Intramolecular nonbonded interactions

Functions and partly also constants for nonbonded interactions within single molecules (intramolecular interactions) have been taken over in many cases from investigations of interactions between different molecules (intermolecular interactions) (7,3). The derivation of parameters for nonbonded interactions presents further difficulties, e.g. the problem of the anisotropy of such interactions (8, 23) and parameter correlations (Section 2.4.). There is no agreement on the question whether pairs of atoms separated by a chain of only three bonds should be counted as nonbonded interactions. Some authors include these pairs,... 

The polydihalophosphazenes are examined by conformational analysis using nonbonding intramolecular interactions based on a 6-12 Lennard-Jones potential and a Coulombic term. The results provide an insight into the reasons for the low glass transition temperatures, the high chain flexibilities, and the conformational preferences of these molecules. Minimum energy conformations are discussed. 

Another example of geometrical consequences of intramolecular interactions can be demonstrated by the structure of a few carbon-cage molecules. Whereas the adamantane molecule [57] has only one kind of C-C distance, due to its high symmetry, there is a distribution of C-C distances in, for example, heptacy-clotetradecane (Figure 12(a)) [67] and fenestrane (Figure 12(b)) [68] due to intramolecular nonbonded interactions. 

Some of the results of our MD simulations of proteins on clay mineral surfaces are summarized in Fig. 8-5. When proteins are placed in the interlayer space of clay minerals, interactions between the surface and the protein compete with intramolecular protein nonbonded interactions. As a result, a protein molecule can gel stretched out along the mineral surface, significantly denatured from its native stale. In the case ol mhredoxiii adsorbed by pyropliyllite. for example, the mole-... 

In practice, one usually defines a training set of molecules and associated experimental properties and fits the relevant data with an assumed force field.The next step is to test the results on molecules and data outside the training set. Experimental data that depend on the energy surface and that may be used to determine the parameters of the intramolecular interactions consist mainly of gas-phase structural data derived from microwave spectra or electron diffraction patterns, crystal structures derived from X-ray and inelastic neutron scattering measurements, and vibrational frequencies obtained from infrared and Raman spectra. Torsional barriers are derived from NMR band shapes and relaxation times, whereas conformational energies are determined from spectroscopic and thermochemical data. Nonbonded parameters are determined mainly from... 

The number of trial sites at any given step, km, can be chosen freely (k = 1 corresponds to an unbiased insertion) and should thus be optimized to improve efficiency [38]. For chain molecules with intramolecular potentials (e.g., bond bending and dihedral potentials), it is more convenient to divide the energy into a bonded part and a nonbonded part. The bonded part can then be used to efficiently bias the selection of trial positions and only the nonbonded part is used for the selection of trial sites and the calculation of the Rosenbluth weights [34,35,37]. Using an isolated chain with intramolecular interactions as the reference state, the excess chemical potential can now be obtained from... 

Interactions between the nonbonded atoms of a molecule play an important role in determining conformational energies and geometries as well as barriers to internal rotation. It seems reasonable that such interactions are of the same type as those between atoms in different molecules, and thus the theory to describe nonbonded intramolecular interactions is the same as that used to describe intermolecular forces. The physical origins of such forces, which are all of the electromagnetic type, are... 

In contrast, in this study modeling ensembles of chains at a realistic bulk density, any constraint to the reorientational motion of a bond is possibly exerted not only by the covalently bonded neighbors but also by the nonbonded neighbors. Our results in fact suggest that the mtermolectdar interaction is more important than the intramolecular interaction in causing the anisotropy. This conclusion is based on the following two observations. First, the intramolecular... 

A force field that focusses on intramolecular interactions, and particularly on the force constants that determine vibrational frequencies, is the spectroscopically determined force field of Krimm and co-workers (50-52). They advocate very high level quantum calculations to fix the geometries, force constants, and electrostatic terms while using OPLS nonbond Lennard-Jones parameters. The recent focus of this work has been on highly polar molecules, as are discussed later. While this force field reproduces gas-phase IR data very accurately, it does not appear to have been tested on condensed phases. 

The Hamiltonian of a multiple-chain system consisting of n chains is split into two parts H = H o -F W, where H o is the Hamiltonian of a reference (ideal) system composed of n noninteracting chains but with all the intramolecular interaction terms, while the intermolecular interactions are accounted for by the second term W that is assumed to be dependent on the particle positions only through the particle density distribution. One of the simplest expressions for this nonbonded interaction is as follows ... 

The cause of this phenomenon can undoubtedly be attributed, at least in part, to inductive effects due to the low electronegativity of the silyl group (10), but it has been suggested, based also on ultraviolet (42) and NMR data, that intramolecular interaction between the nonbonding electrons of the ketone oxygen and the d orbitals of silicon occur in the compounds" (43), i.e., o(p-d) bonding. 

Brant et al [11] who used the dipole approximation, stressed the importance of the electrostatic term in the calculation of intramolecular interactions in the case of a dipeptide. They have also stressed that when only the nonbonded and torsional interactions are considered, the minimum in energy does not correspond to the experimentally observed conformation. Earlier studies (Rein et al, [15]) on the conformations of simple molecules, such as hydrogen peroxide and methanol, have shown that the monopole and dipole approximations may be insufficient for the electrostatic calculations. Lassetre and Dean [16] considered the interactions in terms of a series of multipoles localized at bond midpoints and included terms up to quadrupole interactions. Tang Au-Chin [17] included interactions up to octopole terms. However, at the time of their work [16, 17], wave functions sufficiently accurate for the calculation of reliable electrical moments were not available. As a result, only rough orders of magnitude were used in their calculations. 

The first step is the same as that of the RD algorithm. First the nonbonded forces F are computed. The result is summed into both fa and ff Next, each processor computes a fraction NjP of the bonded interactions. A critical point here is that in a preprocessing step of the run, we should guarantee that each processor knows all the atom positions needed for the bonded (intramolecular) interactions. This step again scales as NjP. 

The external potential energy accounts for all interactions with other molecules and for all the nonbonded intramolecular interactions. In addition, interactions with any external field that may be present are also included in... 

In what follows we shall denote a chain in the absence of the external interactions as the ideal chain. Note that this is a purely fictitious concept, as real chains always have nonbonded intramolecular interactions. 

We started our OFF analysis of hydrogen bonded crystals (Hagler, Huler and Lifson, 1974) about a decade ago, after we concluded a OFF analysis of intra- and intermolecular potentials for alkanes. The nonbonded interactions in the alkane force field were selected to be of the "n-6-1" type, namely composed additively from a Lennard-Jones ("n-6") potential, Eqs. (17) or (19), and a Coulomb ("1") potential (Eq. (21)). Atoms of the same molecule were considered as nonbonded if they were separated by at least 3 consecutive bonds. The Lennard-Jones (LJ) potential is commonly considered to be a "12-6" potential, that is, the exponent n in the repulsive term Ar is taken to be n = 12 (see above). Examining the LJ potential for alkanes, we found that the LJ parameters optimized for intramolecular interactions were too low for intermolecular interactions, while the LJ parameters optimized for intermolecular interactions were too high for intramolecular interactions. These trends -12... 

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