Electrostatics Coulombic interactions

In this chapter we meet three increasingly sophisticated models of molecular shape. The first considers molecular shape to be a consequence merely of the electrostatic (coulombic) interaction between pairs of electrons. The other two models are theories that describe the distribution of electrons and molecular shape in terms of the occupation of orbitals. 

Term wavefunctions describe the behaviour of several electrons in a free ion coupled together by the electrostatic Coulomb interactions. The angular parts of term wavefunctions are determined by the theory of angular momentum as are the angular parts of one-electron wavefunctions. In particular, the angular distributions of the electron densities of many-electron wavefunctions are intimately related to those for orbitals with the same orbital angular momentum quantum number that is. 

The electrostatic (Coulombic) interaction is a long range order interaction. The electrostatic interaction is inversely proportional to the dielectric constant of the medium. Therefore, this interaction becomes more important in a hydrophobic... 

Electrostatic coulombic interactions Attractive or repulsive interactions... 

In this instance the point-charge simulation is precise, but unlike the covalent case, the primary interaction is not shielded against secondary interference. Each ion is surrounded by six nearest neighbours of opposite charge, at a distance d = a/2, equivalent to an electrostatic coulomb interaction,... 

Interpreting bulk properties qualitatively on the basis of microscopic properties requires only consideration of the long-range attractive forces and short-range repulsive forces between molecules it is not necessary to take into account the details of molecular shapes. We have already shown one kind of potential that describes these intermolecular forces, the Lennard-Jones 6-12 potential used in Section 9.7 to obtain corrections to the ideal gas law. In Section 10.2, we discuss a variety of intermolecular forces, most of which are derived from electrostatic (Coulomb) interactions, but which are expressed as a hierarchy of approximations to exact electrostatic calculations for these complex systems. 

In vacuum, the long-range attractive van der Waals interactions as well as the short-range chemical forces are the predominant interaction between sample and tip (provided that electrostatic Coulomb interactions are carefully compensated or negligible and the tip is non-magnetic). The van der Waals forces are caused by the interaction of fluctuations in the electromagnetic field and are attractive when the tip approaches the surface, the chemical forces originate from Pauli-exclusion and nuclear-repulsion. The attraction increases until tip and sample have approximately the distance of a chemical bond. When distance between tip and surface is further decreased the interaction becomes repulsive (for more details see [83]). 

The basic building blocks of the materials world are electrons and nuclei interacting via electrostatic Coulomb interactions. Thus, the starting point of a theoretical treatment of the chemical and physical properties of materials is the Hamiltonian... 

The model and theory, like that of the Debye-Htickel treatment of non-ideality, were based on consideration of long range electrostatic coulombic interactions only. The model was most likely to be inadequate because it did not take into account specific short range interactions corresponding to ion-ion, ion-solvent, and solvent-solvent interactions. 

Many properties of disperse systems are related to the distribution of charges in the vicinity of the interface due to the adsorption of electrolytes. The adsorption of molecules is driven by the van der Waals attraction, while the driving force for the adsorption of electrolytes is the longer-range electrostatic (Coulomb) interaction. Because of this, the adsorption layers in the latter case are less compact than in the case of molecular adsorption (i.e., they are somewhat extended into the bulk of the solution), and the discontinuity surface acquires noticeable, and sometimes even macroscopic thickness. This diffuse nature of the ionized adsorption layer is responsible for such important features of disperse systems as the appearance of electrokinetic phenomena (see Chapter V) and colloid stability (Chapters VII, VIII). Another peculiar feature of the adsorption phenomena in electrolyte solutions is the competitive nature of the adsorption in addition to the solvent there are at least two types of ions (even three or four, if one considers the dissociation of the solvent) present in the system. Competition between these ions predetermines the structure of the discontinuity surface in such systems -i.e. the formation of spatial charge distribution, which is referred to as the electrical double layer (EDL). The structure and theory of the electrical double layer is described in detail in textbooks on electrochemistry. Below we will primarily focus on those features of the EDL, which are important in colloid... 

There are several types of intermolecular interactions, each of which involves electrostatic forces of some kind or other. An example is provided by the ion-ion interactions between cations and anions. Pure electrostatic (Coulombic) interactions are long-range and many, such as hydrogen bonding, are directional. Molecules can, however, be distorted by the electric fields of surrounding molecules, even if the molecules themselves are electrically neutral. 

Atoms by comparison are familiar objects, and the forces which govern atomic structures are simply the electrostatic Coulomb interactions of nuclei and electrons. These forces follow the law of inverse squares and provide the central accelerations required to maintain the electrons in orbital motion about the nuclei. The numbers and modes of disposition of electrons are governed not by laws of force but by quantum rules, a matter which has already been discussed in some detail. 

When electronic excited states in the QM region are considered, each electronic state possesses unique electronic density and thus interacts differently with polarizable environment. Purely electrostatic (Coulomb) interactions between solvent and electronically excited solute are automatically taken into account due to a presence of the one-electron Coulomb term in the QM Hamiltonian (Eq. 5.10). A part of polarization interactions is also represented in a similar way due to an explicit inclusion of EFP induction terms in the QM Hamiltonian, as given by Eq. 5.11. 

The belief that electrostatic (Coulomb) interactions exhibit little directionality (i.e., that their energy hardly depends on the bond angle) is widespread. This is because the concept of net atomic charges (atom-centered monopoles) has become ingrained in chemists thinking, so that Coulomb interactions with a polar atom are believed to be necessarily isotropic and directionahty of Coulomb interactions only to be the result of secondary interactions with more distant atoms. Neither of these assumptions is correct and the reasons have been known for decades. Nonetheless, directionality in noncovalent interactions is still often attributed to covalent contributions or donor-acceptor interactions because the Coulomb interaction is believed not to be able to give rise to significant directionality. The purpose of this chapter is to discuss Coulomb interactions with special emphasis on directionality and anisotropy of the molecular electrostatic potential (MEP) [1] around atoms. 

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