Force field transferability

Transferability of the functional form and parameters is an important feature of a force field. Transferability means that tire same set of parameters can be used to model a series of related molecules, rather than having to define a new set of parameters for each individual molecule. For example, we would expect to be able to use the same set of parameters for all u-alkanes. Transferability is clearly important if we want to use the force field to make predictions. Only for some small systems, where particularly accurate work is required, may it be desirable to develop a model specific to that molecule. 

Harmonic frequencies of PHJ were obtained by scaled SCF MO calculations [19] and from the ab initio calculated geometry combines with a force field (transferred from SiH4) [31]. 

Force field transferability is important in practical simulations. When parameters have been carefully refined to reproduce observation for only a model system, one needs to ask How will they perform when transferred to new chemical environments For example, if potentials are available and are known to describe adequately AI2O3 and Li20, how effective will these potential models be in the description of Li migration in AI2O3 How effective will... 

While simulations reach into larger time spans, the inaccuracies of force fields become more apparent on the one hand properties based on free energies, which were never used for parametrization, are computed more accurately and discrepancies show up on the other hand longer simulations, particularly of proteins, show more subtle discrepancies that only appear after nanoseconds. Thus force fields are under constant revision as far as their parameters are concerned, and this process will continue. Unfortunately the form of the potentials is hardly considered and the refinement leads to an increasing number of distinct atom types with a proliferating number of parameters and a severe detoriation of transferability. The increased use of quantum mechanics to derive potentials will not really improve this situation ab initio quantum mechanics is not reliable enough on the level of kT, and on-the-fly use of quantum methods to derive forces, as in the Car-Parrinello method, is not likely to be applicable to very large systems in the foreseeable future. 

This situation, despite the fact that reliability is increasing, is very undesirable. A considerable effort will be needed to revise the shape of the potential functions such that transferability is greatly enhanced and the number of atom types can be reduced. After all, there is only one type of carbon it has mass 12 and charge 6 and that is all that matters. What is obviously most needed is to incorporate essential many-body interactions in a proper way. In all present non-polarisable force fields many-body interactions are incorporated in an average way into pair-additive terms. In general, errors in one term are compensated by parameter adjustments in other terms, and the resulting force field is only valid for a limited range of environments. 

Very early force fields were used in an attempt to calculate structures, enthalpies of formation, and vibrational spectra, but it was soon found that accuracy suffered severely in either the structure-energy calculations or the vibrational spectra. Force constants were, on the whole, not transferable from one field to another. The result was that early force fields evolved so as to calculate either structure and energy or spectra, but not both. 

In order for the transferability of parameters to be a good description of the molecule, force fields use atom types. This means that a sp carbon will be described by different parameters than a. sp - carbon, and so on. Usually, atoms in aromatic rings are treated differently from sp atoms. Some force fields even parameterize atoms for specific functional groups. For example, the carbonyl oxygen in a carboxylic acid may be described by different parameters than the carbonyl oxygen in a ketone. 

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... 

Of the biomolecular force fields, AMBER [21] is considered to be transferable, whereas academic CHARMM [20] is not transferable. Considering the simplistic form of the potential energy functions used in these force fields, the extent of transferability should be considered to be minimal, as has been shown recently [52]. As stated above, the user should perform suitable tests on any novel compounds to ensure that the force field is treating the systems of interest with sufficient accuracy. 

I mentioned earlier that molecular-mechanics force fields have to be transferable from molecule to molecule, and that it was found many years ago that extra terms were needed apart from the pure valence ones. Non-bonded interactions are usually taken as the Lennard-Jones 12-6 potential... 

The parameterization process may be done sequentially or in a combined fashion. In the sequential method a certain class of compound, such as hydrocarbons, is parameterized first. These parameters are held fixed, and a new class of compound, for example alcohols and ethers, is then parameterized. Tins method is in line with the basic assumption of force fields parameters are transferable. The advantage is that only a fairly small number of parameters are fitted at a time. The ErrF is therefore a relatively low-dimensional function, and one can be reasonably certain that a good minimum has been found (although it may not be the global minimum). The disadvantage is that the final set of parameters necessarily provides a poorer fit (as defined from the value of the ErrF) than if all the parameters are fitted simultaneously. 

The approach presented above is referred to as the empirical valence bond (EVB) method (Ref. 6). This approach exploits the simple physical picture of the VB model which allows for a convenient representation of the diagonal matrix elements by classical force fields and convenient incorporation of realistic solvent models in the solute Hamiltonian. A key point about the EVB method is its unique calibration using well-defined experimental information. That is, after evaluating the free-energy surface with the initial parameter a , we can use conveniently the fact that the free energy of the proton transfer reaction is given by... 

MM, UFF, molecular mechanics, universal force field. Ref. (14). Charge transfer reactive force field. Ref. (92). 

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