Coupled cluster theory with emphasis on selected new developments

Coupled cluster (CC) methods for the description of the correlated motion of electrons and nuclei are reviewed with emphasis on selected new initiatives. The basic aspects of standard electronic CC theory are described including the rationale behind the most widely used methods like coupled cluster singles and doubles (CCSD) and the CCSD(T) approach. The hierarchy of coupled cluster models consisting of coupled cluster singles (CCS), CC2, CCSD and CC3 is also described. A brief account of the theory behind the calculation of molecular properties using CC methods, and the description of response properties and excited states using CC response theory is followed by a discussion of the use of CC theory in the context of effective models for describing molecules in solution. In another part of the review we consider recent initiatives aimed at the development of coupled cluster methods for describing the correlated motion of the atomic nuclei. A recently developed second quantization formulation of many-mode dynamics for distinguishable degrees of freedom forms the basis for developing new quantum dynamical methods in particular vibrational coupled cluster (VCC) methods. The VCC theory is reviewed and discussed in comparison with vibrational configuration interaction (VCI), and vibrational Moller-Plesset (VMP) perturbation theory. The review concludes with a discussion of some important future research topics.