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 t...
| मुख्य लेखकों: | , |
|---|---|
| स्वरूप: | Journal article |
| भाषा: | English |
| प्रकाशित: |
American Institute of Physics
2003
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| _version_ | 1826288208126672896 |
|---|---|
| author | Wales, D Doye, J |
| author_facet | Wales, D Doye, J |
| author_sort | Wales, D |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T02:10:14Z |
| format | Journal article |
| id | oxford-uuid:a0622f1b-c5ce-48fa-9977-e0bd85c4df1a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:10:14Z |
| publishDate | 2003 |
| publisher | American Institute of Physics |
| record_format | dspace |
| spelling | oxford-uuid:a0622f1b-c5ce-48fa-9977-e0bd85c4df1a2022-03-27T02:05:03ZSome Further Results for the Stationary Points and Dynamics of Supercooled LiquidsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a0622f1b-c5ce-48fa-9977-e0bd85c4df1aEnglishSymplectic Elements at OxfordAmerican Institute of Physics2003Wales, DDoye, JWe 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. |
| spellingShingle | Wales, D Doye, J Some Further Results for the Stationary Points and Dynamics of Supercooled Liquids |
| title | Some Further Results for the Stationary Points and Dynamics of
Supercooled Liquids |
| title_full | Some Further Results for the Stationary Points and Dynamics of
Supercooled Liquids |
| title_fullStr | Some Further Results for the Stationary Points and Dynamics of
Supercooled Liquids |
| title_full_unstemmed | Some Further Results for the Stationary Points and Dynamics of
Supercooled Liquids |
| title_short | Some Further Results for the Stationary Points and Dynamics of
Supercooled Liquids |
| title_sort | some further results for the stationary points and dynamics of supercooled liquids |
| work_keys_str_mv | AT walesd somefurtherresultsforthestationarypointsanddynamicsofsupercooledliquids AT doyej somefurtherresultsforthestationarypointsanddynamicsofsupercooledliquids |