Modern atomistic simulations increasingly employ localized orbitals to represent quantum operators, yielding sparse block matrices whose block shapes vary with chemical species and basis choice. Conventional scalar sparse formats store the entries of each block individually, obscuring this local structure and limiting the use of efficient block algorithms. We present VBCSR, a distributed sparse matrix library that preserves variable-size atomic blocks and accelerates the core linear algebra of large-scale atomistic simulations. A unified interface automatically maps scalar, uniform-basis, and multispecies operators to compressed sparse row (CSR), block sparse row (BSR), or variable-block compressed sparse row (VBCSR). Our advanced acceleration method groups blocks of equal shape and dispatches them to optimized dense kernels. In the reported benchmarks, VBCSR outperforms the tested Python-accessible reference implementations for several block-sparse benchmarks. We further demonstrate VBCSR in an InP nanoparticle application containing more than \(10^6\) atoms.

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