Curve fit

Curve Fit is a function used to decompose the area of heavily overlapping bands into constituent components. The implemented procedure is based on the least-squares minimization algorithm. Each band is characterized by the parameters band position, intensity, and width. Furthermore, the type of the band shape is taken into account, whereby you can choose a Gaussian or Lorentzian function or a linear combination of both. 

Note that before the fitting calculation is started, it is essential to generate a model consisting of an estimated number of bands and a baseline. The model can be setup interactively on the display and is optimized during the calculation. Since the result of the calculation is highly dependent on the model chosen, care must be taken that the model is reasonable from the chemical point of view. An indispensable part of any fitting procedure is a good choice of initial parameter values. 

Calling up Curve Fit from the Evaluate menu, a dialog box (Fig. 11.2) appears to select the spectrum and the spectral range. On the first page, the spectrum to be fitted is selected by dragging it from the browser window into the File to Fit box. Note that the spectrum needs to be of absorbance type and baseline 

IR and Raman Spectroscopy Fundamental Processing. Siegfried Wartewig Copyright 2003 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim ISBN 3-527-30245-X 

In order to perform a curve fit, an appropriate method must first be created. By clicking on the button Start Interactive Mode, the spectrum you selected will be opened in the curve fit setup window (see Fig. 11.3). In the upper window, the spectrum to be fitted is displayed, whereas in the bottom window the difference between the original spectrum and the fitted spectrum is shown. As there was no fitting carried out at this point, both windows show the same spectrum. 

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Fig. XVin-6. Curve-fitted Mo XPS 3d spectra of a 5 wt% Mo/Ti02 catalyst (a) in the oxidic +6 valence state (b) after reduction at 304°C. Doublets A, B, and C refer to Mo oxidation states +6, +5, and +4, respectively [37]. (Reprinted with permission from American Chemical Society copyright 1974.)...

In the first pari of this project, the analytical form of the functional relationship is not used because it is not known. Integration is carried out directly on the experimental data themselves, necessitating a rather different approach to the programming of Simpson s method. In the second part of the project, a curve fitting program (TableCurve, Appendix A) is introduced. TableCurve presents the area under the fitted curve along with the curve itself. 

To anyone who has carried out curve-fitting calculations with a mechanical calculator (yes, they once existed) TableCurve (Appendix A) is equally miraculous. TableCurve fits dozens, hundreds, or thousands of equations to a set of experimental data points and ranks them according to how well they fit the points, enabling the researcher to select from among them. Many will fit poorly, but usually several fit well. 

Along with the curve fitting process, TableCurve also calculates the area under the curve. According to the previous discussion, this is the entropy of the test substance, lead. To find the integral, click on the numeric at the left of the desktop and find 65.06 as the area under the curve over the range of x. The literature value depends slightly on the source one value (CRC Handbook of Chemistry and Physics) is 64.8 J K mol. ... 

The situation is similar for a linear curve fit, except that now the data set is two-dimensional and the number of degrees of freedom is reduced to (n — 2). The analogs of the one-dimensional variance )/( 1) the standard... 

Solved using the BASIC curve fitting program QLLSQ we get as a partial output block 10 POINTS, FIT WITH STD DEV OF THE REGRESSION. 2842293... 

COMPUTER PROJECT 3-1 Linear Curve Fitting KF Solvation... 

The quadr atic curve fit leads to a number of residuals equal to the number of points in the data set. The sum of squares of residuals gives SSE by Eqs. (3-23) and MSE by Eq. (3-30), except that now the number of degrees of freedom for n points is... 

Using the expanded determinants from Problem 6, write explicit algebraic expressions for the three minimization parameters a, b, and c for a parabolic curve fit. 

Write the determinant for a sixth-degree curve fitting procedure. 

We now have two ways of inserting the correct parameters into the STO-2G calculation. We can write them out in a gen file like Input File 8-1 or we can use the stored parameters as in Input File 8-2. You may be wondering where all the parameters come from that are stored for use in the STO-xG types of calculation. They were determined a long time ago (Hehre et al, 1969) by curve fitting Gaussian sums to the STO. See Szabo and Ostlund (1989) for more detail. There are parameters for many basis sets in the literature, and many can be simply called up from the GAUSSIAN data base by keywords such as STO-3G, 3-21G, 6-31G, etc. 

Mortimer, R. G., 1999. Mathematics for Physical Chemistry, 2nd ed. Academic Press, San Diego, CA. [This book contains an introduction to computer use with brief comments, references and sources to BASIC, Excel, graphics, curve fitting, and Mathematica.]... 

One very popular technique is to use QSAR. It is, in essence, a curve-fitting... 

Understanding how the force field was originally parameterized will aid in knowing how to create new parameters consistent with that force field. The original parameterization of a force field is, in essence, a massive curve fit of many parameters from different compounds in order to obtain the lowest standard deviation between computed and experimental results for the entire set of molecules. In some simple cases, this is done by using the average of the values from the experimental results. More often, this is a very complex iterative process. 

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