Force fields methods

Spellmeyer and Houk provided a valuable alternative flexible force-field method in which transition state parameters were developed from ah initio data on simple 

Radical Beckwith-Schiesser A s [exo) AEg [endo) Spellmeyer-Houk A s [exo) Aits [endo) Experimental A [exo) AE [endo)  

Streamlined with the incorporation of the SH model into the commercially available MacroModcl modeling package [lO]. Both models have been used extensively to model a large cross-section of intramolecular homolytic addition reactions. Not only can regio- and stereochemical trends be modeled accurately, but the rate-altering effects of substitution are also well reproduced (Table 2). Some calculated transition structures are displayed in Fig, 1, 

Houk and coworkers investigated the diastereofacial selectivity in radical additions of substituted cyclohexyl radicals to alkenes [13]. In this work, the force field developed by Spellmeyer and Houk was applied to intermolecular homolytic addition with success and demonstrated the added versatility of the HS model over the BS procedure which is limited to intramolecular systems. Extraordinarily accurate predictions of diastereoselectivity were made. For example, acrylonitrile is predicted to react with the 4-ter -butyl-2-methylcyclohexyl radical 28 to alford the products 

29 in a 79 21 trans.cis ratio experimentally this ratio was determined to be 79 21 

Molecules are described by a ball and spring model in force field methods, with atoms having different sizes and softness and bonds having different lengths and stiffness . Force field methods are also referred to as molecular mechanics (MM) methods. Many different force fields exist, and in this Chapter we will use Allinger s MM2 and MM3 (Molecular Mechanics versions 2 and 3) to illustrate specific details.  

Introduction to Computational Chemistry, Second Edition. Frank Jensen. 2007 John Wiley Sons, Ltd 

Type Symbol Description Type Symbol Description  

Note that special atom types are defined for carbon atoms involved in small rings, such as cyclopropane and cyclobutane. The reason for this will be discussed in Section 2.2.2. 

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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]). 

The range of systems that have been studied by force field methods is extremely varied. Some force fields liave been developed to study just one atomic or molecular sp>ecies under a wider range of conditions. For example, the chlorine model of Rodger, Stone and TUdesley [Rodger et al 1988] can be used to study the solid, liquid and gaseous phases. This is an anisotropic site model, in which the interaction between a pair of sites on two molecules dep>ends not only upon the separation between the sites (as in an isotropic model such as the Lennard-Jones model) but also upon the orientation of the site-site vector with resp>ect to the bond vectors of the two molecules. The model includes an electrostatic component which contciins dipwle-dipole, dipole-quadrupole and quadrupole-quadrupole terms, and the van der Waals contribution is modelled using a Buckingham-like function. 

II. Ab Initio, Semi-Empirical and Empirical Force Field Methods... 

Chem comes with default parameter sets, Amber2 and Amber3 in the case of the AMBER method. It is possible, however, to define an arbitrary number of additional parameter sets for the AMBER method (or for any of the other three force field methods). These user-defined parameter sets can be specified in the Parameters dialog box and integrated into HyperChem, in the same way as the default sets. 

Molecula.rMecha.nics. Molecular mechanics (MM), or empirical force field methods (EFF), ate so called because they are a model based on equations from Newtonian mechanics. This model assumes that atoms are hard spheres attached by networks of springs, with discrete force constants. 

It should be clear that force field methods are models of the real quantum mechanical systems. The total neglect of electrons as individual particles forces the user to define explicitly the bonding present in the molecule prior to any calculations. The user must decide how to describe a given molecule in terms of the selected force field. The input to a calculation consists of three sets of information. 

Finally, force field methods are zero-dimensional . It is not possible to asses the probable error of a given result within the method. The quality of the result can only be judged by comparison with other calculations on similar types of molecules, for which relevant experimental data exist. 

Atoms are assigned types , much as in force field methods, i.e. the parameters depend on the nuclear charge and the bonding situation. The a a and /3ab parameters for atom types A and B are related to the corresponding parameters for sp -hybridized carbon by means of dimensionless constants /ia and /cab-... 

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