Generation of Initial Guesses

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. 

Generate an initial guess for the path connecting the initial and final coordinates of the system using an MEP algorithm, such as self-penalty walk (SPW) or nudged-elastic band. ... 

We now discnss the numerical solution of (4.128). We first generate an initial guess of the new state vector, from an explicit rule such as (4.118). Then, we use Newton s... 

When this initial guess is poor, you need a more sophisticated—albeit more expensive—means of generating the force constants. This is especially important for transition state optimizations. Gaussian provides a variety of alternate ways of generating them. Here are some of the most useful associated keywords consult the Gaussian User s Reference for a full description of their use ... 

As seen, there is significant variability in the estimates. This is the reason why we should avoid using this technique if possible (unless we wish to generate initial guesses for the Gauss-Newton method for ODE systems). As it was mentioned earlier, the numerical computation of derivatives from noisy data is a risky business ... 

A suitable transformation of the model equations can simplify the structure of the model considerably and thus, initial guess generation becomes a trivial task. The most interesting case which is also often encountered in engineering applications, is that of transformably linear models. These are nonlinear models that reduce to simple linear models after a suitable transformation is performed. These models have been extensively used in engineering particularly before the wide availability of computers so that the parameters could easily be obtained with linear least squares estimation. Even today such models are also used to reveal characteristics of the behavior of the model in a graphical form. 

As expected, the estimated values were found to be closer to the correct ones compared with the estimated values when the water-oil ratios are only matched. In the 2nd run, the horizontal permeabilities of layers 5 to 10 (6 zones) were estimated using the value of 200 md as initial guess. It was found necessary to use the pseudo-inverse option in this case to ensure convergence of the computations. The initial and converged profiles generated by the model are compared to the observed data in Figures 18.25a and 18.25b. 

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