Critical assessment of coupled cluster method in quantum chemistry

Methods based on the coupled-cluster (CC) Ansatz and most widely applied fo r the computation of molecular properties and electronic structure are revi ewed. The applications of each method are presented, and its performance is evaluated. Following introductory remarks and a brief historical overview of CC methodology and its applications, we first outline the scope of our r eview, establish the required notation, and recall the foundations and orig ins of the CC Ansatz. We begin with single-reference CC approaches, which h ave greatly matured since the first ab initio study in early seventies, and are currently used to solve many diverse problems. The handling of nondege nerate closed-shell states being nowadays routine, we focus on open-shell s ystems and the important role of spin adaptation, as well as on methods ext ending or improving the ubiquitous CC method with singles and doubles (CCSD ). Multireference CC approaches still defy routine usage and are therefore given only a cursory treatment. Their main purpose is to provide a basis fo r the so-called state-selective, or state-specific, CC approaches that empl oy a single, yet possibly multideterminantal, reference. Perturbative and t he so-called quadratic configuration interaction methods are briefly addres sed from the viewpoint of CC theory. We also make an attempt to assess and interrelate numerous CC-based approaches to molecular properties, ranging f rom those related to the shape of the potential-energy surfaces (geometry, harmonic force fields, etc.) to properties characterizing the interaction w ith electromagnetic fields (static moments, polarizabilities, etc.). We the n conclude the methodological part of our review with a few comments concer ning the computational aspects. The subsequent part, devoted to application s, presents various examples that illustrate the scope, efficiency, and rel iability of various CC methods, particularly those of recent provenance. We focus on the general account of correlation effects, potential-energy surf aces and related properties, ionization potentials and electron affinities, vertical electronic excitation energies, and various static and dynamical properties. The final section of this review attempts to summarize the stat us quo of the CC methodology and its applications, as well as to ponder its future prospects.