Fig. 2: Categorical compression within the small-tensor-product distributed active space (STP-DAS) framework.
From: Numerically exact configuration interaction at quadrillion-determinant scale
A The STP-DAS framework decomposition of a complete active space configuration interaction (CASCI) calculation into a direct sum of categorical excitations. The large excitation lists can be factored into much smaller categorical excitation lists. Purple sections within active spaces represent electron-occupied orbitals. B The exact two-component full configuration interaction (X2C-FCI) ground state energy of the Mg2+ ion within the cc-pVNZ-DK142,143 (N = 2, 3, 4) basis sets, along with the extrapolated complete basis set limit. Source data are provided as a Source data file. C Average execution time (in seconds) of the compression-compatible STP-DAS algorithm per σ-build of a thallium hydride (TlH) test case versus the node count (5 iterations, 1 message passing interface (MPI) process per node, 40 symmetric multiprocessing (SMP) threads per MPI process). Here, H is the Hamiltonian, C is the CI vector, and σ is their product. The dashed lines illustrate the ideal strong scaling behavior of each CASCI calculation. Source data are provided as a Source data file. D The representation of the subspace expansion vector in a traditional configuration interaction (CI) picture, the decomposed subspace vector in the STP-DAS framework, and the numerically exact compression of the subspace expansion vector in the categorically compression-compatible STP-DAS representation. The color of CI coefficients indicates their configuration category, while their brightness symbolizes their magnitude. White indicates a magnitude of zero. E A schematic representation of the lossless, compression-compatible, STP-DAS σ-build algorithm. The Hamiltonian matrix is represented as a heatmap, where brighter elements have larger magnitudes. The color of the vector elements indicates the configuration category of the corresponding CI coefficients. Note that the σ-build preserves categorical compression. F An illustration comparing the traditional Davidson preconditioner with the compression-compatible preconditioner to generate successive subspace expansion vectors. The compression-compatible preconditioner appends the subspace with the same effective search direction as the traditional Davidson preconditioner without compromising its compression.
