Inherent structures landscapes

Figure 22. Potential energy landscape explored by the model calamitic system GB(3, 5, 2, 1) (N = 256) as the system makes a transit through mesophases upon cooling, (a) Temperature dependence of the average inherent structure energy per particle, (< /s), along three isochors at densities p = 0.31,0.32, and 0.33. (b) Evolution of the average second-rank orientational order parameter S with temperature both for the inherent structures (filled) and for the instantaneous configurations (opaque). (Reproduced from Ref. 144.)...

Intuitively, D appears to be well-placed to capture the dynamical signature of the coupling between orientational and translational order. In the energy landscape formalism the time-dependent position rft) of a particle i can be resolved into two components rft) = Rft) + Sft), where Rft) is the spatial position of the particle i in the inherent structure for the basin inhabited at time and S ft) is the intrabasin displacement away from that inherent structure [159], It has been theoretically argued that the replacement of the real positions r (f) by the corresponding inherent structure positions in the Einstein relation yields an equivalent diffusion description [159, 160]. Such a proposition, which has been verified in simulations [159, 160], forms the foundation of the analysis presented here. 

Structural Models for Supercooled Liquids. - This approach focuses on the molecular order in the supercooled liquid. The potential energy surface or landscape (r ) where = n, 2. .. is a 3A-dimensional vector in phase space has a characteristic appearance in the various states of matter. In a liquid, the 4>-landscape has a distribution of many shallow energy minima. In a crystal there are a few steep and deep minima representing the collapse of the system into the crystalline states with long-range order. In a liquid simulation, each of these deep minima, or inherent structures as they are called, will be surromided... 

Figure 3. The potential energy landscape and its connection to dynamics. Shown are (a) inherent structure energy cis. (b) configurational entropy S, and (c) diffiisivity D as functions of T for three isochores at p = 3.90 g/cm (5.13 cm /mol, triangles), p = 3.01 g/cm (6.65 cm /mol, squares), and p = 2.36 g/cm (8.50 cm /mol, circles). In panel (c). Sc is given per, Si02 unit. Panel (d) shows a test of the Adam-Gibbs relationship. Molar quantities are per mole ions.

In the energy landscape view, the polymorphs are the inherent structures of the sol phase and shall be obtained when the vibrational degrees of freedom and the kinetic energy are removed from the molecules. Thus, the polymorphs form a rugged landscape with the most stable structure at the bottom of the energy ladder, just like in the folding funnel of a protein. 

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