Lennard-Jones parameter

The calculation of diffusion, viscosity and thermal diffusion coefficients, requires a knowledge of the values of the LENNARD-JONES parameters a and e/kg. Tables XIV.3 give these values for a few species. Other compilations in the literature allow the values of supplementary species to be obtained. However, it is useful to have correlations between these properties and other properties of the molecules most frequently tabulated, which is especially true of the critical pressure and temperature (p and T ) and of the PITZER ((o) acentric factor, which constitutes a macroscopic 

It is assumed that isopentane has a negligible dipolar moment formulae (29) and (30) give the following e/kg = 293.7 K and a = 6.1 IxlO m. 

References in ref. [57] Pyrophyllite Montmorillonite deav Mica deav Principal charges [e] Principal well depths (kcal/mol)  

The strong influence of principal atomic charges and Lennard-Jones well depths on computed surface tensions and cleavage energies can be seen. tetrahedral oxygen coordination and Al refers to Al in octahedral oxygen coordination. 

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McDonald I R and Singer K 1967 Calculation of thermodynamic properties of liquid argon from Lennard-Jones parameters by a Monte Carlo method Discuss. Faraday Soc. 43 40-9... 

Lennard-Jones parameters are / ,nh,/ in angsU oms and kilocalories per mole, respectively. 

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. 

The second approach is to derive Lennard-Jones parameters for the quantum atoms that are specific to the problem in hand. This is a less common approach but has been shown to improve the quantitative accuracy of the QM-MM approach in specific cases [53,54]. The disadvantage of this approach, however, is that it is necessary to derive Lennard-Jones parameters for the quanmm region for every different study. Since the derivation of Lennard-Jones parameters is not a trivial exercise, this method of finding van der Walls parameters for the QM-MM interaction has not been widely used. 

The issue of the theoretical maximum storage capacity has been the subject of much debate. Parkyns and Quinn [20] concluded that for active carbons the maximum uptake at 3.5 MPa and 298 K would be 237 V/V. This was estimated from a large number of experimental methane isotherms measured on different carbons, and the relationship of these isotherms to the micropore volume of the corresponding adsorbent. Based on Lennard-Jones parameters [21], Dignum [5] calculated the maximum methane density in a pore at 298 K to be 270 mg/ml. Thus an adsorbent with 0.50 ml of micropore per ml could potentially adsorb 135 mg methane per ml, equivalent to about 205 V/ V, while a microporc volume of 0.60 mEml might store 243 V/V. Using sophisticated parallel slit... 

One of the more difficult decisions to be made is the proper value for the Lennard-Jones parameters. These relate to the interaction between the quantum mechanical atoms and the MM atoms. At the time of writing (1999), there does not appear to be a consensus amongst researchers. Some authors recommend a 10% scaling of the traditional 12-6 parameters. Some authors scale the MM atom charges. 

In the other extreme, quantum chemistry is impractical for Lennard-Jones parameters of most molecules of interest to simulators, since the description of dispersive interactions needs huge basis sets and a high-order treatment of electron correlation. DFT methods seem to have similar difficulties, since in... 

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. 

Yin DX, Mackerell AD (1998) Combined ab initio empirical approach for optimization of Lennard-Jones parameters. J Comput Chem 19(3) 334-348... 

Intermediate states do not have to be physically meaningful, i.e., they do not have to correspond to systems that actually exist. As an example, assume that we want to calculate the difference in hydration free energies of a Lennard-Jones particle and an ion with a positive charge q of le. For simplicity, we further assume that the Lennard-Jones parameters remain unchanged upon charging the particle. Since a direct calculation of the free energy difference is not likely to succeed in this case, we construct intermediate states in which the particle carries fractional charges [Pg.46]

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. 

Fig. 9.4. Pa (e) and (e) as a function of the binding energy. The simulations treated 216 water molecules, utilizing the SPC/E water model, and the Lennard-Jones parameters for methane were from [63]. The number density for both the systems is fixed at 0.03333 A 3, and T = 298 K established by velocity rescaling. These calculations used the NAMD program (www.ks.uiuc.edu/namd). After equilibration, the production run comprised 200 ps in the case of the pure water simulation and 500 ps in the case of the methane-water system. Configurations were saved every 0.5 ps for analysis...

The data were obtained in an electrostatic balance, and phase functions were recorded to determine the droplet size as a function of time. The slopes of the three data sets are S12 = - 7.54 x 10 (/an)Vs, S,3 = — 1.70 X 10 (/im)Vs, and S14 = — 1.10 x 10 ( m)Vs. From these and additional data obtained at different temperatures, Ravindran et al. reported aoBS = 9.97 0.26A, Sobs/ b = 688 72 K, and pges(293 K) = 207//Pa. They also reported Lennard-Jones parameters and vapor pressures measured in this way for dibutyl phthalate and dioctyl phthalate. 

In Fig. 1, various elements involved with the development of detailed chemical kinetic mechanisms are illustrated. Generally, the objective of this effort is to predict macroscopic phenomena, e.g., species concentration profiles and heat release in a chemical reactor, from the knowledge of fundamental chemical and physical parameters, together with a mathematical model of the process. Some of the fundamental chemical parameters of interest are the thermochemistry of species, i.e., standard state heats of formation (A//f(To)), and absolute entropies (S(Tq)), and temperature-dependent specific heats (Cp(7)), and the rate parameter constants A, n, and E, for the associated elementary reactions (see Eq. (1)). As noted above, evaluated compilations exist for the determination of these parameters. Fundamental physical parameters of interest may be the Lennard-Jones parameters (e/ic, c), dipole moments (fi), polarizabilities (a), and rotational relaxation numbers (z ,) that are necessary for the calculation of transport parameters such as the viscosity (fx) and the thermal conductivity (k) of the mixture and species diffusion coefficients (Dij). These data, together with their associated uncertainties, are then used in modeling the macroscopic behavior of the chemically reacting system. The model is then subjected to sensitivity analysis to identify its elements that are most important in influencing predictions. 

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