Hopping criterion

The quasiclassical SH model employs the simple and physically appealing picture in which a molecular sj tem always evolves on a single adiabatic potential-energy surface (PES). When the trajectory reaches an intersection of the electronic PESs, the transition probability pk k to the other PES is calculated according to some hopping criterion and, depending on the comparison of pk w with a random number, the trajectory hops to... 

Since the hopping procedure accounts for the coupling of electronic and nuclear degrees of freedom, the key problem of the SH approach is to establish a dynamically consistent hopping criterion and momentum adjustment. As already mentioned, any rigorous way to derive such a formulation leads to complicated equations of motion that in general are quite cumbersome to implement (see, e.g. Sec. 5.2). Many workers have therefore developed simple but practical models of Here the most popular formulation... 

Fig. 5.13. Relaxation time r3 plotted vs. temperature for the coarse-grained model of PE with N = 20, using the random hopping algorithm (upper set of data) or the slithering snake algorithm (lower set of data), respectively. The time r3 is of the same order as the Rouse relaxation time of the chains, and is defined in terms of a crossing criterion for the mean-square displacements [41], g3(t = r3) = g2(t = r3) [See Eqs. (5.2) and 5.3)]. From [32]...

It is important to do local optimizations as efficiently as possible because they are a time-consuming part of minima hopping. In our implementation, we perform local minimization in two steps. The first optimization uses the limited memory L-BFGS method [64, 65] with a loose convergence threshold. The optimization is refined in the second step which uses Davidon s optimally conditioned variable metric method [66] and a more stringent convergence criterion. 

Foaming is an important criterion of the taste of beer. A distinction is made between foam volume (produced by the content of carbon dioxide), foam density, and especially foam stability (caused by protein degradation products, bitter hop compounds, and pentosans). Lower fatty acids that are present in beer bouquet act as de-foamers. 

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