Elliptic cone model

The elliptic cone model of the potential energy surface at a conical intersection point discussed above is not general enough to give a correct description of the relaxation in realistic molecules. First, more than two possible IRDs may originate from the tip of the cone. Second, the first-order approximation (i.e., elliptic cone) may break down at larger distances, and some IRDs may lie out of the branching plane because the real... 

In Figure 14b we show the potential energy surface for a model elliptic conical intersection46 plotted in the branching plane (xt, x2). Because, as stated earlier, the cone is elliptic in the linear approximation (i.e., the base of the cone is an ellipse rather than a circle), there are two steep sides of the ground state cone surface and two ridges . There are two preferred directions for downhill motion located on the steep sides of the ground state cone surface. A simple... 

Many common geometric surfaces, such as sphere, cone, elliptic cylinder, and paraboloid, can be represented as quadric surfaces. The quadric surfaces have been employed by engineers for solid model generation from measured point data (Chivate and Jablokow, 1993), and reverse engineering physical modeling (Weir et al., 1996). 

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