Nonbonding interaction

The internal tenns are associated with covalently connected atoms, and the external terms represent the noncovalent or nonbonded interactions between atoms. The external terms are also referred to as interaction, nonbonded, or intermolecular terms. 

These sense in which terms like conjugative interactions, nonbonded interactions, etc., are meant will become clear when we discuss each individual type of interaction or effect. Suffice to say that, in many instances, conjugative interactions as well as geminal interactions or bond ionicity effects contain implicitly the idea of nonbonded interactions. Thus, it should be emphasized that the labels of the basic types of interactions proposed here reflect the way in which the problem is formulated rather than different electronic principles. 

The numerical coefficient of 2 appears because one electron is present in each of the interacting nonbonding orbitals. An analogous approach (structures 14-16) shows that the resonance energies of 9,10 and 11 are... 

Torsional contribution cf. structure with no gauche-butane interactions nonbond(snti—CH3/CH3) + ] nonbond(83UChe—CH3/CH3)... 

Bonding interaction Bonding interaction Nonbonding (no interaction)... 

Nonbonded interactions are possible between atoms that are neither bound to one another (1,2 interactions) nor bound to a common atom (1,3 interactions). They include both van der Waals and electrostatic interactions. Nonbonded interactions with the metal are often omitted in calculations that have been performed with either the VFF or the POS approach. The reason for the omission is that the majority of metal complexes that have been modeled are coordinatively saturated. In these structures, the metal center is shielded from nonbonded interactions by a shell of donor atoms followed by a second shell of ligand atoms. It is not possible for the outer shells of ligand atoms, i.e., those with 1,4 or greater connection to the metal, to achieve close contacts with the metal center. It has been demonstrated that the inclusion of M-X van der Waals terms does not significantly alter calculated geometries or relative energies for different conformers of hexamine Co(III) and Cr(III) complexes and pentacoordinate nitrogen macrocyclic complexes of Co(III) and Cu(II). ... 

Guenot, J., Kollman, P.A. Conformational and energetic effects of truncating nonbonded interactions in an aqueous protein dynamics simulation. J. Comput. Chem. 14 (1993) 295-311. 

In LN, the bonded interactions are treated by the approximate linearization, and the local nonbonded interactions, as well as the nonlocal interactions, are treated by constant extrapolation over longer intervals Atm and At, respectively). We define the integers fci,fc2 > 1 by their relation to the different timesteps as Atm — At and At = 2 Atm- This extrapolation as used in LN contrasts the modern impulse MTS methods which only add the contribution of the slow forces at the time of their evaluation. The impulse treatment makes the methods symplectic, but limits the outermost timestep due to resonance (see figures comparing LN to impulse-MTS behavior as the outer timestep is increased in [88]). In fact, the early versions of MTS methods for MD relied on extrapolation and were abandoned because of a notable energy drift. This drift is avoided by the phenomenological, stochastic terms in LN. 

Formally, we describe the LN method with the above force splitting below for the triplet protocol At, Atm, At. The fast, medium, and slow force components are distinguished by subscripts we take the medium forces as those nonbonded interactions within a 6 A region. 

In an atomic level simulation, the bond stretch vibrations are usually the fastest motions in the molecular dynamics of biomolecules, so the evolution of the stretch vibration is taken as the reference propagator with the smallest time step. The nonbonded interactions, including van der Waals and electrostatic forces, are the slowest varying interactions, and a much larger time-step may be used. The bending, torsion and hydrogen-bonding forces are treated as intermediate time-scale interactions. 

Fig. 1. Nonbonded force evaluation may be distributed among processors according to atomic coordinates, as in spatial decomposition (left), or according to the indices of the interacting atoms, as in force-matrix decomposition (right). Shades of gray indicate processors to which interactions are assigned.

Parallel molecular dynamics codes are distinguished by their methods of dividing the force evaluation workload among the processors (or nodes). The force evaluation is naturally divided into bonded terms, approximating the effects of covalent bonds and involving up to four nearby atoms, and pairwise nonbonded terms, which account for the electrostatic, dispersive, and electronic repulsion interactions between atoms that are not covalently bonded. The nonbonded forces involve interactions between all pairs of particles in the system and hence require time proportional to the square of the number of atoms. Even when neglected outside of a cutoff, nonbonded force evaluations represent the vast majority of work involved in a molecular dynamics simulation. 

Methods of decomposing the nonbonded force evaluation fall into two classes, spatial decomposition [15] in which atoms and their interactions are divided among processors based on their coordinates, and force-matrix decomposition [16] in which the calculation of the interaction between a pair of atoms is assigned to a processor without considering the location of either atom (Fig. 1). Spatial decomposition scales better to large numbers of... 

Fig. 2. Patches divide the simulation space into a regular grid of cubes, each larger than the nonbonded cutoff. Interactions between atoms belonging to neighboring patches are calculated by one of the patches which receives a positions message (p) and returns a force message (f). Shades of gray indicate processors to which patches are assigned.

In order to improve parallelism and load balancing, a hybrid force-spatial decomposition scheme was adopted in NAMD 2. Rather than decomposing the nonbonded computation into regions of space or pairwise atomic interactions, the basic unit of work was chosen to be interactions between atoms... 

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