Christopher Hillenbrand

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.

Over the past decade, the Python-based Simulations of Chemistry Framework (PySCF) has developed into a widely used open-source platform for electronic-structure theory and quantum chemical method development. This article reviews the major advances since the previous overview in 2020, covering new modules and methodology, infrastructure changes, and performance benchmarks.

Periodic equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD) has shown promise for quantitative calculations of band structures in solids. However, its steep computational scaling has limited calculations to relatively coarse k-point meshes, leading to sizable finite-size errors and discrepant estimates of thermodynamic-limit band gaps in recent benchmarks. In this work, we revisit EOM-CCSD band gaps for ten semiconductors and insulators using interacting-bath dynamical embedding theory (ibDET), a systematically improvable Green’s function embedding framework that enables dense Brillouin-zone sampling at modest computational cost. By pushing the k-point sampling up to 10 × 10 × 10, well beyond the system sizes accessible in canonical periodic EOM-CCSD calculations, we significantly reduce finite-size errors and obtain stable thermodynamic-limit extrapolations. We further compare G0W0@PBE, G0W0@HF, and EOM-CCSD on an equal footing using the same numerical settings in PySCF. We find that EOM-CCSD yields a mean absolute error of 0.32 eV relative to experimental band gaps for a test set of ten semiconductors and insulators, which is lower than that of G0W0@PBE. For ZnO, EOM-CCSD also accurately describes the Zn 3d-band binding energy, despite overestimating the band gap. These results demonstrate that ibDET offers a practical route to high-accuracy many-body electronic structure calculations in periodic systems.

We present an energy-specific Bethe–Salpeter equation (BSE) implementation for efficient core and valence optical spectrum calculations. In the energy-specific BSE, high-lying excitation energies are obtained by constructing trial vectors and expanding the subspace targeting excitation energies above the predefined energy threshold in the Davidson algorithm. To calculate optical spectra over a wide energy range, energy-specific BSE can be applied to multiple consecutive small energy windows, where trial vectors for each subsequent energy window are made orthogonal to the subspace of preceding windows to accelerate the convergence of the Davidson algorithm. For seven small molecules, energy-specific BSE combined with G0W0 provides small errors around 0.8 eV for absolute and relative K-edge excitation energies when starting from a hybrid PBEh solution with 45% exact exchange. We further showcase the computational efficiency of this approach by simulating the N 1s K-edge excitation spectrum of the porphine molecule and the valence optical spectrum of silicon nanoclusters involving 6000 excited states using G0W0-BSE. This work expands the applicability of the GW-BSE formalism for investigating high-energy excited states of large systems.