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Electron correlation methods form a systematically improvable hierarchy, which allows one to obtain a desired level of accuracy at the cost of steeply increasing computational cost. It is well-recognized that exploiting spatial locality is the key to eliminating the unphysical scaling of computational cost with system size that is seen in textbook implementations of many body correlation methods such as perturbation theory and coupled cluster theory. Despite impressive computational achievements in local correlation research, including demonstration of linear scaling, there are not yet simple standard models for local correlation. Therefore there is still much for researchers in this area to accomplish! In this talk, I shall discuss two recent developments in my group that attempt to address existing challenges for local correlation methods. The first one is the problem of obtaining smooth potential energy surfaces when adaptive domains are employed in local coupled cluster singles and doubles (LCCSD). A domain here refers to the set of virtual orbitals which are used to correlate a given pair of occupied orbitals. A method with adaptive domains is in principle most suitable to exploring electronic structure along a reaction coordinate where the extent of locality electron correlation changes. However it is difficult to ensure that potential curves are smooth if the number of correlating functions for a given pair of occupied levels changes along a geometric path. We describe the latest developments in our use of bump functions to obtain smooth potential curves with high efficiency. The second problem is related and deals with issue of artifacts such as symmetry breaking that arise in local correlation methods that use fixed domains. While such methods in principle yield smooth potential curves, they will tend to perform better in regions where the electronic structure is more localized. This can give rise to inaccuracies and artifacts, such as symmetry breaking in perfect pairing active space methods. The classic example is benzene, but many aromatic molecules exhibit similar problems in perfect pairing, and more complete local correlation models such as imperfect pairing that are built within the same pair-based framework. We discuss first the magnitude of the problem and second the extent to which non-local electron correlations must be included in order to remove artifacts of this type. It is not necessarily obvious that the very high efficiency of perfect and imperfect pairing can be retained if the solution to the problem is inclusion of non-local correlation effects. |
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