Atom-pair interactions

Additionally, to optimize task 4, we applied a conventional, atom pair interaction based multiple-time-step scheme to the force computation within Ihe innermost distance class. Here, for atom pairs closer than 5 A, the Coulomb sum is calculated every step, and for all other atom pairs the Coulomb sum is extrapolated every second step from previously explicitly calculated forces. 

With the molecular structure thus determined, NVR subtract the computed function 3m(s) from the total structure function [Eq. (3.6)] and obtain the distinct structure function 3 (s). The resulting curve is shown in Fig. 7 e. The function 3a (s) is related to the structure functions descriptive of atom pair interactions in D20(as) by Eq. (3.4). With the structure functions oo(s) known from X-ray diffraction, it is instructive to compute a neutron structure function. 

Helmholtz Free Energies of Atom Pair Interactions in Proteins. 

Sippl MJ, Ortner M, Jaritz M, Lackner P, Flockner H (1996) Helmholtz free energies of atom pair interactions in proteins, Fold Des, 1 289-298... 

This appears not to be the case. On average, the crystal field forces have a distortion effect. This was realized from some of the earliest analyses of hydrogen-bond lengths [52]. It arises from two factors one is the influence of many-atom effects, such as cooperativity. The second is the fact that all other atom-pair interactions are striving toward the equilibrium minimum. Since hydrogen-bonded functional groups tend to protrude from molecules, this results in an overall distortion. The most obvious example of this difference is that between the values for the H 0 distances of 1.7 to 1.8 A observed in the ices and 2.0 A for the water dimer (see Thble 4.3). Similarly, the distribution for two-center OwH O bonds in the hydrates of small molecules, discussed in Part IV, has a mean value of 1.80 A, in agreement with the ices. 

The concepts of quantum mechanics are used in formulating the appropriate expressions for the nonbonding atom-to-atom interactions which are treated as sums of pairwise interactions. Box 4.2 shows the components of these atom-pair interactions which are applied, with different emphasis, depending upon the type of molecules involved. 

Atom-Pair Interaction Potentials. Affinities can be calculated based on ligand-receptor atom-pair interaction potentials that are statistical in nature rather than empirical. Muegge and Martin (320) derived these potentials from crystallographic data in the Protein... 

The simple model of bonds between atoms, reducing chemical bonding to formal atom pair interactions is unsatisfactory for many molecules, since it fails to represent the actual bonding in conjugated or aromatic systems. In reality, chemical bonding is a molecular property, not a property of atom pairs. 

Factors 1 and 2 are universally found in sorption systems, and the approximate additivity of dispersion energies for all atom pair interactions ensures the sorption, at low temperatures, of large molecules, even n-paraffins. When a sorbent is composed of positive and negative ions (as in a zeolite), there exist local electrostatic fields, F, that polarize the sorbate of polarizability a. Thus = — olF, where the negative sign implies exothermal reaction. Such effects could be visualized in terms of distortion of electron clouds in certain p- or 7r-electron systems. 

Knowledge-based functions are based on the derivation of statistical preferences in the form of potentials for protein ligand atom pair interactions. Similar to potentials derived for protein folding and protein structure evaluation (e.g., Ref. 148), pair potentials akin to potentials of mean force (PMFs) are derived for various protein and ligand atom types using the PDB as a knowledge base. The PMF scoring function [118]... 

Van der Waals Interactions. The van der Waals term in (16.94) is usually taken as the sum of interactions involving all possible 1,4,1,5,1,6,... atom-pair interactions Kdw = 2i,s4 Kdw, /. where atoms i and j are in a 1,4 or greater relation.The 1,2 and 13 van der Waals interactions and electrostatic interactions are considered to be implicitly included in the bond-stretching and bond-bending parameters. Each van der Waals pair term Vvdw.iy the sum of an attraction due to London dispersion forces and a repulsion due mainly to Pauli repulsion. The AMBER, CHARMM, DREIDING, UFF, and TRIPOS force fields take as a Lennard-Jones 12-6 potential (Fig. 16.12 and... 

So, in summary, up to this point the take-home messages are that dispersion interactions are (a) ubiquitous and always attractive, (b) per atom-pair interaction on the order of a factor 100 weaker than covalent ones, (c) more long-ranged (typical distance range of 3-5 A compared to 1-2 A for covalent bonds), and (d) additive in character. These properties lead to a wide variety of dispersion bonds and by their admixture to other bonding mechanisms overall to a significant impact in chemistry. 

Another way of representing atom-pair interactions, which lends itself particularly well to computational methods is the spline potential. A least-squares calculation fits various accurately known sets of numerical interaction energies at certain interatomic regions (perhaps from various theoretical and/or empirical investigations) into a functional form under conditions of matching first and second derivatives, so that a potential and its derivatives may be invoked at an arbitrary atom separation. 

Except for the Coulombic contributions, which are computed by an Ewald-type summation, as described in Section 2.3, a potential cutoff distance is imposed to avoid unnecessary computing time calculating negligible contributions by short-range interactions from most of the V 2N N— 1) atom pairs in the system. In the commonly used nearest-image convention, if the cutoff obeys the condition re < VtJL, Then atom pair interactions included are between atom i in the central box and either atomj in the same box or one of its imagesf in an adjacent one, depending on whichever distance x/ - Xy or x/ - f is least (see Fig. 5.4). 

A set which we have found to be satisfactory for conjugated polymers are those contained in the DREIDING generic force field,in which atomic pair interactions depend more on features describing the bonding than on the identities of the atoms themselves. The energy barriers vq specified for a particular type of torsion may then be used in the simple function of Eq. (6), and data which may be useful to simulate common molecular chains are given in Table 5.4. 

Even when the particles are spherical, at separations much shorter than the particle diameter, the particles see each other as thick plates and their surfaces may be regarded as planar. Snch a geometry is now considered in more detail, as shown in Figure 16.1. The total dispersion interaction between the particles is obtained by summation of all atom-pair interactions. The interaction between the atoms in the disk-like volume dV"i in plate 1 and the ring-like volnme dl 2 in plate 2 is found by applying Equation 16.3 to each atom-pair interaction ... 

In an effort to lengthen the feasible simulation time scale of molecular simulations, Streett and co-workers introduced the multiple time-step method in 1978. " These authors recognized that the components of the force that vary most rapidly, and hence require small time steps for numerical resolution, are typically associated with atom pair interactions at small separations. This spatial localization is important because each of the N particles in the simulation has such an interaction with only a few, say [Pg.372]

The latter equation includes a so-called nonbond term which is part of almost all force fields. It adds an explicit atom-atom pair interaction term (equation 2) for the interactions between atoms in a molecule which are separated by at least three or four bonds ... 

Non-bonded interactions. A distance-corrected Morse potential is used to describe atom-pair interactions, with excessively high repulsions between bonded atoms avoided by including a shielded interaction. 

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