Coupled-cluster theory and its equation-of-motion extensions

Coupled-cluster theory offers today's reference quantum chemical method for most of the problems encountered in electronic structure theory. It has been instrumental in establishing the now well-known paradigm of converging, many-body methods, MBPT2 < CCD < CCSD < MBPT4 < CCSD(T) < CCSDT-n < CCSDT < CCSDT(Q) < CCSDTQ-n < CCSDTQ < fullCI. Many-body perturbation theory (MBPT) for second, MBPT2, and fourth-order MBPT4; and coupled-cluster (CC) theory for different categories of excitations, singles, doubles, triples, quadruples (SDTQ). Although built on the same basic concept as configuration interaction (CI), many-body methods fundamentally improve upon CI approximations by introducing the property of size extensivity, meaning that contrary to any truncated CI all terms properly scale with the number of electrons in the problem. This fundamental aspect of many-electron methods leads to the exceptional performance of CC theory and its finite-order MBPT approximations plus its equation-of-motion extensions for excited, ionized, and electron attached states. This brief overview will describe formal aspects of the theory which should be understood by perspective users of CC methods. We will also comment on some current developments that are improving the theory's accuracy or applicability. (c) 2011 John Wiley & Sons, Ltd.