London Dispersion Forces

An important extension of these ideas is to cases where an ion interacts with polar molecules (ion-dipole forces). In such cases the polarity of the molecule is increased because of the inductive effect caused by the ion. Polar solvent molecules that surround an ion in the solvation sphere do not have the same polarity as do the molecules in the bulk solvent. 

In addition to the intermolecular forces that exist as a result of permanent charge separations in molecules, there must be some other type of force. Sometimes referred to as electronic van der Waals 

In order to arrive at a mathematical relationship to describe London forces, we will use an intuitive approach. First, the ability of the electrons to be moved within the molecule is involved. Atoms or molecules in which the electrons are highly localized cannot have instantaneous dipoles of any great magnitude induced in them. A measure of the ability of electrons in a molecule to be shifted is known as the electronic polarizability, a. In fact, each of the interacting molecules has a polarizability, so the energy arising from London forces, Ei, is proportional to a2. London forces are important only at short distances, which means that the distance of separation is in the denominator of the equation. In fact, unlike Coulomb s law, which has r2 in the denominator, the expression for London forces involves r6. Therefore, the energy of interaction as a result of London forces is expressed as 

It is interesting to note that many different types of molecules have ionization potentials that do not differ greatly. Table 6.3 shows typical values for molecular ionization potentials for a wide variety of substances. 

If two different types of molecules having polarizabilities a1 and a2 are interacting, the London energy between them can be expressed as 

Dipole-dipole and dipole-induced dipole interactions result from the attraction of species having charge separations. However, molecules having no charge separation can be liquefied. Helium, H2, N2. 02. and other nonpolar molecules still interact weakly. The nature of this interaction is determined by the fact that even for nonpolar atoms and molecules the electrons are not always distributed symmetrically. It is certainly possible that for He the two electrons can be found at some particular instant on the same side of the nucleus  

There is an instantaneous dipole that will cause there to be an instantaneous change in the electron distribution in the neighboring atom. As a result, there is a weak attraction between the nuclei in one molecule and the electrons in another. The ability to have the electrons shifted in this way is related to the polarizability, a, of the molecule. This type of force is called the London or dispersion force, and the energy of this type of interaction, L, can be expressed by the equation 

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Attractive and Repulsive Forces. The force that causes small particles to stick together after colliding is van der Waals attraction. There are three van der Waals forces (/) Keesom-van der Waals, due to dipole—dipole interactions that have higher probabiUty of attractive orientations than nonattractive (2) Debye-van der Waals, due to dipole-induced dipole interactions (ie, uneven charge distribution is induced in a nonpolar material) and (J) London dispersion forces, which occur between two nonpolar substances. 

There are probably several factors which contribute to determining the endo exo ratio in any specific case. These include steric effects, dipole-dipole interactions, and London dispersion forces. MO interpretations emphasize secondary orbital interactions between the It orbitals on the dienophile substituent(s) and the developing 7t bond between C-2 and C-3 of the diene. There are quite a few exceptions to the Alder rule, and in most cases the preference for the endo isomer is relatively modest. For example, whereas cyclopentadiene reacts with methyl acrylate in decalin solution to give mainly the endo adduct (75%), the ratio is solvent-sensitive and ranges up to 90% endo in methanol. When a methyl substituent is added to the dienophile (methyl methacrylate), the exo product predominates. ... 

Among all the low energy interactions, London dispersion forces are considered as the main contributors to the physical adsorption mechanism. They are ubiquitous and their range of interaction is in the order 2 molecular diameters. For this reason, this mechanism is always operative and effective only in the topmost surface layers of a material. It is this low level of adhesion energy combined with the viscoelastic properties of the silicone matrix that has been exploited in silicone release coatings and in silicone molds used to release 3-dimensional objects. However, most adhesive applications require much higher energies of adhesion and other mechanisms need to be involved. 

In this equation, AG°CS is taken to be negligible for p- and y-cyclodextrin systems and to be constant, if there is any, for the a-cyclodextrin system. The AG W term is virtually independent of the kind of guest molecules, though it is dependent on the size of the cyclodextrin cavity. The AG dw term is divided into two terms, AG°,ec and AGs°ter, which correspond to polar (dipole-dipole or dipole-induced dipole) interactions and London dispersion forces, respectively. The former is mainly governed by the electronic factor, the latter by the steric factor, of a guest molecule. Thus, Eq. 2 is converted to Eq. 3 for the complexation of a particular cyclodextrin with a homogeneous series of guest molecules ... 

Matsui75) has computed energies (Emin) which correspond to the minimal values of Evdw in Eq. 1 for cyclodextrin-alcohol systems (Table 2). Besides normal and branched alkanols, some diols, cellosolves, and haloalkanols were involved in the calculations. The Emi values obtained were adopted as a parameter representing the London dispersion force in place of Es. Regression analysis gave Eqs. 9 and 10 for a- and P-cyclodextrin systems respectively. 

Kristyan, S., Pulay, P., 1994, Can (Semi)Local Density Functional Theory Account for the London Dispersion Forces , Chem. Phys. Lett., 229, 175. 

The physical forces involved in the hydrogen bond must include electrostatic and inductive forces in addition to London dispersion forces... 

Although the fact that the cycloamyloses include a variety of substrates is now universally accepted, the definition of the binding forces remains controversial. Van der Waals-London dispersion forces, hydrogen bonding, and hydrophobic interactions have been frequently proposed to explain the inclusion phenomenon. Although no definitive criteria exist to distinguish among these forces, several qualitative observations can be made. 

When the hydrophobic effect brings atoms very close together, van der Waals interactions and London dispersion forces, which work only over very short distances, come into play. This brings things even closer together and squeezes out the holes. The bottom line is a very compact, hydrophobic core in a protein with few holes. 

In nature, the halogens exist as nonpolar diatomic molecules. London dispersion forces are the only forces of attraction acting between the molecules. These forces increase with increasing molecular size. 

The discussion thus far has focused on the forces between an array of atoms connected together through covalent bonds and their angles. Important interactions occur between atoms not directly bonded together. The theoretical explanation for attractive and repulsive forces for nonbonded atoms i and j is based on electron distributions. The motion of electrons about a nucleus creates instantaneous dipoles. The instantaneous dipoles on atom i induce dipoles of opposite polarity on atom j. The interactions between the instantaneous dipole on atom i with the induced instantaneous dipole on atom j of the two electron clouds of nonbonded atoms are responsible for attractive interactions. The attractive interactions are know as London Dispersion forces,70 which are related to r 6, where r is the distance between nonbonded atoms i and j. As the two electron clouds of nonbonded atoms i and j approach one another, they start to overlap. There is a point where electron-electron and nuclear-nuclear repulsion of like charges overwhelms the London Dispersion forces.33 The repulsive... 

The electron density changes continually, so induced dipoles never last more than about 10-11 s. Nevertheless, they last sufficiently long for an interaction to form with the induced dipole of another nitrogen molecule nearby. We call this new interaction the London dispersion force after Fritz London, who first postulated their existence in 1930. 

The weakest of all the intermolecular forces in nature are always London dispersion forces. 

In general, polarizability increases as the orbital increases in size negative electrons orbit the positive nucleus at a greater distance in such atoms, and consequently experience a weaker electrostatic interaction. For this reason, London dispersion forces tend to be stronger between molecules that are easily polarized, and weaker between molecules that are not easily polarized. 

The strength of the London dispersion forces becomes stronger with increased polarizability, so larger molecule (or atoms) form stronger bonds. This observation helps explain the trends in physical state of the Group VII(b) halogens I2 is a solid, Br2 is a liquid, and Cl2 and L2 are gases. 

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