Contour plots, superimposed

Figure Al.6.27. Equipotential contour plots of (a) the excited- and (b), (c) ground-state potential energy surfaces. (Here a hamionic excited state is used because that is the way the first calculations were perfomied.) (a) The classical trajectory that originates from rest on the ground-state surface makes a vertical transition to the excited state, and subsequently undergoes Lissajous motion, which is shown superimposed, (b) Assuming a vertical transition down at time (position and momentum conserved) the trajectory continues to evolve on the ground-state surface and exits from chaimel 1. (c) If the transition down is at time 2 the classical trajectory exits from chaimel 2 (reprinted from [52]).

The Nichols chart shown in Figure 6.26 is a rectangular plot of open-loop phase on the x-axis against open-loop modulus (dB) on the jr-axis. M and N contours are superimposed so that open-loop and closed-loop frequency response characteristics can be evaluated simultaneously. Like the Bode diagram, the effect of increasing the open-loop gain constant K is to move the open-loop frequency response locus in the y-direction. The Nichols chart is one of the most useful tools in frequency domain analysis. 

Figure 12.10c shows a contour plot of the nanolaser index profile superimposed on a cross-section of the modal field intensity profile in the center of the active medium. As shown in the figure, the modal profile of the nanocavity is confined almost completely in the 300-nm wide central pillar with a modal volume of 0.213 (1/n)3 (0.024 pm3) only 1.75 times the theoretically possible limit of a cubic half... 

Lowest 5 kcal mol 1 of the calculated overall potential energy surface for a model peptide of Ser-DHype(trans propyl)-Oic-Arg. The contour interval is 0.5 Kcalmol"1 and the highest (outermost) and lowest contour energy values are labeled. Superimposed on the contour plots are values for j/i+1 and fi+2 from each of the thirty structures generated from the NMR data corresponding to the tetrapeptide... 

Fig. 5. A contour plot representing a two-dimensional slice of the molecular electrostatic potential for vinyl sulfone in the plane of the molecule with a sample uniform cubic grid superimposed grid points would be placed at the intersections of the perpendicular lines. (Reproduced from [71] copyright-John Wiley Sons)...

Fig. 9.9. Contour plot of the potential energy surface of H2O in the AlB state the bending angle is fixed at 104°. Superimposed are the total stationary wavefunctions I tot( ) defined in (2.70). The total energies are —2.6 eV and -2.0 eV corresponding to wavelengths of A = 180 nm and 165 nm, respectively. Energy normalization is such that E = 0 corresponds to three ground-state atoms.

Fig. 13.7. Contour plot of the A-state PES for a bending angle ae = 104°. Energy normalization is such that E — 0 corresponds to H+O+H. Superimposed are contours of luAX Oil2 where hax is the X —> A transition dipole function and 04 is the bound-state wavefunction of HOD with four quanta of excitation in the O-H bond. The filled circle indicates the barrier and the two especially marked contours represent the energies for the two photolysis wavelengths A2 = 239.5 and 218.5 nm used in the experiment. Adapted from Vander Wal et al. (1991).

Figure 5.1 displays, in the form of contour plots, the ground-state charge distributions of LiF, LiO, and LiH, each at its equilibrium intemuclear separation. Superimposed on each of these plots is the intersection of the... 

Figure 5. Calculated GRID contours for the active site of sialidase superimposed onto some of the amino acid residues and bound NeuSAc (yellow) (a) Contours plotted at —10.0 kcal mol for a carbox-ylate oxygen probe, (b) Contours plotted at —8.5 kcal mol for an sp amino nitrogen probe.

Figure 2. Superimposed plots of 4 contour plots at 145°C and 10 min for rehydration ratio (RR), bulk density (BD), non-enzymatic browning (NEB) and expressible fluid (EF) of dehydrated potato cubes.

The differences in the CMC and EMC predictions can be traced to the different pair probability densities estimated by these methods from the given time series. In fig. 9.4, we show a contour plot of the pair distribution function p Xi, Xg) as calculated by a semi-nonparametric (SNP) method [10] with the time-series simulations for these two species superimposed. In comparison, we show in fig. 9.5 a Gaussian pair probability distribution, as is consistent with CMC, with the same means and variances as those of the EMC distribution. The deviations of the EMC from the Gaussian distribution show that higher than second moments contribute. Since the information entropy for... 

Figure 11.5(a) shows contour plots of two-dimension histograms that count the number of xJ/C-pcm 1X21 points, as a function of the value of q/C-PCM j-jjg dimensionless distance rij/[RiRjy. Various anal) ic interpolating functions I y are superimposed on top of these contours. Much more so than the function the... 

Figure 4 Superimposed contour plots for the panicle size (-ation (-----i. (Reprinted from Ref. 7.)...

In a second step, a simplex centroid design was realized with seven design points and six check points. Two responses were optimized consistency and whiteness. Using the second-order equations from this matrix, it is possible to obtain isoresponse graphs. The contour plots are given in Figs. S and 6. The optimal gel must correspond to a gel similar to petrolatum. This optimal zone is reported in Fig. 7 where contour plots of the two responses are superimposed. 

Fig. 7 Plots of Vx versus x for LG layers separated from the bottom wall by one (o), two (X), three (+) and four ( ) lattice constants, superimposed on a contour plot of m, for the same system as in Fig. 6...

In Fig. 10, we compaxe the structure of the three-ring defect obtained from simulation and theory for s = 0.3ii with R = Soq. In both cases, the director field is shown superimposed to a contour plot of 5, the scalar order parameter. Both theory and simulation exhibit the third ring in addition to the usual two Saturn rings. In these plots we can observe how the strength of S decreases continuously from its bulk value to a minimum at the defects. Once more, in contrast to the field theory results, the Monte Carlo data show layers of low and high values of S close to the spheres surfaces that are correlated with modulations in density see Fig. 10). 

Fig. 2.3 Electron density contour plot of HC = N superimposed to its gradient vector field, which consists of an infinite multitude of gradient paths, here represented by a few dozen paths originating at infinity and terminating at the respective nuclei. A special bundle of gradient paths starts at infinity and ends up at the little squares, which are bond critical points. From each bond critical point emerge two gradient paths, each of which is attracted to a different nucleus. This pair of gradient paths is called the atomic interaction line, or in this case of a local ena-gy minimum, the bond path. The carbon is placed at the origin and the bold square box marks the -6 a.u. and +6 a.u. horizontal and vertical boundaries of the plot. The electron density values of the contour lines are 1 X 10 , 2 X 10 , 4 X 10 and 8 x 10 " au where n starts at -3 and increases with unity increments...

Fig.10 A local energy minimum of the water (darfc).. jnethanal (light) complex. Bond paths and interatomic surfaces (both in bold) are superimposed on an electron density contour plot...

Fortunately, the IGLO method provides the full chemical shift tensor, and not just the isotropic value. The contour plot in Fig. 28.b shows an isotropic/anisotropic separation spectrum of atactic polypropylene, which has been recorded at T 250 K with a home-built DAS probehead [98] on a BRUKER MSL-300 spectrometer. For every isotropic shift on the x-axis, the intensity distribution along the y-axis displays the corresponding powder pattern the edges correspond to Oxx and Ozz as indicated in the figure. The theoretical values of the xx- and the zz-component are superimposed on the experimental contour plot in Fig. 6 and symbolized by the small rhombi (o). The absolute values were adjusted in the same way as for the isotropic chemical shift. The spectral position of Gyy is not easily seen in the experimental spectrum to keep the figure simple, the theoretical values for Gyy have been... 

Experimental spectrum of the methylene region of glassy atactic poly(propylene) (b) recorded atT 240 K on a BRUKER MSL-300 with a DAS probehead. The two angles for evolution and detection, respectively, were =81.7° and = S m = 54.7°. The rotation frequency was 3000 Hz, and 128 fi-increments were recorded. The theoretical values (o) are superimposed on the experimental contour plot. The absolute positions were adjusted like in the ID spectrum. A qualitative agreement of theory and experiment is seen... 

The most elementary example of course is just the H2 molecule. As described by equations (4) or (17), there are two orbitals, 0a and 0b which overlap. These are displayed in Figure 3. On the right of the figure, contour plots of the two orbitals are shown, while on the left, orbital 0a is shown as a three-dimensional shape with the intemuclear axis superimposed. As the intemuclear distance R increases, the deformation of each orbital 0a and 0b decreases to 0, leaving just a pure hydrogen Is orbital on each atom. 

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