Molecular mechanics functions

Some of these software packages also have semiempirical or molecular mechanics functionality. However, the primary strength of each is ah initio calculation. There are also ah initio programs bundled with the Unichem, Spartan, and Hyperchem products discussed previously in this appendix. 

The simple harmonic terms used to represent the energy of bond stretching in typical protein molecular mechanics force fields cannot model the making and breaking of chemical bonds. Also, molecular mechanics parameters are usually developed based on the properties of stable molecules, and so might not be applicable to transition states and intermediates. Molecular mechanics functions and parameters can be developed specifically for reactions, an approach that has been... 

The photonic activation of molecular mechanical functions in solution is often limited by its lack of integration. The electrochemical transduction of... 

The classical approach appropriately known as molecular mechanics has been used with conspicuous success to predict molecular geometries, chemical reactivities and even magnetic, electronic and spectral properties of molecular systems. Molecular mechanics functions with no intention or pretence to elucidate the essential nature of molecules it applies concepts that pertain to the nineteenth-century classical model of the molecule, i.e, bond length, bond order, force constant, torsional rigidity and steric congestion. Transferable numerical values are empirically... 

Potential energy functions of molecules have become the basis for the calculation of a wide range of physical properties, and have been of particular interest in the study of macromolecules. Such so-called MM (molecular mechanics) functions can be used to determine minimum energy structures, relative energies of different conformers, barriers between these structures, and many other properties. 

There is, of course, a mass of rather direct evidence on orientation at the liquid-vapor interface, much of which is at least implicit in this chapter and in Chapter IV. The methods of statistical mechanics are applicable to the calculation of surface orientation of assymmetric molecules, usually by introducing an angular dependence to the inter-molecular potential function (see Refs. 67, 68, 77 as examples). Widom has applied a mean-held approximation to a lattice model to predict the tendency of AB molecules to adsorb and orient perpendicular to the interface between phases of AA and BB [78]. In the case of water, a molecular dynamics calculation concluded that the surface dipole density corresponded to a tendency for surface-OH groups to point toward the vapor phase [79]. 

The situation is more complicated in molecular mechanics optimizations, which use Cartesian coordinates. Internal constraints are now relatively complicated, nonlinear functions of the coordinates, e.g., a distance constraint between atoms andJ in the system is — AjI" + (Vj — + ( , - and this... 

For this reason, there has been much work on empirical potentials suitable for use on a wide range of systems. These take a sensible functional form with parameters fitted to reproduce available data. Many different potentials, known as molecular mechanics (MM) potentials, have been developed for ground-state organic and biochemical systems [58-60], They have the advantages of simplicity, and are transferable between systems, but do suffer firom inaccuracies and rigidity—no reactions are possible. Schemes have been developed to correct for these deficiencies. The empirical valence bond (EVB) method of Warshel [61,62], and the molecular mechanics-valence bond (MMVB) of Bemardi et al. [63,64] try to extend MM to include excited-state effects and reactions. The MMVB Hamiltonian is parameterized against CASSCF calculations, and is thus particularly suited to photochemistry. 

Stanton, R.V., Heutsough, D.S., Merz, K.M. Jr An Examination of a Density Functional-Molecular Mechanical Coupled Potential. J. Comput. Chem. 16 (1995) 113-128. 

Additionally, as in all Tl-based approaches, the free energy differences are linear functions of the potential. Thus non-rigorous decompositions may be made into contributions from the different potential energy terms, parts of system and individual coordinates, providing valuable insight into the molecular mechanisms of studied processes [8, 9, 10). 

To see the contributions to the molecular mechanics potential energy function and their mathematical representation... 

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]. 

A Fortran90 library for the simulation of molecular systems using molecular mechanics (MM) and hybrid quantum mechanics/molecular mechanics (QM)/ MM) potential energy functions. http //www.ibs.fr/ext/labos/LDM/projet6/... 

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. 

Molecular Mechanic use an aiialyLical, dil fereiiliable, aiui relatively simple potential energy function, -(R). for describing the inieraciions between a set of atoms specified by their Cartesian coordinates R. 

Hach molecular mechanics method has its own functional form MM+. AMBER, OPL.S, and BIO+. The functional form describes the an alytic form of each of th e term s in th e poteri tial. For exam pie, MM+h as both a quadratic and a cubic stretch term in th e poten tial whereas AMBER, OPES, and BIO+ have only c nadratic stretch term s, I h e functional form is referred to here as the force field. For exam pie, th e fun ction al form of a qu adratic stretch with force constant K, and equilibrium distance i q is ... 

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