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Improved sampling in Monte Carlo simulations of small clusters

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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    Item Type: University of Pittsburgh ETD
    ETD Committee:
    ETD Committee TypeCommittee MemberEmail
    Committee ChairJordan, Kenneth Djordan@pitt.edu
    Committee MemberPratt, David Wpratt@pitt.edu
    Committee MemberMadura, Jeffery Dmadura@duq.edu
    Committee MemberCoalson, Rob Drob@ringo.chem.pitt.edu
    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    Status: Unpublished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; Release the ETD 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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