Electrostatic and van der Waals Interactions

A molecular dynamics force field is a convenient compilation of these data (see Chapter 2). The data may be used in a much simplified fonn (e.g., in the case of metric matrix distance geometry, all data are converted into lower and upper bounds on interatomic distances, which all have the same weight). Similar to the use of energy parameters in X-ray crystallography, the parameters need not reflect the dynamic behavior of the molecule. The force constants are chosen to avoid distortions of the molecule when experimental restraints are applied. Thus, the force constants on bond angle and planarity are a factor of 10-100 higher than in standard molecular dynamics force fields. Likewise, a detailed description of electrostatic and van der Waals interactions is not necessary and may not even be beneficial in calculating NMR strucmres. 

In Eq. (6) Ecav represents the energy necessary to create a cavity in the solvent continuum. Eel and Eydw depict the electrostatic and van-der-Waals interactions between solute and the solvent after the solute is brought into the cavity, respectively. The van-der-Waals interactions divide themselves into dispersion and repulsion interactions (Ed sp, Erep). Specific interactions between solute and solvent such as H-bridges and association can only be considered by additional assumptions because the solvent is characterized as a structureless and polarizable medium by macroscopic constants such as dielectric constant, surface tension and volume extension coefficient. The use of macroscopic physical constants in microscopic processes in progress is an approximation. Additional approximations are inherent to the continuum models since the choice of shape and size of the cavity is arbitrary. Entropic effects are considered neither in the continuum models nor in the supermolecule approximation. Despite these numerous approximations, continuum models were developed which produce suitabel estimations of solvation energies and effects (see Refs. 10-30 in 68)). 

From (2.70), it follows that the free energy cannot be divided simply into two terms, associated with the interactions of type a and type b. There are also coupling terms, which would vanish only if fluctuations in AUa and AUb were uncorrelated. One might expect that such a decoupling could be accomplished by carrying out the transformations that involve interactions of type a and type 6 separately. In Sect. 2,8.4, we have already discussed such a case for electrostatic and van der Waals interactions in the context of single-topology alchemical transformations. Even then, however, correlations between these two types of interactions are not... 

Hirshfeld and Mirsky (1979) evaluated the relative contributions to the lattice energy for the crystal structures of acetylene, carbon dioxide, and cyanogen, using theoretical charge distributions. Local charge, dipole and quadrupole moments are used in the evaluation of the electrostatic interactions. When the unit cell dimensions are allowed to vary, inclusion of the electrostatic forces causes an appreciable contraction of the cell. In this study, the contributions of the electrostatic and van der Waals interactions to the lattice energy are found to be of comparable magnitude. 

When the KCl(lOO) substrates are held at RT we can observe that the microcrystals are equally distributed in perpendicular directions. In addition to the increase in size with increasing Tgub, the microcrystals in the same direction tend to agglomerate leaving, however, the hnal microcrystal distribution unaltered no temperature-induced in-plane preferential orientation is observed. In case 3 a considerable number of microcrystals become curved. This is due to the triggering of in-plane growth directions other than the equivalent [110] directions caused by the contributions of the electrostatic and van der Waals interactions to the total energy at the interface (Caro et al, 1997). 

In this section, we calculate the energy for the preparation of monolayer particle-coated powder. Firstly, the energy is calculated on the assumption that the pure electrostatic interaction works mainly on adhesion between particles (11). Second, the energy is calculated on the basis of the assumption that the electrostatic and van der Waals interaction work together (12). 

In atomic force microscopy (AFM), the sharp tip of a microscopic probe attached to a flexible cantilever is drawn across an uneven surface such as a membrane (Fig. 1). Electrostatic and van der Waals interactions between the tip and the sample produce a force that moves the probe up and down (in the z dimension) as it encounters hills and valleys in the sample. A laser beam reflected from the cantilever detects motions of as little as 1 A. In one type of atomic force microscope, the force on the probe is held constant (relative to a standard force, on the order of piconewtons) by a feedback circuit that causes the platform holding the sample to rise or fall to keep the force constant. A series of scans in the x and y dimensions (the plane of the membrane) yields a three-dimensional contour map of the surface with resolution near the atomic scale—0.1 nm in the vertical dimension, 0.5 to 1.0 nm in the lateral dimensions. The membrane rafts shown in Figure ll-20b were visualized by this technique. 

When instead assemblies of helices are taken into account, it is well known that for many aspects DNA duplexes in solution can be treated as a charged anisotropic particle [2]. Accordingly, steric, electrostatic, and Van der Waals interactions, together with the mechanical properties of the helix (bending and torsional rigidity), play a major role in the formation of DNA mesophases. In addition, all these different kinds of interactions combine in a subtle and still poorly understood way to generate other forces relevant for the case of DNA. A notable example is the helix-specific, chiral interaction, whose importance for DNA assemblies will be discussed below. 

The disulfide bond differs from other types of interactions in folded proteins, such as hydrogen bonds and hydrophobic, electrostatic and van der Waals interactions. The disulfide bond is a covalent bond that is able to significantly stabilize folded conformations by 2-5 kcal/ mol for each disulfide.11 The effect is presumed to be due mainly to a decrease in the configurational chain entropy of the unfolded polypeptide.21 On the other hand, another view is that the disulfide bond destabilizes folded structures entropically, but stabilizes them enthalpically to a greater extent.31... 

The last term in the formula (1-196) describes electrostatic and Van der Waals interactions between atoms. In the Amber force field the Van der Waals interactions are approximated by the Lennard-Jones potential with appropriate Atj and force field parameters parametrized for monoatomic systems, i.e. i = j. Mixing rules are applied to obtain parameters for pairs of different atom types. Cornell et al.300 determined the parameters of various Lenard-Jones potentials by extensive Monte Carlo simulations for a number of simple liquids containing all necessary atom types in order to reproduce densities and enthalpies of vaporization of these liquids. Finally, the energy of electrostatic interactions between non-bonded atoms is calculated using a simple classical Coulomb potential with the partial atomic charges qt and q, obtained, e.g. by fitting them to reproduce the electrostatic potential around the molecule. 

Surface and Colloid Science employs extensively black films in its research. They can be the model of study of molecular interactions between two contacting phases at small distances, such as electrostatic and van der Waals interactions, of the factors related to specific ionic interactions at interfaces, etc. 

The experimental isotherm for films from Cio(EO)4 lays between the two theoretical curves obtained at Oo = const and (po = const. Therefore, it can be supposed that in this case the DLVO-theory describes well the electrostatic and van der Waals interactions in foam films in both cases of constant surface charge or ( -potential [e.g. 264],... 

The stability of colloidal systems consisting of charged particles can be essentially explained by the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory [1-7]. According to this theory, the stability of a suspension of colloidal particles is determined by the balance between the electrostatic interaction and the van der Waals interaction between particles. A number of studies on colloid stability are based on the DLVO theory. In this chapter, as an example, we consider the interaction between lipid bilayers, which serves as a model for cell-cell interactions [8, 9]. Then, we consider some aspects of the interaction between two soft spheres, by taking into account both the electrostatic and van der Waals interactions acting between them. 

In the molecular mechanical force fields, the intermolecular interactions are most often described by the electrostatic and Van der Waals interactions. The MM atoms are normally represented by point charges and Lennard-Jones parameters (usually centered on atoms) in the calculation of intermolecular interactions. Therefore, a simple coupling can be established as shown schematically in Figure 2 and the corresponding Hamiltonian as in eq.(7). [12]... 

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