Forces mechanical

In a more general stress field, the force (which is always perpendicular to the dislocation line) can have a component in the glide plane of the dislocation as well as a component normal to the glide plane. In such a case, the overall force will tend to produce both glide and climb. However, if the temperature is low enough that no significant diffusion is possible, only glide will occur. 

2The Burgers circuit is constructed so that it will close if mapped step by step into a perfect reference crystal. See Hirth and Lothe [2]. 

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Much of chemistry is concerned with the short-range wave-mechanical force responsible for the chemical bond. Our emphasis here is on the less chemically specific attractions, often called van der Waals forces, that cause condensation of a vapor to a liquid. An important component of such forces is the dispersion force, another wave-mechanical force acting between both polar and nonpolar materials. Recent developments in this area include the ability to measure... 

Convection is the movement of a species due to external mechanical forces. This can be of two types natural convection, which arises from thennal gradients or density differences within the solution, and forced convection, which can take the fomi of gas bubbling, pumping or stirrmg. The fomier is undesirable and can occur m any solution... 

Equation (C3.5.3) shows tire VER lifetime can be detennined if tire quantum mechanical force-correlation Emotion is computed. However, it is at present impossible to compute tliis Emotion accurately for complex systems. It is straightforward to compute tire classical force-correlation Emotion using classical molecular dynamics (MD) simulations. Witli tire classical force-correlation function, a quantum correction factor Q is needed 5,... 

Figure C3.5.6. The computed Fourier transfonn at frequency co, of tire classical mechanical force-force correlation function for liquid O2 at 70 K from [M]- The VER rate is proportional to the value of ( " at tire O2...

Experimental techniques based on the application of mechanical forces to single molecules in small assemblies have been applied to study the binding properties of biomolecules and their response to external mechanical manipulations. Among such techniques are atomic force microscopy (AFM), optical tweezers, biomembrane force probe, and surface force apparatus experiments (Binning et al., 1986 Block and Svoboda, 1994 Evans et ah, 1995 Israelachvili, 1992). These techniques have inspired us and others (see also the chapters by Eichinger et al. and by Hermans et al. in this volume) to adopt a similar approach for the study of biomolecules by means of computer simulations. 

A number of issues need to be addressed before this method will become a routine tool applicable to problems as the conformational equilibrium of protein kinase. E.g. the accuracy of the force field, especially the combination of Poisson-Boltzmann forces and molecular mechanics force field, remains to be assessed. The energy surface for the opening of the two kinase domains in Pig. 2 indicates that intramolecular noncovalent energies are overestimated compared to the interaction with solvent. 

Figure 7-8. Bonded (upper row) and non-bonded (lower row) contributions to a typioal molecular mechanics force field potential energy function. The latter two types of Interactions can also occur within the same molecule.

The mathematical formulation of a typical molecular mechanics force field, which is also called the potential energy function (PEF), is shown in Eq. (18). Do not wony yet about the necessary mathematical expressions - they will be explained in detail in the following sections ... 

Many problems in force field investigations arise from the calculation of Coulomb interactions with fixed charges, thereby neglecting possible mutual polarization. With that obvious drawback in mind, Ulrich Sternberg developed the COSMOS (Computer Simulation of Molecular Structures) force field [30], which extends a classical molecular mechanics force field by serai-empirical charge calculation based on bond polarization theory [31, 32]. This approach has the advantage that the atomic charges depend on the three-dimensional structure of the molecule. Parts of the functional form of COSMOS were taken from the PIMM force field of Lindner et al., which combines self-consistent field theory for r-orbitals ( nr-SCF) with molecular mechanics [33, 34]. 

T. Fox, C. Chipot, A. PohorUle, The development/application of a minimalisf organic/biochemical molecular mechanic force field using a combination of ab-initio calculations and experimental data, in Computer Simulation of Biomolecular Systems. 

A descriptor for the 3D arrangement of atoms in a molceulc can be derived in a similar manner. The Cartesian coordinates of the atoms in a molecule can be calculated by semi-empirical quantum mechanical or molecular mechanics (force field) methods, For larger data sets, fast 3D structure generators are available that combine data- and rule-driven methods to calculate Cartesian coordinates from the connection table of a molecule (e.g., CORINA [10]). 

Th is discussion focuses on th e individual compon en ts of a typical molecular mechanics force field. It illustrates the mathematical functions used, wdi y those functions are chosen, and the circiim -Stan ces u n der wh ich the fun ction s become poor approxirn atiori s. Part 2 of th is book, Theory and Melhadx, includes details on the implementation of the MM+,. AM BHR, RlO-g and OPl.S force fields in HyperChem. 

TlypcrC hcm oilers four molecular mechanics force fields MM+, AMBER, BIO+, and OPES (sec References on page 106). To run a molecular mechanics calciilaLion. yon miisi lirsi choose a force Eeld. The following sections discuss considerations in choosing a force field. 

Wofe." rh c BIO + force field is an im plern en lation oflheCH. ARMM (Chcmistry at H.ARvard MacromoIceular Mechanics ) force field developed in the group of Martin Karplusat Harvard University, l.ike. AMBER and OP1.S, it is primarily designed to explore rnacro-moleciilcs. 

For biological polymers, molecular mechanics force fields arc not well substantiated by experirn eri tal data. You should be cautious about relying on predictions from thesc calculations. 

Molecular mechanics force fields have much information built into them and can be accurate for the molecules used in their param eten/ation. For molecules outside the limited scope for 40. Dewar. J. S. Dicier, K. M../. Am. Chem. Soc. 108 807. ), 1086. 

Some General Features of Molecular Mechanics Force Fields... 

Landis C R, D M Root and T Cleveland 1995. Molecular Mechanics Force Fields for Modeling Inorgani and Organometallic Compounds. In Lipkowitz K B and D B Boyd (Editors). Reviews in Compute tional Chemistry Volume 6. New York, VCH Publishers, pp. 73-148. 

Halgren T A 1992. Representation of van der Waals (vdW) Interactions in Molecular Mechanics Force Fields Potential Form, Combination Rules, and vdW Parameters. Journal of the American Chemical Society 114 7827-7843. 

FIGURE 6.2 Hannonic, cubic, and Morse potential curves used to describe the energy due to bond stretching in molecular mechanics force fields. 

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