Applications of Traditional Modeling Techniques

Internally, molecules can be represented several different ways. One possibility is to use a bond-order matrix representation. A second possibility is to use a list of bonds. Matrices are convenient for carrying out mathematical operations, but they waste memory due to many zero entries corresponding to pairs of atoms that are not bonded. For this reason, bond lists are the more widely used technique. 

Some programs incorporate very simple energy calculations. These are very quickly calculated estimations of electronegativity and other properties. Although not accurate enough to be completely reliable, these techniques are useful in weeding out undesirable reaction routes. 

Computer-Assisted Organic Synthesis W. T. Wipke, W. J. Howe, Eds., ACS, Washington (1977). 

Hladka, J. Koca, M. Kratochvil, V. Kvasnicka, L. Matyska, J. Pospichal, V. Potucek, Computer Chemistry Springer-Verlag, Berlin (1993). 

Barone, M. Chanon, Computer Aids to Chemistry 19 G. Vernin, M. Chanon, Eds., Ellis Horwood-John Wiley, New York (1986). 

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The identification of plant models has traditionally been done in the open-loop mode. The desire to minimize the production of the off-spec product during an open-loop identification test and to avoid the unstable open-loop dynamics of certain systems has increased the need to develop methodologies suitable for the system identification. Open-loop identification techniques are not directly applicable to closed-loop data due to correlation between process input (i.e., controller output) and unmeasured disturbances. Based on Prediction Error Method (PEM), several closed-loop identification methods have been presented Direct, Indirect, Joint Input-Output, and Two-Step Methods. 

Characterizing the overall uncertainties associated with the PBPK model estimates is also an important component of the PBPK model evaluation and application. This includes characterizing the uncertainties in model outputs resulting from the uncertainty in the PBPK model parameters. Traditionally, Monte Carlo has been employed for performing uncertainty analysis of PBPK models (39, 40). Some of the recent techniques that have been applied for the uncertainty analysis of PBPK models include the stochastic response surface method (SRSM) (38, 41) and the high-dimensional model reduction (HDMR) technique (42). 

A further restriction on the use of many-body perturbation techniques arises from the (quasi-) degenerate energy structure, which occurs for most open-shell atoms and molecules. In these systems, a single reference state fails to provide a good approximation for the physical states of interest. A better choice, instead, is the use of a multi-configurational reference state or model space, respectively. Such a choice, when combined with configuration interactions calculations, enables one to incorporate important correlation effects (within the model space) to all orders. The extension and application of perturbation expansions towards open-shell systems is of interest for both, the traditional order-by-order MBPT [1] as well as in the case of the CCA [17]. 

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