Lennard dispersion attraction

Atomic repulsion and induced dipole-induced dipole dispersive attraction are typically described by a Lennard-Jones function [16,17] ... 

The interactions between the QM part and the MM part are treated by a combination of quantum-chemical and force-field contributions. If the system can be separated into a QM solute and an MM solvent, the partitioning of interactions arises naturally The electrons of the QM part feel the electric field of the partial charges of the solvent molecules which enter the one-electron Hamiltonian as additional point charges. The dispersion attraction and the short-range repulsion are modelled by a Lennard-Jones 6-12 potential. If, on the other... 

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. 

The dispersion (attractive) part of the van der Waals potential is usually described by a term with a sixth power, whereas the repulsive part is described by a twelfth-power term (Lennard-Jones 12-6 function, Eq. [12]), or, alternatively, by an exponential function (Eq. [13]). 

In this case the first two sums contain contributions describing pairwise additive atom-atom interactions due to repulsion at short distances and dispersion attraction at large distances. The latter follows from a perturbative treatment of the fluctuations 1). The Lennard-Jones potential is... 

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 dispersion interactions are weak compared with repulsion, but they are longer range, which results in an attractive well with a depth e at an interatomic separation of am n = 21/6a. The interatomic distance at which the net potential is zero is often used to define the atomic diameter. In addition to the Lennard-Jones form, the exponential-6 form of the dispersion-repulsion interaction,... 

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. 

The dispersion and repulsion interactions form the Lennard-Jones (Barrer, 1978 Masel, 1996 Razmus and Hall, 1991 Gregg and Sing, 1982 Steele, 1974 Adamson, 1976 Rigby et al., 1986) potential, with an equilibrium distance (r0) where 4 d + 4 r = 0. This distance is taken as the mean of the van der Waals radii of the interacting pair. Once the attractive, dispersion constant, A, is known, B is readily obtained by setting at chp/dr = 0 at r0. Hence, B = Ar /2. The most commonly used expression for calculating A is the Kirkwood-Muller formula ... 

Physisorption or physical adsorption is the mechanism by which hydrogen is stored in the molecular form, that is, without dissociating, on the surface of a solid material. Responsible for the molecular adsorption of H2 are weak dispersive forces, called van der Waals forces, between the gas molecules and the atoms on the surface of the solid. These intermolecular forces derive from the interaction between temporary dipoles which are formed due to the fluctuations in the charge distribution in molecules and atoms. The combination of attractive van der Waals forces and short range repulsive interactions between a gas molecule and an atom on the surface of the adsorbent results in a potential energy curve which can be well described by the Lennard-Jones Eq. (2.1). 

The interaction between water molecules and silica substrate is described in the framework of the PN-TrAZ model [15] which has proven to model successfiilly the adsorption of simple adsorbates on various zeolites [20]. In this model, the pair potential decomposes in two parts a repulsion term Ae" due to electronic clouds and the attractive dispersion terms. The repulsive parameters (A,b) for silica atoms (Si, O, H) are those obtained from studies of adsorption of simple gazes on various zeolites [20] and mesoporous glass [21]. Those for water oxygen are chosen to fit the repulsive part of Lennard-Jones from SPC model in the range around equilibriiun distance, and those for water hydrogen are taken equal to the parameters for surface hydrogen of vycor. The cross repulsive parameters A and b are obtained by Bohm and Ahlrichs [22] combination mles. The dispersion terms are calculated from polarizabilities and effective niunber of electron Neff according to the PN-TrAZ model up to order r °. Values are listed in table 1. 

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. 

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. 

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