechanical calculations directly, or by quantum mechanical calculations on small molecules, which are used to develop force fields for large molecules. The latter method is exceedingly powerful, now that reasonably accurate calculations on molecules of moderate size can be carried out by ab initio methods. The most reliable force fields result when one can develop the force field from both ab initio methods and from experiment, and obtain results that are acceptably accurate by both methods. 

A number of more general force fields for the study of small molecules are available that can be extended to biological molecules. These force fields have been designed with the goal of being able to treat a wide variety of molecules, based on the ability to transfer parameters between chemical systems and the use of additional terms (e.g., cross terms) in their potential energy functions. Typically, these force fields have been optimized to... 

It should also be noted that a force field for a wide variety of small molecules, CHARMm (note the small m, indicating the commercial version of the program and parameters), is available [39] and has been applied to protein simulations with limited success. Efforts are currently under way to extend the CHARMm small molecule force field to make the nonbonded parameters consistent with those of the CHARMM force fields, thereby allowing for a variety of small molecules to be included in computational smdies of biological systems. 

The rapid rise in computer speed over recent years has led to atom-based simulations of liquid crystals becoming an important new area of research. Molecular mechanics and Monte Carlo studies of isolated liquid crystal molecules are now routine. However, care must be taken to model properly the influence of a nematic mean field if information about molecular structure in a mesophase is required. The current state-of-the-art consists of studies of (in the order of) 100 molecules in the bulk, in contact with a surface, or in a bilayer in contact with a solvent. Current simulation times can extend to around 10 ns and are sufficient to observe the growth of mesophases from an isotropic liquid. The results from a number of studies look very promising, and a wealth of structural and dynamic data now exists for bulk phases, monolayers and bilayers. Continued development of force fields for liquid crystals will be particularly important in the next few years, and particular emphasis must be placed on the development of all-atom force fields that are able to reproduce liquid phase densities for small molecules. Without these it will be difficult to obtain accurate phase transition temperatures. It will also be necessary to extend atomistic models to several thousand molecules to remove major system size effects which are present in all current work. This will be greatly facilitated by modern parallel simulation methods that allow molecular dynamics simulations to be carried out in parallel on multi-processor systems [115]. 

Foloppe N, MacKerell AD (2000) All-atom empirical force field for nucleic acids I. Parameter optimization based on small molecule and condensed phase macromolecular target data. J Comput Chem 21 (2) 86-104... 

A potentially much more adaptable technique is force-field vibrational modeling. In this method, the effective force constants related to distortions of a molecule (such as bond stretching) are used to estimate unknown vibrahonal frequencies. The great advantage of this approach is that it can be applied to any material, provided a suitable set of force constants is known. For small molecules and complexes, approximate force constants can often be determined using known (if incomplete) vibrational specha. These empirical force-field models, in effect, represent a more sophisticated way of exhapolating known frequencies than the rule-based method. A simple type of empirical molecular force field, the modified Urey-Bradley force field (MUBFF), is introduced below. 

The molecular mechanics method is extremely parameter dependent. A force field equation that has been empirically parameterized for calculating peptides must be used for peptides it cannot be applied to nucleic acids without being re-parameterized for that particular class of molecules. Thankfully, most small organic molecules, with molecular weights less than 800, share similar properties. Therefore, a force field that has been parameterized for one class of drug molecules can usually be transferred to another class of drug molecules. In medicinal chemistry and quantum pharmacology, a number of force fields currently enjoy widespread use. The MM2/MM3/MMX force fields are currently widely used for small molecules, while AMBER and CHARMM are used for macromolecules such as peptides and nucleic acids. 

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