Jones force field

Munoz Munoz, Y.M., Guevara-Carrion, G., Llano-Restrepo, M., Vrabec, J. Lennard-Jones force field parameters for cyelie alkanes from cyclopropane to cyclohexane. Fluid Phase Eq. 404, 150-160 (2015)... 

Atomistically detailed models account for all atoms. The force field contains additive contributions specified in tenns of bond lengtlis, bond angles, torsional angles and possible crosstenns. It also includes non-bonded contributions as tire sum of van der Waals interactions, often described by Lennard-Jones potentials, and Coulomb interactions. Atomistic simulations are successfully used to predict tire transport properties of small molecules in glassy polymers, to calculate elastic moduli and to study plastic defonnation and local motion in quasi-static simulations [fy7, ( ]. The atomistic models are also useful to interiDret scattering data [fyl] and NMR measurements [70] in tenns of local order. 

But the methods have not really changed. The Verlet algorithm to solve Newton s equations, introduced by Verlet in 1967 [7], and it s variants are still the most popular algorithms today, possibly because they are time-reversible and symplectic, but surely because they are simple. The force field description was then, and still is, a combination of Lennard-Jones and Coulombic terms, with (mostly) harmonic bonds and periodic dihedrals. Modern extensions have added many more parameters but only modestly more reliability. The now almost universal use of constraints for bonds (and sometimes bond angles) was already introduced in 1977 [8]. That polarisability would be necessary was realized then [9], but it is still not routinely implemented today. Long-range interactions are still troublesome, but the methods that now become popular date back to Ewald in 1921 [10] and Hockney and Eastwood in 1981 [11]. 

A 6-12 function (also known as a Lennard-Jones function) frequently simulates van der Waats in tcraction s in force fields (ec iia-tion t 1). 

Ihi.. same molecule but separated by at least three bonds (i.e. have a 1, h relationship where n > 4). In a simple force field the non-bonded term is usually modelled using a Coulomb piilential term for electrostatic interactions and a Lennard-Jones potential for van der IV.uls interactions. 

Some force fields replace the Lennard-Jones 6-12 term between hydrogen-bonding atoms by ail explicit hydrogen-bonding term, which is often described using a 10-12 Lennard-Jones potential ... 

The range of systems that have been studied by force field methods is extremely varied. Some force fields liave been developed to study just one atomic or molecular sp>ecies under a wider range of conditions. For example, the chlorine model of Rodger, Stone and TUdesley [Rodger et al 1988] can be used to study the solid, liquid and gaseous phases. This is an anisotropic site model, in which the interaction between a pair of sites on two molecules dep>ends not only upon the separation between the sites (as in an isotropic model such as the Lennard-Jones model) but also upon the orientation of the site-site vector with resp>ect to the bond vectors of the two molecules. The model includes an electrostatic component which contciins dipwle-dipole, dipole-quadrupole and quadrupole-quadrupole terms, and the van der Waals contribution is modelled using a Buckingham-like function. 

Finally, the parametrization of the van der Waals part of the QM-MM interaction must be considered. This applies to all QM-MM implementations irrespective of the quantum method being employed. From Eq. (9) it can be seen that each quantum atom needs to have two Lennard-Jones parameters associated with it in order to have a van der Walls interaction with classical atoms. Generally, there are two approaches to this problem. The first is to derive a set of parameters, e, and G, for each common atom type and then to use this standard set for any study that requires a QM-MM study. This is the most common aproach, and the derived Lennard-Jones parameters for the quantum atoms are simply the parameters found in the MM force field for the analogous atom types. For example, a study that employed a QM-MM method implemented in the program CHARMM [48] would use the appropriate Lennard-Jones parameters of the CHARMM force field [52] for the atoms in the quantum region. 

I mentioned earlier that molecular-mechanics force fields have to be transferable from molecule to molecule, and that it was found many years ago that extra terms were needed apart from the pure valence ones. Non-bonded interactions are usually taken as the Lennard-Jones 12-6 potential... 

Some force fields make special provision for hydrogen-bonded atoms A-H B, and modify the Lennard-Jones 12-6 potential to a 12-10 model ... 

Most force fields employ the Lennard-Jones potential, despite the known inferiority to an exponential type function. Let us examine the reason for this in a little more detail. 

In some force fields, especially those using the Lennard-Jones form in eq. (2.12), the /fg parameter is defined as the geometrical mean of atomic radii, implicitly via the geometrical mean rale used for the C and C2 constants. 

The significance of force constants of general quadratic valence force fields application to Au(CN)2. PtCl42-, AuC14, AuBr4- and Au(CN)2Cl2. L. H. Jones, Coord. Chem. Rev., 1966,1, 351-378 (15). 

Fig. 1. The Lennard Jones 12 6 pair potential plotted for a pair of CH2 united atoms using the OPTS united force field. Enonbond = 4e((o /r) (o /r) ), where s is the well depth for the potential and cr is the distance at which the repulsive energy exactly cancels the attractive energy...

Table 5.1 Parameters of the united atom force field for polyethylene used as the atomistic input for the coarse-graining procedure. The Lennard-Jones parameters pertain to CH2-group interaction, since chain ends were not considered in the coarse-graining. 

Here, avaw is a positive constant, and and ctJ are the usual Lennard-Jones parameters found in macromolecular force fields. The role played by the term avdw (1 — A)2 in the denominator is to eliminate the singularity of the van der Waals interaction. Introduction of this soft-core potential results in bounded derivatives of the potential energy function when A tends towards 0. 

Consider the case of an ion in water. The force field for the ion may be described using a Lennard-Jones and electrostatic potential with charge q. Assume that we... 

Many force fields use a Lennard-Jones 6-12 potential71 to reproduce nonbonded interactions, see Equation 7. As two atoms approach one another, the steepness or hardness of the energy curve is proportional to r 12. The use of an exponential term instead of the r12 term in force field equations better reproduces experimental data for organic structures, and it is more consistent with quantum chemical calculations. 

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