Pair parameters

The first general parameterization to be reported by Dewar and co-workers was a third-generation modified INDO model (MINDO/3 Bingham, Dewar, and Lo, 1975). Some of the specific modifications to the INDO framework included the use of different t exponents in s and p type STOs on the same atom, the definition of pair parameters /Iab between two atoms A and B that were not averages of atomic parameters (actually, four such parameters... 

Reactive absorption processes occur mostly in aqueous systems, with both molecular and electrolyte species. These systems demonstrate substantially non-ideal behavior. The electrolyte components represent reaction products of absorbed gases or dissociation products of dissolved salts. There are two basic models applied for the description of electrolyte-containing mixtures, namely the Electrolyte NRTL model and the Pitzer model. The Electrolyte NRTL model [37-39] is able to estimate the activity coefficients for both ionic and molecular species in aqueous and mixed solvent electrolyte systems based on the binary pair parameters. The model reduces to the well-known NRTL model when electrolyte concentrations in the liquid phase approach zero [40]. 

Here z is the coordination number in the two-dimensional adsorbate, w the lateral interaction pair parameter. 

The classical expressions for ai, pf , and up are similar to the pure-gas expressions with the slight added complication of having two sets of isolated-molecule parameters o oo, fio,. Fo, The determination of the mixed-pair parameters involved in uq is much more difficult. The determination of these parameters from mixed viscosities and pressure virial coefficients is hampered by a shortage of experimental data, and the usual procedure is to employ a set of empirical combining rules which relate the mixed parameters to those of the pure gases. A number of such rules have been proposed for the 6-12 potential, the most widely used for dielectric calculations being... 

Step 5 In the list on the left, choose Property/Specifications. In property method, scroll down to get RK-Soave (see Figure 2.4). To eliminate the red pair parameters, open the window and click on the designated (recommended) data set. 

The development of the PF method culminated in molecular mechanics, a reliable method of prediction of conformational eneigy and equilibrium structure of nonpolar molecules. For molecules having several heteroatoms, a modified parameterization was developed, with the lone-pair parameters as a part of the force field, and with their inclusion into all types of intramo-... 

Hubbard initiated a treatment where some electron interaction is included in a localized description with the aim to deal with magnetic features. His model has become a popular and widely used vehicle for the study of electron correlation. It is based on the reduction of the electron repulsion terms to intraatomic ones and to use only the form with the largest pair parameter, (Hint)Ao gAO gAO, for each atom A. Interatomic coupling is represented by a one-particle operator which moves particles from one atom to another, so-called hopping terms. The Hamiltonian is then... 

The present calculations of activities and compositions have been made using Equations 1-7 group counts or assignments are given in Table I and group-pair parameters are given in Table II. 

The group pair parameters are summarized in Table II. Parameters for CH2-CA, CHjj-OH, CH2-MCOO, CH2-KCO, and CHjr-Cl were computer generated by satisfying activity coefficient data (II) for heptane-benzene, heptane-ethanol, hexane-ethyl acetate, heptane-acetone, and heptane-chlorobenzene systems, respectively. In generating the CB2/C1 parameters, previously determined CH2/CA values were used. In order that no more than a single pair of parameters be sought in a given determination, it is important that proper sequence be maintained. 

Pitzer s equations and available ion-pair parameters allow calculation of mean-ion activity coefficients Y+ in complex, concentrated electrolyte solutions with an accuracy estimated to be better than + 25% in the range 25° - 55°C. The accuracy of calculated activity coefficients is limited to about the same degree by uncertainties in the estimated parameters and by simplifications introduced in the theory both to reduce the number of parameters to be estimated and to reflect the uncertainties of the estimates. Because activity coefficients are determined to quite an extent by the form of Pitzer s equations and are not extremely sensitive to the exact values of parameters, ion-pair parameters only have to be estimated within a reasonable range. 

The simplest way to handle hydrogen bonding is to rely on the other nonbonded potentials to reproduce hydrogen bonds. Some methods include specific pair parameters [19] while others use special potentials for the nonbonded interactions between hydrogen bond donors and acceptors [20,21],... 

In the development of MINDO/3, nearly all quantities that entered the Fock matrix and the energy expression were treated as free parameters. The orbital exponents that entered into the basis, set were varied, and it was found advantageous to allow the s and p exponents to be different. In addition, the core integral V (Eq. [12a]) were also freely varied. Finally, the resonance integral, 3, was chosen to be a pair parameter rather than the average of two atomic parameters. As a result of the introduction of these parameters, the MINDO/3 model achieved a rather impressive qualitative as well as quantitative predictive power. 

Definitions of helical and base pair parameters in DNA and PNA helices. 

The interaction parameters between molecules and electrolytes are called pair parameters. They are described with a slightly different temperature dependence ... 

It must be emphasized that the pair parameters are not specific for an ion but for an electrolyte,... 

Figure 6. Intrabase-pair parameters shear, stretch, stagger, buckle, propeller twist and opening of CGCGAATTCGCG simulated with a cis, syn dimer at T7-T8. (Reproduced with permission from ref. 29. Copyright 1996 American Chemical Society)...

There are two ways to use the UNIFAC model. One is to use the UNIFAC model to describe all binary pairs in the whole component system. The other is to only use the UNIFAC model to estimate the binary pair parameters for the particular pair where the built-in parameters are not available in Aspen. We will discuss these two situations in the following. 

For the like-pair interaction the remaining parameters (e, o, n, 5x, or 2) were determined as those giving the best fit to the saturated liquid density and vapor pressure data (13). The like-pair parameters are shown in Table 2. For the unlike-pair interactions one must also know the parcuneters a3 03 > %3 where 1 is 1 or 2. The last two parameters were estimated from the combining rules... 

The PM3-PIF models that have been developed in the past decade were aimed to enable more realistic studies of solutes in aqueous solutions. The fact that at the center of the model there is a correct structural and energetic description of the intermolecular forces governing the physical and chemical behavior of a condensed phase makes of these PM3-PIF models an excellent choice for a large exploration of the dynamic and structural properties of solutions. A clear obstacle for an ample use of these models is the need to obtain specific atomic pair parameters for each system and, as recently found, they are not necessarily transferable [34]. However, the advantage of having an inexpensive model including implicit polarizability and molecular flexibility with a satisfactory description of interactions makes worth the parameterization challenge. 

The non-bonded interaction van der Waals parameters Cn i,j) and j) in equation (23) depend on the non-bonded atom types / and J, of atoms i and j, respectively. In contrast to the standard practice of defining atom pair parameters Ci2(/, J) in terms of the single atom parameters Ci2(/, /) and C iiJ,J) using so-called combination rules, e.g.,... 

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