Pillardy J., Piela L., Molecular dynamics on deformed potential energy hypersurfaces, J. Phys.Chem., 99, 11805-11812 (1995)  Home/Search   Document Not in Database   Summary   Related Articles   Check

....(or a set of best solutions) found during the first phase. In [14] and later in [18] many of the currently putative global minima for N up to 147 have been detected. But further research revealed that the conjecture was not correct. The first counterexample was the N = 38 case. In [3] 6] and [15] a new solution was found whose structure is not the icosahedral one but is a truncated octahedron. It is again interesting to note that the Kissing Number problem can also be solved by placing the 12 points at the vertices of a truncated octahedron. Icosahedral structure usually have a larger ....

Pillardy J., Piela L., Molecular dynamics on deformed potential energy hypersurfaces, J. Phys.Chem., 99, 11805-11812 (1995)

.... 14, 16, 26, 27] The latter encompasses a wider variety of techniques, including molecular dynamics and statistical mechanics [3, 5, 11, 22] Monte Carlo and genetic algorithms [4, 19] underestimation or tunneling methods [6, 7, 21] such as CGU, and procedures for smoothing energy landscapes [15, 17, 20, 25]. Instead of utilizing a single refinement technique, we have here coupled a discrete algorithm with a continuous one. While this idea was arrived at independently, it most certainly can be found in the work of others. We cite as just one example the AutoDock suite [18] which performs a discrete ....

Pillardy, J., and Piela, L. (1995), Molecular Dynamics on Deformed Potential Energy Hypersurfaces. J. Phys. Chem., 99: 11805-12.

....CGU home page at: http: cgu.cs.uw ec.edu. The latterencompassesawidervariety oftechniques,includingmoleculardynamicsand statisticalmechanics[3,11,16, 23] Mon teCarloand geneticalgorithms[4,20] underestimationor tunneling methods[6,7,22]such asCGU, and proceduresforsmoothingenergylandscapes[15,18,21,26]. Insteadofutilizinga singlereflnement technique,we have herecoupleda discretealgorithmwitha continuousone. Whilethisideawasarrived atindependently,itmost certainlycanbe foundintheworkofothers.W e citeasjust oneexampletheAutoDock suite[19] which performsa ....

Pillardy,J.,and Piela,L.(1995),MolecularDynamics on Deformed PotentialEnergy Hypersurfaces. J.Phys. Chem.,99:11805-12.

....will be found at the same position and value for any value of t. Pillardy and Piela use the method to study clusters of Lennard Jones atoms up to 66 atoms, combining their deformation technique with molecular dynamics. They carry out a number of studies, starting from different configurations. In [9] they report on a number of different ways to combine molecular dynamics with the distance scaling method. They conclude that their final results are independent of the starting configuration to a considerable degree and that the lowest minima have energies that are lower than the minima found by ....

J. Pillardy, L. Piela, Molecular dynamics on deformed potential energy hypersurfaces, J. Phys. Chem. 99 (1995), 11805.

....icosahedral solutions have been improved e.g. in (Coleman et al. 1994) Deaven et al. 1996) Xue, 1994) but a remarkable step was the detection of lower energy configurations for some values of N which do not have an icosahedral structure. In (Doye et al. 1995) Gomez and Romero, 1994) and (Pillardy and Piela, 1995) a Face Centered Cubic (FCC) solution has been detected for N = 38. Decahedral structures were detected in (Doye et al. 1995) and (Doye and Wales, 1995) for N = 75 Gamma 77; 102 Gamma 104. Very recently in (Leary and Doye, 1999) a tetrahedral structure has been detected for N = 98. In ....

Pillardy, J. and L. Piela: 1995, `Molecular dynamics on deformed potential energy hypersurfaces'. Journal of Physical Chemistry 99, 11805--11812.

....for N = 38 has a FCC (Face Centered Cubic) structure, and many algorithmic approaches, such as the lattice search in (Northby, 1987) and (Xue, 1994) biased towards icosahedral structures, are unable to detect this solution. The new putative global optimum was first observed only recently in (Pillardy and Piela, 1995) using a direct approach based on molecular dynamics; more recently, in (Leary, 1997) the putative global optimum was found using the big bang global optimization algorithm employing on the average 330 local searches, while for the basin hopping algorithm proposed in (Wales and Doye, 1997) the ....

Pillardy, J. and L. Piela: 1995, `Molecular dynamics on deformed potential energy hypersurfaces'. Journal of Physical Chemistry 99, 11805--11812.

....infinity. In addition, when fl 0 and P 1, equation (3.1) has a zero derivative at r = 0. Fig. 3.3 clearly illustrates the independence of the y intercept upon the parameter P , as well as the zero derivative at r = 0. While preparing this paper for publication, we discovered a recent paper [17] that proposes a smoothing function quite similar to (3.1) They propose a smoothing function where r in (1.1) is replaced with (r ff) 1 ff) for some positive constant ff. Note that our smoothing function (3.1) may be viewed as replacing r 6 in (1.1) by (r P fl) 1 fl) It would be ....

Pillardy, J., and Piela, L. Molecular Dynamics on Deformed Potential Energy Hypersurfaces, J. Phys. Chem., 99, 11805-11812, 1995.

....from the true Lennard Jones potential as t # 0. Still, in the Section 5 we will see that our new family and the di#usion equation family behave quite similarly in trajectory tracking experiments on a Lennard Jones cluster. While making the present study, we discovered a recent paper [18] that proposes a smoothing function quite similar to (20) This smoothing function replaces r in (1) with (r #) 1 #) so the smoothing function is written as p(r) 1 # r # ) 12 2 # ( 1 # r # ) 6 . 24) where # is some positive constant. One major di#erence between (20) ....

Pillardy, J., and Piela, L. Molecular Dynamics on Deformed Potential Energy Hypersurfaces, J. Phys. Chem., 99, 11805-11812, 1995.

....15 smoothing methods, the global search involves tracking local minima from highly deformed states to the original energy hypersurface. This approach has only been tested on the molecular cluster problem [158] A qualitatively similar technique has also been used in molecular dynamics simulations [145]. An alternative method smoothes the energy hypersurface using local minima to construct separable quadratic underestimating functions. The local minima of these fitted functions are then used to initiate searches on the original energy surface [42, 142] 3.5. Branch and Bound Methods. Typically, ....

J. Pillardy and L. Piela, Molecular dynamics on deformed potential energy hypersurfaces, J. Phys. Chem., 99, (1995), 11805-11812.

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Pillardy, J. and Piela L., Molecular Dynamics on Deformed Potential Energy Hypersurfaces, J. Phys. Chem. 99, 11805--12, 1995.

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