Gaussian landscapes

Gaussian Landscape Parameters for 1-Propanol and 3-Methylpentane Calculated from Heat Capacity Measurements ... 

Several useful relations can be written for systems with Gaussian landscapes. The excitation profile satisfies the relation... 

Thus, all thermodynamic (equilibrium) properties of a macroscopic system with a Gaussian landscape can be calculated from knowledge of ,-<> (p) (the density dependence of the basin depth per particle in the high-temperature limit), rrdensity dependence of the configurational entropy... 

M. Oresic, D. Shalloway, Hierarchical characterization of energy landscapes using Gaussian packet states, J. Chem. Phys. 101 (1994), 9844. 

The kernel defined by Eqs. (2.5) will be inefficient when pB is multimodal. In this situation we must dissect the conformation space into separate macrostate regions a, b, c,. .. and find Gaussian kernels that match pB in each region. This can be accomplished using window functions and characteristic packets, concepts that have previously been introduced in the context of global optimization [14,15], potential-energy landscape analysis... 

Figure 4 A sketch of the process of metadynamics. First the system evolves according to a normal dynamics, then a Gaussian potential is deposited (solid gray line). This lifts the system and modifies the free-energy landscape (dashed gray line) in which the dynamics evolves. After a while the sum of Gaussian potentials fills up the first metastable state and the system moves into the second metastable basin. After this the second metastable basin is filled, at this point, the system evolves in a flat landscape. The summation of the deposited bias (solid gray profile) provides a first rough negative estimate of the free-energy profile.

To estimate this deviation from the flat histogram behavior quantitatively, one should assume that the added Gaussians are narrower than the features of the underlying free-energy landscape and thus can be considered equivalent to 8 functions with the proper normalization ... 

While the time evolution of the free-energy landscape (see Figure 19) is similar to the conventional MetaD case (Figure 12) we point out that WTMetaD is depositing less potential than the standard case, because of the diminishing Gaussian height. 

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