Force fields parameter derivation

Force field parameters derived from the work of Rey and Skolnick for use with Eq. l. ... 

One of the greatest disadvantages is that a large number of carefully selected parameters is required to model the experimental properties and behavior of molecules. The derivation of these parameters can be difficult. Moreover, it is by no means guaranteed that force field parameters derived for one system will work equally well for another system. Whereas ab initio methods are capable of giving physically reasonable results in most instances, it is usually necessary to check the accuracy of a force field when it is to be transferred to a system outside its area of development. ... 

Early force field parameter derivations were completely empirical owing to the lack of reliable first-principles, quantum mechanical data, plus a relative abundance of experimental data. As described in preceding sections, ab initio methods are capable of providing a reasonable description of many molecular... 

Most of the force fields described in the literature and of interest for us involve potential constants derived more or less by trial-and-error techniques. Starting values for the constants were taken from various sources vibrational spectra, structural data of strain-free compounds (for reference parameters), microwave spectra (32) (rotational barriers), thermodynamic measurements (rotational barriers (33), nonbonded interactions (1)). As a consequence of the incomplete adjustment of force field parameters by trial-and-error methods, a multitude of force fields has emerged whose virtues and shortcomings are difficult to assess, and which depend on the demands of the various authors. In view of this, we shall not discuss numerical values of potential constants derived by trial-and-error methods but rather describe in some detail a least-squares procedure for the systematic optimisation of potential constants which has been developed by Lifson and Warshel some time ago (7 7). Other authors (34, 35) have used least-squares techniques for the optimisation of the parameters of nonbonded interactions from crystal data. Overend and Scherer had previously applied procedures of this kind for determining optimal force constants from vibrational spectroscopic data (36). 

A comparison of force fields as derived and used by different authors is therefore possible only to a limited extent. Any meaningful comparison has to be performed by calculating a large set of molecular properties which comprises the ranges of validity of all force fields under comparison. By experience, calculated structural parameters are generally less sensitive to changes of potential constants than energetical and vibrational quantities. 

The final part is devoted to a survey of molecular properties of special interest to the medicinal chemist. The Theory of Atoms in Molecules by R. F.W. Bader et al., presented in Chapter 7, enables the quantitative use of chemical concepts, for example those of the functional group in organic chemistry or molecular similarity in medicinal chemistry, for prediction and understanding of chemical processes. This contribution also discusses possible applications of the theory to QSAR. Another important property that can be derived by use of QC calculations is the molecular electrostatic potential. J.S. Murray and P. Politzer describe the use of this property for description of noncovalent interactions between ligand and receptor, and the design of new compounds with specific features (Chapter 8). In Chapter 9, H.D. and M. Holtje describe the use of QC methods to parameterize force-field parameters, and applications to a pharmacophore search of enzyme inhibitors. The authors also show the use of QC methods for investigation of charge-transfer complexes. 

The next two steps in the procedure of Leonard and Ashman are the conversion of the diagonal elements from atomic units into force field units and calculation of scaling factors for bond lengths and angles. The calculated force constants had to be scaled down by approximately 25% and 70% to yield force constants comparable in numerical size with those included in MM2. Neither force constants nor scaling factors can be incorporated directly into a different force field. A modification of the described procedure that meets the requirements of CVFF was developed. Fragments with known force field parameters were chosen. After a full geometry optimization (HF/6-31G ) second derivatives and vibrational frequencies were calculated. The force... 

Moreover, as discussed in more detail later, force field parameters are not statistically orthogonal, so optimized values can be skewed by coupling with other parameters. With all of these caveats in mind, however, there are still instances where valuable physical insights derive from a term-by-term analysis of the torsional coordinate. 

For molecular dynamics (MD) simulations to accurately reflect chain motions and conformational changes at various temperatures, the rotational barriers must be correct whether they arise from an explicit dihedral term, vdW interactions, or both. Barriers that are too low will allow disorder to occur at simulated temperatures far below experimental temperatures at which transitions and disorders in PTFE are observed. The validity of the barrier heights, especially the one at trans, obtained from the MOPAC AMI calculations and derived force field parameters above was called into question upon comparison to high level ab initio calculations on perfluorobutane (PFB), perfluoropentane (PFP), and... 

The molecular structures used in the calculations were optimized using a molecular force field program. The force field parameters were derived from various sources The bond length was taken into accound according to a model of Dewar and Llano (7). The VALBOND method of Root et al. (8) was used for the calculation of bond angels. The dihedral angles were parametrized according to the PIMM method (9). 

The set of functions, together with the collection of terms that parameterize them (kb, r0, etc.), is referred to as the force field. In some cases force field parameters can be related to experimentally determinable values. For example, the bond stretching force constant kb is approximately equivalent to the vibrational force constant derived from an infrared spectrum. However, in general die force field terms are derived empirically with the target of reproducing experimental structures and energy distributions. 

Molecular mechanics and dynamics studies of metal-nucleotide and metal-DNA interactions to date have been limited almost exclusively to modeling the interactions involving platinum-based anticancer drugs. As with metal-amino-acid complexes, there have been surprisingly few molecular mechanics studies of simple metal-nucleotide complexes that provide a means of deriving reliable force field parameters. A study of bis(purine)diamine-platinum(II) complexes successfully reproduced the structures of such complexes and demonstrated how steric factors influenced the barriers to rotation about the Pt(II)-N(purine) coordinate bonds and interconversion of the head-to-head (HTH) to head-to-tail (HTT) isomers (Fig. 12.4)[2011. In the process, force field parameters for the Pt(II)/nucleotide interactions were developed. A promising new approach involving the use of ab-initio calculations to calculate force constants has been applied to the interaction between Pt(II) and adenine[202]. 

An additional advantage of second-derivative methods is that frequencies of infrared vibrations can be calculated from the final Hessian matrix. This is only likely to be of relevance to small-molecule systems where good-quality spectra can be obtained. However, in such cases there is the potential to predict spectra and so characterize an unknown compound (see Chapter 9, Section 9.1). The ability to reproduce infrared frequencies should also provide a good test of the force field parameters, but little use has been made so far of this approach [43 5]. 

When changing force field parameters of a compound, overall exactness of the model is determined by the parameterization criteria. As this work was parameterized to reproduce the solubility, which is related to the thermodynamic quantity of free energy, this raises the question of solvent structure, as the structure-energy relationship is evident even in the gas phase interactions. One way to test the solvent structure is to check the density of the aqueous solution as a rough estimate of the ability of the model to reproduce the correct intermolecular interaction between the solute and the solvent. For this purpose, additional MC simulations were carried out on the developed models to test their ability to reproduce the experimental density of solution, at the specified concentration. The density was calculated using the experimentally derived density equations for carbon dioxide in aqueous solution from Teng et al., which is calculated from the fyj, of the C02(aq) and the density of the pure solvent [36, 37]. 

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