Contour maps plots

Fig. 3. Oxide removal rate and WIWNU (3 mm EE)contour map plotted against normalized...

If a iTioleciile is rotated by chan gin g th c position of the viewer (left mouse btiLlon rotation) ih en the moleetile s position in ihetnolee-ular eoorditi ale system h as not ch an ged and anolb er con lour plot can be requested without recotn pu tin g the wave ftinetion. fb at is, m any orbitals can he plotted after a sin gle poin t ah initio or setn i-einpirical calculation,. iti y contour map is available without recotn putation of the wave function. 

If a molecule is rotated by changing the position of the viewer (left mouse button rotation) then the molecule s position in the molecular coordinate system has not changed and another contour plot can be requested without recomputing the wave function. That is, many orbitals can be plotted after a single point ab initio or semi-empirical calculation. Any contour map is available without recomputation of the wave function. 

The results of electrostatic potential calculations can be used to predict initial attack positions of protons (or other ions) during a reaction. You can use the Contour Plot dialog box to request a plot of the contour map of the electrostatic potential of a molecular system after you done a semi-empirical or ab initio calculation. By definition, the electrostatic potential is calculated using the following expression ... 

Comparison of Alignment Charts and Cartesian Graphs. There are typically fewer lines on an alignment chart as compared to Cartesian plots. This reduces error introduced by interpolation and inconsistency between scales. For example, to find a point (x,j) on a Cartesian graph one draws two lines, one perpendicular to each axis, and these reference lines intersect at the point x,j). This point (x,j) may correspond to some finite value found by rea ding a contour map represented by a family of curves corresponding to different values of the function. 

Figure 13 shows contour maps at an instant in time when 75% of the fuel is left in the calculation domain. Each contour plot shows contour values for the following percentages of the maximum in the plane in question 0.95, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.05. In the plots the highest value is denoted... 

Figure 6.17 Contour map of p in the interatomic surface associated with the CC bond critical point in ethene. The plane of the plot is perpendicular to the molecular plane. The C and two H nuclei are projected onto the plane of the plot to indicate the orientation of the molecule. We see that electronic charge is preferentially accumulated in the direction perpendicular to the molecular plane, giving an elliptical shape to the electron density in this plane.

Figure 6.18 Contour maps of the ground state electronic charge distributions for the period 2 diatomic hydrides (including H2) showing the positions of the interatomic surfaces. The outer density contour in these plots is 0.001 au. (Reproduced with permission front Bader [1990].)...

Figure 2. Contour maps of the electron density of (a) SCI2 and (b) H2O. The density increases from the outermost 0.001 au isodensily contour in steps of 2 x 10", 4 x 10", and 8 x 10" au with n starting at 3 and increasing in steps of unity. The lines connecting the nuclei are the bond paths, and the lines delimiting each atom are the intersection of the respective interatomic surface with the plane of the drawing. The same values for the contours apply to subsequent contour plots in this paper.

Fig. 13a and b. Intensity contour maps around the 5.9-nm and 5.1-nm actin layer lines (indicated by arrows) a resting state b contracting state. Z is the reciprocal-space axial coordinate from the equator. M5 to M9 are myosin meridional reflections indexed to the fifth to ninth orders of a 42.9-nm repeat, (c) intensity profiles (in arbitrary units) of the 5.9- and 5.1-nm actin reflections. Dashed curves, resting state solid curves, contracting state. Intensity distributions were measured by scanning the intensity data perpendicular to the layer lines at intervals of 0.4 mm. The area of the peak above the background was adopted as an integrated intensity and plotted as a function of the reciprocal coordinate (R) from the meridian... 

Response surface plot a graphical representation of the response surface as a contour map of the dependent variable on a coordinate scale of two of the independent variables. 

Fig. 22. Electron density contour maps of the three frontier orbitals of electron-deficient M(it-C5Hs)2 fragments. The plots represent a section through the yz plane. [Reproduced from Lauher and Hoffmann (134), by permission of the American Chemical Society.]...

Fig. 15.7 Conceptual illustration of the behavior of a Newton iteration on a nonlinear, stiff system of algebraic equations. A contour map of a norm of the residual vector F is plotted. The curvature represents nonlinear behavior, and the elongation represents disparate scaling, or stiffness. The desired solution of the problem is represented by the X the current iteration is marked by a dot. The elliptical contours represent residuals of the local linearization at the current iterate.

The two-dimensional matrix can be recorded by an analog plotter, or much faster by a digital plotter or a graphic display. Stacked plots as drawn in Fig. 2.50(d) can be obtained, providing a panoramic picture of the carbon-13 signals (3) and their individual multiplets (JCHj. Useful for practical evaluation, the contour plot is like a contour map of the signal mountains, giving a type of aerial view of the CH multiplets (Fig. 2.50(e)). 

Fig. 3. (Top) A two-dimensional nuclear magnetic resonance spectrum of a sugar (Bottom) conventional NMR spectrum of same sugar. Tile two-dimensional spectrum also can be plotted as a contour map with intensities denoted by color. (JEOL Inc)...

Plots the adiab equation surface as a 2D contour map with the contour = 0 7. curve marked in black. 

Figure 5.1 Seasonable February morning in Maine. Lines of constant temperature (isotherms) allow plotting a two-dimensional function without using the third dimension. This is a contour map of t(x,y), giving the temperature t at all locations x,y). Along each contour line lie all points having the same temperature. A planar contour map of a function of two variables takes the form of contour lines on the plane. In contrast, a contour map of a function of three variables takes the form of contour surfaces in three dimensions (see Plate 2).

Figure 6.11 a Diels-Alder reaction of N-2-alkenoyl-l, 3-oxazolidin-2-one with cyclopentadiene. b alignment of all 23 bisoxazoline and phosphinoxazoline ligands used in the CoMFA study. Regions of space where steric bulk should enhance or decrease stereo-induction are plotted using iso-contour mapping. 

Once the characteristic absorbance frequencies for the components have been determined, one can view the image data with contour plots (intensity versus spatial position). A contour plot for a given frequency is a representation of the data in three dimensions spectral intensity (shown by colors), and plotted in the x- and y-dimensions. From the contour map, one can determine initially whether the acquired image is homogeneous or heterogeneous. If the image is homogenous and is expected... 

The results may be displayed either as an isometric 3-D plot of intensity vs temperature and wavelength or as a contour map. Individual interferograms can also be summed to display a conventional 2-D glow-curve over the full temperature range. 

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