Molecular mechanics modelling methods

Molecular Mechanics Models. Methods for structure, conformation and strain energy calculation based on bond stretching, angle bending and torsional distortions, together with Non-Bonded Interactions, and parameterized to fit experimental data. 

One tool for working toward this objective is molecular mechanics. In this approach, the bonds in a molecule are treated as classical objects, with continuous interaction potentials (sometimes called force fields) that can be developed empirically or calculated by quantum theory. This is a powerful method that allows the application of predictive theory to much larger systems if sufficiently accurate and robust force fields can be developed. Predicting the structures of proteins and polymers is an important objective, but at present this often requires prohibitively large calculations. Molecular mechanics with classical interaction potentials has been the principal tool in the development of molecular models of polymer dynamics. The ability to model isolated polymer molecules (in dilute solution) is well developed, but fundamental molecular mechanics models of dense systems of entangled polymers remains an important goal. 

The second problem also reflects the exceptional difficulty of exploring complex conformational energy surfaces. Quite simply, only the lowest-cost methods are applicable to anything but molecules with only a few degrees of conformational freedom. In practice and at the present time, this translates to molecular mechanics models. (Semi-empirical quantum chemical models might also represent practical alternatives, except for the fact that they perform poorly in this role.) Whereas molecular mechanics models such as MMFF seem to perform quite well, the fact of the matter is, outside the range of their explicit parameterization, their performance is uncertain at best. 

Molecular mechanics models are restricted to the description of molecular equilibrium geometry and conformation. They are the method of choice for conformational searching on complex systems. 

Whilst these difficulties do not invalidate application of molecular mechanics methods to such systems, they do mean that the interpretation of the results must be different from what is appropiate for small-molecule systems. For these reasons, the real value of molecular modeling of macromolecule systems emerges when the models are used to make predictions that can be tested experimentally or when the modeling is used as an adjunct to the interpretation of experiments. Alternatively, the relatively crude molecular mechanics models, while not of quantitative value, are an excellent aid to the visualization of problems not readily accessible in any other way. Molecular dynamics is needed, especially for large molecules, to scan the energy surface and find low-energy minima. The combination of computational studies with experimental data can help to assign the structure. 

From its inception, the combined Quantum Mechanics/Molecular Mechanics (QM/MM) method [1-3] has played an important roll in the explicit modeling of solvent [4], Whereas Molecular Mechanics (MM) methods on their own are generally only able to describe the effect of solvent on classical properties, QM/MM methods allow one to examine the effect of the solvent on solute properties that require a quantum mechanical (QM) description. In most cases, the solute, sometimes together with a few solvent molecules, is treated at the QM level of theory. The solvent molecules, except for those included in the QM region, are then treated with an MM force field. The resulting potential can be explored using Monte Carlo (MC) or Molecular Dynamics (MD) simulations. Besides the modeling of solvent, QM/MM methods have been particularly successful in the study of biochemical systems [5] and catalysis [6],... 

The combination of molecular mechanics like methods and multidimensional NMR has formed the basis for numerous studies of peptides, proteins and DNA fragments. Paramagnetic shifts in metalloproteins have also been used to obtain structural information that is used as constraints in molecular mechanics and molecular dynamics calculations. For a number of reasons there are relatively few reported applications of combined NMR-molecular modeling studies involving metal complexes (see Section 10.4). 

Methods for molecular mechanics modeling of coordination compounds . 

For solvation modeling, see C. J. Cramer and D. G. Truhlar, this volume. Continuum and Solvation Models Classical and Quantum Mechanical Implementation. For molecular mechanics, see D. B. Boyd and K. Lipkowitz, /. Chem. Educ., S9, 269 (1982). Molecular Mechanics. The Method and Its Underlying Philosophy. 

This type of selectivity originates solely from steric interactions between the auxiliary ligands, polymer chain, and the incoming propene. It was first explained qualitatively by means of visualization of the structure of the catalyst precursors. A more quantitative approach led naturally to molecular mechanics models in order to explain and even predict the stereospecificity of catalysts with different ligand environments. Due to the limitations of MM models to describe metallocene complexes as well as bond breaking and bond formation processes (see Section 3.1.2.1), the models were initially based on some rigid core structures derived from the measured structures, e. g., of the dichloride precursors [25, 26]. In order to achieve more accurate results, core structures, calculated by ab initio methods, were employed later. A further step in this direction is the joint description of the... 

Standard molecular mechanics (MM) methods (e.g. the popular force fields developed for AMBER, CHARMM and GROMOS decribed in Section 2 above) provide a good description of protein structure and dynamics, but cannot be used to model chemical reactions. This limitation is due their simple functional forms (e.g. harmonic terms for bond stretching) and inability to model changes in electronic polarization (because of the invariant point partial atomic charge used by these molecular mechanics methods to represent electrostatic interactions). 

Many systems of interest are too large to be tackled using ab initio methods and here force field methods can be useful. Force field methods do not explicitly include the electrons, rather the energy of a system is a function only of the nuclear coordinates. The main application of molecular mechanics modelling is in the area of big systems (thousands of atoms are not uncommon). The calculations can be performed in a fraction of the computer time that would be required for an ab initio calculation. Their accuracy is determined by the quality of the parameterization of the force field. 

Hay BP. Methods for molecular mechanics modeling of coordination compounds. Coord Chem Rev 1993 126 177-236. 

Semiempirical methods are the middle ground between highly accurate ab initio methods and completely empirical molecular mechanical (MM) methods [155]. For the treatment of very large biomolecules, hybrid approaches have been developed where the reactive center is described by a semiempirical method and the inert rest of the molecule by a classical force field [3,156,157], This technique can also be applied for the description of solvent effects. The solvent molecules are then described by the MM method. If an even higher accuracy is required for the reactive center of the system, a hybrid approach of three different methods can be applied, e.g., in the ONIOM model by Vreven and Morokuma [158], Here the center is described at DFT or post-HF level, the nearest-neighbor atoms at semiempirical level, and the outer surrounding at MM level. There also exist hybrid schemes between semiempirical and DFT methods only [159],... 

The molecular mechanics model is extremely popular among chemists and there is an overwhelming number of articles reporting the application of this method. Their broad application also is considered to raise our understanding and our capability to explain the structural features of the treated molecules.5 But still, as the last example shows, there exist upper limits concerning the size of the molecules for which a proper prediction of structure can be made. Especially in the case of proteins, such predictions can have tremendous practical importance. The last model, I discuss is a method used to predict the secondary structure of a protein, i.e., its folding mode, starting with only information on its primary structure, i.e., its amino acid sequence. 

---