Potential energy landscape

Fig. 5. The left hand side figure shows a contour plot of the potential energy landscape due to V4 with equipotential lines of the energies E = 1.5, 2, 3 (solid lines) and E = 7,8,12 (dashed lines). There are minima at the four points ( 1, 1) (named A to D), a local maximum at (0, 0), and saddle-points in between the minima. The right hand figure illustrates a solution of the corresponding Hamiltonian system with total energy E = 4.5 (positions qi and qs versus time t).

Based on the theoretical electrochemistry method outlined above in combination with DFT calculations, the potential energy of the intermediates can be obtained at a given potential, (Fig. 3.5). Since aU steps involve exactly one proton and electron transfer, the height of the different steps scales directly with the potential. To calculate the potential energy landscape at the equilibrium potential, the levels are moved down hyn X 1.23 eV, where n is the number of the electrons at the given state (the horizontal axis in Fig. 3.5). 

At the equilibriuni potential, some steps are uphill in free energy, meaning that the reaction on the surface is slow. A perfect catalyst in this analysis would be characterized by a flat potential energy landscape at the equilibrium potential, i.e., by all steps having the same height at zero potential. Whereas no such catalyst has yet been found, we can define the highest potential at which all steps are just downhill in free energy, C/qrr-Below we would say that the reaction starts to be transport-limited. At potentials... 

F. Sciortino, J. Stat. Mech., P05015 (2005). Potential Energy Landscape Description of... 

Fragile-to-Strong Crossover in Liquid Silica as Expressed by Its Potential-Energy Landscape. 

A. Crisanti and F. Ritort, Potential energy landscape of finite-size mean-field models for glasses. 

W. Wenzel and K. Hamacher. Stochastic tunneling approach for global optimization of complex potential energy landscapes. Phys. Rev. Lett, 82 3003, 1999. 

Figure 7.3 In a system with 3N spatial coordinates, the potential-energy landscape...

The concept of fragility is a qualitative one and is related to deviations of the relaxation time of a liquid from Arrhenius-like behavior and to the topology of the potential energy landscape of the system. The classification of liquids into strong and fragile thus provides a fundamental framework for quantitatively describing equilibrium and dynamical properties of supercooled liquids and glassy states of matter [1-6,8,9,22,37,38,52,54—56,88-91,103]. 

Thus, the configurational entropy. S, (7. p) expresses the number of local potential energy minima and hence can be evaluated by potential energy landscape and thermodynamic integration methodology [53]. The vibration entropy was calculated within the framework of a harmonic approximation to each basin [165,166], an approximation that is valid at low temperatures [53]. Three notable results were obtained by Sastry [53] ... 

The characteristics of the potential energy landscape was linked to fragility via the following steps [53] ... 

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