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London dispersion force
Encyclopedia
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Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
s and molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
s. They are part of the van der Waals forces. The LDF is named after the German-American physicist Fritz London
Fritz London
Fritz Wolfgang London was a German theoretical physicist. His fundamental contributions to the theories of chemical bonding and of intermolecular forces are today considered classic and are discussed in standard textbooks of physical chemistry.With his brother Heinz, he made a significant...
.
The LDF is a weak intermolecular force
Intermolecular force
Intermolecular forces are forces of attraction or repulsion which act between neighboring particles: atoms, molecules or ions. They are weak compared to the intramolecular forces, the forces which keep a molecule together...
arising from quantum
Quantum
In physics, a quantum is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization". This means that the magnitude can take on only certain discrete...
induced instantaneous polarization multipoles in molecules. They can therefore act between molecules without permanent multipole moments
Multipole moments
In mathematics, especially as applied to physics, multipole moments are the coefficients of a series expansion of a potential due to continuous or discrete sources . A multipole moment usually involves powers of the distance to the origin, as well as some angular dependence...
.
London forces are exhibited by nonpolar molecules because of the correlated movements of the electrons
Electronic correlation
Electronic correlation is the interaction between electrons in the electronic structure of a quantum system.- Atomic and molecular systems :...
in interacting molecules. Because the electrons from different molecules start "feeling" and avoiding each other, electron density
Electron density
Electron density is the measure of the probability of an electron being present at a specific location.In molecules, regions of electron density are usually found around the atom, and its bonds...
in a molecule becomes redistributed in proximity to another molecule, (see quantum mechanical theory of dispersion forces). This is frequently described as formation of "instantaneous dipoles" that attract each other. London forces are present between all chemical groups and usually represent the main part of the total interaction force in condensed matter
Condensed Matter
Condensed matter may refer to several things*Condensed matter physics, the study of the physical properties of condensed phases of matter*European Physical Journal B: Condensed Matter and Complex Systems, a scientific journal published by EDP sciences...
, even though they are generally weaker than ionic bonds and hydrogen bond
Hydrogen bond
A hydrogen bond is the attractive interaction of a hydrogen atom with an electronegative atom, such as nitrogen, oxygen or fluorine, that comes from another molecule or chemical group. The hydrogen must be covalently bonded to another electronegative atom to create the bond...
s.
This is the only attractive intermolecular force present between neutral atoms (e.g., a noble gas
Noble gas
The noble gases are a group of chemical elements with very similar properties: under standard conditions, they are all odorless, colorless, monatomic gases, with very low chemical reactivity...
). Without London forces, there would be no attractive force between noble gas
Noble gas
The noble gases are a group of chemical elements with very similar properties: under standard conditions, they are all odorless, colorless, monatomic gases, with very low chemical reactivity...
atoms, and they wouldn't exist in liquid form.
London forces become stronger as the atom or molecule in question becomes larger. This is due to the increased polarizability of molecules with larger, more dispersed electron clouds. This trend is exemplified by the halogen
Halogen
The halogens or halogen elements are a series of nonmetal elements from Group 17 IUPAC Style of the periodic table, comprising fluorine , chlorine , bromine , iodine , and astatine...
s (from smallest to largest: F2, Cl2, Br2, I2). Fluorine
Fluorine
Fluorine is the chemical element with atomic number 9, represented by the symbol F. It is the lightest element of the halogen column of the periodic table and has a single stable isotope, fluorine-19. At standard pressure and temperature, fluorine is a pale yellow gas composed of diatomic...
and chlorine
Chlorine
Chlorine is the chemical element with atomic number 17 and symbol Cl. It is the second lightest halogen, found in the periodic table in group 17. The element forms diatomic molecules under standard conditions, called dichlorine...
are gas
Gas
Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...
es at room temperature, bromine
Bromine
Bromine ") is a chemical element with the symbol Br, an atomic number of 35, and an atomic mass of 79.904. It is in the halogen element group. The element was isolated independently by two chemists, Carl Jacob Löwig and Antoine Jerome Balard, in 1825–1826...
is a liquid, and iodine
Iodine
Iodine is a chemical element with the symbol I and atomic number 53. The name is pronounced , , or . The name is from the , meaning violet or purple, due to the color of elemental iodine vapor....
is a solid. The London forces also become stronger with larger amounts of surface contact. Greater surface area
Surface area
Surface area is the measure of how much exposed area a solid object has, expressed in square units. Mathematical description of the surface area is considerably more involved than the definition of arc length of a curve. For polyhedra the surface area is the sum of the areas of its faces...
means closer interaction between different molecules.
Quantum mechanical theory of dispersion forces
The first explanation of the attraction between noble gas atoms was given by Fritz London in 1930. He used a quantum mechanical theory based on second-order perturbation theoryPerturbation theory (quantum mechanics)
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an...
. The perturbation is the Coulomb interaction V between the electrons and nuclei of the two monomers (atoms or molecules) that constitute the dimer. The second-order perturbation expression of the interaction energy contains a sum over states. The states appearing in this sum are simple products of the stimulated electronic states of the monomers. Thus, no intermolecular antisymmetrization of the electronic states is included and the Pauli exclusion principle
Pauli exclusion principle
The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions may occupy the same quantum state simultaneously. A more rigorous statement is that the total wave function for two identical fermions is anti-symmetric with respect to exchange of the particles...
is only partially satisfied.
London developed the method perturbation V in a Taylor series
Taylor series
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point....
in
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Center of mass
In physics, the center of mass or barycenter of a system is the average location of all of its mass. In the case of a rigid body, the position of the center of mass is fixed in relation to the body...
of mass of the monomers.
This Taylor expansion is known as the multipole expansion
Multipole expansion
A multipole expansion is a mathematical series representing a function that depends on angles — usually the two angles on a sphere. These series are useful because they can often be truncated, meaning that only the first few terms need to be retained for a good approximation to the original...
of V because the terms in this series can be regarded as energies of two interacting multipoles, one on each monomer. Substitution of the multipole-expanded form of V into the second-order energy yields an expression that resembles somewhat an expression describing the interaction between instantaneous multipoles (see the qualitative description above). Additionally an approximation, named after Albrecht Unsöld
Albrecht Unsöld
Albrecht Otto Johannes Unsöld was a German astrophysicist known for his contributions to spectroscopic analysis of stellar atmospheres.-Career:...
, must be introduced in order to obtain a description of London dispersion in terms of dipole polarizabilities
Polarizability
Polarizability is the measure of the change in a molecule's electron distribution in response to an applied electric field, which can also be induced by electric interactions with solvents or ionic reagents. It is a property of matter...
and ionization potential
Ionization potential
The ionization energy of a chemical species, i.e. an atom or molecule, is the energy required to remove an electron from the species to a practically infinite distance. Large atoms or molecules have a low ionization energy, while small molecules tend to have higher ionization energies.The property...
s.
In this manner the following approximation is obtained for the dispersion interaction
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Note that this final London equation does not contain instantaneous dipoles (see molecular dipoles). The "explanation"
of the dispersion force as the interaction between two such dipoles was invented after London gave the proper quantum mechanical theory. See the authoritative work for a criticism of the instantaneous dipole model and for a modern and thorough exposition of the theory of intermolecular forces.
The London theory has much similarity to the quantum mechanical theory of light dispersion
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...
, which is why London coined the phrase "dispersion effect".
Relative magnitude
Dispersion forces are usually dominant of the three van der Waals forces (orientation, induction, dispersion) between atoms and molecules, with the exception for molecules that are small and highly polar, like of water. The following contribution of the dispersion to the total intermolecular interaction energy has been given:Molecule pair | % of the total energy of interaction |
---|---|
Ne Neon Neon is the chemical element that has the symbol Ne and an atomic number of 10. Although a very common element in the universe, it is rare on Earth. A colorless, inert noble gas under standard conditions, neon gives a distinct reddish-orange glow when used in either low-voltage neon glow lamps or... -Ne |
100 |
CH4 Methane Methane is a chemical compound with the chemical formula . It is the simplest alkane, the principal component of natural gas, and probably the most abundant organic compound on earth. The relative abundance of methane makes it an attractive fuel... -CH4 |
100 |
HCl Hydrogen chloride The compound hydrogen chloride has the formula HCl. At room temperature, it is a colorless gas, which forms white fumes of hydrochloric acid upon contact with atmospheric humidity. Hydrogen chloride gas and hydrochloric acid are important in technology and industry... -HCl |
86 |
HBr Hydrogen bromide Hydrogen bromide is the diatomic molecule HBr. HBr is a gas at standard conditions. Hydrobromic acid forms upon dissolving HBr in water. Conversely, HBr can be liberated from hydrobromic acid solutions with the addition of a dehydration agent, but not by distillation. Hydrogen bromide and... -HBr |
96 |
HI Hydrogen iodide Hydrogen iodide is a diatomic molecule. Aqueous solutions of HI are known as iohydroic acid or hydroiodic acid, a strong acid. Gas and aqueous solution are interconvertible... -HI |
99 |
CH3Cl Chloromethane Chloromethane, also called methyl chloride, R-40 or HCC 40, is a chemical compound of the group of organic compounds called haloalkanes. It was once widely used as a refrigerant. It is a colorless extremely flammable gas with a minorly sweet odor, which is, however, detected at possibly toxic levels... -CH3Cl |
68 |
NH3 Ammonia Ammonia is a compound of nitrogen and hydrogen with the formula . It is a colourless gas with a characteristic pungent odour. Ammonia contributes significantly to the nutritional needs of terrestrial organisms by serving as a precursor to food and fertilizers. Ammonia, either directly or... -NH3 |
57 |
H2O Water Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a... -H2O |
24 |
HCl-HI | 96 |
H2O-CH4 | 87 |