High-performance parallel implementation of spin-free high-order coupled-cluster theories

High-order coupled-cluster theories with iterative triples (CCSDT), perturbative quadruples [CCSDT(Q)], and iterative quadruples (CCSDTQ) provide benchmark-quality correlation energies, but their steep computational scalings, O(N8), O(N9), and O(N10), together with the large memory requirements of high-order amplitude tensors, have historically limited their application to small molecules. In this work, we develop efficient open-source implementations of spin-restricted CCSDT (RCCSDT), RCCSDT(Q), and RCCSDTQ within the pyscf package and a Message Passing Interface (MPI)-based extension, distributed-cc. The shared-memory implementation combines compact triangular storage of the highest-order amplitude tensors with the multithreaded tensor contraction backend pytblis, enabling efficient use of modern many-core central processing unit (CPU) architectures. This design delivers near-ideal thread scaling up to 90 cores and achieves wall times shorter than or comparable to existing single-node implementations for representative benchmark molecules. We further extend RCCSDT, RCCSDT(Q), and RCCSDTQ to distributed-memory architectures using MPI-based algorithms. By distributing compact high-order amplitudes across MPI ranks and overlapping communication with computation through nonblocking data transfers, the distributed implementation achieves near-ideal strong scaling on up to 32 nodes, corresponding to ∼3000 CPU cores. These developments substantially extend the practical reach of canonical high-order coupled-cluster theory, enabling CCSDT and CCSDT(Q) calculations on systems with ∼100 correlated electrons in 450 orbitals and CCSDTQ calculations on systems with ∼50 correlated electrons in 115 orbitals. Applications to π-stacked noncovalent dimers, the CO dissociation energy of Cr(CO)6, and the Cope rearrangement of semibullvalene demonstrate that canonical high-order coupled-cluster benchmarks are now feasible for chemically realistic molecular systems.