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 theory. 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 is only partially satisfied.
London developed the method perturbation V in a Taylor series in, where is the distance between the nuclear centers of mass of the monomers.
This Taylor expansion is known as the multipole expansion 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, must be introduced in order to obtain a description of London dispersion in terms of dipole polarizabilities and ionization potentials.
In this manner the following approximation is obtained for the dispersion interaction between two atoms and . Here and are the dipole polarizabilities of the respective atoms. The quantities and are the first ionization potentials of the atoms and is the intermolecular distance.
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, which is why London coined the phrase "dispersion effect". In physics the term "dispersion" describes the variation of a quantity with frequency which is the fluctuation of the electrons in case of the London dispersion.
For endohedral fullerene, such as He@C60, the inside atom typically locates at the center of the outer shell. In this case, the intermolecular distance, is zero if the multipole expansion centers are set at the centers of the two subsystems. The London equation would not be applicable. Another formula has been derived in literature
here is a new polarizability.
Read more about this topic: London Dispersion Force
Famous quotes containing the words quantum, mechanical, theory, dispersion and/or forces:
“A personality is an indefinite quantum of traits which is subject to constant flux, change, and growth from the birth of the individual in the world to his death. A character, on the other hand, is a fixed and definite quantum of traits which, though it may be interpreted with slight differences from age to age and actor to actor, is nevertheless in its essentials forever fixed.”
—Hubert C. Heffner (1901–1985)
“We are caught up Mr. Perry on a great wave whether we will or no, a great wave of expansion and progress. All these mechanical inventions—telephones, electricity, steel bridges, horseless vehicles—they are all leading somewhere. It’s up to us to be on the inside in the forefront of progress.”
—John Dos Passos (1896–1970)
“There could be no fairer destiny for any physical theory than that it should point the way to a more comprehensive theory in which it lives on as a limiting case.”
—Albert Einstein (1879–1955)
“The slogan offers a counterweight to the general dispersion of thought by holding it fast to a single, utterly succinct and unforgettable expression, one which usually inspires men to immediate action. It abolishes reflection: the slogan does not argue, it asserts and commands.”
—Johan Huizinga (1872–1945)
“There exists, at the bottom of all abasement and misfortune, a last extreme which rebels and joins battle with the forces of law and respectability in a desperate struggle, waged partly by cunning and partly by violence, at once sick and ferocious, in which it attacks the prevailing social order with the pin-pricks of vice and the hammer-blows of crime.”
—Victor Hugo (1802–1885)