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Lennard-Jones parameters used

As before, M is the molecular weight of the rigid sphere, T is the absolute temperature, and a and are the same Lennard-Jones parameters used in Eq. (4.6) (note that... [Pg.344]

Lennard-Jones parameters used for chloro- and fluoro- and chlorofluoro-carbons in zeolites. [Pg.722]

Table II. Lennard-Jones Parameters used in Molecular Dynamics... Table II. Lennard-Jones Parameters used in Molecular Dynamics...
Table 1. Lennard-Jones Parameters Used in GCMC simulations... Table 1. Lennard-Jones Parameters Used in GCMC simulations...
Table 10. Charges and Lennard-Jones parameters used in the MD simulations corresponding to Table 9.2 ... Table 10. Charges and Lennard-Jones parameters used in the MD simulations corresponding to Table 9.2 ...
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. [Pg.225]

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. [Pg.226]

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... [Pg.281]

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. [Pg.120]

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... 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...
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. [Pg.99]

The gas-phase diffusivity of sodium in helium Dvl may then be evaluated from the experimental data by using Equation 15. A value of 1.96 cm.2/sec. was obtained, which compares favorably with 2.11 cm.2/ sec. estimated from an equation given by Hirschfelder, Curtiss, and Bird (8), using Lennard-Jones parameters given by Chapman (5). The close agreement obtained here seems to justify the assumption of a stagnant gas layer through which both sodium and cesium diffuse. [Pg.85]

Also estimate e/kg and o for Ar from the critical temperature Tc = — 122°C and critical pressure pc = 48 atm. Calculate the thermal conductivity as a function of temperature using these Lennard-Jones parameters. [Pg.535]

Evaluate the viscosity of ethane using these Lennard-Jones parameters over the temperature range 300 to 700 K. Fit the temperature dependence of the viscosity using Eq. 12.114, and report the values of the polynomial fitting coefficients that you obtained. [Pg.535]

Figure 2. Experimental and simulated fluorescence Stokes shift function 5(f) for coumarin 343 in water. The curve marked Aq is a classical molecular dynamics simulation result using a charge distribution difference, calculated by semiempirical quantum chemical methods, between ground and excited states. Also shown is a simulation for a neutral atomic solute with the Lennard-Jones parameters of the water oxygen atom (S°). (From Ref. 4.)... Figure 2. Experimental and simulated fluorescence Stokes shift function 5(f) for coumarin 343 in water. The curve marked Aq is a classical molecular dynamics simulation result using a charge distribution difference, calculated by semiempirical quantum chemical methods, between ground and excited states. Also shown is a simulation for a neutral atomic solute with the Lennard-Jones parameters of the water oxygen atom (S°). (From Ref. 4.)...
A1P04-31 (structure type ATO) has unidimensional channels with nominal diameter 5.4 A. To model Xe/AlP04-31 atomistically, we assume that A1P04-31 is rigid and defect free with the experimentally determined crystal structure [7]. Xe atoms are represented as spheres, and Xe-Xe and Xe-0 interactions are taken to be Lennard-Jones potentials using previously derived parameters [5,8]. [Pg.650]

The solute charge distribution obtained from the quantum calculation is then used as input in the molecular dynamics calculation. The solute-solvent Lennard-Jones parameters and the complete solvent-solvent force field are obtained from the literature. [Pg.583]

In order to include curvature-dependence in both the covalent and non-bonding interactions, we used the adaptive intermolecular reactive bond-order (AIREBO) potential,24 with modified van der Waals interactions. This potential uses the same bonding interactions as Brenner s REBO potential,25,26 both of which correctly account for local curvature dependence in the covalent bonding interactions. Chemisorption is thus treated accurately, but there is no explicit or implicit curvature dependence in the Lennard-Jones (L-J) parameters used to describe the non-bonded van der Waals interactions (physisorption). Consequently, we modified the Lennard-Jones parameters to make them explicitly dependent on the curvature of the nanotube. [Pg.472]


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