4,909 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
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
Theoretical study of finite temperature spectroscopy in van der Waals clusters. II Time-dependent absorption spectra
Using approximate partition functions and a master equation approach, we
investigate the statistical relaxation toward equilibrium in selected CaAr
clusters. The Gaussian theory of absorption (previous article) is employed to
calculate the average photoabsorption intensity associated with the 4s^2->
4s^14p^1 transition of calcium as a function of time during relaxation. In
CaAr_6 and CaAr_10 simple relaxation is observed with a single time scale.
CaAr_13 exhibits much slower dynamics and the relaxation occurs over two
distinct time scales. CaAr_37 shows much slower relaxation with multiple
transients, reminiscent of glassy behavior due to competition between different
low-energy structures. We interpret these results in terms of the underlying
potential energy surfaces for these clusters.Comment: 10 pages, 9 figure
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
- …