Contour, of constant energy

At this point you should be hearing warning bells—in Section 6.3 we saw that small nonlinear terms can easily destroy a center predicted by the linear approximation. But that s not the case here, because of energy conservation. The trajectories are closed curves defined by the contours of constant energy, i.e.,... 

In the phase-stability diagrams of Figure 14.7, contours of constant energy are shown that result from a numerical integration of Equation 14.4 for OH radicals in the 7 = 3/2, Af = - 9/4 state. The computations were carried out with the parameters of a Stark decelerator operated in our laboratory, at the values of the synchronous... 

Fig. XVII-18. Contours of constant adsorption energy for a krypton atom over the basal plane of graphite. The carbon atoms are at the centers of the dotted triangular regions. The rhombuses show the unit cells for the graphite lattice and for the commensurate adatom lattice. (From Ref. 8. Reprinted with permission from American Chemical Society, copyright 1993.)...

Fig. 4. Curves in the N-Z plane representing isodeformation contours left, empirical contours of E2+1 energies right, contours of constant Np-Nn.

Fig. 34a-c. Results of a model calculation of a Xe atom adsorbed on a high electron density jellium surface (e.g. aluminium), (a) Contours of constant electron density in a cut perpendicular to the surface through the center of the Xe atom, (b) Xe valence p-elechon density vs. distance (difference density between metal-adatom system and sum of clean metal plus single Xe atom except 5p level), (c) Effective single particle potential energy contributions due to electrostatic dipole, Ves, and the exchange-correlation interaction, Vxc, respectively, [82Lan],... 

FIG. 4 Cartoon of a zig-zag approximation of the IRC (bold dot-dash line). The thin solid path that repeatedly crosses the IRC (dot-dash path) is likely to result when no Hessian information is used, such as with Eqs. (14) and (15). Dashed and dotted lines indicate contours of constant potential energy. 

Figure 11.17 Dependence of Gibbs energy on volume and pressure, at constant temperature, in a closed system containing an ideal gas mixture of A and B. The reaction is A->2B with ArG°=0. Solid curves contours of constant G plotted at an interval of O.SnAfiRT. Dashed curve states of reaction equilibrium (ArG = 0). Dotted curves limits of possible values of the advancement. Open circle position of minimum G (and an equilibrium state) at the constant pressure p = 1,02p°. Filled circle position of minimum G for a constant volume of 1.41 Fo. where Vq is the initial volume at pressure p°.

Figure 6. Contours of constant bonding valence electron density (calculated by adding the contributions from energy levels between -4 and 0 eV) for the most stable structure of the Li4Pb solid in a plane containing Pb atoms.

Suppose, then, we consider the independent variation through the interface of two density or composition variables, say x and y. As in 3.3, we now have a density of excess free energy, —W(x, y), still defined at prescribed values of the c - p+2 independent fields. Contours of constant W in the x, y-plane will be as in Figs 3.5 or 3.7, but now, with p = 3, they will show three peaks of equal height, as depicted in Fig. 8.6. The peate... 

Figure 3.21 Sketch iUustrating the instability of a planar interface (a) during growth. Dashed fines represent contours of constant solvent concentration.The outwardly directed part of the fluctuation in part (b) has increased the gradient in the z direction, leading to faster growth at point A than at point B. Inclusion of interfacial energy further modifies the gradient as discussed in the text. From Danger [34] with kind permission from the author and the American Physical Society.

Fig. 1. Schematic contours of constant potential energy V for an atom interacting with the CO2 molecule in a fixed conformation. The dash-dot line corresponds to V=0.

Figure 6.6 Illustration of two two-dimensional PESs for benzene in De symmetry. The surfaces differ in choice of coordinates, which may affect optimizer efficiency, ease of input, etc., but will have no effect on the equilibrium structure. Contour lines reflect constant energy intervals of arbitrary magnitude. No attempt is made to illustrate the full 30-dimensional PES, on which it would be considerably more taxing to search for a minimum-energy structure...

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