Lennard-Jones intermolecular

Figure 9.5 Molecular dynamics calculations of the nondimcnsional surface pressure (difference between pressure inside a drop and the gas) for a Lennard-Jones intermolecular potential. Classical liquid drop theory begins to break down fordroplei radii smallcrihan about 10 times the Lennard-Jones diameter CTij. Calculations for Ar/su = 0.71 and = 0,58. (After Thompson et al, 1984.)...

Figure 3 presents minus P vs. v, where A(v). This represents a hypothetical isotherm at absolute zero. The negative sign is taken to emphasize the similarity between this plot and the Lennard-Jones intermolecular potential function [3], The algebraic form, taken from the latter, is... 

The intercept function, which was seen in Fig. 3 to suggest a Lennard-Jones intermolecular potential function, is adopted in the form... 

Using the Lennard-Jones intermolecular potential, which accounts for the repulsive and attractive forces, for the interaction of spherical substances A and B in (A -I- B), mabW is given by ... 

Table 1 Parameters of the Lennard-Jones intermolecular potential (e in kcal/mol and cr in A) and different sets of atomic charges (in e) and dipole moment (ji in D) for mesityl oxide at optimized geometry with B3LYP/6-31- -G(d) ...

Critical Properties and Lennard-Jones Intermolecular Force Parameters... 

Lennard-Jones intermolecular force parameter or constant for inter-... 

Lennard-Jones intermolecular force parameter or constant for intermolecular interactions or collision diameter Charge conductivity Electronic conductivity Ionic conductivity or electrolyte conductivity Reference conductivity Proton conductivity... 

One fascinating feature of the physical chemistry of surfaces is the direct influence of intermolecular forces on interfacial phenomena. The calculation of surface tension in section III-2B, for example, is based on the Lennard-Jones potential function illustrated in Fig. III-6. The wide use of this model potential is based in physical analysis of intermolecular forces that we summarize in this chapter. In this chapter, we briefly discuss the fundamental electromagnetic forces. The electrostatic forces between charged species are covered in Chapter V. 

A proportionality between the theoretical spall strength and the bulk modulus is obtained when a two-parameter model is chosen to represent the intermolecular potential. Other two-parameter representations of the intermolecular potential, such as the Lennard-Jones 6-12 potential, will yield a similar proportionality although the numerical coefficients will differ slightly. 

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... 

Finally, it was found necessary to add a Lennard-Jones (LJ) 12-6 intermolec-ular term between each pair of quantum-mechanical and MM atoms, in order to obtain good interaction energies as well as good geometries for intermolecular interactions. 

The main difference between the three functions is in the repulsive part at short distances the Lennard-Jones potential is much too hard, and the Exp.-6 also tends to overestimate the repulsion. It furthermore has the problem of inverting at short distances. For chemical purposes these problems are irrelevant, energies in excess of lOOkcal/mol are sufficient to break most bonds, and will never be sampled in actual calculations. The behaviour in the attractive part of the potential, which is essential for intermolecular interactions, is very similar for the three functions, as shown in... 

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... 

A key to both methods is the force field that is used,65 or more precisely, the inter- and possibly intramolecular potentials, from which can be obtained the forces acting upon the particles and the total energy of the system. An elementary level is to take only solute-solvent intermolecular interactions into account. These are typically viewed as being electrostatic and dispersion/exchange-repulsion (sometimes denoted van der Waals) they are represented by Coulombic and (frequently) Lennard-Jones expressions ... 

Fig. 5.1 A schematic projection of the 3n dimensional (per molecule) potential energy surface for intermolecular interaction. Lennard-Jones potential energy is plotted against molecule-molecule separation in one plane, the shifts in the position of the minimum and the curvature of an internal molecular vibration in the other. The heavy upper curve, a, represents the gas-gas pair interaction, the lower heavy curve, p, measures condensation. The lighter parabolic curves show the internal vibration in the dilute gas, the gas dimer, and the condensed phase. For the CH symmetric stretch of methane (3143.7 cm-1) at 300 K, RT corresponds to 8% of the oscillator zpe, and 210% of the LJ well depth for the gas-gas dimer (Van Hook, W. A., Rebelo, L. P. N. and Wolfsberg, M. /. Phys. Chem. A 105, 9284 (2001))...

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