Group Molecular Mechanics

In the remainder of the chapter, we consider molecular mechanics as applied to systems involving main group elements. To make this review manageable, some topics were excluded. Specifically, strictly organic MM applications are not included in this review, nor are heterocyclic systems such as crown ethers and porphyrins. -  

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The conformation of the chains of isotactic polymers in the crystalline state is generally helical and corresponds to a succession of nearly trans and gauche torsion angles, the exact values depending on the bulkiness of the side groups. Molecular mechanics calculations have been extensively used for the prediction of the chain conformation of polymers in the crystal.29... 

Besides the requirement of accurate algorithms to integrate the equation of motions in MD simulations the accuracy of the forces plays a pivotal role. Methodologies to derive intermolecular forces can be divided into two main groups - molecular mechanics (MM) or quantum mechanics (QM). 

This material on main group molecular mechanics is divided into two major parts applications on small molecules (generally organized by group number, with a couple of miscellaneous subdivisions at the end covering several groups) and larger systems, subdivided into extended lattices and polymers. 

Structure determinations of cyclopropyl derivatives using X-ray crystallography, microwave spectroscopy, electron diffraction, and theoretical calculations has been increasingly emphasized in recent years, and as discussed in later sections the molecular geometries obtained by these methods have been particularly informative as to the substituent interactions of cyclopropyl groups. Molecular mechanics methods have also been applied to structural studies of cyclopropyl derivatives . 

Molecular mechanics methods, based on Westheimer s approach (see chapter 6), were refined into software packages by a number of groups. Molecular mechanics calculations depend heavily on input data from known... 

In molecular mechanics and molecular dynamics studies of proteins, assig-ment of standard, non-dynamical ionization states of protein titratable groups is a common practice. This assumption seems to be well justified because proton exchange times between protein and solution usually far exceed the time range of the MD simulations. We investigated to what extent the assumed protonation state of a protein influences its molecular dynamics trajectory, and how often our titration algorithm predicted ionization states identical to those imposed on the groups, when applied to a set of structures derived from a molecular dynamics trajectory [34]. As a model we took the bovine... 

The primary problem with explicit solvent calculations is the significant amount of computer resources necessary. This may also require a significant amount of work for the researcher. One solution to this problem is to model the molecule of interest with quantum mechanics and the solvent with molecular mechanics as described in the previous chapter. Other ways to make the computational resource requirements tractable are to derive an analytic equation for the property of interest, use a group additivity method, or model the solvent as a continuum. 

This method does not attempt to distinguish between the various energy contributions. The surface tension parameter acts to include all interactions as much as possible. There are a number of algorithms for implementing this method, most of which differ in the means for determining the surface area associated with a particular group. This method is particularly popular for very large molecules, which can only be modeled by molecular mechanics. 

Computed optical properties tend not to be extremely accurate for polymers. The optical absorption spectra (UV/VIS) must be computed from semiempiri-cal or ah initio calculations. Vibrational spectra (IR) can be computed with some molecular mechanics or orbital-based methods. The refractive index is most often calculated from a group additivity technique, with a correction for density. 

Figure 2 A glutamate side chain partitioned into quantum and classical regions. The terminal CH2C02 group IS treated quantum mechanically, and the backbone atoms are treated with the molecular mechanics force field.

The treatment of electrostatics and dielectric effects in molecular mechanics calculations necessary for redox property calculations can be divided into two issues electronic polarization contributions to the dielectric response and reorientational polarization contributions to the dielectric response. Without reorientation, the electronic polarization contribution to e is 2 for the types of atoms found in biological systems. The reorientational contribution is due to the reorientation of polar groups by charges. In the protein, the reorientation is restricted by the bonding between the polar groups, whereas in water the reorientation is enhanced owing to cooperative effects of the freely rotating solvent molecules. 

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