London quantum dispersive attraction

In addition to the static induction effects included in I/scf, the hot Drude oscillators give rise to a 1/r6, temperature-dependent, attractive term. This jkg Ta2/r6 term is the classical thermodynamic equivalent of the London quantum dispersive attraction IEa2/r6. It corresponds to a small perturbation to the London forces, because k T is at least two orders of magnitude smaller than the typical ionization energy IE. The smaller the temperature of the Drude motion, the closer the effective potential is to the SCF potential, making Eq. (9-57) independent of mo, the mass of the oscillators. 

The dispersion attractive interactions were first characterized by London (1930) and arise from the rapid fluctuations in electron density in one atom, which induce an electrical moment in a neighbouring atom. By making use of quantum-mechanical perturbation theory, London arrived at the well-known expression for the potential energy, eD(r), of two isolated atoms separated by a distance r ... 

On the other hand the description of basis stacking provided by the empirical potential study of Poltev and Shulyupina was quite successful [22]. This unexpected agreement between modem quantum-chemical and empirical potential results can be easily understood. The most demanding part of a quantum-chemical treatment of base stacking is a proper description of intermolecular electron correlation which is responsible for the dispersion attraction. Semi-empirical methods have never succeeded in including this contribution, and it is still not within the reach of DFT techniques. The use of the MP2 method is the minimal requirement. On the other hand, the dispersion attraction is a rather isotropic contribution. It can be well described by the simple empirical London dispersion energy proportional to polarizabilities and the sixth power of the reciprocal interatomic distance. 

London or dispersion forces are the weakest of all of the dipole-dipole. These are best described in quantum mechanical terms, but may be viewed qualitatively as the consequence of the transient asymmetry in the charge distribution in a neutral atom that induces a favorable dipole in a neighboring neutral atom thus leading to a weak attraction. These forces are inversely pro-... 

Van der Waals forces are very complex and manifest themselves even at distances at which it is unreasonable to assume that orbital interactions can occur. An explanation due to London in terms of the mutual attraction of induced dipoles (dispersion forces) accounts for the long-range behavior. The unoccupied-occupied orbital interactions will be the dominant component of van der Waals forces at short range. See Kauzmann, W., Quantum Chemistry, Academic, New York, 1957, Chapter 13, for a discussion of dispersion forces. 

One of the more profound manifestations of quantum mechanics is that this curve does not accurately describe reality. Instead, because the motions of electrons are correlated (more properly, the electronic wave functions are correlated), the two atoms simultaneously develop electrical moments that are oriented so as to be mutually attractive. The force associated with tills interaction is referred to variously as dispersion , the London force, or the attractive van der Waals force. In the absence of a permanent charge, the strongest such interaction is a dipole-dipole interaction, usually referred to as an induced dipole-induced dipole interaction, since the moments in question are not permanent. Such an interaction has an inverse sixtli power dependence on the distance between the two atoms. Thus, the potential energy becomes increasingly negative as the two noble gas atoms approach one another from infinity. 

Also, in the 1930 s London (9) indicated the quantum mechanical origin of dispersion forces between apolar molecules and in subsequent work extended these ideas to interaction between particles (10). It was shown that whereas the force between molecules varied inversely as the seventh power of the separation distance, that between thick flat plates varied inversely as the third power of the distance of surface separation. These ideas lead directly to the concept of a "long range van der Waals attractive force. A similar relationship was found for interaction between spheres (10). 

Physical adsorption is a universal phenomena, producing some, if not the major, contribution to almost every adhesive contact. It is dependent for its strength upon the van der Waals attraction between individual molecules of the adhesive and those of the substrate. Van der Waals attraction quantitatively expresses the London dispersion force between molecules that is brought about by the rapidly fluctuating dipole moment within an individual molecule polarizing, and thus attracting, other molecules. Grimley (1973) has treated the current quantum mechanical theories involved in simplified mathematical terms as they apply to adhesive interactions. 

The third contribution to the attractive forces comes from London dispersion forces. These arise from the instantaneous dipoles on the molecules formed by the moving electrons. Thus, inert gas atoms such as helium and argon possess instantaneous dipole moments formed by the electron cloud, which is constantly in motion. Dispersion forces were analyzed using quantum mechanics by London [2] who derived the following expression for the attractive potential ... 

A quantum mechanical interpretation of temporary dipoles was provided by Fritz London in 1930. London showed that the magnitude of this attractive interaction is directly proportional to the polarizability of the atom or molecule. As we might expect, dispersion forces may be quite weak. This is certainly true for helium, which has a boiling point of only 4.2 K, or 269°C. (Note that hehum has only two electrons, which are tightly held in the Is orbital. Therefore, the helium atom has low polarizability.)... 

Polarizability plays the central role in the most universal intermolecular force. Up to this point, we ve discussed forces that depend on an existing charge, of either an ion or a polar molecule. But what forces cause nonpolar substances like octane, chlorine, and argon to condense and solidify Some force must be acting between the particles, or these substances would be gases under any conditions. The intermolecular force primarily responsible for the condensed states of nonpolar substances is the dispersion force (or London force, named for Fritz London, the physicist who explained the quantum-mechanical basis of the attraction). 

Attractive forces between neutral molecules may be partially explained with electric dipole interactions. Keesom explained attractive forces between permanent dipoles in thermal motion, and Debyeinvestigated permanent and induced dipoles. The induced-induced dipole interaction could be understood adequately only after the advent of quantum theory. The general character of these forces was explained by London as a perturbation of zero-point energies. He also made a connection with the dispersion... 

The most frequent and important effect of the intermolecular forces is the London dispersion effect [123-125] between neutral atoms of the film and the atoms of the substrate surface. These quantum mechanical dispersion forces, which are based on a common influencing of the electron movement, produce the attraction. The adsorption energy E a of a film atom onto a surface atom may be expressed ... 

As van der Waals postulated, the attractive forces between neutral molecules also originate from electrical interactions (Hiemenz 1986). Although there are several types of van der Waals attractive forces that originate from electrical interactions, the most important for colloids is that operating between nonpolar molecules. These forces are due to the polarization of one molecule by quantum fluctuations in the charge distribution in the second molecule, and vice versa. They are known as the London dispersion forces, their origin having first been explained by F. London in 1930. 

The curve in Figure 4.32 is usually considered to arise from a balance between attractive and repulsive forces. The attractive forces are long-range, whereas the repulsive forces act at short distances. The attractive contribution is due to dispersive forces. London first showed how the dispersive force could be explained using quantum mechanics [London 1930] and so this interaction is sometimes referred to as the London force. The dispersive force... 

The sum of the two energies given by (i.iy) and (1.19) still does not give the correct interaction between molecules. This is obvious, since these equations allow no attraction between molecules lacking a permanent dipole moment (x, whereas we know that the attractive force between such molecules is by no means negligible. The additional force, which is of quantum origin and universal effect, is called a dispersion force (London, 1937). 

Dispersion forces arise because of the fluctuations and uncertainties which are fundamental in quantum mechanics. Thus, though the expectation value of a molecular dipole may be zero, the instantaneous value fluctuates about zero because <(x —<(i = <(x > —<( ,> does not vanish. This instantaneous fluctuating dipole can cause polarization effects in a neighbouring molecule in the same way as does a permanent dipole and this leads to an attractive potential varying as Details of the calculation are given by London (1937) and Buckingham (1965) and in standard texts on quantum mechanics and we will not repeat them here. The approximate result found by London was... 

As discussed above, significant discrepancies were observed between quantum benchmarks and force fields for non-bonded interactions in the benzene dimer (Sherrill et al., 2009a). Analysis of the discrepancies was greatly aided by the use of energy component analysis, specifically the SAPT method. A detailed analysis of the parallel-displaced benzene dimer at a fixed vertical distance of 3.4 A is shown in Fig. 3.4. As seen from the figure, the London dispersion interaction computed by the force field through the attractive part of the Lennard-Jones potential is fairly accurate compared to the quantum SAPT results. Moreover, in this system, SAPT shows that... 

Dispersion forces are often called London forces, afterthe German-born physicist Fritz London (1900-1954). He initially postulated their existence in 1930, on the basis of quantum theory. Yet another name is van der Waals attractive forces. You should be familiar with all three names. 

---