Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and Supercooled Liquids
The properties of higher-index saddle points have been invoked in recent theories of the dynamics of supercooled liquids. Here we examine in detail a mapping of configurations to saddle points using minimization of $|\nabla E|^2$, which has been used in previous work to support these theories. The e...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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American Institute of Physics
2001
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| _version_ | 1826303621759762432 |
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| author | Doye, J Wales, D |
| author_facet | Doye, J Wales, D |
| author_sort | Doye, J |
| collection | OXFORD |
| description | The properties of higher-index saddle points have been invoked in recent theories of the dynamics of supercooled liquids. Here we examine in detail a mapping of configurations to saddle points using minimization of $|\nabla E|^2$, which has been used in previous work to support these theories. The examples we consider are a two-dimensional model energy surface and binary Lennard-Jones liquids and solids. A shortcoming of the mapping is its failure to divide the potential energy surface into basins of attraction surrounding saddle points, because there are many minima of $|\nabla E|^2$ that do not correspond to stationary points of the potential energy. In fact, most liquid configurations are mapped to such points for the system we consider. We therefore develop an alternative route to investigate higher-index saddle points and obtain near complete distributions of saddles for small Lennard-Jones clusters. The distribution of the number of stationary points as a function of the index is found to be Gaussian, and the average energy increases linearly with saddle point index in agreement with previous results for bulk systems. |
| first_indexed | 2024-03-07T06:05:30Z |
| format | Journal article |
| id | oxford-uuid:edb2e5a6-652d-4b07-8bdc-c11ee7336cff |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:05:30Z |
| publishDate | 2001 |
| publisher | American Institute of Physics |
| record_format | dspace |
| spelling | oxford-uuid:edb2e5a6-652d-4b07-8bdc-c11ee7336cff2022-03-27T11:27:04ZSaddle Points and Dynamics of Lennard-Jones Clusters, Solids and Supercooled LiquidsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:edb2e5a6-652d-4b07-8bdc-c11ee7336cffEnglishSymplectic Elements at OxfordAmerican Institute of Physics2001Doye, JWales, DThe properties of higher-index saddle points have been invoked in recent theories of the dynamics of supercooled liquids. Here we examine in detail a mapping of configurations to saddle points using minimization of $|\nabla E|^2$, which has been used in previous work to support these theories. The examples we consider are a two-dimensional model energy surface and binary Lennard-Jones liquids and solids. A shortcoming of the mapping is its failure to divide the potential energy surface into basins of attraction surrounding saddle points, because there are many minima of $|\nabla E|^2$ that do not correspond to stationary points of the potential energy. In fact, most liquid configurations are mapped to such points for the system we consider. We therefore develop an alternative route to investigate higher-index saddle points and obtain near complete distributions of saddles for small Lennard-Jones clusters. The distribution of the number of stationary points as a function of the index is found to be Gaussian, and the average energy increases linearly with saddle point index in agreement with previous results for bulk systems. |
| spellingShingle | Doye, J Wales, D Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and Supercooled Liquids |
| title | Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and
Supercooled Liquids |
| title_full | Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and
Supercooled Liquids |
| title_fullStr | Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and
Supercooled Liquids |
| title_full_unstemmed | Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and
Supercooled Liquids |
| title_short | Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and
Supercooled Liquids |
| title_sort | saddle points and dynamics of lennard jones clusters solids and supercooled liquids |
| work_keys_str_mv | AT doyej saddlepointsanddynamicsoflennardjonesclusterssolidsandsupercooledliquids AT walesd saddlepointsanddynamicsoflennardjonesclusterssolidsandsupercooledliquids |