556 research outputs found
Rearrangements and Tunneling Splittings in Small Water Clusters
Recent far-infrared vibration-rotation tunneling (FIR-VRT) experiments pose
new challenges to theory because the interpretation and prediction of such
spectra requires a detailed understanding of the potential energy surface (PES)
away from minima. In particular we need a global description of the PES in
terms of a complete reaction graph. Hence all the transition states and
associated mechanisms which might give rise to observable tunneling splittings
must be characterized. It may be possible to guess the detailed permutations of
atoms from the transition state alone, but experience suggests this is unwise.
In this contribution a brief overview of the issues involved in treating the
large amplitude motions of such systems will be given, with references to more
detailed discussions and some specific examples. In particular we will consider
the effective molecular symmetry group, the classification of rearrangement
mechanisms, the location of minima and transition states and the calculation of
reaction pathways. The application of these theories to small water clusters
ranging from water dimer to water hexamer will then be considered. More details
can be found in recent reviews.Comment: 15 pages, 5 figures. This paper was prepared in August 1997 for the
proceedings volume of the NATO-ASI meeting on "Recent Theoretical and
Experimental Advances in Hydrogen Bonded Clusters" edited by Sotiris
Xantheas, which has so far not appeare
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
Comment on ``Quasisaddles as relevant points of the potential energy surface in the dynamics of supercooled liquids'' [J. Chem. Phys. 116, 10297 (2002); cond-mat/0203301]
Recently, the properties of supercooled liquids have been studied by mapping
instaneous configurations onto minima of the gradient squared. It was
originally suggested that this mapping would probe higher-order saddle points
of the potential energy surface. However, it was subsequently shown that the
majority of the minima of this function are only local minima and so do not
correspond to saddles. In this comment, we provide a critique of the suggestion
made by Angelani et al. [J. Chem. Phys. 116, 10297 (2002); cond-mat/0203301]
that although these minima are not true saddles, they are almost saddles (hence
the term quasisaddles). This issue has important implications for the
interpretation of the results obtained by this approach.Comment: 2 page
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
Structural trends in clusters of quadrupolar spheres
The influence of quadrupolar interactions on the structure of small clusters
is investigated by adding a point quadrupole of variable strength to the
Lennard-Jones potential. Competition arises between sheet-like arrangements of
the particles, favoured by the quadrupoles, and compact structures, favoured by
the isotropic Lennard-Jones attraction. Putative global potential energy minima
are obtained for clusters of up to 25 particles using the basin-hopping
algorithm. A number of structural motifs and growth sequences emerge, including
star-like structures, tubes, shells and sheets. The results are discussed in
the context of colloidal self-assembly.Comment: 8 pages, 6 figure
- …