Basin hopping

Smart Darting and Basin Hopping Monte Carlo... 

Prentiss, M.C., Wales, D.J., Wolynes, P.G. Protein structure prediction using basin-hopping. J. Chem. Phys. 2008, 128, 225106. 

Abstract. We present a quantum-classieal determination of stable isomers of Na Arii clusters with an electronically excited sodium atom in 3p P states. The excited states of Na perturbed by the argon atoms are obtained as the eigenfunctions of a single-electron operator describing the electron in the field of a Na Arn core, the Na and Ar atoms being substituted by pseudo-potentials. These pseudo-potentials include core-polarization operators to account for polarization and correlation of the inert part with the excited electron . The geometry optimization of the excited states is carried out via the basin-hopping method of Wales et al. The present study confirms the trend for small Na Arn clusters in 3p states to form planar structures, as proposed earlier by Tutein and Mayne within the framework of a first order perturbation theory on a "Diatomics in Molecules" type model. 

Figure 3. Energy vs. RMSB plot for the final energies of the twenty basin hopping simulations described in the text (diamonds). For comparison we also indicate the best energy result for the STUN method (circle) and for the thirty processor PT simulation (square).

Table 1. Energies (in kcal/mol) of the 10 lowest energy decoys obtained in the basin hopping simulations of the HIV accessory protein. The table shows the backbone RMS deviation to the NMR structure and secondary structure content. The first row designates the secondary structure content of the NMR structure.

Turning to the more recent work, we mention the study of Sebetci and Guveng86 on Ft v clusters with 22 < N < 56. They used an embedded-atom approach in describing the interatomic interactions and two different approaches in optimizing the structures, i.e., the basin-hopping algorithm and a molecular-dynamics approach. Their approach allowed for a comparison... 

In two works, Flikkema and Bromley113,114 used a specifically tailored semiempirical potential for describing the interatomic interactions of (Si02)2v clusters. In order to optimize the structure, they used the basin-hopping algorithm. Subsequently, parameter-free density-functional calculations were carried through for the optimized structures. 

By dealing with the evolution of constraints (i.e., Ramachandran basins) rather than the backbone torsional coordinates themselves, the dynamics are judiciously simplified [31]. The algorithm consists of a stochastic simulation of the coarsely resolved dynamics, simplified to the level of time-evolving Ramachandran basin assignments. An operational premise is that steric restrictions imposed by the side chains on the backbone may be subsumed into the basin-hopping dynamics. The side chain constraints define regions in the Ramachandran map that can be explored in order to obtain an optimized pattern of nonbonded interactions. 

In the present work we have generally located the global minimum of the PES using a basin-hopping approach [190-192]. The following transformation is applied to the energy landscape ... 

The success of the basin-hopping approach has been explained in terms of the thermodynamics of the transformed landscape [182,195]. The plateau transformation broadens the temperature range of thermodynamic transitions, so that the global minimum has a significant occupation probability at temperatures where the free energy barriers between different funnels are still surmountable. 

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