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Recent advances in selected CI, including the adaptive sampling configurationinteraction (ASCI) algorithm and its heat bath extension, have made the ASCIapproach competitive with the most accurate techniques available, and hence anincreasingly powerful tool in solving quantum Hamiltonians. In this work, weshow that a useful paradigm for generating efficient selected CI/exactdiagonalization algorithms is driven by fast sorting algorithms, much in thesame way iterative diagonalization is based on the paradigm of matrix vectormultiplication. We present several new algorithms for all parts of performing aselected CI, which includes new ASCI search, dynamic bit masking, fast orbitalrotations, fast diagonal matrix elements, and residue arrays. The algorithmspresented here are fast and scalable, and we find that because they are builton fast sorting algorithms they are more efficient than all other approaches weconsidered. After introducing these techniques we present ASCI results appliedto a large range of systems and basis sets in order to demonstrate the types ofsimulations that can be practically treated at the full-CI level with modernmethods and hardware, presenting double- and triple-zeta benchmark data for theG1 dataset. The largest of these calculations is Si$_{2}$H$_{6}$ which is asimulation of 34 electrons in 152 orbitals. We also present some preliminaryresults for fast deterministic perturbation theory simulations that use hashfunctions to maintain high efficiency for treating large basis sets.

Modern Approaches to Exact Diagonalization and Selected Configuration Interaction with the Adaptive Sampling CI Method