Force field methods computational considerations

The molecular mechanics (MM) or force field method is an empirical method based on classical mechanics and adjustable parameters. It has the disadvantage of being limited in its application to certain kinds of compounds for which the required parameters have been determined (experimentally or by theoretical calculations). Its advantage is a considerably shorter computation time in comparison with other procedures having the same purpose. This method has been shown to be very reliable and efficient in determing molecular geometries, energies, and other properties for a wide variety of compounds. 

The use of semi-empirical or even force field methods, which are generally used for problems of this size, is nevertheless not apt for the description of these systems [3]. On the other hand, the application of ab initio methods requires a considerable computational effort so that attempts to improve the efficiency of computational techniques are well worthwhile. 

Force-field methods form the basis of molecular dynamics. They use a parameterised quasi-classical description of interatomic forces to model the trajectory of systems typically composed of hundreds or even thousands of atoms. One good feature of these types of calculations is that with large systems the computational effort increases linearly with the size of the problem. This means that increased computational power allows considerably larger systems to be studied. Further gains can also be made by using parallel processors since energy calculations in molecular dynamics simulations are inherently parallel. 

Apart from the different approaches to calculating hole sizes of macrocyclic ligands, there are also considerable differences in the force fields that have been used13,4,45,78,80,84 89]. Unfortunately, no comparative study that systematically analyzes the various methods and force fields is available. It is therefore worth noting that the computation of the cavity size of 12- to 16-membered tetraaza macrocycles with two very different models and force fields led to remarkably similar results (Table 8.2). 

The determination of the charge distribution in a molecule, needed here for the latter term, (Ges), has been a considerable problem in force field calculations, especially for transition metal compounds (see Sections 3.2.6 and 3.3.6). Most promising but not yet fully tested for transition metal complexes are semi-empiri-cal quantum-mechanical methods[ 103,1041. Future studies might show whether a combination of approximate methods for the computation of charge distributions and solvation will lead to a reliable approximation of solvation parameters of coordination compounds. 

In spite of these caveats, there is intense activity in the application of these methods to polymorphic systems and considerable progress has been made. Two general approaches to the use of these methods in the study of polymorphism may be distinguished. In the first, the methods are utilized to compute the energies of the known crystal structures of polymorphs to evaluate lattice energies and determine the relative stabilities of different modifications. By comparison with experimental thermodynamic data, this approach can be used to evaluate the methods and force fields employed. The ofher principal application has been in fhe generation of possible crystal structures for a substance whose crystal structure is not known, or which for experimental reasons has resisted determination. Such a process implies a certain ability to predict the crystal structure of a system. However, the intrinsically approximate energies of different polymorphs, the nature of force fields, and the inherent imprecision and inaccuracy of the computational method still limit the efificacy of such an approach (Lommerse et al. 2000). Nevertheless, in combination with other physical data, in particular the experimental X-ray powder diffraction pattern, these computational methods provide a potentially powerful approach to structure determination. The first approach is the one applicable to the study of conformational polymorphs. The second is discussed in more detail at the end of this chapter. 

This synopsis summarises three applications of the hybrid method, two of which actually involve chemical reactions. The combination of a semiempirical kernel and a force-field environment has been very successful in these application and has yielded information that could - at present - be obtained by other means (experimental or computational) only with considerable difficulty or not at all. One has to realise, though, that in practice there is a window of usefulness of the method If the energy differences are large enough the energetics will be mainly determined by vacuum values, i.e. environment effects will be negligible. If, on the other hand, the energy differences are small compared to the intrinsic inaccuracies of semiempirical method and force field the results cannot be trusted. 

It is impossible to predict the complete dissipation factor (tan 8) curves of polymers as functions of temperature and frequency without detailed consideration of relaxation times. At present, the a priori estimation of relaxation times requires detailed computer-intensive calculations, such as force field or quantum mechanical methods to estimate rotation barriers, and molecular dynamics simulations. A much less ambitious goal was therefore pursued. A simple variable was sought, for use in an order of magnitude estimate of the "lossiness" of a polymer at room temperature over the most important frequency range for typical applications. 

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