Torsional and nonbonding

Transferring torsional and nonbonded terms between force helds is much less reliable. These are lower-energy terms that are much more interdependent. It is quite common to hnd force helds with signihcantly different parameters for these contributions, even when the exact same equations are used. 

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. 

Figure 7). Osawa s recent force-field calculation study (21) of cage-shaped molecules with ethano bridges affords an excellent demonstration of this twist deformation at the molecular level. In six achiral cage-shaped molecules so far studied, his calculations showed that each molecule assumed a twisted, chiral conformation to minimize torsional and nonbonding strain. Tricyclo[4.2.2.2.2,s]dodecane (5) was shown to be 1.1 kcal/mol more stable in a twisted D2 than in the eclipsed D2h conformation, and his calculation also suggests that perhydrotriquinacene and C16-hexaquinane should assume C3 rather than conformations, contrary to naive pictures obtained by a casual observation of molecular models. 

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. 

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. 

MD simulations of polymer systems, in particular, require computation of two kinds of interactions bonded forces (bond length stretching, bond angle bending, torsional) and nonbonded forces (van der Waals and Coulombic). Parallel techniques developed [31-33] include the atom-decomposition (or replicated-datd) method, the force-decomposition method, and the spatial (domain)-decomposition method. The three methods differ only in the way atom coordinates are distributed among the processors to perform the necessary computations. Although all methods scale optimally with respect to computation, their different data layouts incur different interprocessor communication costs which affect the overall performance of each method. 

These differences clearly reflect the close coupling between torsion and nonbonded terms. 

---