Two-dimensional contour

Figure A3.7.1. Two-dimensional contour plot for direct collinear reaction A + BC —> AB + C. Transition state is indicated by J.

Figure A3.7.7. Two-dimensional contour plot of the Stark-Wemer potential energy surface for the F + H2 reaction near the transition state. 0 is the F-H-H bend angle.

HyperChem allows the visualization of two-dimensional contour plots for a certain number of variables, fh esc contour plots show the values of a spatial variable (a property f(x,y,z) in normal th rce-dimensional Cartesian space ) on a plane that is parallel to the screen. To obtain these contour plots the user needs to specify ... 

Figure 6.4 shows a third and commonly used way of representing electron density profiles the two-dimensional contour map. This map for the SCI2 molecule corresponds to the relief map in Figure 6.2. Although this map is able to show very detailed information, we are restricted to a particular choice of plane, or to a selection of planes. To obtain an approximately equally dense distribution of contour lines, contour values used in this book increase in the nearly geometrical sequence, I0 3, 2 X 10 3, 4 X 10 3, 8 X 10-3. 2 X 10-3.

For a homonuclear diatomic molecule such as Cl2 the interatomic surface is clearly a plane passing through the midpoint between the two nuclei—in other words, the point of minimum density. The plane cuts the surface of the electron density relief map in a line that follows the two valleys leading up to the saddle at the midpoint of the ridge between the two peaks of density at the nuclei. This is a line of steepest ascent in the density on the two-dimensional contour map for the Cl2 molecule (Fig. 9). 

Figure 75-3 Two-dimensional contour plot of data matrix A found in Table 75-1.

The first graphical representation using MATLAB software is that of a two-dimensional contour surface plot of the data from Table 75-1 [2], This Figure 75-3 plot can represent multiple levels of j-axis data (absorbance) by the use of contours and color schemes. The MATLAB commands for generating this image are given in Table 75-2 where A represents the raster data matrix shown in Table 75-1. 

Figure 75-5 Two-dimensional contour plot overlay onto three-dimensional surface plot of data matrix A found in Table 75-1. (see Color Plate 24)...

Figure 3. Two-dimensional contours of total spin density of Ag°(C2Fl4) and Ag°(C2Fl4)2 complexes as the result of DFT calculations (B3LYP/A1CF//R-level)...

This behavior can be shown graphically by constructing the rD-7 -/A relation from equation 5.3-16, in which kp kr, and Keq depend on T. This is a surface in three-dimensional space, but Figure 5.2 shows the relation in two-dimensional contour form, both for an exothermic reaction and an endothermic reaction, with /A as a function of T and ( rA) (as a parameter). The full line in each case represents equilibrium conversion. Two constant-rate ( -rA) contours are shown in each case (note the direction of increase in (- rA) in each case). As expected, each rate contour exhibits a maximum for the exothermic case, but not for the endothermic case. 

What has been done more typically, however, is to evaluate V(r) only at or beyond some appropriate distances from the nuclei. For instance, what was formerly often done was to compute two-dimensional contour plots of V(r) in planes passing through a molecule (but omitting the regions near the nuclei) or in planes well removed from the nuclei, e.g., 1.75 A [3,14,16,17], This approach is of course more straightforward for planar molecules than for nonplanar ones. Another possibility that is sometimes utilized is to show just one, presumably important, three-dimensional outer contour of Hr) [18]. This introduces the problem of choosing which one to show. 

As discussed in Chapter 1, given a sample mixture-fraction field16 f (x, t) x e L3, this joint PDF could be estimated and plotted in terms of z and as a two-dimensional contour plot. 

Figure 6.29 shows mass spectra recorded during elution reduced to a two-dimensional contour plot. Each point is produced from pseudo-molecular ions, cluster formation or fragmentation. AU ions eluting in parallel with respect to time, at c. 29 min are assumed to belong to the main component, but there are some points clearly seen on the front edge of the main peak that indicate the presence of an impurity. This was confirmed by the production of a mass chromatogram of miz 486. 

Figure 629 (a) UV trace of the drug, (b) mass chromatogram of mJz 486 of an impurity component and (c) two-dimensional contour plot of the mass spectra from mIz 400 to mIz 550. Reproduced from [22] with permission of John Wiley and Sons Ltd. 

Figure 6 Two-dimensional contour plot of the sum of the harmonic-oscillator and of the electron-repulsion potentials for two electrons in the internal space (xa, ya) for coxy = 5.0 (a), 1.0 (b), and 0.1 (c). The maximum potential height Vmax and the domain of the xa and ya coordinates displayed are the same as used in Figure 3. The red spot at the origin of the contours represents the potential pole of the electron repulsion potential. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this book.)...

Fig. 1.11. Two-dimensional contour maps of the potential energy surfaces of cis-CHsONO in the three lowest singlet states So, Si, and 2- The coordinates are defined in Figure 1.10(a). The energy contours are given in eV and the normalization is such that CH3O + NO(re) corresponds to E = 0 in all three cases.

Figure 28 Two-dimensional contour plots of the calculated PES for die CT2O3 (0 00 l)-CO system. 4>—X dependence at ground state (bottom) and at die excited a3 n state (top) with a snapshot of die wave packet after a time evolution of 50 fs. Inset cluster model, only two Cr ions are shown [79].

Figure 1 Two-dimensional contour plots of the log of the Raman-echo correlation function, In Cre(ti, T3), showing the effect of changing the rate of solvent-induced perturbations. All cases give a Raman line with the same FWHM (5 cm-1) and FIDs with similar decay times but give very different Raman echo results, (a) Fast modulation (b) intermediate modulation (A, = 3.32 cm-1, r( = 1.60 ps) (c) slow modulation. Calculations are based on a single Kubo-Anderson process [Equations (7)-(9)].

Several of the spectra in this workbook were obtained using techniques such as proton-detected C-H shift correlation and multiple-quantum-filtered phase-sensitive COSY which were not covered in detail in our main text because they have come into general use since it was written. This is a measure of the rate at which practical NMR is progressing but presents no problem in the interpretation of the spectra. Various field strengths and modes of presentation, ranging from continuous-wave traces to phase-sensitive two-dimensional contour plots, were used for the spectra. In part, this reflects the history of individual problems, but it is also intentional. It is important to be able to extract the essential message of a spectrum independently of the way it is presented. 

Figure 15 Two-dimensional contour plots of the Werner-Keller-Schinke potential energy surface of HCO. Reprinted, with permission of the American Institute of Physics, from Ref. 51.

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