Quantitative quantum chemistry

We review the current status of quantum chemistry as a predictive tool of chemistry and molecular physics, capable of providing highly accurate, quantitative data about molecular systems. We begin by reviewing wave-function based electronic-structure theory, emphasizing the N-electron hierarchy of coupled-cluster theory and the one-electron hierarchy of correlation-consistent basis sets. Following a discussion of the slow basis-set convergence of dynamical correlation and basis-set extrapolations, we consider the methods of explicit correlation, from the early work of Hylleraas in the 1920s to the latest developments in such methods, capable of yielding high-accuracy results in medium-sized basis sets. Next, we consider the small corrections to the electronic energy (high-order virtual excitations, vibrational, relativistic, and diagonal Born-Oppenheimer corrections) needed for high accuracy and conclude with a review of the composite methods and computational protocols of electronic-structure theory.