Number of contours

You can specify the number and values of visible contour lines. You specify the total number of contour lines to be shown by simple stating the number, n>0. You normally specify the values of the contour lines as default values. For this case, HyperChem computes the maximum and minimum values on the grid and then draws contours at these values plus n-2 contour lines evenly spaced in between these maximum and minimum values. If you need non-default values, you can specify the starting value and then an increment to define the other n-1 evenly spaced contour lines. If default values were computed previously, HyperChem suggests the starting value and increment of the previous default computation for the new non-default option. 

Similar options are available for the Contour plots, as shown in Figure D.14. You can set e number of contours to be plotted, and you can choose Vector with isolevels and type in e numerical values of the contours you want [1.5 1.6 2.0 3.0]. If you want your plot to have only contours, then unclick the box under e Surface tab, or go to the General tab and unclick the box next to Surface. 

FIGURE 3.12 The first of three plots of a 2-D gttSQC NMR spectrum, showing the effect of spacing and number of contour lines. This plot shows (up to) 40 lines spaced 110% apart. 

Limiting the number of contour lines to just 5 or 10 likely will result in a plot with open, circular (or elliptical) cross peaks (Figure 3.14). This technique is often used by those in the bioNMR subdisdplme because bioNMR plots are often so full of cross peaks that having a large number of filled-in cross peaks is displeasing to the eye. 

Limiting the number of contour lines to 15, 20, or 30 can also be used to help illustrate which cross peaks are most intense. This enhancement occurs because a weaker cross peak will have its middle completely filled in by the contour lines, but a stronger cross peak will appear as an open circle, much like a snow-capped mountain (Figure 3.14). That is, a strong cross peak will have an intensity at its center that rises above the maximum intensity denoted by the highest contour line. Therefore, the centers of the stronger cross peaks will be devoid of contour lines. 

Usually the 2D NMR spectnun is either for the spin-spin interaction (COSY) or for the NOE (NOESY). Spectra of 2D NMR are plotted on two frequency axes, which show a crosspeak at the frequencies corresponding to each pair of nuclei that interact. The magnitude of the interaction effect is represented by the intensity of the crosspeak. It is shown by the number of contours (like a contour map) at the point of interaction the more contours, the higher the peak corresponding to the interaction. The diagonal represents ID spectrum of the contour line of peaks, which also plot along both axes. 

Figure 3.44 shows the electron density in the plane of the molecule. By counting the number of contour lines for each atom, it is easy to distinguish C from N. The electron density at the center of N is 14.5 e A " and at the center ofC12.5 A". The electron density of H is too small to be visible in this figure, but these atoms can, in fact, be seen by choosing a finer contour interval. 

It follows from Cauchy s theorem that if there is a finite number of contours Cl, C2,. .., C inside C, and f z) is analytic in the region between them, then... 

Figure 5.12 shows a number of contour lines for yield and selectivity. Observe that there are many points of intersection with the AR for these functions. Both Yg and BD become larger as the reaction approaches the equilibrium point [0,0] mol/L. This suggests that a reactor operating near the equilibrium point produces the largest instantaneous yield and... 

Many chemical processes require unusual vessel configurations. The heads of such vessels can have an infinite number of contours. One such contour is shown in Fig. 9. Ig. The design of these heads is very complicated and there are no simple methods of analysis. Experience, proof testing, and sophisticated analyses are generally used to detennine required thicknesses. 

An alternative method of analysis of NOESY data, which is usually sufficient for resolved peaks with a digital resolution much greater than the intrinsic line width and coupling constants, is to measure the maximum peak amplitude or to count the number of contours. NOESY cross peaks can then be classified as strong, medium or weak and can be translated into upper distance restraints of around 2.5, 3.5 and 5.0 A respectively. The lower distance constraint is usually the sum of the van der Waals radii (1.8 A for protons). This simple approach is reasonably insensitive to the effects of spin diffusion or non-uniform correlation times and can usually lead to definition of the global fold of the protein, provided a sufficiently large number of NOEs have been identified. 

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