Interaction between two atoms

Assume the following functions for the interaction energy between two atoms of a molecule of common salt (NaCl)  

Compare the result of the calculation with the interatomic distance calculated for a NaCl crystal with a density of = 2.165g/cm l The molar mass of Na is 23g/mol, that of chlorine is 35.4g/mol. Avogadro s constant (the number of molecules in a mol) is Aa = 6.022 x lO mol b Estimate Young s modulus of NaCl in the (100) direction Neglect the bonds between next-nearest neighbours and those even further away Note leV= 1.602 X 10 J. 

The elastic constants of NaCl are Cn = 48.7 GPa, C12 = 12.6 GPa and C44 = 12.75 GPa. Use these values to calculate A ioo) Compare this value to your estimate  

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The raie gas atoms reveal through their deviation from ideal gas behavior that electrostatics alone cannot account for all non-bonded interactions, because all multipole moments are zero. Therefore, no dipole-dipole or dipole-induced dipole interactions are possible. Van der Waals first described the forces that give rise to such deviations from the expected behavior. This type of interaction between two atoms can be formulated by a Lennaid-Jones [12-6] function Eq. (27)). 

We see that the shortcomings of the quasi-chemical theory for dilute solutions also lead to the idea that the interaction between two atoms in solution may be very different from the interaction between the same atoms in the pure state. This is a point of view that can be reached from a consideration of the screening11 by localized or by conduction-band electrons that must occur about... 

The constancy of the ligand radii, in contrast to van der Waals radii, suggests that gem-inal ligands on molecules of period 2 elements are squeezed together almost to their limit of compressibility. The repulsive interaction between two atoms is usually represented by a steeply rising potential such as that shown in Figure 5.7. This potential is often approximately represented by a function of the type... 

We just remark that E P C also includes the leading contribution to the van-der-Waals interaction between two atoms [19]. 

A strongly stabiliztng interaction between two atoms in which certain of their atomic orbitals overlap, thereby resulting in a region of high electron density. This sharing of two electrons in the orbital by the two bonded atoms describes a molecular orbital. 

A secondary bond , as defined by Alcock [6-8], is an interaction between two atoms characterized by a distance longer than the sum of the covalent radii but shorter than the sum of the van der Waals radii of the corresponding atoms. Such secondary interactions are weaker than normal covalent or dative bonds, but strong enough to connect individual molecules and to modify the coordination geometry of the atoms involved. They are often present in a crystal, thus resulting in self-assembled supermolecules or supramolecular architectures. For gold complexes,... 

Fortunately, the same rules apply to interaction between two molecular orbitals as apply to interaction between two atomic orbitals. We shall be able to make a new model to cover the interacting situation by adding and subtracting the molecular orbital functions that were correct for the separate molecules before the interaction occurred. 

For atoms in a vacuum, the induced dipole of the neighboring atom moves in phase with the original dipole. Thus, the energy of interaction between two atoms i and j separated by a distance s is obtained by [London, 1937]... 

Having similar energies is not the only criterion for good interaction between two atomic orbitals. It also matters how the orbitals overlap. We have seen that p orbitals overlap better in an end-on fashion (forming a C bond) than they do side-on (forming a n bond). Another factor is the size of the atomic orbitals. For best overlap, the orbitals should be the same size—a 2p orbital overlaps much better with another 2p orbital than it does with a 3p or 4p orbital. 

Where 0ae(r) is the interaction between two atoms of type a and B and r v means the minimum image distance consistent with periodic boundary conditions. In addition, there can be... 

In some molecular geometries, the so-called intramolecular 1,3 separations are remarkably constant. The 1,3 label refers to the interactions between two atoms in the molecule which are separated by a third atom. The near equality of the nonbonded distances in the ONF3 molecule is a special case. What is more commonly observed is the constancy of a certain 1,3 nonbonded distance throughout a series of related molecules. Significantly, this constancy of 1,3-distances may be accompanied by considerable changes in the bond lengths... 

Some sample potential energy curves for covalent and noncovalent interactions between two atoms are given in Fig. 4.1. The left side shows an interaction curve for the two oxygen atoms in the 0, molecule. This has a large dissociation energy (about 117 kcal/ mol in this case), so that at room temperature where RT approximates 0.6 kcal/mol R is the universal gas constant and T is the absolute temperature), the fraction of "broken" bonds at equilibrium is very small. By con-... 

Before analyzing a general potential function used to describe the interaction between two atomic or polyatomic systems, it is worth briefly recalling the main interaction types, as summarized in Table 1. 

Isolated atoms show spherical symmetry, and it is natural to model atoms by spheres of some suitably defined radii. The potential energy of interaction between two atoms rises very sharply at short internuclear distances during atomic collisions, not unlike the potential energy increase in the collisions of hard, macroscopic bodies. In a somewhat crude, approximate sense, atoms behave as hard balls. This analogy can be used for a simple molecular model where atoms are represented by hard spheres. Once a choice of atomic radii is made, the approximate atomic surfaces can be defined as the surfaces of these spheres. 

Bond valence The strength of an interaction between two atoms expressed in terms of electrostatics. It is used particularly for a description of metal coordination. In coordination, both shared electrons in a bond are provided by one of the two atoms. 

The closer in energy the two interacting orbitals are, the greater their interaction. The better the overlap is between the two orbitals, the greater the interaction. Greater orbital interaction between two atoms means a stronger bond between them. 

Pauling s definition is exhaustive only for interactions between two atoms for instance, the van der Waals bond in the Ar Ar interaction, or the bond in the H2 molecule. However, for more complex systems, it only recognizes the existence of a bond, but not the atoms involved in such a bond, or how many bonds are present. For instance, Pauling s definition recognizes that benzene is an entity with bonds, but does not determine their number or the atoms involved. The same is true for intermolecular bonds, where it cannot determine how many bonds can be found in... 

The energy of the dispersion interaction between two atoms can be presented with fine precision as a sum of three terms ... 

There are different types of forces that make up the interaction between two atoms over a large range of separation. Both experimental phenomena and theoretical considerations suggest that the forces can be categorized as short- and long-range forces. 

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