Dipole moments instantaneous

In the crystals of inherent gases the cohesion between atoms is given by the van der Waals interaction. The origin of this interaction consists in the fact that the electrons are in movement around the nucleus, even in the lowest energetic state, so even for OK. The electrons movement produces a dipole moment instantaneous non-null, which will induce a dipole moment instantaneous in the neighboring atom and so one. The van der Waals interaction is un-oriented, thereby, in these structures will appear the tendency that an atom will be siuroimded with a maximum number from other atoms. 

The average cloud is spherically synnnetric with respect to the nucleus, but at any instant of time there may be a polarization of charge givmg rise to an instantaneous dipole moment. This instantaneous dipole induces a corresponding instantaneous dipole in the other atom and there is an interaction between the instantaneous dipoles. The dipole of either atom averages to zero over time, but the interaction energy does not because the instantaneous and induced dipoles are correlated and... 

Fi E- Zi eri F2 >. Here erj is the one-eleetron operator deseribing the interaetion of an eleetrie field of magnitude and polarization E with the instantaneous dipole moment... 

To understand the origins of dispersion forces, let us consider two Bohr atoms, each of which consists of an electron orbiting around a nucleus comprised of a proton, having a radius ao, often referred to as the first Bohr radius . It is obvious that a Bohr atom has no permanent dipole moment. However, the Bohr atom can be considered to have an instantaneous dipole moment given by... 

The dispersion (London) force is a quantum mechanieal phenomenon. At any instant the electronic distribution in molecule 1 may result in an instantaneous dipole moment, even if 1 is a spherieal nonpolar moleeule. This instantaneous dipole induces a moment in 2, which interacts with the moment in 1. For nonpolar spheres the induced dipole-induced dipole dispersion energy function is... 

An instantaneous dipole moment on one molecule distorts the electron cloud on a neighboring molecule and gives rise to a dipole moment on that molecule the two instantaneous dipoles attract each other. An instant later, the swirling electron cloud of the first molecule will give rise to a dipole moment in a different direction,... 

FIGURE 5.5 The rapid fluctuations in the electron distribution in two neighboring molecules result in two instantaneous electric dipole moments that attract each other. The fluctuations flicker into different positions, but each new arrangement in one molecule induces an arrangement in the other that results in mutual attraction. 

FIGURE 5.7 (a) The instantaneous dipole moments in two neighboring rod-shaped molecules tend to be close together and interact strongly over a relatively broad region of the molecule, (b) Those on neighboring spherical molecules tend to be farther apart and interact weakly over only a small region of the molecule. 

The transfer of the electron takes place very rapidly compared to nuclear motion, and will only take place when the combination of internal and librational coordinates is such that the curves interact. Thus, the [Fe(H20)6] + species must first distort and/or experience a dipole moment field from the instantaneous positions of the water molecules such that it attains the cross-over point. At this point, the electron may tunnel from the [Fe(H20)6]2+ ion to the metal, leaving behind an [Fe(H20)6]3 + ion with a non-equilibrium geometry, This then relaxes by heat transfer to the solvent to the equilibrium point, q0. 

As well as these permanent dipole moments, random motion of electron density in a molecule leads to a tiny, instantaneous dipole, which can also induce an opposing dipole in neighbouring molecules. This leads to weak intermolecu-lar attractions which are known as dispersive forces or London forces, and are present in all molecules, ions and atoms - even those with no permanent dipole moment. Dispersive forces decrease rapidly with distance, and the attractions are in proportion to 1/r6, where r is the distance between attracting species. 

Like the Coulombic forces, the van der Waals interactions decrease less rapidly with increasing distance than the repulsive forces. They include interactions that arise from the dipole moments induced by nearby charges and permanent dipoles, as well as interactions between instantaneous dipole moments, referred to as dispersion forces (Israelachvili 1992). Instantaneous dipole moments can be thought of as arising from the motions of the electrons. Even though the electron probability distribution of a spherical atom has its center of gravity at the nuclear position, at any very short instance the electron positions will generally not be centered on the nucleus. 

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