Dispersion Lennard-Jones potential

The Lennard-Jones potential is characterised by an attractive part that varies as r ° and a repulsive part that varies as These two components are drawn in Figure 4.35. The r ° variation is of course the same power-law relationship foimd for the leading term in theoretical treatments of the dispersion energy such as the Drude model. There are no... 

Forces Molecules are attracted to surfaces as the result of two types of forces dispersion-repulsion forces (also called London or van der Waals forces) such as described by the Lennard-Jones potential for molecule-molecule interactions and electrostatic forces, which exist as the result of a molecule or surface group having a permanent electric dipole or quadrupole moment or net electric charge. 

The interaction between atoms separated by more than two bonds is described in terms of potentials that represent non-bonded or Van der Waals interaction. A variety of potentials are being used, but all of them correspond to attractive and repulsive components balanced to produce a minimum at an interatomic distance corresponding to the sum of the Van der Waals radii, V b = R — A. The attractive component may be viewed as a dispersive interaction between induced dipoles, A = c/r -. The repulsive component is often modelled in terms of either a Lennard-Jones potential, R = a/rlj2, or Buckingham potential R = aexp(—6r ). 

The major forms of van der Waals forces between molecules that are not bonded together are the permanent dipole-dipole interaction, the dispersion-induced temporary dipole interaction, and the hydrogen bond. They are short-range forces that operate only when two atoms or molecules are in close proximity. The Lennard-Jones potential of 6-12 is a model of this potential field ... 

The first term on the right-hand side of Eq. 12.9 or 12.14 describes the short-range, repulsive interaction between molecules as they get very close to one another. The second term accounts for the longer-range, attractive potential (i.e the dispersion interaction between the molecules). The final term is the longest-range interaction, between the dipole moments JTj and JTj of the two molecules. In the case where one or both of the dipole moments are zero, the Stockmayer potential reduces to the Lennard-Jones potential discussed in Sec 12.2.1. 

When taken together with dispersion, the short-range repulsion is thus modeled by the Lennard-Jones potential ... 

As an example of application of the method we have considered the case of the acrolein molecule in aqueous solution. We have shown how ASEP/MD permits a unified treatment of the absorption, fluorescence, phosphorescence, internal conversion and intersystem crossing processes. Although, in principle, electrostatic, polarization, dispersion and exchange components of the solute-solvent interaction energy are taken into account, only the firsts two terms are included into the molecular Hamiltonian and, hence, affect the solute wavefunction. Dispersion and exchange components are represented through a Lennard-Jones potential that depends only on the nuclear coordinates. The inclusion of the effect of these components on the solute wavefunction is important in order to understand the solvent effect on the red shift of the bands of absorption spectra of non-polar molecules or the disappearance of... 

One of the simplest and therefore computationally less expensive potential functions for ion-water consists of the sum of long-range Coulorabic electrostatic interactions plus short-range dispersion interactions usually represented by the Lennard-Jones potential. This last term is a combination of 6 and 12 powers of the inverse separation between a pair of sites. Two parameters characterize the interaction an energetic parameter e, given by the minimum of the potential energy well, and a size parameter a, that corresponds to the value of the pair separation where the potential energy vanishes. The 6-th power provides the contribution of the attractive forces, while repulsive forces decay with the 12-th power of the inverse separation between atoms or sites. 

After ealeulating discrete values of frequency and relaxation time for the polarization mode and different wave veetors, a continuous function for the relaxation time and dispersion relations can be established for eaeh mode. The results shown in Fig. 3 are obtained with the Lennard-Jones potential for Argon. An approach similar to that described above can be applied with the Stillinger-Weber potential for silieon. 

Short-range repulsions and London dispersion attractions are balanced by a shallow energy minimum at the van der Waals distance (Eq. (8)), describing the Lennard Jones potential, used by most force fields. Here the parameters A and B are calculated based on atomic radii and the minimum found at the sum of the two radii. 

Lennard-Jones potential As two atoms approach one another there is the attraction due to London dispersion forces and eventually a van der Waals repulsion as the interatomic distance r gets smaller than the equilibrium distance. A well-known potential energy function to describe this behavior is the Lennard-Jones (6-12) potential (LJ). The LJ (6-12) potential represents the attractive part as r-6-dependent whereas the repulsive part is represented by an r n term. Another often used nonbonded interaction potential is the Buckingham potential which uses a similar distance dependence for the attractive part as the LJ (6-12) potential but where the repulsive part is represented by an exponential function. 

Dispersion forces are attractive forces between atoms at close distances. Even molecules with no permanent dipole moment have, due to the movement of their electrons, local dipole moments which induce dipoles in the opposite molecule, leading to fluctuating electrostatic attractions. At a closer distance repulsive forces develop due to an unfavorable overlap of the van der Waals spheres of both molecules. These relationships are typically described by the Lennard Jones potential, with an r attractive term and an r repulsive term (Figure 2) [59, 116]. Dipole-dipole interactions and dispersion forces are much weaker than other electrostatic interactions. Nevertheless, if there is a close contact between both molecules over a relatively large surface area, they may sum up to large values of overall interaction energies. 

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