## Final Report Summary - LCC (Coupled Cluster Calculations on Large Molecular Systems)

Today science is driven by the mutual interaction of three fundamental pillars: experiment, theory, and simulation. In this ERC project we aim to improve on the theory and simulation pillars with focus on high precision calculations of large molecular systems of interest in e.g. biological and material sciences.

Within the field of high precision electronic structure calculations, coupled cluster (CC) theory is preeminent due to its hierarchy of accurate models. However, conventional implementations of the CC methods have suffered from unphysical scaling issues, which have limited their use to small molecular systems. For example, the "gold standard" of electronic structure theory, the so-called CCSD(T) model, scales with the system size to the seventh power. This implies that if a computer calculation on a single amino acid takes 1 hour, then a calculation on a small protein like insulin (containing 51 amino acids) would take 897 billion hours, corresponding to 100 million years! Clearly, this inhibits the practical application of CC models to large molecular systems. The goal of the present ERC project is to address the computational scaling problem of CC methods to enable calculations on large molecular systems.

We have recently developed the Divide-Expand-Consolidate (DEC) CC scheme which scales only linearly with system size and furthermore is well suited for large supercomputer architectures. This implies that calculations on large systems take hours or days rather than millions of years. In the DEC-CC scheme the local nature of electron interactions is used to partition the calculation of a large molecular systems into many small and independent fragment calculations. Importantly, this is done in a way where the precision of the DEC calculation compared to a conventional CC calculation is fully under control.

We have undertaken collaboration with the Oak Ridge National Lab (ORNL) for the U.S Department of Energy, which is home for one of the largest supercomputers in the world, Titan. Furthermore, we have had access to the Partnership for Advanced Computing in Europe (PRACE) supercomputers.

We have developed a scalable cross-platform hybrid MPI/OpenMP/OpenACC implementation of the Divide–Expand–Consolidate (DEC) formalism with portable performance on heterogeneous HPC architectures and applied the DEC-RI-MP2 method to 1-aza-adamantane-trione supramolecular wires containing up to 40 monomers (2440 atoms, 6800 correlated electrons, 24440 basis functions and 91280 auxiliary functions). This represents the largest molecular system treated at the MP2 level of theory, demonstrating an efficient removal of the scaling wall pertinent to conventional quantum many-body methods.

While a lot of effort has been spent on developing the DEC methodology, several other theoretical projects have also been carried out.

We have derived a new series of the perturbative triples models (the CCSD(T-n) series), in which the CCSD state is considered as the unperturbed reference and the fluctuation potential of ordinary Møller-Plesset perturbation theory as the perturbation. The CCSD(T-n) series systematically approaches the CCSDT energies and may provide an alternative to the CCSD(T) model.

We have developed a completely new class of hybrid wave-function models – the cluster perturbation (CP) models, primed to challenge the state-of-the-art methods for the calculation not only of the energy but in particular for molecular properties.

Finally, we have created a Local framework for excitation energies, a first very promising step towards a general cost-effective high-accuracy simulation tool capable of providing a wide range of molecular properties for large molecular systems, such as multi-photon absorption spectra.

Our theoretical developments and their implementations have been carried out with focus on enabling high-accuracy calculations on large molecular systems. The developments are being implemented in the LSDALTON program package, which is available, free-of-charge, to the general user.

Within the field of high precision electronic structure calculations, coupled cluster (CC) theory is preeminent due to its hierarchy of accurate models. However, conventional implementations of the CC methods have suffered from unphysical scaling issues, which have limited their use to small molecular systems. For example, the "gold standard" of electronic structure theory, the so-called CCSD(T) model, scales with the system size to the seventh power. This implies that if a computer calculation on a single amino acid takes 1 hour, then a calculation on a small protein like insulin (containing 51 amino acids) would take 897 billion hours, corresponding to 100 million years! Clearly, this inhibits the practical application of CC models to large molecular systems. The goal of the present ERC project is to address the computational scaling problem of CC methods to enable calculations on large molecular systems.

We have recently developed the Divide-Expand-Consolidate (DEC) CC scheme which scales only linearly with system size and furthermore is well suited for large supercomputer architectures. This implies that calculations on large systems take hours or days rather than millions of years. In the DEC-CC scheme the local nature of electron interactions is used to partition the calculation of a large molecular systems into many small and independent fragment calculations. Importantly, this is done in a way where the precision of the DEC calculation compared to a conventional CC calculation is fully under control.

We have undertaken collaboration with the Oak Ridge National Lab (ORNL) for the U.S Department of Energy, which is home for one of the largest supercomputers in the world, Titan. Furthermore, we have had access to the Partnership for Advanced Computing in Europe (PRACE) supercomputers.

We have developed a scalable cross-platform hybrid MPI/OpenMP/OpenACC implementation of the Divide–Expand–Consolidate (DEC) formalism with portable performance on heterogeneous HPC architectures and applied the DEC-RI-MP2 method to 1-aza-adamantane-trione supramolecular wires containing up to 40 monomers (2440 atoms, 6800 correlated electrons, 24440 basis functions and 91280 auxiliary functions). This represents the largest molecular system treated at the MP2 level of theory, demonstrating an efficient removal of the scaling wall pertinent to conventional quantum many-body methods.

While a lot of effort has been spent on developing the DEC methodology, several other theoretical projects have also been carried out.

We have derived a new series of the perturbative triples models (the CCSD(T-n) series), in which the CCSD state is considered as the unperturbed reference and the fluctuation potential of ordinary Møller-Plesset perturbation theory as the perturbation. The CCSD(T-n) series systematically approaches the CCSDT energies and may provide an alternative to the CCSD(T) model.

We have developed a completely new class of hybrid wave-function models – the cluster perturbation (CP) models, primed to challenge the state-of-the-art methods for the calculation not only of the energy but in particular for molecular properties.

Finally, we have created a Local framework for excitation energies, a first very promising step towards a general cost-effective high-accuracy simulation tool capable of providing a wide range of molecular properties for large molecular systems, such as multi-photon absorption spectra.

Our theoretical developments and their implementations have been carried out with focus on enabling high-accuracy calculations on large molecular systems. The developments are being implemented in the LSDALTON program package, which is available, free-of-charge, to the general user.