Dynamic Variational Principles and Extended Coupled Cluster Techniques

Abstract

We present a description of the so-called extended coupled cluster method (ECCM), and show how it provides a rather powerful and general treatment for the quantum-mechanical many-body problem. Since this method has to date not yet been applied to systems of interest in quantum chemistry, we compare and contrast the method with both the configuration-interaction (CI) and (normal) coupled cluster (CC) techniques which have been so successfully applied to a wide variety of many-body systems, including atoms and molecules. We indicate the potential advantages of the ECCM over these other methods, and show how in some very real sense it completes the process begun but not completed by the normal CC method in attempting to overcome the (size-extensivity) problems associated with the CI method. The ECCM provides, in principle, an exact parametrisation of the many-body Hilbert space in terms of a complete set of linked-cluster amplitudes, all of which obey the cluster property. By contrast, none of the corresponding CI amplitudes, and only half of the normal CC amplitudes, obey this property. This has important consequences if one is interested in arbitrary expectation values or geometric (topological) properties. Both static and dynamic properties are describable, and we sketch the ECCM description of both ground and excited states.KeywordsRandom Phase ApproximationCouple ClusterDynamic MatrixDyson EquationArbitrary OperatorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.