1,273 research outputs found
Protein Structure Prediction Using Basin-Hopping
Associative memory Hamiltonian structure prediction potentials are not overly
rugged, thereby suggesting their landscapes are like those of actual proteins.
In the present contribution we show how basin-hopping global optimization can
identify low-lying minima for the corresponding mildly frustrated energy
landscapes. For small systems the basin-hopping algorithm succeeds in locating
both lower minima and conformations closer to the experimental structure than
does molecular dynamics with simulated annealing. For large systems the
efficiency of basin-hopping decreases for our initial implementation, where the
steps consist of random perturbations to the Cartesian coordinates. We
implemented umbrella sampling using basin-hopping to further confirm when the
global minima are reached. We have also improved the energy surface by
employing bioinformatic techniques for reducing the roughness or variance of
the energy surface. Finally, the basin-hopping calculations have guided
improvements in the excluded volume of the Hamiltonian, producing better
structures. These results suggest a novel and transferable optimization scheme
for future energy function development
Thermodynamics and the Global Optimization of Lennard-Jones clusters
Theoretical design of global optimization algorithms can profitably utilize
recent statistical mechanical treatments of potential energy surfaces (PES's).
Here we analyze the basin-hopping algorithm to explain its success in locating
the global minima of Lennard-Jones (LJ) clusters, even those such as \LJ{38}
for which the PES has a multiple-funnel topography, where trapping in local
minima with different morphologies is expected. We find that a key factor in
overcoming trapping is the transformation applied to the PES which broadens the
thermodynamic transitions. The global minimum then has a significant
probability of occupation at temperatures where the free energy barriers
between funnels are surmountable.Comment: 13 pages, 13 figures, revte
Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms
We describe a global optimization technique using `basin-hopping' in which
the potential energy surface is transformed into a collection of
interpenetrating staircases. This method has been designed to exploit the
features which recent work suggests must be present in an energy landscape for
efficient relaxation to the global minimum. The transformation associates any
point in configuration space with the local minimum obtained by a geometry
optimization started from that point, effectively removing transition state
regions from the problem. However, unlike other methods based upon hypersurface
deformation, this transformation does not change the global minimum. The lowest
known structures are located for all Lennard-Jones clusters up to 110 atoms,
including a number that have never been found before in unbiased searches.Comment: 8 pages, 3 figures, revte
The effect of compression on the global optimization of atomic clusters
Recently, Locatelli and Schoen proposed a transformation of the potential
energy that aids the global optimization of Lennard-Jones clusters with
non-icosahedral global minima. These cases are particularly difficult to
optimize because the potential energy surface has a double funnel topography
with the global minimum at the bottom of the narrower funnel. Here we analyse
the effect of this type of transformation on the topography of the potential
energy surface. The transformation, which physically corresponds to a
compression of the cluster, firstly reduces the number of stationary points on
the potential energy surface. Secondly, we show that for a 38-atom cluster with
a face-centred-cubic global minimum the transformation causes the potential
energy surface to become increasingly dominated by the funnel associated with
the global minimum. The transformation has been incorporated in the
basin-hopping algorithm using a two-phase approach.Comment: 9 pages, 6 figures, revte
Evolution of the Potential Energy Surface with Size for Lennard-Jones Clusters
Disconnectivity graphs are used to characterize the potential energy surfaces
of Lennard-Jones clusters containing 13, 19, 31, 38, 55 and 75 atoms. This set
includes members which exhibit either one or two `funnels' whose low-energy
regions may be dominated by a single deep minimum or contain a number of
competing structures. The graphs evolve in size due to these specific size
effects and an exponential increase in the number of local minima with the
number of atoms. To combat the vast number of minima we investigate the use of
monotonic sequence basins as the fundamental topographical unit. Finally, we
examine disconnectivity graphs for a transformed energy landscape to explain
why the transformation provides a useful approach to the global optimization
problem.Comment: 13 pages, 8 figures, revte
Fragile vs strong liquids: a saddles ruled scenario
In the context of the energy landscape description of supercooled liquids, we
propose an explanation for the different behaviour of fragile and strong
liquids. Above the Goldstein crossover temperature Tx, diffusion is interpreted
as a motion in the phase space among unstable stationary points of the
potential energy, that is among saddles. In this way two mechanisms of
diffusion arise: mechanism A takes place when the system crosses potential
energy barriers along stable uphill directions, while mechanism B consists in
finding unstable downhill directions out of a saddle. Depending on the mutual
value of the efficiency temperatures of A and B, we obtain two very different
behaviours of the viscosity, reproducing the usual classification of liquids in
fragile and strong. Moreover, this scenario very naturally predicts the
possibility of a fragile-to-strong crossover when lowering the temperature.Comment: Revised versio
- …