Bonds van der Waals interactions

N is the number of point charges within the molecule and Sq is the dielectric permittivity of the vacuum. This form is used especially in force fields like AMBER and CHARMM for proteins. As already mentioned, Coulombic 1,4-non-bonded interactions interfere with 1,4-torsional potentials and are therefore scaled (e.g., by 1 1.2 in AMBER). Please be aware that Coulombic interactions, unlike the bonded contributions to the PEF presented above, are not limited to a single molecule. If the system under consideration contains more than one molecule (like a peptide in a box of water), non-bonded interactions have to be calculated between the molecules, too. This principle also holds for the non-bonded van der Waals interactions, which are discussed in Section 7.2.3.6. 

The stereoelectronic features produce actions at a distance by the agency of the recognition forces they create. These forces are the hydrophobic effect, and the capacity to enter ionic bonds, van der Waals interactions and H-bonding interactions. The most convenient and informative assessment of such recognition forces is afforded by computahon in the form of MIFs, e.g. lipophilicity fields, hydrophobicity fields, molecular electrostatic potentials (MEPs) and H-bonding fields (see Chapter 6) [7-10]. 

Substrates bind to the active site of the enzyme through a variety of interactions such as ionic bonding, hydrogen bonding, van der Waals interaction or dipole-dipole Interachon (Fig. 16.1). 

Eagland et al. ( 3) propose a different scheme. The helix formation is compared to a first order reaction concerning only individual chains. In the first step the helices are nucleated and stabilized by the solvent. Next, the chains slowly fold back and the helical sequences associate by hydrogen bonds. Van der Waals interactions or entanglements between the folded chains are responsible for the gel gormation (see Figure 1-b). 

Non-Bonded Interactions. Interactions between atoms which are not directly bonded, van der Waals Interactions and Coulombic Interactions are non-bonded interactions. 

In order that the contribution from random-coil sequences might be more correctly evaluated, Miller and Flory (43) carried out a calculation, taking into account the hindrance to internal rotation of bonds, van der Waals interactions of non-bonded atoms, dipole-dipole interactions between atomic groups, and so forth. However, no excluded-volume effect was allowed for. Actually, they... 

The fundamental assumption underlying the molecular mechanics (MM) method is that the positions of the atoms of a molecule, ion, solvate, or crystal lattice are determined by forces between pairs of atoms (bonds, van der Waals interactions, hydrogen bonding and electrostatic interactions), and between groups of three (valence angles) and groups of four (torsional angles, planes) atoms (Fig. 2.1). 

The quantum theory of atoms in molecules (QTAIM) [25, 26] is based on analyses of the electron density distribution. The electron density of such systems such as simple molecules or ions, and also complexes, complex molecular and ionic aggregates, as well as crystals may be analyzed using this approach. QTAIM is a powerful tool that allows characterizing of various interactions covalent bonds, ionic bonds, van der Waals interactions and, what is the most important for this review, also HBs. The analysis of critical points of the electron density is very useful. For the critical points (CPs), the gradient of electron density, p(r), vanishes ... 

In order to include curvature-dependence in both the covalent and non-bonding interactions, we used the adaptive intermolecular reactive bond-order (AIREBO) potential,24 with modified van der Waals interactions. This potential uses the same bonding interactions as Brenner s REBO potential,25,26 both of which correctly account for local curvature dependence in the covalent bonding interactions. Chemisorption is thus treated accurately, but there is no explicit or implicit curvature dependence in the Lennard-Jones (L-J) parameters used to describe the non-bonded van der Waals interactions (physisorption). Consequently, we modified the Lennard-Jones parameters to make them explicitly dependent on the curvature of the nanotube. 

Molecular self-assembly is defined as the spontaneous condensation of molecules into ordered arrays by noncovalent forces [refs. 20,24]. For molecular self-assembly to be reversible, the free energy of interaction, AG°, between two molecules must be comparable to the average thermal energy, kT, of molecules. Molecular self-assembly ordinarily involves weak interactions (e.g. hydrogen bonds, van der Waals interactions, and hydrophobic interactions). Although one, two, or all three dimensions of the final array may extend into the millimeter... 

Generally, however, the specific stacking patterns found in crystals of purine derivatives are surprisingly consistent, especially when the influences of additional factors such as hydrogen bonding, van der Waals interactions and steric factors are taken into account. 

Noncovalent Bonds. Noncovalent bonds are weaker than covalent bonds but arc crucial for biochemical processes such as the formation of a double helix, hour lundamental noncovalent bond types are electrostatic interactions, hydrot en bonds, van der Waals interactions, and hydrophobic inlerac-turns. T hey differ in geometry, strength, and specificity. Furthermore, these bunds are allected in vastly different ways by the presence of water. Let us consider the characteristics of each ... 

Keywords Hydrogen bonds van der Waals interactions C-H- - -X interactions ab initio calcu-... 

Four main types of noncovalent Interactions occur In biological systems Ionic bonds, hydrogen bonds, van der Waals Interactions, and Interactions due to the hydrophobic effect. 

Supramolecular chemistry may be defined as "chemistry beyond the molecule." bearing on the organized entities of higher complexity that result from the association of two or more chemical species held together by intermo-lecular noncovalent forces, such as metal ion coordination, electrostatic forces, hydrogen bonding, van der Waals interactions, and others.These supramolecular entities derived from supramolecular association are generally called supermolecules or supramolecular compounds. Thus, one may say that "supramolecules are to... 

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