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The underlying reasons for the poor convergence of the venerated many-body expansion (MBE) for higher-order response properties are investigated, with a particular focus on the impact of basis set superposition errors. Interaction energies, dipole moments, dynamic polarizabilities, and specific rotations are computed for three chiral solutes in explicit water cages of varying sizes using the MBE including corrections based on the site–site function counterpoise (or “full-cluster” basis) approach. In addition, we consider other possible causes for the observed oscillatory behavior of the MBE, including numerical precision, basis set size, choice of density functional, and snapshot geometry. Our results indicate that counterpoise corrections are necessary for damping oscillations and achieving reasonable convergence of the MBE for higher order properties. However, oscillations in the expansion cannot be completely eliminated for chiroptical properties such as specific rotations due to their inherently nonadditive nature, thus limiting the efficacy of the MBE for studying solvated chiral compounds. 

We propose a modified coupled cluster Monte Carlo algorithm that stochastically samples connected terms within the truncated Baker–Campbell–Hausdorff expansion of the similarity-transformed Hamiltonian by construction of coupled cluster diagrams on the fly. Our new approach—diagCCMC—allows propagation to be performed using only the connected components of the similarity-transformed Hamiltonian, greatly reducing the memory cost associated with the stochastic solution of the coupled cluster equations. We show that for perfectly local, noninteracting systems diagCCMC is able to represent the coupled cluster wavefunction with a memory cost that scales linearly with system size. The favorable memory cost is observed with the only assumption of fixed stochastic granularity and is valid for arbitrary levels of coupled cluster theory. Significant reduction in memory cost is also shown to smoothly appear with dissociation of a finite chain of helium atoms. This approach is also shown not to break down in the presence of strong correlation through the example of a stretched nitrogen molecule. Our novel methodology moves the theoretical basis of coupled cluster Monte Carlo closer to deterministic approaches. 

We discuss from a pedagogical perspective the use of tensors in many-body electronic structure methods, especially the relevant storage and computational aspects used by modern quantum chemistry software packages. We consider the implementational consequences of the various symmetries—spin, spatial, and permutational—that appear in tensors representing the Hamiltonian, wave functions, and other important quantities in many-body methods. In addition, we review a number of state-of-the-art approaches to tensor frameworks on modern high-performance computing architectures.