Liu, Hanbin (2005) *Improved sampling in Monte Carlo simulations of small clusters.* Doctoral Dissertation, University of Pittsburgh.

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## Abstract

In this thesis, improved sampling algorithms are applied to atomic and molecular clusters. The parallel-tempering Monte Carlo procedure is used to characterize the (CO2)n, n = 6, 8, 13, 19, and 38, clusters. The heat capacity curves of the n = 13 and 19 clusters are found to have pronounced peaks that can be associated with cluster melting. In addition, there is evidence of a low temperature "solid -> solid" transition in the case of (CO2)19. The low-energy minima and rearrangement pathways are determined and used to examine the complexity of the potential energy surfaces of the clusters. An algorithm combining the Tsallis generalized ensemble and the parallel tempering algorithm is introduced and applied to a 1D model potential and to Ar38. The convergence of parallel tempering Monte Carlo simulations of the 38-atom Lennard-Jones cluster starting from the Oh global minimum and from the C5v second lowest-energy minimum is also investigated. It is found that achieving convergence is appreciably more difficult, particularly at temperatures in the vicinity of the Oh -> C5v transformation, when starting from the C5v structure. Compared to PTMC, the hybrid algorithm is about 10 times faster for reaching equilibrium in the 1D model potential and is about 3 times faster for reaching equilibrium in the LJ38 system when starting from the second lowest energy minimum. The Wang-Landau free random walk algorithm is also applied to Ar13 and Ar38.

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## Details | |||||||||

Item Type: | University of Pittsburgh ETD | ||||||||
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Creators/Authors: |
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Title: | Improved sampling in Monte Carlo simulations of small clusters | ||||||||

Status: | Unpublished | ||||||||

Abstract: | In this thesis, improved sampling algorithms are applied to atomic and molecular clusters. The parallel-tempering Monte Carlo procedure is used to characterize the (CO2)n, n = 6, 8, 13, 19, and 38, clusters. The heat capacity curves of the n = 13 and 19 clusters are found to have pronounced peaks that can be associated with cluster melting. In addition, there is evidence of a low temperature "solid -> solid" transition in the case of (CO2)19. The low-energy minima and rearrangement pathways are determined and used to examine the complexity of the potential energy surfaces of the clusters. An algorithm combining the Tsallis generalized ensemble and the parallel tempering algorithm is introduced and applied to a 1D model potential and to Ar38. The convergence of parallel tempering Monte Carlo simulations of the 38-atom Lennard-Jones cluster starting from the Oh global minimum and from the C5v second lowest-energy minimum is also investigated. It is found that achieving convergence is appreciably more difficult, particularly at temperatures in the vicinity of the Oh -> C5v transformation, when starting from the C5v structure. Compared to PTMC, the hybrid algorithm is about 10 times faster for reaching equilibrium in the 1D model potential and is about 3 times faster for reaching equilibrium in the LJ38 system when starting from the second lowest energy minimum. The Wang-Landau free random walk algorithm is also applied to Ar13 and Ar38. | ||||||||

Date: | 05 October 2005 | ||||||||

Date Type: | Completion | ||||||||

Defense Date: | 05 July 2005 | ||||||||

Approval Date: | 05 October 2005 | ||||||||

Submission Date: | 07 July 2005 | ||||||||

Access Restriction: | No restriction; The work is available for access worldwide immediately. | ||||||||

Patent pending: | No | ||||||||

Institution: | University of Pittsburgh | ||||||||

Thesis Type: | Doctoral Dissertation | ||||||||

Refereed: | Yes | ||||||||

Degree: | PhD - Doctor of Philosophy | ||||||||

URN: | etd-07072005-093427 | ||||||||

Uncontrolled Keywords: | CO2 cluster; LJ38 cluster; parallel tempering Monte Carlo; parallel tempering Tsallis statistics; Wang-Laudua algorithm | ||||||||

Schools and Programs: | Dietrich School of Arts and Sciences > Chemistry | ||||||||

Date Deposited: | 10 Nov 2011 14:50 | ||||||||

Last Modified: | 18 Jun 2012 12:10 | ||||||||

Other ID: | http://etd.library.pitt.edu/ETD/available/etd-07072005-093427/, etd-07072005-093427 |

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