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LCSphysicist
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Hello there. Do you know any paper that derive the Lennard Jones potential ##V = \epsilon [(\delta / r)^{12}-2(\delta / r)^6]## theorically? If you know a book instead, let me know. Thank you
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A derivation can also be found in the 3-volume QM textbook by Cohen-Tannoudji, Diu and Laloe, Chapter XI.C.TeethWhitener said:The ##\frac{1}{r^6}## portion comes from treating the dipole-dipole interaction perturbatively to second order. This is actually the short-distance limit of the full interaction, not taking into account retardation effects. The full derivation in all its gory details of both short (London) and long (Casimir-Polder) limits is given in "Molecular Quantum Electrodynamics" by Craig and Thirunamachandran (p. 152ff): https://www.google.com/books/editio...rpbdozIZt3sC?hl=en&gbpv=1&printsec=frontcover
Van der Waal repulsion is a type of intermolecular force that occurs between non-polar molecules. It is caused by the temporary dipole moments that arise due to the uneven distribution of electrons in a molecule. These temporary dipoles can induce similar temporary dipoles in neighboring molecules, resulting in a repulsive force between them.
The Lennard Jones potential is a mathematical model used to describe the potential energy between two neutral atoms or molecules. It takes into account both the attractive forces, such as Van der Waal forces, and the repulsive forces, such as the Pauli exclusion principle, between the particles.
Van der Waal repulsion is one of the factors that contribute to the shape of the Lennard Jones potential curve. At very short distances, the repulsive force dominates and the potential energy increases rapidly. However, at longer distances, the attractive forces start to dominate and the potential energy decreases.
Van der Waal repulsion and the Lennard Jones potential are important concepts in understanding the behavior of non-polar molecules and their interactions with each other. They help explain phenomena such as the boiling point of a substance, the stability of molecules, and the properties of gases.
Yes, Van der Waal repulsion and the Lennard Jones potential can be applied to a wide range of molecules, including polar molecules and ions. However, the strength and nature of these interactions may vary depending on the specific properties of the molecules involved.