Speaker: Susi Lehtola
Title: Single-reference coupled-cluster treatment of strong correlation via the perfect pairing hierarchy
Abstract: I will discuss the treatment of systems with strong correlation with single-reference coupled-cluster (CC) theory based on the perfect pairing, perfect quadruples (PQ) [1] and perfect hextuples (PH) [2] models. The methods are obtained as tensor block decompositions of conventional coupled-cluster theory. Thanks to the truncation, coupled-cluster diagrams of high order – up to quadruples in PQ and up to hextuples in PH – can be included, which grant exactness for problems with four electrons in four orbitals (PQ) and six electrons in six orbitals (PH). Naturally, the obtained models can also be applied to much larger systems, and due to the coupled cluster ansatz, the exactness of the models is also valid for an arbitrary number of local strongly interacting subsets of electrons and orbitals. PQ and PH have storage requirements that scale as the square, and the cube of the number of active electrons, respectively, and exhibit quartic scaling of the computational effort for large systems.
Using the novel implementations [3], active spaces of hundreds of electrons in hundreds of orbitals can be solved with PQ in a matter of minutes on a single core workstation. While the truncation results in huge speedups for the models, it also makes them no longer invariant to rotations in the occupied-occupied and virtual-virtual blocks, and so the orbitals need to be optimized. We have recently implemented orbital optimization [4] and will discuss applications including π-space only as well as full-valence calculations on linear polyacenes, with active spaces nearing 200 electrons in 200 orbitals. Furthermore, we will also discuss the extension of the pairing models to beyond singlet references, which may yield powerful models for the description of radicals in the near future. Unfortunately, not all types of systems are amenable to a single-reference CC treatment, but these may be identified using a cluster decomposition approach [5].
[1] J. A. Parkhill, K. Lawler and M. Head-Gordon, Journal of Chemical Physics 130, 084101 (2009).
[2] J. A. Parkhill and M. Head-Gordon, Journal of Chemical Physics 133, 024103 (2010).
[3] S. Lehtola, M. Head-Gordon, and J. A. Parkhill, Journal of Chemical Physics 145, 134110 (2016). arXiv:1609.00077.
[4] S. Lehtola, J. Parkhill, and M. Head-Gordon, Mol. Phys. 116, 547 (2018). arXiv:1705.01678.
[5] S. Lehtola, N. M. Tubman, K. B. Whaley, and M. Head-Gordon, J. Chem. Phys. 147, 154105 (2017). arXiv:1707.04376.
Susi Lehtola from the University of Helsinki is visiting Oslo for two months (June and July) to work with Rolf and Simen in connection with the BIVAQUM project.
The Hylleraas seminars alternate between Oslo (room V205) and Tromsø (room C302), and are broadcasted by video conference to the other place. It is possible to follow the seminars externally upon request.