The key to successful description of many-electron and other many-fermion systems is an accurate assessment of particle correlations. This is particularly true in studies of molecular potential energy surfaces involving bond breaking, chemical reaction pathways involving radicals and biradicals, and electronic excitations in molecules, where one has to provide an accurate and balanced description of electron correlations of the short-range (or dynamical) and long-range (or non-dynamical) type. Other examples of many-body systems where particle correlations are very important are atomic nuclei.
In this presentation, I will focus on the recently developed ideas in quantum many-body theory that have resulted in the discovery and development of renormalized coupled-cluster methods. I will show that the renormalized coupled-cluster methods, which are based on a new type of the asymmetric energy expression that defines the formalism of the method of moments of coupled-cluster equations, enable an accurate and balanced description of molecular potential energy surfaces involving bond breaking, reaction pathways in organic and bioinorganic chemistries, singlet-triplet gaps in magnetic systems, and several important classes of excited electronic states, including challenging excited states of closed- and open-shell molecular systems dominated by two-electron transitions. I will emphasize that the renormalized coupled-cluster methods extend the applicability of conventional single-reference quantum-chemical approaches to bond breaking, reaction pathways, and electronically excited states with an ease of a black-box calculation that can be performed by experts as well as non-experts. I will also show that one can extend coupled-cluster theories, including renormalized coupled-cluster methods, to large molecular systems with dozens or even hundreds of atoms, while retaining the high accuracies coupled-cluster methods offer for smaller molecular species.
If time permits, I will demonstrate that the applicability of quantum chemistry inspired coupled-cluster approximations, including the renormalized coupled-cluster methods, is not limited to many-electron systems. I will discuss the results of applying the conventional and renormalized coupled-cluster methods, which have previously been developed in the context of electronic structure calculations, to ground and excited states of the 4He and 16O nuclei, and valence systems around 16O exploiting modern nucleon-nucleon interactions derived from effective-field theory. I will also discuss the results of our most recent coupled-cluster calculations for low-lying states of the heavier 56Ni nucleus demonstrating that practical coupled-cluster approximations developed in quantum chemistry may offer a useful alternative to the traditional and considerably more expensive shell-model calculations.