Explanation
The r−12 term, which is the repulsive term, describes Pauli repulsion at short ranges due to overlapping electron orbitals and the r−6 term, which is the attractive long-range term, describes attraction at long ranges (van der Waals force, or dispersion force). Whereas the functional form of the attractive term has a clear physical justification, the repulsive term has no theoretical justification. It is used because it approximates the Pauli repulsion well, and is more convenient due to the relative computational efficiency of calculating r12 as the square of r6.
The Lennard-Jones (12,6) potential can be further approximated by the (exp-6) potential later proposed by R. A. Buckingham, in which the repulsive part is exponential:
The L-J potential is a relatively good approximation and due to its simplicity is often used to describe the properties of gases, and to model dispersion and overlap interactions in molecular models. It is particularly accurate for noble gas atoms and is a good approximation at long and short distances for neutral atoms and molecules.
The lowest energy arrangement of an infinite number of atoms described by a Lennard-Jones potential is a hexagonal close-packing. On raising temperature, the lowest free energy arrangement becomes cubic close packing and then liquid. Under pressure the lowest energy structure switches between cubic and hexagonal close packing. Real materials include BCC structures as well.
Other more recent methods, such as the Stockmayer potential, describe the interaction of molecules more accurately. Quantum chemistry methods, Møller–Plesset perturbation theory, coupled cluster method or full configuration interaction can give extremely accurate results, but require large computational cost.
Read more about this topic: Lennard-Jones Potential
Famous quotes containing the word explanation:
“To develop an empiricist account of science is to depict it as involving a search for truth only about the empirical world, about what is actual and observable.... It must involve throughout a resolute rejection of the demand for an explanation of the regularities in the observable course of nature, by means of truths concerning a reality beyond what is actual and observable, as a demand which plays no role in the scientific enterprise.”
—Bas Van Fraassen (b. 1941)
“The explanation of the propensity of the English people to portrait painting is to be found in their relish for a Fact. Let a man do the grandest things, fight the greatest battles, or be distinguished by the most brilliant personal heroism, yet the English people would prefer his portrait to a painting of the great deed. The likeness they can judge of; his existence is a Fact. But the truth of the picture of his deeds they cannot judge of, for they have no imagination.”
—Benjamin Haydon (1786–1846)
“Natural selection, the blind, unconscious, automatic process which Darwin discovered, and which we now know is the explanation for the existence and apparently purposeful form of all life, has no purpose in mind. It has no mind and no mind’s eye. It does not plan for the future. It has no vision, no foresight, no sight at all. If it can be said to play the role of the watchmaker in nature, it is the blind watchmaker.”
—Richard Dawkins (b. 1941)