Torsional and nonbonding interactions

A modified boat conformation of cyclohexane, known as the twist boat (Figure 1.9), or skew boat, has been suggested to minimize torsional and nonbonded interactions. This particular conformation is estimated to be about 1.5kcal mol-1 (bklmol-1) lower in energy than the boat form at room temperature. 

The parameter sets, defining the bond lengths, angles, torsion, and nonbonded interactions can be very specific for a given application, such as proteins or nucleic acids. This specificity can lead to surprising failures due to missing parameters even for relatively common atom types and combinations. 

The above discussion has focused on one particular element of the force constant matrix (the Hessian) and examined its characteristic behavior along the coordinate of interest. This kind of analysis of specific force constants turns out to be quite useful for various types of interactions and will be used later for the torsional and nonbonded interactions. 

In summary, this section, along with the previous one, has presented an overview of the theory of energy derivatives, especially second derivatives, and of the technique that enables the extraction of force field functions from ab initio quantum mechanical calculations. In the following sections we shall discuss in further detail extensions to the crucially important torsional and nonbonded interactions. 

First determine what parameters will be used for describing bond lengths and angles. Then determine torsional, inversion, and nonbonded interaction parameters. 

Rigid-geometry ab initio MO calculations of 86 torsional isomers of the dimethylphosphate anion (CH30)2P02 led to the determination of parameters for the Lennard-Jones type of nonbonded interaction, two- and three-fold torsional, and electrostatic interaction potential functions (215). Extension of this approach to full relaxation ab initio and MM schemes will be extremely useful, not only for phosphorus but also for other heteroatoms. 

Interactions between atoms that are not transmitted through bonds are referred to as nonbonded interactions. Most interactions are between centers of atoms, while some force fields use through-space interactions between points that are not centered on nuclei, such as lone pairs and bond-center dipoles. Interactions between atoms separated by only one or two bonds are normally not calculated, whereas atoms in the 1, 4-position with three intervening bonds interact both via torsional and nonbonded potentials. Thus these interactions become partially dependent. Introduction of scalable parameters for nonbonded 1,4-interactions can reduce this interdependence. 

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