Intermolecular potential Lennard-Jones form

A complete set of intermolecular potential functions has been developed for use in computer simulations of proteins in their native environment. Parameters have been reported for 25 peptide residues as well as the common neutral and charged terminal groups. The potential functions have the simple Coulomb plus Lennard-Jones form and are compatible with the widely used models for water, TIP4P, TIP3P and SPC. The parameters were obtained and tested primarily in conjunction with Monte Carlo statistical mechanics simulations of 36 pure organic liquids and numerous aqueous solutions of organic ions representative of subunits in the side chains and backbones of proteins... 

There are presently two main difficulties which handicap attempts at exact calculation. The first concerns the intermolecular potential, and the hazards of extrapolation from models derived from viscosity measurements have been discussed. Furthermore, such a method is of dubious validity for polyatomic molecules, because the intermolecular repulsive potential will generally appear to become progressively shallower with increasing molecular dimensions if the viscosity data are cast, for example, in the Lennard-Jones form. Energy transfer depends... 

Carbon tetrafluoride. Carbon tetra-fluoride, which undergoes a transition to a plastically crystalline (orientationally disordered) phase, has been investigated by the Parrinello-Rahman molecular dynamics method under constant-pressure conditions (6). A simple intermolecular potential model of the Lennard-Jones form was derived by taking into account the experimen-... 

For the intermolecular potential, the Lennard-Jones form as modified by Rushbrooke,... 

After the pioneering quantum mechanical work not much new ground was broken until computers and software had matured enough to try fresh attacks. In the meantime the study of intermolecular forces was mainly pursued by thermodynamicists who fitted model potentials, often of the Lennard-Jones form [10] 4e[(cr/R) — (cr// ) ], to quantities like second virial coefficients, viscosity and diffusion coefficients, etc. Much of this work is described in the authoritative monograph of Hirschfelder et al. [11] who, incidentally, also gave a good account of the relationship of Drude s classical work to that of London. 

The remaining critical component in the simulations is the potential functions that describe the intra- and intermolecular energetics for the system. The intermolecular part is usually represented in a Coulomb plus Lennard-Jones form with the interactions occurring between sites located on the nuclei. Simple potential functions are now available that give excellent thermodynamic and structural results for many pure liquids including water,... 

The Lennard-Jones interaction is often used as the intermolecular potential function to estimate transport properties. The form of the Lennard-Jones interaction between molecules i and j as a function of distance is... 

All of the transport properties from the Chapman-Enskog theory depend on 2 collision integrals that describe the interactions between molecules. The values of the collision integrals themselves, discussed next, vary depending on the specified intermolecular potential (e.g., a hard-sphere potential or Lennard-Jones potential). However, the forms of the transport coefficients written in terms of the collision integrals, as in Eqs. 12.87 and 12.89, do not depend on the particular interaction potential function. 

The Lennard-Jones ( 6-12 ) potential Vu(/ ) provides a simple 2-parameter approximation to the intermolecular potential between closed-shell molecular species. This function can be written in the form (with empirical parameters a, b)... 

The intermolecular potential term is represented by a simple Lennard-Jones function that is attenuated at short interatomic distances by a cubic spline so that at small (covalent) intemuclear distances, the description of the interaction is that of the intramolecular term only. The original form of... 

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). 

For atomic gases the intermolecular potential most used in calculations of B, has been the Lennard-Jones 6-12, with the parameters e and r determined from gas viscosities and pressure virial coefScients. For non-dipolar gases possessing higher moments, most authors have used the 6-12 potential together with the appropriate terms from equations (27) and (28), while for dipolar gases some form of equations (26)—(28) is used with a shape-dependent term added to uq. 

Thus, the usual approach to deriving intermolecular potentials from experimental data is to choose a functional form for the model potential, for example, the Lennard-Jones 12-6 potential ... 

Corresponding States (CS) The principle of CS applies to conformal fluids [Lehmd, T. L., Jr., and P. S. Chappelear, Ind. Eng. Chem., 60 (1968) 15]. Two fluids are conformal if their intermolecu-lar interactions are equivalent when scaled in dimensionless form. For example, the Lennard-Jones (LJ) intermolecular pair potential energy U can be written in dimensionless form as... 

With these simplifying assumptions, the classical expression of surface energy is obtained in the form of the increase in potential energy per unit surface area when an infinite face-centered cubic lattice is divided into two semi-infinite halves. The intermolecular potential will be assumed to have the form of the Lennard-Jones 6—12 function... 

The form of the intermolecular potential is assumed to be of the form of the Lennard-Jones type, that is, as given by Eq. III.2. The reduced values... 

The first extension of this approach to ionic energetic crystals was done by Sorescu and Thompson [104] for ADN. Using the rigid-ion approximation, the intermolecular potential used was composed by pairwise Lennard-Jones (LJ), hydrogen bonding (HB), and Coulombic (C) terms of the form... 

Hansen and Verlet [156] observed an invariance of the intermediate-range (at and beyond two molecular diameters) form of the radial distribution function at freezing, and from this postulated that the first peak in the structure factor of the liquid is a constant on the freezing curve, and approximately equal to the hard-sphere value of 2.85. They demonstrated the rule by application to the Lennard-Jones system. Hansen and Schiff [157] subsequently examined g r) of soft spheres in some detail. They found that, although the location and magnitude of first peak of g r) at crystallization is quite sensitive to the intermolecular potential, beyond the first peak the form of g(r) is nearly invariant with softness. This observation is consistent with the Hansen-Verlet rule, and indeed Hansen and Schiff find that the first peak in the structure factor S k) at melting varies only between 2.85 n = 8) to 2.57 (at n= ), with a maximum of 3.05 at n = 12. 

The liquid structure factor of CCI4 and its derivatives with respect to temperature at fixed pressure or fixed volume, needed by eq. (2), were evaluated by Molecular Dynamics (MD) simulations. We have used the OPLS model for tetrachloromethane [9] In this model, the CCI4 molecules are described as rigid tetrahedra (dc-ci = 1 -769 A) and the intermolecular potentials are atom centered 6-12 Lennard-Jones potentials plus the coulombic interaction with partial charges on C and Cl. We performed NVT simulations with 512 molecules for about 1 ns each. The different x-ray structure factors were obtained from the accumulated partial radial distribution functions [10], using the atomic form-factors from the DABAX database [11]. In order to estimate the partial derivatives of the structure factor, we have used finite differences we considered two different temperatures, Ti = 300 K and T2 = 328 K, and two molar volumes, Vi = 97.3 cm mol and V2 = 100.65 cm mol which are the molar volumes along the liquid-vapor coexistence line for the two temperatures Tj and Tz respectively [12]. Three simulations were then run for the temperature and molar volume conditions (TiiVi), T2,V )... 

In the description of the intermolecular bonding, the Lennard-Jones 6-12 potential function (8) is one of the most common, consisting of an attractive and repulsive contribution to the van der Waals component of the lattice energy (Vydw) as shown in Equation 1. "A" and "B" are the atom-atom parameters for describing a particular atom-atom interaction and "r" is the interatomic distance. This potential function has formed the basis of a variety of different force fields (9-11) that were utilized in this paper. A modified (10-12 version of this potential can also be employed (10,11) to describe hydrogen bonding. The 10-12 potential is very similar in construction to Equation 1 except that the attractive part is dependent on r ° rather than r. ... 

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