OPLS model

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 ... 

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... 

With increasing use of such models, methods are likely to become more concisely defined in the near future. At present, the models for which protocols and parameters have been most clearly defined and where a fair number of applications have appeared applying those models in a consistent fashion include the aheady noted AM1/TIP3P model (more generally AMl/OPLS when solvents other than water are employed in the MM region) and a similarly fashioned HF/3-21G/OPLS model (Freindorf and Gao 1996). Implementations carrying the QM level as far as coupled-cluster theory have been reported (Kongsted et al. 2003). 

Figure 6. Comparison of calculated (computer simulation results for the OPLS model) and experimental heats of vaporization in kcal mol- for the liquids in Table 1 and TIP4P water. Reprinted with permission from W. L. Jorgensen and J. Tirado-Rives, J. Am. Chem. Soc. 110, 1657 (1988) [8], Copyright 1988 American Chemical Society.

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 )... 

Here, we consider NIR spectra that have been recorded in order to analyze the protein content in wheat (cf. Example 6.10). The original 30 spectra shown in Figure 6.6a are of less regular structure in comparison to the spectra of Figure 6.6b corrected by the OPLS model of Eq. (6.69). 

Van der Waals non bonded potential parameters are obtained by fitting some experimentally observed properties. At present, the limited capacity of computers prevents us from using efficiently all atoms descriptions (AA potential), in which each atom is represented by a separate Lennard-Jones center. Consequently, several authors proposed united atom (UA) potential, such as the NERD potential (Nath et al., 1998) or the TraPPE model (Martin and Siepmann, 1998), where a group like CH2 or CHj is represented by a single force center, this approach was pioneered in the early work by Jorgensen (1984) with its OPLS model. While each force center is located on the carbon in the more classic UA potentials, it is shifted in the Anisotropic United Atoms (AUA) potential proposed by Toxvaerd (1990) for n-alkanes, so that it is placed between the carbon and the hydrogen atoms of the related group. Here, the AUA formalism is used. 

Figure 6 Vapor-liquid curve of octane comparison of Oibb.s-ense-mble simulations using the OPLS model of Jorgensen and co-workers, the model of Toxvaeid, and the model of Siepmann et al. ...

Optimized potentials for liquid simulation (OPES) was designed for modeling bulk liquids. It has also seen significant use in modeling the molecular dynamics of biomolecules. OPLS uses five valence terms, one of which is an electrostatic term, but no cross terms. 

Another difference between the force fields is the calculation of electrostatic interactions. AMBER, BIO+, and OPLS use point charges to model electrostatic interactions. MM+ calculates electrostatic interactions using bond dipoles. The bond dipole method may not adequately simulate very polar or charged systems. 

The term "lag" refers to the delay in transporting heat from one part of the extruder to another. For example, "Lag 11" refers to the delay in heat conduction from the "OPl" heater to the first measurement, node number 5 ("Tn5"), in the model. Similarly, "Lag 12" refers to the delay in heat conduction from the "OPl" heater to the second measurement, node number 55 ("Tn55"), in the model. 

Kaminski, G. Duffy, E. M. Matsui, T. Jorgensen, W. L., Free-energies of hydration and pure liquid properties of hydrocarbons from the OPLS all-atom model, J. Phys. Chem. 1994, 98, 13077-13082. 

From a structural point of view the OPLS results for liquids have also shown to be in accord with available experimental data, including vibrational spectroscopy and diffraction data on, for Instance, formamide, dimethylformamide, methanol, ethanol, 1-propanol, 2-methyl-2-propanol, methane, ethane and neopentane. The hydrogen bonding in alcohols, thiols and amides is well represented by the OPLS potential functions. The average root-mean-square deviation from the X-ray structures of the crystals for four cyclic hexapeptides and a cyclic pentapeptide optimized with the OPLS/AMBER model, was only 0.17 A for the atomic positions and 3% for the unit cell volumes. 

ILOG OPL Studio 3.71 hosts the optimization model and provides... 

This model extension is tested with ILOG OPL Studio 3.71 using ILOG CPLEX 9.1 and examined industry case test data on an Intel Pentium 4 Processor with 1,598 Mhz and 256 MB RAM. The extension is tested for an excerpt of the value chain network including nine sales locations, one procurement location and one production and having one multi-purpose and one continuous production resource as shown in fig. 101. 

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