| Popis: |
This thesis improves computational efficiency in two domains of quantum chemistry. Firstly, we improve the efficiency of computing atomic orbital (AO) integrals. We efficiently compute effective core potential integrals, relying on novel recursion relations and rigorous screening strategies. Inspired by PRISM, we create an adaptive algorithm to compute two-electron Gaussian geminal integrals, efficiently handling the contracted nature of both the contracted Gaussian-type orbital and geminal. We implement an efficient non-robust density fitting (DF) algorithm for computing the three-electron energy term in the Unsöld-W12 functional using new integral and screening routines. Secondly, we develop low computational scaling and highly parallel algorithms for MP2 energies. These algorithms rely on spatial quadratures of the electronic co-ordinates. We begin with a Localised Molecular Orbital formalism. This algorithm computes the opposite-spin (OS) MP2 energy and scales formally O(N^6) but, with screening strategies, scales asymptotically O(N^2). Unfortunately, the screened quantities reach their asymptotic scaling too slowly. Instead, we adopt a more local AO formalism. This algorithm demonstrates an almost ideal parallel speedup with more than 800 cores and competitive timings against DF-MP2-OS. In our improved AO algorithm, we develop rigorous screening strategies for eliminating insignificant AOs, extend the method to computing the same-spin MP2 energy, remove the prior sparse memory access bottleneck and implement a hybrid parallelisation strategy. We demonstrate a 51% parallel efficiency on 4644 cores, competitive timings and accuracy compared to DF-MP2. Finally, we extend this methodology to compute the MP2-F12(3*A) correction. We present a novel scaled Coulomb-like term approximation and develop efficient quadrature methods and screening strategies. Our scaled approximation and algorithm achieves chemical accuracy across a range of test sets. |
