2,254 research outputs found
Some Further Results for the Stationary Points and Dynamics of Supercooled Liquids
We present some new theoretical and computational results for the stationary
points of bulk systems. First we demonstrate how the potential energy surface
can be partitioned into catchment basins associated with every stationary point
using a combination of Newton-Raphson and eigenvector-following techniques.
Numerical results are presented for a 256-atom supercell representation of a
binary Lennard-Jones system. We then derive analytical formulae for the number
of stationary points as a function of both system size and the Hessian index,
using a framework based upon weakly interacting subsystems. This analysis
reveals a simple relation between the total number of stationary points, the
number of local minima, and the number of transition states connected on
average to each minimum. Finally we calculate two measures of localisation for
the displacements corresponding to Hessian eigenvectors in samples of
stationary points obtained from the Newton-Raphson-based geometry optimisation
scheme. Systematic differences are found between the properties of eigenvectors
corresponding to positive and negative Hessian eigenvalues, and localised
character is most pronounced for stationary points with low values of the
Hessian index.Comment: 16 pages, 2 figure
NP-hardness of the cluster minimization problem revisited
The computational complexity of the "cluster minimization problem" is
revisited [L. T. Wille and J. Vennik, J. Phys. A 18, L419 (1985)]. It is argued
that the original NP-hardness proof does not apply to pairwise potentials of
physical interest, such as those that depend on the geometric distance between
the particles. A geometric analog of the original problem is formulated, and a
new proof for such potentials is provided by polynomial time transformation
from the independent set problem for unit disk graphs. Limitations of this
formulation are pointed out, and new subproblems that bear more direct
consequences to the numerical study of clusters are suggested.Comment: 8 pages, 2 figures, accepted to J. Phys. A: Math. and Ge
Landscapes, dynamic heterogeneity and kinetic facilitation in a simple off-lattice model
We present a simple off-lattice hard-disc model that exhibits glassy
dynamics. The inherent structures are enumerated exactly, transitions between
metabasins are well understood, and the particle configurations that act to
facilitate dynamics are easily identified. The model readily maps to a coarse
grained dynamic facilitation description.Comment: 5 pages, 5 figures, submitted to PR
Understanding the role of ions and water molecules in the NaCl dissolution process
The dissolution of NaCl in water is one of the most common everyday
processes, yet it remains poorly understood at the molecular level. Here we
report the results of an extensive density functional theory study in which the
initial stages of NaCl dissolution have been examined at low water coverages.
Our specific approach is to study how the energetic cost of moving an ion or a
pair of ions to a less coordinated site at the surface of various NaCl crystals
varies with the number of water molecules adsorbed on the surface. This
"microsolvation" approach allows us to study the dependence of the defect
energies on the number of water molecules in the cluster and thus to establish
when and where dissolution becomes favorable. Moreover, this approach allows us
to understand the roles of the individual ions and water molecules in the
dissolution process. Consistent with previous work we identify a clear
preference for dissolution of Cl ions over Na ions. However, the detailed
information obtained here leads to the conclusion that the process is governed
by the higher affinity of the water molecules to Na ions than to Cl ions. The
Cl ions are released first as this exposes more Na ions at the surface creating
favorable adsorption sites for water. We discuss how this mechanism is likely
to be effective for other alkali halides
Assessing the efficiency of first-principles basin-hopping sampling
We present a systematic performance analysis of first-principles
basin-hopping (BH) runs, with the target to identify all low-energy isomers of
small Si and Cu clusters described within density-functional theory. As
representative and widely employed move classes we focus on single-particle and
collective moves, in which one or all atoms in the cluster at once are
displaced in a random direction by some prescribed move distance, respectively.
The analysis provides detailed insights into the bottlenecks and governing
factors for the sampling efficiency, as well as simple rules-of-thumb for
near-optimum move settings, that are intriguingly independent of the distinctly
different chemistry of Si and Cu. At corresponding settings, the observed
performance of the BH algorithm employing two simple, general-purpose move
classes is already very good, and for the small systems studied essentially
limited by frequent revisits to a few dominant isomers.Comment: 11 pages including 8 figures; related publications can be found at
http://www.fhi-berlin.mpg.de/th/th.htm
Excess entropy, Diffusivity and Structural Order in liquids with water-like anomalies
The excess entropy, Se, defined as the difference between the entropies of
the liquid and the ideal gas under identical density and temperature
conditions, is shown to be the critical quantity connecting the structural,
diffusional and density anomalies in water-like liquids. Based on simulations
of silica and the two-scale ramp liquids, water-like density and diffusional
anomalies can be seen as consequences of a characteristic non-monotonic density
dependence of Se. The relationship between excess entropy, the order metrics
and the structural anomaly can be understood using a pair correlation
approximation to Se.Comment: 9 pages, 5 figues in ps forma
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
The double-funnel energy landscape of the 38-atom Lennard-Jones cluster
The 38-atom Lennard-Jones cluster has a paradigmatic double-funnel energy
landscape. One funnel ends in the global minimum, a face-centred-cubic (fcc)
truncated octahedron. At the bottom of the other funnel is the second lowest
energy minimum which is an incomplete Mackay icosahedron. We characterize the
energy landscape in two ways. Firstly, from a large sample of minima and
transition states we construct a disconnectivity tree showing which minima are
connected below certain energy thresholds. Secondly we compute the free energy
as a function of a bond-order parameter. The free energy profile has two
minima, one which corresponds to the fcc funnel and the other which at low
temperature corresponds to the icosahedral funnel and at higher temperatures to
the liquid-like state. These two approaches show that the greater width of the
icosahedral funnel, and the greater structural similarity between the
icosahedral structures and those associated with the liquid-like state, are the
cause of the smaller free energy barrier for entering the icosahedral funnel
from the liquid-like state and therefore of the cluster's preferential entry
into this funnel on relaxation down the energy landscape. Furthermore, the
large free energy barrier between the fcc and icosahedral funnels, which is
energetic in origin, causes the cluster to be trapped in one of the funnels at
low temperature. These results explain in detail the link between the
double-funnel energy landscape and the difficulty of global optimization for
this cluster.Comment: 12 pages, 11 figures, revte
Energy Landscape and Global Optimization for a Frustrated Model Protein
The three-color (BLN) 69-residue model protein was designed to exhibit frustrated folding. We investigate the energy landscape of this protein using disconnectivity graphs and compare it to a Go model, which is designed to reduce the frustration by removing all non-native attractive interactions. Finding the global minimum on a frustrated energy landscape is a good test of global optimization techniques, and we present calculations evaluating the performance of basin-hopping and genetic algorithms for this system.Comparisons are made with the widely studied 46-residue BLN protein.We show that the energy landscape of the 69-residue BLN protein contains several deep funnels, each of which corresponds to a different β-barrel structure
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