AH model

Wadley, S. et ah, Modeling of nanofiltration applied to the recovery of salt from waste brine at a sugar decolorization plant, J. Membr. Sci., 102, 163, 1997. 

Comparison of Anthony-Howard and Coats-Redfern Equations. Because the CR equation and the CN equation yielded similar results, the CR equation was chosen as a basis for comparison with the AH equation. The correlated results based on the AH multiple reaction model and the CR model are presented in Table VIII. The kinetic parameters were determined using an equally weighted regression method. From Table VIII, it can be seen that the AH model yields... 

Multiple Heating Rate Data. The major effort of this study has been to correlate the data in a model which will be valid for multiple heating rates. The advantage of the AH model was more evident for this purpose. Three models were used to correlate the multiple heating rate data 1) CR-LM, 2) AH-LM, and 3) CR-AH-LM. A comparison of the correlated results of these three models is presented in Table IX. From Table IX, it can be seen that ... 

The output data from reformer II for the process gas and the calculated results of the dusty gas model and simplified models I and II are presented in Table 6.16. The measured and calculated temperatures, pressures and concentrations of the process gas at the exit of reformer II are in good agreement (Table 6.16). AH models give almost the same exit conversion and yield for methane and carbon dioxide. This unit is operating relatively close to thermodynamic equilibrium, though it is slightly shifted away from equilibrium compared with unit I. 

The difference between the Kramers-Grote-Hynes one-dimensional reaction coordinate (KGH) model and the Agmon-Hopfield two-dimensional reaction coordinate (AH) model can be seen clearly by comparing Figs 3.2a and b. 

The slopes of the plots in Fig. 3.10 were around —0.7 and, hence, smaller than unity as expected. Again, in all of the cases studied similar linearity was observed. On the basis of these results, we concluded that the AH model is a better description of our slow reaction systems. Now the next step is to examine whether it is possible to obtain further information on the extent of correlation of the two coordinates. Figure 3.10 gives an important hint on this point. The isoviscous tern-... 

Considering the significant difference in the isomerization rate and in the pressure range where dynamic solvent effects were observed for the two carbocyanines, it is interesting to examine whether the dynamic solvent effect appears at a similar level in the relative time scales of the solvent and the chemical coordinate. It has earlier been shown [20, 21] that the product kxsT x Z can be used in the AH model to describe the balance of the characteristic times of the reaction system and the solvent the greater the product, the higher the anisotropy of the two time scales as... 

The coupling of the ID SFR equations with the chemical processes in and on the catalytic plate is straightforward. AH models discussed in Section 2.3 can be coupled via the species mass fluxes at the boundary between fluid phase and catalytic plate (Karadeniz, 2014 Karadeniz et al., 2013). Even more sophisticated models for the description of mass transport and chemical reactions in porous media such as the dusty-gas model (DGM) and also energy balances can be implemented into the numerical simulation (Karadeniz, 2014). 

Sterman, J. D. (2002). AH models are wrong reflections on becoming a systems scientist. System Dynamics Review, iS(4), 525-526. 

Table 8.1 Ab Initio Computations Required to Generate Input Data for Simulation of Vibrationally Resolved Electronic Spectra with VG, AS, and AH Models in FC and FCHT Framework...

As far as the comparison of the predictions of VG and AH models are concerned, they show remarkable differences in some cases, especially for TPCD, suggesting that the more complex a signal is (in the sense that it depends on many transition amplitudes) and the more important the HT effects are, the larger are the differences that can arise between the different models used to approximate the... 

Because of the number of unit-level and kinehc models available in the literature and commercially, it is impossible to prescribe a single cahbrahon method that wiU work for ah models and methods. However, there are significant common features in ah of the models to allow for general recommendahons. These recom-mendahons form a simple workflow to manage the large number of parameters that many occur in a many models. 

The PEOE procedure has been incorporated into practically ah molecular modeling packages, e.g., SYBYL of Tripos and Catalyst of Accelrys, because of its high speed and the quality of the charge values obtained. 

The molecular electronic polarizability is one of the most important descriptors used in QSPR models. Paradoxically, although it is an electronic property, it is often easier to calculate the polarizability by an additive method (see Section 7.1) than quantum mechanically. Ah-initio and DFT methods need very large basis sets before they give accurate polarizabilities. Accurate molecular polarizabilities are available from semi-empirical MO calculations very easily using a modified version of a simple variational technique proposed by Rivail and co-workers [41]. The molecular electronic polarizability correlates quite strongly with the molecular volume, although there are many cases where both descriptors are useful in QSPR models. 

Model Builder lo get a reasonable starting geometry, with the possibility of refilling the geometry by sem i-empirical calculations before submitting it to ah initio computation. 

The success of simple theoretical models m determining the properties of stable molecules may not carry over into reaction pathways. Therefore, ah initio calcii lation s with larger basis sets ni ay be more successful in locatin g transition structures th an semi-empir-ical methods, or even methods using minimal or small basis sets. 

Witir the correct choice of the parameters k and the ah initio data in Figure 4.50 could be reproduced very well. In this force field a Urey-Bradley term was also included between the silicon atoms in such angles to model the lengthening of the Si—O bond as the angle decreased. 

Williams D E 1991. Net Atomic Charge and Multipole Models for the Ah Initio Molecula Electric Potential. In Lipkowitz K B and D B Boyd (Editors). Reviews in Computational Chemistr Volume 2. New York, VCH Publishers, pp. 219-271. 

In formulating a mathematical representation of molecules, it is necessary to define a reference system that is defined as having zero energy. This zero of energy is different from one approximation to the next. For ah initio or density functional theory (DFT) methods, which model all the electrons in a system, zero energy corresponds to having all nuclei and electrons at an infinite distance from one another. Most semiempirical methods use a valence energy that cor-... 

The complete neglect of differential overlap (CNDO) method is the simplest of the neglect of differential overlap (NDO) methods. This method models valence orbitals only using a minimal basis set of Slater type orbitals. The CNDO method has proven useful for some hydrocarbon results but little else. CNDO is still sometimes used to generate the initial guess for ah initio calculations on hydrocarbons. 

There are three modihed intermediate neglect of differential overlap (MINDO) methods MINDO/1, MINDO/2, and MINDO/3. The MINDO/3 method is by far the most reliable of these. This method has yielded qualitative results for organic molecules. However its use today has been superseded by that of more accurate methods such as Austin model 1 (AMI) and parameterization method 3 (PM3). MINDO/3 is still sometimes used to obtain an initial guess for ah initio calculations. 

The PRDDO (partial retention of diatomic differential overlap) method is an attempt to get the optimal ratio of accuracy to CPU time. It has been parameterized for the periodic elements through Br, including the 3rd row transition metals. It was parameterized to reproduce ah initio results. PRDDO has been used primarily for inorganic compounds, organometallics, solid-state calculations, and polymer modeling. This method has seen less use than other methods of similar accuracy mostly due to the fact that it has not been incorporated into the most widely used semiempirical software. 

The most severe limitation of ah initio methods is the limited size of the molecule that can be modeled on even the largest computers. Semiempirical calculations can be used for large organic molecules, but are also too computation-intensive for most biomolecular systems. If a molecule is so big that a semiempirical treatment cannot be used elfectively, it is still possible to model its behavior avoiding quantum mechanics totally by using molecular mechanics. 

Once a PES has been computed, it is often fitted to an analytic function. This is done because there are many ways to analyze analytic functions that require much less computation time than working directly with ah initio calculations. For example, the reaction can be modeled as a molecular dynamics simulation showing the vibrational motion and reaction trajectories as described in Chapter 19. Another technique is to fit ah initio results to a semiempirical model designed for the purpose of describing PES s. 

The simplest and most quickly computed models are those based solely on steric hindrance. Unfortunately, these are often too inaccurate to be trusted. Molecular mechanics methods are often the method of choice due to the large amount of computation time necessary. Semiempirical methods are sometimes used when molecular mechanics does not properly represent the molecule. Ah initio methods are only viable for the very smallest molecules. These are discussed in more detail in the applicable chapters and the sources mentioned in the bibliography. 

Another technique is to use an ah initio method to parameterize force field terms specific to a single system. For example, an ah initio method can be used to compute the reaction coordinate for a model system. An analytic function can then be fitted to this reaction coordinate. A MM calculation can then be performed, with this analytic function describing the appropriate bonds, and so on. 

One very popular technique is an adaptation of the Born model for orbital-based calculations by Cramer and Truhlar, et. al. Their solvation methods (denoted SMI, SM2, and so on) are designed for use with the semiempirical and ah initio methods. Some of the most recent of these methods have a few parameters that can be adjusted by the user in order to customize the method for a specific solvent. Such methods are designed to predict ACsoiv and the geometry in solution. They have been included in a number of popular software packages including the AMSOL program, which is a derivative of AMPAC created by Cramer and Truhlar. 

The self-consistent reaction held (SCRF) method is an adaptation of the Poisson method for ah initio calculations. There are quite a number of variations on this method. One point of difference is the shape of the solvent cavity. Various models use spherical cavities, spheres for each atom, or an isosurface... 

The conductor-like screening model (COSMO) is a continuum method designed to be fast and robust. This method uses a simpler, more approximate equation for the electrostatic interaction between the solvent and solute. Line the SMx methods, it is based on a solvent accessible surface. Because of this, COSMO calculations require less CPU time than PCM calculations and are less likely to fail to converge. COSMO can be used with a variety of semiempirical, ah initio, and DFT methods. There is also some loss of accuracy as a result of this approximation. 

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