Lennard-Jones terms

The OPLS model is an example of pair potential where non-bonded interactions are represented through Coulomb and Lennard-Jones terms interacting between sites centred on nuclei (equation (51). Within this model, each atomic nucleus has an interaction site, except CH groups that are treated as united atoms centered on the carbon. It is important to note that no special functions were found to be needed to describe hydrogen bonding and there are no additional interaction sites for lone pairs. Another important point is that standard combining rules are used for the Lennard-Jones interactions such that An = (Ai As )1/2 and Cu = (C Cy)1/2. The A and C parameters may also be expressed in terms of Lennard-Jones o s and e s as A = 4ei Oi and C ... 

The OPLS parameters (charges and Lennard-Jones terms) were obtained primarily via Monte Carlo simulations with particular emphasis on reproducing the experimental densities and heats of vaporization of liquids. Those simulations were performed iteratively as part of the parametrization, so better agreement with experiment is obtained than in previous studies where the simulations were usually carried out after the parametrization. Once the OPLS parametrization was completed, further simulations were also performed in order to test the new set of parameters in the calculation of other thermodynamic and structural properties of the system, besides its density and its heat of vaporization. Parameters have now been generated, among others, for water, alkanes, alkenes, alcohols, amides, alkyl chlorides, amines, carboxylic esters and acids, various sulfur and nitrogen compounds, and nitriles. A protein force field has been established as well. 

In the study of reactivity, Jorgensen and col. have normally used both, the OPLS model and potential functions derived from ab initio calculations. As we have already indicated, when intermolecular pair potentials are applied to the study of a chemical process, the evolution of charges, as well as the Lennard-Jones terms, along the reaction coordinate, has to be considered. For the SN2 reaction in water between chloride anion... 

Thus, die electrostatic interaction term of Eq. (13.2) has been separated into an operator acting on die QM electrons (the first tenn on the r.h.s. of Eq. (13.3)) and the classical term for the interacdon of the MM atoms widi the solute nuclei. The Lennard-Jones term is the same in Eqs. (13.2) and (13.3) (although the parameters may certainly be different from one model to another). 

The inverse power dependence of Lennard-Jones terms... 

Benzene-benzene interactions were modeled with a Buckingham potential that was shown to yield reasonable predictions of the properties of liquid and solid benzene. Benzene-zeolite interactions were modeled by a short-range Lennard-Jones term and a long-range electrostatic term. In total, 16 benzene molecules were simulated in a unit cell of zeolite Y, corresponding to a concentration of 2 molecules per supercage. Calculations ran for 24 ps (after an initial 24-ps equilibration time) for diffusion at 300 K. 

The Lennard-Jones term describes the nonbonded interaction between the hydrogen atom of an N—H group and the oxygen atom of a C=0 group. The second term describes the electrostatic interaction between two point dipoles centered on the oxygen atom and the hydrogen atom and having the orientation of the C=0 and N—H bonds. 

Fig. 9. Potential function [U(r), which is the same as Ubb] for the amide hydrogen bond, with e = 5-5 kcal mole"1. Curve A is the analogue of eq. 13, using a Buckingham potential with repulsive part Arep and attractive part Aatt Curve B is eq. 13. In both cases, S(r) is added to either the Buckingham or Lennard-Jones terms to obtain U(r) (Poland and Scheraga, 1967).

To illustrate the SS-LMBW methodology, we calculated the stractuie of the planar liquid/vapour as well as liquid/liquid interfaces of non-polar and polar molecular fluids hexane and methanol at ambient conditions. The site-site interaction potentials to appear in the closure (7) were specified in the form comprising the Coulomb and 12-6 Lennard-Jones terms,... 

The interaction Hamiltonian for many hybrid potentials contains a term which accounts for the electrostatic interaction between the MM atoms and the QM electrons and nuclei and a Lennard-Jones term that mimics the effects of the exchange repulsion and dispersion interactions between the MM and QM atoms. For an ab initio QM method, it takes the form ... 

In many force fields, truncation schemes are often used to reduce the number of non-bonded electrostatic and Lennard-Jones interactions that need to be calculated. Such schemes, are readily incorporated into the.inter-action Hamiltonian either by omitting all interactions that have a distance greater than some cutoff or by multiplying the appropriate interactions by a tapering function that reduces the interactions to zero beyond a certain distance. It is to be noted that in some hybrid force fields (see, for example, [35]) the electrostatic interaction terms are not included and the QM/MM interaction is due solely to the Lennard-Jones terms (and link-atoms if they are present). This could be a reasonable approximation in non-polar systems (such as the transition metal complexes for which some of these force fields were developed) but it will not be sufficiently accurate in the general case. 

The empirical XI potential (3.1) [248] consisting of a Lennard-Jones term for the nonelectrostatic part and a three-point-charge model for the electrostatics is used [140] to describe the N2-N2 interactions. The substrate-mediated dispersion energy as formulated by McLachlan [49, 225] is included... 

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