The evaluation of molecular integrals is a vital but computationally expensive part of electronic structure calculations. This computational expense is particularly problematic for the explicitly correlated methods, in which complicated and numerous integrals over more than two-electrons must be evaluated. The successful R12/F12 methods overcome this difficulty by decomposition of these many-electron integrals by means of approximate resolutions of the identity (RIs). To obtain accurate results with this approach, however, requires large auxiliary basis sets with high angular momentum functions. To address this issue, we present a new RI-free variant of MP2-F12 theory, which uses density fitting to approximate three-electron integrals, rather than RIs. This approach demonstrates improved convergence of calculated energies with respect to the size and maximum angular momentum of the auxiliary basis set compared to the standard RI-based approach. For the systems on which the method was tested, relatively small auxiliary basis sets were sufficient to reduce errors in the correlation energy to less than a millihartree. The software implementation of the three-electron integral types needed in the new MP2-F12 variant proved to be extremely time-consuming. This difficulty inspired us to develop "Intception", a code generator which generates code for molecular integral evaluation. Intception is capable of automatically implementing code for evaluating a wide range of molecular integral types, using a general theoretical framework based on Obara-Saika-type recurrence relations [1] . To flexibly express integral definitions for use in Intception, a new domain-specific language was created. Testing revealed that the generated code evaluated integrals to a high numerical accuracy and on a reasonable timescale, though somewhat slower than existing optimized implementations. A detailed analysis of the performance of the generated code was undertaken, which suggested some possible routes to improving the efficiency of the code.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:687429 |
| Date | January 2015 |
| Creators | Womack, James Christopher |
| Publisher | University of Bristol |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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